social responsibility 2

What Is Social Responsibility? Being Socially Responsible means that people and organisations must behave ethically and with sensitivity toward social, cultural, economic and environmental issues. Striving for social responsibility helps individuals, organisations and governments have a positive impact on development, business and society with a positive contribution to bottom-line results. Individual Social Responsibility (ISR) to achieve Corporate Social Responsibility (CSP) ISP may appear to be a new concept in relation to CSP, but it is a concept as old as The Golden Rule — Do unto others as you would have them do unto you. ISR expands on this by promoting a proactive stance towards positively influencing and affecting the people and environments outside your immediate circle. ISR is at the roots of CSR, because a corporate comprises of individuals and hence determines the social responsibility culture it creates. This is the intermingled relationship between CSR and ISR. Individuals are becoming more socially responsible and, in response to this Corporations and Companies need to become more socially responsible to meet consumer demand. The International Organisation for Standardisation (ISO) states: “In the wake of increasing globalisation, we have become increasingly conscious not only of what we buy, but also how the goods and services we buy have been produced. Environmentally harmful production, child labor, dangerous working environments and other inhumane conditions are examples of issues being brought into the open. All companies and organisations aiming at long-term profitability and credibility are starting to realise that they must act in accordance with norms of right and wrong.” Socially responsible individuals are demanding companies and organisations to become more socially responsible. How Does an Individual Become Socially Responsible? The Workshop for Civic Initiatives Foundation (WCIF), Bulgaria, describes ISR in its position statement on Social Responsibility as, “The individual social responsibility includes the engagement of each person towards the community where he lives, which can be expressed as an interest towards what’s happening in the community, as well as in the active participation in the solving of some of the local problems. Under community we understand the village, the small town or the residential complex in the big city, where lives every one of us. Each community lives its own life that undergoes a process of development all the time. And everyone of us could take part in that development in different ways, for example by taking part in cleaning of the street on which he lives, by taking part in organization of an event, connected with the history of the town or the village or by rendering social services to children without parents or elderly people. The individual social responsibility also could be expressed in making donations for significant for the society causes – social, cultural or ecological. There are many ways of donating, as for example donating of goods or donating money through a bank account or online” Social Responsibility can be “negative,” in that it is a responsibility to refrain from acting (resistance stance) or it can be “positive,” meaning there is a responsibility to act (proactive stance). Being socially responsible not only requires participating in socially responsible activities like recycling, volunteering and mentoring, but to actually make it a lifestyle. Only through a commitment to embrace and embed social responsibility into your personal value and belief system can you truly become socially responsible in all you do. According to The Harris Poll ®#57 , June 18, 2007[7], when it comes to individual social responsibility, there are three types of people: 1. Two-thirds of U.S. adults have “Good Intentions” – they believe that social responsibility is a good idea, and they do what they can in terms of volunteering, but they do not sacrifice huge amounts of time or money. 2. At the top end of the spectrum, 8 percent of U.S. adults “Practice What They Preach” and for this group, individual, as well as corporate, social responsibility is extremely important. 3. One-quarter of U.S. adults, however, follow a philosophy of “To Thine Own Self Be True” and, for this group, social responsibility has little consequence in their lives. On the other hand the trends show that the biggest growth for big charitable organisations in the world is coming through individuals and not through Corporations and Governments [8]. To take a proactive stance, ISR can start off as a simple act of philanthropic behaviour. My husband and I actually budget for giving, just like we do for living or car expenses. Add to this the campaigner, volunteer and activist in you that picks-up and supports issues affecting society. You may just start off volunteering once a month somewhere that suits your skills, abilities or interests. The other day, I asked a friend if he could teach my son guitar. We determined a tuition cost but instead of me paying him, he asked me if I could pay the charity of his choice. If you have the choice of two products and one product supports a good cause or was produced in a more ethical way, then purchase that product. You may only be one person but if everyone did their part, we could change the world! All Social responsibility, both individual and corporate, is voluntary; it is about going above and beyond what is called for by the law(legal responsibility). It involves an idea that it is better to be proactive toward a problem rather than reactive to a problem. Social responsibility means eliminating corrupt, irresponsible or unethical behavior that might bring harm to the community, its people, or the environment before the behavior happens. CORPORATE/BUSINESS SOCIAL RESPONSIBILITY Corporate social responsibility (CSR) can be defined as the "economic, legal, ethical, and discretionary expectations that society has of organizations at a given point in time" (Carroll and Buchholtz 2003, p. 36). The concept of corporate social responsibility means that organizations have moral, ethical, and philanthropic responsibilities in addition to their responsibilities to earn a fair return for investors and comply with the law. A traditional view of the corporation suggests that its primary, if not sole, responsibility is to its owners, or stockholders. However, CSR requires organizations to adopt a broader view of its responsibilities that includes not only stockholders, but many other constituencies as well, including employees, suppliers, customers, the local community, local, state, and federal governments, environmental groups, and other special interest groups. Collectively, the various groups affected by the actions of an organization are called "stakeholders." The stakeholder concept is discussed more fully in a later section. Corporate social responsibility is related to, but not identical with, business ethics. While CSR encompasses the economic, legal, ethical, and discretionary responsibilities of organizations, business ethics usually focuses on the moral judgments and behavior of individuals and groups within organizations. Thus, the study of business ethics may be regarded as a component of the larger study of corporate social responsibility. Carroll and Buchholtz's four-part definition of CSR makes explicit the multi-faceted nature of social responsibility. The economic responsibilities cited in the definition refer to society's expectation that organizations will produce good and services that are needed and desired by customers and sell those goods and services at a reasonable price. Organizations are expected to be efficient, profitable, and to keep shareholder interests in mind. The legal responsibilities relate to the expectation that organizations will comply with the laws set down by society to govern competition in the marketplace. Organizations have thousands of legal responsibilities governing almost every aspect of their operations, including consumer and product laws, environmental laws, and employment laws. The ethical responsibilities concern societal expectations that go beyond the law, such as the expectation that organizations will conduct their affairs in a fair and just way. This means that organizations are expected to do more than just comply with the law, but also make proactive efforts to anticipate and meet the norms of society even if those norms are not formally enacted in law. Finally, the discretionary responsibilities of corporations refer to society's expectation that organizations be good citizens. This may involve such things as philanthropic support of programs benefiting a community or the nation. It may also involve donating employee expertise and time to worthy causes. HISTORY The nature and scope of corporate social responsibility has changed over time. The concept of CSR is a relatively new one—the phrase has only been in wide use since the 1960s. But, while the economic, legal, ethical, and discretionary expectations placed on organizations may differ, it is probably accurate to say that all societies at all points in time have had some degree of expectation that organizations would act responsibly, by some definition. In the eighteenth century the great economist and philosopher Adam Smith expressed the traditional or classical economic model of business. In essence, this model suggested that the needs and desires of society could best be met by the unfettered interaction of individuals and organizations in the marketplace. By acting in a self-interested manner, individuals would produce and deliver the goods and services that would earn them a profit, but also meet the needs of others. The viewpoint expressed by Adam Smith over 200 years ago still forms the basis for free-market economies in the twenty-first century. However, even Smith recognized that the free market did not always perform perfectly and he stated that marketplace participants must act honestly and justly toward each other if the ideals of the free market are to be achieved. In the century after Adam Smith, the Industrial Revolution contributed to radical change, especially in Europe and the United States. Many of the principles espoused by Smith were borne out as the introduction of new technologies allowed for more efficient production of goods and services. Millions of people obtained jobs that paid more than they had ever made before and the standard of living greatly improved. Large organizations developed and acquired great power, and their founders and owners became some of the richest and most powerful men in the world. In the late nineteenth century many of these individuals believed in and practiced a philosophy that came to be called "Social Darwinism," which, in simple form, is the idea that the principles of natural selection and survival of the fittest are applicable to business and social policy. This type of philosophy justified cutthroat, even brutal, competitive strategies and did not allow for much concern about the impact of the successful corporation on employees, the community, or the larger society. Thus, although many of the great tycoons of the late nineteenth century were among the greatest philanthropists of all time, their giving was done as individuals, not as representatives of their companies. Indeed, at the same time that many of them were giving away millions of dollars of their own money, the companies that made them rich were practicing business methods that, by today's standards at least, were exploitative of workers. Around the beginning of the twentieth century a backlash against the large corporations began to gain momentum. Big business was criticized as being too powerful and for practicing antisocial and anticompetitive practices. Laws and regulations, such as the Sherman Antitrust Act, were enacted to rein in the large corporations and to protect employees, consumers, and society at large. An associated movement, sometimes called the "social gospel," advocated greater attention to the working class and the poor. The labor movement also called for greater social responsiveness on the part of business. Between 1900 and 1960 the business world gradually began to accept additional responsibilities other than making a profit and obeying the law. In the 1960s and 1970s the civil rights movement, consumerism, and environmentalism affected society's expectations of business. Based on the general idea that those with great power have great responsibility, many called for the business world to be more proactive in (1) ceasing to cause societal problems and (2) starting to participate in solving societal problems. Many legal mandates were placed on business related to equal employment opportunity, product safety, worker safety, and the environment. Furthermore, society began to expect business to voluntarily participate in solving societal problems whether they had caused the problems or not. This was based on the view that corporations should go beyond their economic and legal responsibilities and accept responsibilities related to the betterment of society. This view of corporate social responsibility is the prevailing view in much of the world today. The sections that follow provide additional details related to the corporate social responsibility construct. First, arguments for and against the CSR concept are reviewed. Then, the stakeholder concept, which is central to the CSR construct, is discussed. Finally, several of the major social issues with which organizations must deal are reviewed. ARGUMENTS FOR AND AGAINST CORPORATE SOCIAL RESPONSIBILITY The major arguments for and against corporate social responsibility are shown in Exhibit 1. The "economic" argument against CSR is perhaps most closely associated with the American economist Milton Friedman, who has argued that the primary responsibility of business is to make a profit for its owners, albeit while complying with the law. According to this view, the self-interested actions of millions of participants in free markets will, from a utilitarian perspective, lead to positive outcomes for society. If the operation of the free market cannot solve a social problem, it becomes the responsibility of government, not business, to address the issue. FOR AGAINST The rise of the modern corporation created and continues to create many social problems. Therefore, the corporate world should assume responsibility for addressing these problems. Taking on social and moral issues is not economically feasible. Corporations should focus on earning a profit for their shareholders and leave social issues to others. In the long run, it is in corporations' best interest to assume social responsibilities. It will increase the chances that they will have a future and reduce the chances of increased governmental regulation. Assuming social responsibilities places those corporations doing so at a competitive disadvantage relative to those who do not. Large corporations have huge reserves of human and financial capital. They should devote at least some of their resources to addressing social issues. Those who are most capable should address social issues. Those in the corporate world are not equipped to deal with social problems. The "competitive" argument recognizes the fact that addressing social issues comes at a cost to business. To the extent that businesses internalize the costs of socially responsible actions, they hurt their competitive position relative to other businesses. This argument is particularly relevant in a globally competitive environment if businesses in one country expend assets to address social issues, but those in another country do not. According to Carroll and Buchholtz, since CSR is increasingly becoming a global concern, the differences in societal expectations around the world can be expected to lessen in the coming years. Finally, some argue that those in business are ill-equipped to address social problems. This "capability" argument suggests that business executives and managers are typically well trained in the ways of finance, marketing, and operations management, but not well versed in dealing with complex societal problems. Thus, they do not have the knowledge or skills needed to deal with social issues. This view suggests that corporate involvement in social issues may actually make the situation worse. Part of the capability argument also suggests that corporations can best serve societal interests by sticking to what they do best, which is providing quality goods and services and selling them at an affordable price to people who desire them. There are several arguments in favor of corporate social responsibility. One view, held by critics of the corporate world, is that since large corporations create many social problems, they should attempt to address and solve them. Those holding this view criticize the production, marketing, accounting, and environmental practices of corporations. They suggest that corporations can do a better job of producing quality, safe products, and in conducting their operations in an open and honest manner. A very different argument in favor of corporate social responsibility is the "self-interest" argument. This is a long-term perspective that suggests corporations should conduct themselves in such a way in the present as to assure themselves of a favorable operating environment in the future. This view holds that companies must look beyond the short-term, bottom-line perspective and realize that investments in society today will reap them benefits in the future. Furthermore, it may be in the corporate world's best interests to engage in socially responsive activities because, by doing so, the corporate world may forestall governmental intervention in the form of new legislation and regulation, according to Carroll and Buchholtz. Finally, some suggest that businesses should assume social responsibilities because they are among the few private entities that have the resources to do so. The corporate world has some of the brightest minds in the world, and it possesses tremendous financial resources. (Wal-Mart, for example, has annual revenues that exceed the annual GNP of some countries.) Thus, businesses should utilize some of their human and financial capital in order to "make the world a better place." THE STAKEHOLDER CONCEPT According to Post, Lawrence, and Weber, stakeholders are individuals and groups that are affected by an organization's policies, procedures, and actions. A "stake" implies that one has an interest or share in the organization and its operations, per Carroll and Buchholtz. Some stakeholders, such as employees and owners, may have specific legal rights and expectations in regard to the organization's operations. Other stakeholders may not have specific rights granted by law, but may perceive that they have moral rights related to the organization's operations. For example, an environmental group may not have a legal right in regard to a company's use of natural resources, but may believe that they have a moral right to question the firm's environmental policies and to lobby the organization to develop environmentally friendly policies. All companies, especially large corporations, have multiple stakeholders. One way of classifying stakeholder groups is to classify them as primary or secondary stakeholders. Primary stakeholders have some direct interest or stake in the organization. Secondary stakeholders, in contrast, are public or special interest groups that do not have a direct stake in the organization but are still affected by its operations. Exhibit 2 classifies some major stakeholder groups into primary and secondary categories. The owners of a firm are among the primary stakeholders of the firm. An organization has legal and moral obligations to its owners. These obligations include, but are not limited to, attempting to ensure that owners receive an adequate return on their investment. Employees are also primary stakeholders who have both legal and moral claims on the organization. Organizations also have specific responsibilities to their customers in terms of producing and marketing goods and services that offer functionality, safety, and value; to local communities, which can be greatly affected by the actions of resident organizations and thus have a direct stake in their operations; and to the other companies with whom they do business. Many social commentators also suggest that companies have a direct responsibility to future generations and to the natural environment. An organization's responsibilities are not limited to primary stakeholders. Although governmental bodies and regulatory agencies do not usually have ownership stakes in companies in free-market economies, they do play an active role in trying to ensure that organizations accept and meet their responsibilities to primary stakeholder groups. Organizations are accountable to these secondary stakeholders. Organizations must also contend with civic and special interest groups that purport to act on behalf of a wide variety of constituencies. Trade associations and industry groups are also affected by an organization's actions and its reputation. The media reports on and investigates the actions of many companies, particularly large organizations, and most companies accept that they must contend with and effectively "manage" their relationship with the media. Finally, even an organization's competitors can be considered secondary stakeholders, as they are obviously affected by organizational actions. For example, one might argue that organizations have a social responsibility to compete in the marketplace in a manner that is consistent with the law and with the best practices of their industry, so that all competitors will have a fair chance to succeed. CONTEMPORARY SOCIAL ISSUES Corporations deal with a wide variety of social issues and problems, some directly related to their operations, some not. It would not be possible to adequately describe all of the social issues faced by business. This section will briefly discuss three contemporary issues that are of major concern: the environment, global issues, and technology issues. There are many others. ENVIRONMENTAL ISSUES. Corporations have long been criticized for their negative effect on the natural environment in terms of wasting natural resources and contributing to environmental problems such as pollution and global warming. The use of fossil fuels is thought to contribute to global warming, and there is both governmental and societal pressure on corporations to adhere to stricter environmental standards and to voluntarily change production processes in order to do less harm to the environment. Other issues related to the natural environment include waste disposal, deforestation, acid rain, and land degradation. It is likely that corporate responsibilities in this area will increase in the coming years. GLOBAL ISSUES. Corporations increasingly operate in a global environment. The globalization of business appears to be an irreversible trend, but there are many opponents to it. Critics suggest that globalization leads to the exploitation of developing nations and workers, destruction of the environment, and increased human rights abuses. They also argue that globalization primarily benefits the wealthy and widens the gap between the rich and the poor. Proponents of globalization argue that open markets lead to increased standards of living for everyone, higher wages for workers worldwide, and economic development in impoverished nations. Many large corporations are multinational in scope and will continue to face legal, social, and ethical issues brought on by the increasing globalization of business. Whether one is an opponent or proponent of globalization, however, does not change the fact that corporations operating globally face daunting social issues. Perhaps the most pressing issue is that of labor standards in different countries around the world. Many corporations have been stung by revelations that their plants around the world were "sweatshops" and/or employed very young children. This problem is complex because societal standards and expectations regarding working conditions and the employment of children vary significantly around the world. Corporations must decide which is the responsible option: adopting the standards of the countries in which they are operating or imposing a common standard world-wide. A related issue is that of safety conditions in plants around the world. Another issue in global business is the issue of marketing goods and services in the international marketplace. Some U.S. companies, for example, have marketed products in other countries after the products were banned in the United States. TECHNOLOGY ISSUES. Another contemporary social issue relates to technology and its effect on society. For example, the Internet has opened up many new avenues for marketing goods and services, but has also opened up the possibility of abuse by corporations. Issues of privacy and the security of confidential information must be addressed. Biotechnology companies face questions related to the use of embryonic stem cells, genetic engineering, and cloning. All of these issues have far-reaching societal and ethical implications. As our technological capabilities continue to advance, it is likely that the responsibilities of corporations in this area will increase dramatically. Corporate social responsibility is a complex topic. There is no question that the legal, ethical, and discretionary expectations placed on businesses are greater than ever before. Few companies totally disregard social issues and problems. Most purport to pursue not only the goal of increased revenues and profits, but also the goal of community and societal betterment. Research suggests that those corporations that develop a reputation as being socially responsive and ethical enjoy higher levels of performance. However, the ultimate motivation for corporations to practice social responsibility should not be a financial motivation, but a moral and ethical one. Stakeholders and Corporate Social Responsibility These stakeholder groups form the basis of success and failure of the business. Stakeholders are individuals or groups that have interests, rights, or ownership in an organization and its activities. Customers, suppliers, employees, and shareholders are example of primary stakeholder groups. Each has interest in how an organization performs or interacts with them. These stakeholder groups can benefit from a company’s success and can be harmed by its mistakes. Secondary stakeholders are also important because they can take action that can damage or assist the organization. Secondary stakeholders include governments (especially through regulatory agencies), unions, nongovernmental organizations (NGOs), activities, political action groups, and the media. In orders to serve their stakeholders in an ethical and social manner, more and more organizations are adapting the model of corporate social responsibility. The term Corporate Social Responsibility goes by many other terms such as corporate citizenship, responsible business or simply corporate responsibility. When an organization builds ethical and social elements in its operating philosophy and integrate them in its business model, it is said to have possessed a self-regulating mechanism that guides, monitor and ensure its adherence to law, ethics, and norms in carrying out business activities that ensures the serving the interest of all external and internal stakeholders. In other words, the objective of being socially responsible business is achieved when its activities meet or exceed the expectations of all its stakeholders. Here is a model for evaluating an organization’s social performance. The model indicates that total corporate social responsibility can be subdivided into four criteria-economic, legal, ethical and discretionary responsibilities. These responsibilities are ordered from bottom to top in the following illustration. Let’s discuss each one them briefly. Economic responsibilities: The first criterion of social responsibility is economic responsibility. The business institution is, above all, the basic economic unit of society. Its responsibility is to produce goods and services that a society wants and to maximise profit for its owners and shareholders. Economic responsibilities, carried to the extreme, is called profit-maximizing view; it was advocated by Nobel economist Milton Friedman. This view argued that a company should be operated on a profit-oriented basis, with its sole mission to increase its profits so long as is stays withing the rule of the game. The purely profit-maximizing view is no longer considered an adequate criterion of performance in the world in general. Treating economic gain in the social as the only social responsibility can lead companies into trouble. Legal responsibilities All modern societies lay down ground rules, laws and regulations that businesses are expected to follow. Legal responsibility defines what society deems as important with respect to appropriate corporate behavior. Businesses are expected to fulfil their economic goals within the legal framework. Legal requirements are imposed by local councils, state and federal governments and their regulating agencies. Organizations that knowingly break the law are poor performers in this category. Intentionally manufacturing defective goods or billing a client for work not done is illegal. Legal sanctions may include embarrassing public apologies or corporate ‘confessions’. Ethical responsibilities Ethical responsibility include behavior that is not necessarily codified into law and may not serve the organization’s direct economic interests. To be ethical, organization’s decision makers should act with equity, fairness and impartiality, respect the rights of individuals, and provide different treatments of individual only when differences between them are relevant to the organization’s goals and tasks. Unethical behavior occurs when decisions enable an individual or organization to gain expense of society. Discretionary responsibilities Discretionary responsibility is purely voluntary and guided by an organization’s desire to make social contributions not mandated by economics, laws or ethics. Discretionary activities include generous philanthropic contributions that offer no payback to the organization and are not expected. Discretionary responsibility is the highest criterion of social responsibility, because it goes beyond societal expectations to contribute to the community’s welfare.

constitution

5. (1) Every person shall be entitled to his personal liberty and no person shall be deprived of such liberty save in the following cases and in accordance with a procedure permitted by law - (a) in execution of the sentence or order of a court in respect of a criminal offence of which he has been found guilty; (b) by reason of his failure to comply with the order of a court or in order to secure the fulfilment of any obligation imposed upon him by law; (c) for the purpose of bringing him before a court in execution of the order of a court or upon reasonable suspicion of his having committed a criminal offence, or to such extent as may be reasonably necessary to prevent his committing a criminal offence; (d) in the case of a person who has not attained the age of eighteen years for the purpose of his education or welfare; (e) in the case of persons suffering from infectious or contagious disease, persons of unsound mind, persons addicted to drugs or alcohol or vagrants, for the purpose of their care or treatment or the protection of the community; or (f) for the purpose of preventing the unlawful entry of any person into Nigeria or of effecting the expulsion, extradition or other lawful removal from Nigeria of any person or the taking of proceedings relating thereto: Provided that a person who is charged with an offence and who has been detained in lawful custody awaiting trial shall not continue to be kept in such detention for a period longer than the maximum period of imprisonment prescribed for the offence. 35. (1) Every person shall be entitled to his personal liberty and no person shall be deprived of such liberty save in the following cases and in accordance with a procedure permitted by law - (a) in execution of the sentence or order of a court in respect of a criminal offence of which he has been found guilty; (b) by reason of his failure to comply with the order of a court or in order to secure the fulfilment of any obligation imposed upon him by law; (c) for the purpose of bringing him before a court in execution of the order of a court or upon reasonable suspicion of his having committed a criminal offence, or to such extent as may be reasonably necessary to prevent his committing a criminal offence; (d) in the case of a person who has not attained the age of eighteen years for the purpose of his education or welfare; (e) in the case of persons suffering from infectious or contagious disease, persons of unsound mind, persons addicted to drugs or alcohol or vagrants, for the purpose of their care or treatment or the protection of the community; or (f) for the purpose of preventing the unlawful entry of any person into Nigeria or of effecting the expulsion, extradition or other lawful removal from Nigeria of any person or the taking of proceedings relating thereto: Provided that a person who is charged with an offence and who has been detained in lawful custody awaiting trial shall not continue to be kept in such detention for a period longer than the maximum period of imprisonment prescribed for the offence. (2) Any person who is arrested or detained shall have the right to remain silent or avoid answering any question until after consultation with a legal practitioner or any other person of his own choice. (3) Any person who is arrested or detained shall be informed in writing within twenty-four hours (and in a language that he understands) of the facts and grounds for his arrest or detention. (4) Any person who is arrested or detained in accordance with subsection (1) (c) of this section shall be brought before a court of law within a reasonable time, and if he is not tried within a period of - (a) two months from the date of his arrest or detention in the case of a person who is in custody or is not entitled to bail; or (b) three months from the date of his arrest or detention in the case of a person who has been released on bail, he shall (without prejudice to any further proceedings that may be brought against him) be released either unconditionally or upon such conditions as are reasonably necessary to ensure that he appears for trial at a later date. (5) In subsection (4) of this section, the expression "a reasonable time" means - (a) in the case of an arrest or detention in any place where there is a court of competent jurisdiction within a radius of forty kilometres, a period of one day; and (b) in any other case, a period of two days or such longer period as in the circumstances may be considered by the court to be reasonable. (6) Any person who is unlawfully arrested or detained shall be entitled to compensation and public apology from the appropriate authority or person; and in this subsection, "the appropriate authority or person" means an authority or person specified by law. (7) Nothing in this section shall be construed - (a) in relation to subsection (4) of this section, as applying in the case of a person arrested or detained upon reasonable suspicion of having committed a capital offence; and (b) as invalidating any law by reason only that it authorises the detention for a period not exceeding three months of a member of the armed forces of the federation or a member of the Nigeria Police Force in execution of a sentence imposed by an officer of the armed forces of the Federation or of the Nigeria police force, in respect of an offence punishable by such detention of which he has been found guilty. 36. (1) In the determination of his civil rights and obligations, including any question or determination by or against any government or authority, a person shall be entitled to a fair hearing within a reasonable time by a court or other tribunal established by law and constituted in such manner as to secure its independence and impartiality. (2) Without prejudice to the foregoing provisions of this section, a law shall not be invalidated by reason only that it confers on any government or authority power to determine questions arising in the administration of a law that affects or may affect the civil rights and obligations of any person if such law - (a) provides for an opportunity for the persons whose rights and obligations may be affected to make representations to the administering authority before that authority makes the decision affecting that person; and (b) contains no provision making the determination of the administering authority final and conclusive. (3) The proceedings of a court or the proceedings of any tribunal relating to the matters mentioned in subsection (1) of this section (including the announcement of the decisions of the court or tribunal) shall be held in public. (4) Whenever any person is charged with a criminal offence, he shall, unless the charge is withdrawn, be entitled to a fair hearing in public within a reasonable time by a court or tribunal: Provided that - (a) a court or such a tribunal may exclude from its proceedings persons other than the parties thereto or their legal practitioners in the interest of defence, public safety, public order, public morality, the welfare of persons who have not attained the age of eighteen years, the protection of the private lives of the parties or to such extent as it may consider necessary by reason of special circumstances in which publicity would be contrary to the interests of justice; (b) if in any proceedings before a court or such a tribunal, a Minister of the Government of the Federation or a commissioner of the government of a State satisfies the court or tribunal that it would not be in the public interest for any matter to be publicly disclosed, the court or tribunal shall make arrangements for evidence relating to that matter to be heard in private and shall take such other action as may be necessary or expedient to prevent the disclosure of the matter. (5) Every person who is charged with a criminal offence shall be presumed to be innocent until he is proved guilty; Provided that nothing in this section shall invalidate any law by reason only that the law imposes upon any such person the burden of proving particular facts. (6) Every person who is charged with a criminal offence shall be entitled to - (a) be informed promptly in the language that he understands and in detail of the nature of the offence; (b) be given adequate time and facilities for the preparation of his defence; (c) defend himself in person or by legal practitioners of his own choice; (d) examine, in person or by his legal practitioners, the witnesses called by the prosecution before any court or tribunal and obtain the attendance and carry out the examination of witnesses to testify on his behalf before the court or tribunal on the same conditions as those applying to the witnesses called by the prosecution; and (e) have, without payment, the assistance of an interpreter if he cannot understand the language used at the trial of the offence. (7) When any person is tried for any criminal offence, the court or tribunal shall keep a record of the proceedings and the accused person or any persons authorised by him in that behalf shall be entitled to obtain copies of the judgement in the case within seven days of the conclusion of the case. (8) No person shall be held to be guilty of a criminal offence on account of any act or omission that did not, at the time it took place, constitute such an offence, and no penalty shall be imposed for any criminal offence heavier than the penalty in force at the time the offence was committed (9) No person who shows that he has been tried by any court of competent jurisdiction or tribunal for a criminal offence and either convicted or acquitted shall again be tried for that offence or for a criminal offence having the same ingredients as that offence save upon the order of a superior court. (10) No person who shows that he has been pardoned for a criminal offence shall again be tried for that offence. (11) No person who is tried for a criminal offence shall be compelled to give evidence at the trial. (12) Subject as otherwise provided by this Constitution, a person shall not be convicted of a criminal offence unless that offence is defined and the penalty therefor is prescribed in a written law, and in this subsection, a written law refers to an Act of the National Assembly or a Law of a State, any subsidiary legislation or instrument under the provisions of a law. 1. Accounts of the Government of the Federation, and of offices, courts, and authorities thereof, including audit of those accounts. 2. Arms, ammunition and explosives. 3. Aviation, including airports, safety of aircraft and carriage of passengers and goods by air. 4. Awards of national titles of honour, decorations and other dignities. 5. Bankruptcy and insolvency 6. Banks, banking, bills of exchange and promissory notes. 7. Borrowing of moneys within or outside Nigeria for the purposes of the Federation or of any State. 8. Census, including the establishment and maintenance of machinery for continuous and universal registration of births and deaths throughout Nigeria. 9. Citizenship, naturalisation and aliens. 10. Commercial and industrial monopolies, combines and trusts. 11. Construction, alteration and maintenance of such roads as may be declared by the National Assembly to be Federal trunk roads. 12. Control of capital issues. 13. Copyright 14. Creation of States 15. Currency, coinage and legal tender 16. Customs and excise duties 17. Defence 18. Deportation of persons who are not citizens of Nigeria 19. Designation of securities in which trust funds may be invested. 20. Diplomatic, consular and trade representation. 21. Drugs and poisons. Subject to the provisions of this Constitution, the Court of Appeal shall have jurisdiction to the exclusion of any other court of law in Nigeria, to hear and determine appeals from the Federal High Court, the High Court of the Federation Capital Territory, Abuja, High Court of a state, Sharia Court of Appeal of the Federal Capital Territory, Abuja, Sharia Court of Appeal of a state, Customary Court of Appeal of a state and from decisions of a court martial or other tribunals as may be prescribed by an Act of the National Assembly. 241. (1) An appeal shall lie from decisions of the Federal High Court or a High Court to the Court of Appeal as of right in the following cases - (a) final decisions in any civil or criminal proceedings before the Federal High Court or a High Court sitting at first instance; (b) where the ground of appeal involves questions of law alone, decisions in any civil or criminal proceedings; (c) decisions in any civil or criminal proceedings on questions as to the interpretation or application of this Constitution; (d) decisions in any civil or criminal proceedings on questions as to whether any of the provisions of Chapter IV of this Constitution has been, is being or is likely to be, contravened in relation to any person; (e) decisions in any criminal proceedings in which the Federal High Court or a High Court has imposed a sente

vistor

• 19. How does a receptionist handle (a) visitors with appointments? o Check the Appointment Book to confirm time of the appointment o Ask for the visitor’s business card. o Invite the visitor to take a seat while you inform the staff whom the visitor wishes to see. o Record the details of the business card in the Reception Register. • 20. Invite the visitor to take a seat! Record the visitor’s details in the Reception Register • 21. (b) Visitors without appointments? o Politely ask about the nature of the visit. o Ask for the visitor’s business card. o Invite the visitor to take a seat. o Check with the staff member concerned. o Record the details of the business card in the Reception Register. • 22. (c) Difficult visitors o If a visitor who does not have an appointment insists on seeing an executive who is busy or not around, suggest that he sees another executive or arrange for an appointment. • 23. o Even if the visitor is angry and shouting, it is not good for you to lose your temper and shout back. o A good receptionist should remain calm and deal with the situation in a professional manner. • 24. o Explain to the visitor that the staff member is not available or is busy. _________________________________________ _________________________________________ o Politely ask whether the visitor would like to see another staff who may be able to help. _________________________________________ _________________________________________ • 25. o Politely ask the visitor to leave his/her name card for the staff member to set up an appointment. o Be sensitive, calm, polite and patient!!

types of visitor

TYPES OF VISITORS Visitors With Appointments: Visitors who have appointments will not always arrive at the exact time scheduled. Those who arrive early should realize that they may have to wait. Those who have appointments should not be kept waiting, but realistically an executive may not be able to stay on a precise schedule. If the visitor appear annoyed, you may suggest that another appointment be arranged or perhaps. You offer to get the visitor a cup of coffee and indicate that the latest issue of a magazine. While the person is waiting, you should maintain a business like attitude. Visitors Without Appointments: When you do not recognize those who come to your office without appointments, you need to determine who they are and what they want. Embarrassing situations may result from untrue statements concerning why the executive cannot see a visitor. Your boss may want to be available to some people at all times. Certainly, higher- ranking executives and their secretaries do not need permission to enter your boss’s office, but they usually ask or give an opportunity to indicate whether he or she is busy. Relatives, close friends and executives on the same level generally have access to the boss’s office Problem Visitors: If a visitor to your office becomes irate, you must do all you can to maintain goodwill. One of the best ways to avoid becoming defensive is to remember that unless you are the one whose actions created the problems, the visitor’s remark are not about you. Be attentive listen carefully until the visitor has finished talking. After you have listened to what the visitor has to say you may know how the problem can be resolved. PERSONAL QUALITIES OF A SECRETARY 1 A Secretary Should Be Cost Conscious: He must have ability to organize ideals, improve things and avoid waste in his daily activities. 2 A Secretary Should Be Cheerful And Hospitable: In his day to day activities the office worker interacts with people of different social and psychology disposition. To make such people come again, the secretary ought to radiate joy in his inter-face with them. 3 To Work Well Under Pressure: A secretary must possess the ability to work under pressure. When work and responsibilities mount and unwieldy the secretary should be clam, under there are too many tasks awaiting treatment on your table, you should as a secretary, be peaceful and clam. 4 Be Tactful, Discrete And Diplomatic In Relating To Visitors And Callers: He must release that he is a keeper of secret and should be careful in letting out secret information to authorized person, being tactful required visitors and his employers. 5 To Be A Good Communicator In Speech And Writer: Be “phonogenic” in oral and telephone conversations. To be “phonogenic”, he needs to pronounce word appropriately using the correct consonants, vowels, diphthong, diction and style. A secretary avoids native language interference in his office communication. CONCLUSION A secretary has many reception duties required of him. These duties were mostly related to correspondence, such as typing out letters. The advent of words processing has significant reduced the time that such duties require. A secretary is often the first business contact a person will meet at any organization. These are many qualities that a secretary is expected to possess in order to do the jobs successfully include attentiveness, a well groomed appearance, loyalty, maturity etc. Furthermore it is emphasized that the secretary must possess or be acquainted with some personal qualities/characteristics that will make her quite unique in the office. Her ability to get along with members within and outside the organization is important. The study portrayed those receptionist duties required as a yardstick for any secretary who wishes to be successful in the secretarial profession. RECOMMENDATION 1) A formal study of training programme should be organized for secretaries on receptionist duties this will further enhance the secretary’s performance and in dealing with people in the industry because adequate and better receptionist duties is an essential factor for efficient and effective of nay organization. 2) god receptionist duties is an essential tool and imperative factors that should be cultivated, sustained and maintained by secretaries, management and other members of any establishment for the attainment of organizational goals. REFERENCES Akpan, E. (1987) Senior Secretarial Duties And Office Organization Macdonald And Evans Ltd Great Britain. Akpan, O. (2000) The Perfect Secretary (An Exposition Of The Secretarial Duties Of The Professional Secretary, Enugu, Procession Publishers Ltd. Eni, A. (2000) The Concept And The Meaning Of Secretary, Enugu, Precision Publishers Ltd. Ezekiel, M. (2000) Receptionist Duties Required Of Secretary In Today’s Business Osprey Publication Centre. Harrison, A. (1999) The Effective Secretary Hong Kong London Group. McCarteny, A. (1996) Secretarial Duties Pitman Publishing Ltd London. Ohakwe, S. N. (2010) The Effectiveness Of Office Practices Jude Global Publication.

nepad

INTRODUCTION The new partnership for Africa’s development (NEPAD) is a vision and strategic framework for Africa’s renewal, the NEPAD strategic framework document arises from a mandate given to the five initiating heads of state (Algeria, Egypt, Nigeria, Senegal, south Africa) by the organization of African unity (OAU) to develop an integrated socio-economic development framework for Africa. The 37th summit of the OAU in July 2001 formally adopted the strategic framework document. ORIGIN The New Partnership for Africa's Development (NEPAD) is an economic development program of the African Union. NEPAD was adopted at the 37th session of the Assembly of Heads of State and Government in July 2001 in Lusaka, Zambia. NEPAD aims to provide an overarching vision and policy framework for accelerating economic co-operation and integration among African countries. It is in this regard that the New Partnership for Africa's Development (NEPAD) is the result of three parallel initiatives. The first is the Millennium Africa Recovery Plan (MAP), led by South African President Thabo Mbeki and unveiled at the World Economic Forum in Davos in January 2001. The second initiative is the Omega Plan, crafted by the President of Senegal, Abdoulaye Wade, and presented to the Summit of Francophone African leaders in Cameroon in January 2001. MAP and the Omega Plan were then combined to give birth to a third initiative the New African Initiative (NAI) that then led to NEPAD in 2001. All three initiatives shared a common interest in increasing the pace and impact of Africa's development. While these initiatives share common characteristics, there were also differences reflecting the regional and other priorities of the enactors. Compromises had to be made in order to merge the three proposals into one initiative. NEPAD thus reflects the compromises involved in arriving at a single initiative. Founding member countries of NEPAD included South Africa, Nigeria, Algeria, Egypt and Senegal. NEPAD was adopted by African Heads of State and Government of the OAU in 2001 and was ratified by the African Union (AU) in 2002 to address Africa's development problems within a new paradigm. NEPAD's main objectives are to reduce poverty, put Africa on a sustainable development path, halt the marginalization of Africa, and empower women. The mechanism for Africa's development – today and tomorrow Since its initiation, NEPAD has been promoted widely both within Africa and in the industrialised North. NEPAD is now recognised as Africa's development plan by all the governments of the North, and the international financial institutions, and by many international governance institutions like the United Nations. NEPAD is widely seen as the mechanism through which support to Africa's development efforts can be best delivered. Thus, the NEPAD process has come to be accepted not only by African countries and RECs but also by Africa's development partners as the framework mechanism for their development efforts. NEPAD is a merger of two plans for the economic regeneration of Africa: the Millennium Partnership for the African Recovery Programme (MAP), led by Former President Thabo Mbeki of South Africa in conjunction with Former President Olusegun Obasanjo of Nigeria and President Abdelaziz Bouteflika of Algeria; and the OMEGA Plan for Africa developed by President Abdoulaye Wade of Senegal. At a summit in Sirte, Libya, March 2001, the Organisation of African Unity (OAU) agreed that the MAP and OMEGA Plans should be merged. The UN Economic Commission for Africa (UNECA) developed a "Compact for Africa’s Recovery" based on both these plans and on resolutions on Africa adopted by the United Nations Millennium Summit in September 2000, and submitted a merged document to the Conference of African Ministers of Finance and Ministers of Development and Planning in Algiers, May 2001.[2] In July 2001, the OAU Assembly of Heads of State and Government meeting in Lusaka, Zambia, adopted this document under the name of the New African Initiative (NAI). The leaders of G8 countries endorsed the plan on July 20, 2001; and other international development partners, including the European Union, China, and Japan also made public statements indicating their support for the program. The Heads of State and Government Implementation Committee (HSGIC) for the project finalized the policy framework and named it the New Partnership for Africa's Development on 23 October 2001. NEPAD is now a program of the African Union (AU) that has replaced the OAU in 2002, though it has its own secretariat based in South Africa to coordinate and implement its programmes. NEPAD seeks to attract increased investment, capital flows and funding, providing an African-owned framework for development as the foundation for partnership at regional and international levels. In July 2002, the Durban AU summit supplemented NEPAD with a Declaration on Democracy, Political, Economic and Corporate Governance. According to the Declaration, states participating in NEPAD ‘believe in just, honest, transparent, accountable and participatory government and probity in public life’. Accordingly, they ‘undertake to work with renewed determination to enforce’, among other things, the rule of law; the equality of all citizens before the law; individual and collective freedoms; the right to participate in free, credible and democratic political processes; and adherence to the separation of powers, including protection for the independence of the judiciary and the effectiveness of parliaments. The Declaration on Democracy, Political, Economic and Corporate Governance also committed participating states to establish an African Peer Review Mechanism (APRM) to promote adherence to and fulfilment of its commitments. The Durban summit adopted a document setting out the stages of peer review and the principles by which the APRM should operate; further core documents were adopted at a meeting in Abuja in March 2003, including a Memorandum of Understanding to be signed by governments wishing to undertake the peer review. Current status Ever since it was set up there has been some tension over the place of NEPAD within the African Unity (AU) programs, given its origins outside the framework of the AU, and the continuing dominant role of South Africa—symbolised by the location of the secretariat in South Africa. Successive African Unity (AU) summits and meetings of the HSGIC have proposed the greater integration of NEPAD into the AU's structures and processes. In March 2007 there was a 'brainstorming session' on NEPAD held in Algeria at which the future of NEPAD and its relationship with the AU was discussed by an ad hoc committee of heads of state. The committee again recommended the fuller integration of NEPAD with the AU. In April 2008, a review summit of five heads of state—Presidents Mbeki of South Africa, Wade of Senegal, Bouteflika of Algeria, Mubarak of Egypt and Yar'Adua of Nigeria—met in Senegal with a mandate to consider the progress in implementing NEPAD and report to the next AU summit to be held in Egypt in July 2008. Structure The HSGIC to which the NEPAD secretariat reports comprises three states for each region of the African Union, with former President Obasanjo (Nigeria) as elected chair, and Presidents Bouteflika (Algeria) and Wade (Senegal) as deputy chairmen. The HSGIC meets several times a year and reports to the AU Assembly of Heads of State and Government. There is also a steering committee, comprising 20 AU member states, to oversee projects and program development. The NEPAD Secretariat is based in Midrand, South Africa. The first CEO was Wiseman Nkuhlu of South Africa (2001–2005), and the second Mozambican Firmino Mucavele (2005–2008). On April 1, 2009, Ibrahim Hassane Mayaki accepted the position as the 3rd CEO. The NEPAD Secretariat is not responsible for the implementation of development programs itself, but works with the African Regional Economic Communities—the building blocks of the African Union. The role of the NEPAD Secretariat is one of coordination and resource mobilisation. Many individual African states have also established national NEPAD structures responsible for liaison with the continental initiatives on economic reform and development programs. Partners • UN Economic Commission for Africa (UNECA) • African Development Bank • Development Bank of Southern Africa (DBSA) • Investment Climate Facility (ICF) • African Capacity Building Foundation • Office of the UN Under-Secretary-General and Special Adviser on Africa • IDC (The Industrial Development Corporation) - Sponsor of NEPAD Programs The eight priority areas of NEPAD are: political, economic and corporate governance; agriculture; infrastructure; education; health; science and technology; market access and tourism; and environment. During the first few years of its existence, the main task of the NEPAD Secretariat and key supporters was the popularisation of NEPAD’s key principles, as well as the development of action plans for each of the sectoral priorities. NEPAD also worked to develop partnerships with international development finance institutions—including the World Bank, G8, European Commission, UNECA and others—and with the private sector. After this initial phase, more concrete programs were developed, including: • The Comprehensive Africa Agriculture Development Programme (CAADP), aimed at assisting the launching of a 'green revolution' in Africa, based on a belief in the key role of agriculture in development. • The Programme for Infrastructure Development in Africa (PIDA) which comprises numerous trans-boundary infrastructure projects in the four sectors transport, energy, water and ICT, aimed at boosting intra-African trade and interconnecting the continent. • The NEPAD Science and Technology programme, including an emphasis on research in areas such as water science and energy. • The "e-schools programme", adopted by the HSGIC in 2003 as an initiative to equip all 600,000 primary and secondary schools in Africa with IT equipment and internet access within 10 years, in partnership with several large IT companies. See NEPAD E-School program • The launch of a Pan African Infrastructure Development Fund (PAIDF) by the Public Investment Corporation of South Africa, to finance high priority cross-border infrastructure projects. • Capacity building for continental institutions, working with the African Capacity Building Foundation, the Southern Africa Trust, UNECA, the African Development Bank, and other development partners. One of NEPAD's priorities has been to strengthen the capacity of and linkages among the Regional Economic Communities. • NEPAD was involved with the Timbuktu Manuscripts Project although it is not entirely clear to what extent. Criticism NEPAD was initially met with a great deal of scepticism from much of civil society in Africa as playing into the 'Washington Consensus' model of economic development. In July 2002, members of some 40 African social movements, trade unions, youth and women's organizations, NGOs, religious organizations and others endorsed the African Civil Society Declaration on NEPAD[8] rejecting NEPAD; a similar hostile view was taken by African scholars and activist intellectuals in the 2002 Accra Declaration on Africa's Development Challenges. Part of the problem in this rejection was the process by which NEPAD was adopted was insufficiently participatory—civil society was almost totally excluded from the discussions by which it came to be adopted. More recently, NEPAD has also been criticised by some of its initial backers, including notably Senegalese President Abdoulaye Wade, who accused NEPAD of wasting hundreds of millions of dollars and achieving nothing. Like many other intergovernmental bodies, NEPAD suffers from slow decision-making, and a relatively poorly resourced and often cumbersome implementing framework. There is a great lack of information about the day-to-day activities of the NEPAD secretariat—the website is notably uninformative—that does not help its case. However, the program has also received some acceptance from those initially very critical, and in general its status has become less controversial as it has become more established and its programs have become more concrete. The aim of promoting greater regional integration and trade among African states is welcomed by many, even as the fundamental macroeconomic principles NEPAD endorses remain contested. ACHIEVEMENT NEPAD achievements during the first 5 years, NEPAD has come about as a result of the merger between the Millennium Partnership for Africa’s Recovery Programme (MAP) and OMEGA plan, which was finalised on 3 July 2001. Out of this merger, the New African Initiative (NAI) was formed. The NAI Policy Framework was finalised by the Heads of State and Implementation Committee of the OAU (now AU) on 23 October 2001 and NAI was renamed to NEPAD on the day. This brief makes a summarised assessment of the achievements by NEPAD as it has reached the age of five. It should however be noted that the short term action plan of NEPAD started later in 2002 and what is assessed here is NEPAD itself based on its far-reaching programmes. It is pointed out in this briefing that NEPAD has achieved a lot in terms of gaining international recognition; getting the African civil society on board; promoting good governance through peer reviews; developing regional infrastructure; and promoting agricultural activity. One notable event where NEPAD made its mark on the international stage was the G8 summit that took place in Canada in June 2002. At that meeting, four promoters of NEPAD, together with the UN Secretary-General were invited to discuss challenges facing Africa, and for the G8 to give its first response to the NEPAD plan. This has resulted in the adoption of the G8 African Action Plan as a framework to support African countries whose performance reflects the commitments of NEPAD. Under the plan, the G8 indicated their increased commitment to support Africa under various initiatives, including the HIPC, enhanced HIPC, ODA, and the Global Fund to fight HIV/AIDS, malaria and TB. The organisation of various regional workshops that brought together stakeholders from civil society, business and government sectors were another achievement. The main aim of these workshops is to increase awareness amongst all stakeholders about the plan and to urge stakeholders to implement it. Hanns Seidel Foundation has taken a lead in organising such workshops in Southern and Eastern Africa. Another achievement, which is also linked to the first two, is the extensive coverage of NEPAD in literature and media, in Africa and abroad, and from different disciplines of science. The African Peer Review Mechanism of NEPAD that works to promote democracy and good governance has already produced results. The review reports from Ghana and Kenya have been published, while the same process is at an advanced stage in further nine countries. NEPAD has done well in the area of regional infrastructure development since 2002. Over US$530 million has already been used in the development of roads, communications and energy networks, while projects worth around US$490 million were under consideration during 2005. Furthermore, NEPAD has formulated an Agricultural Development Plan whereby member states of the AU have committed themselves to develop pro-development policies and to allocate sufficient resources to the sector. Among its achievements, that are cited in the NEPAD Briefing 15, are gaining international recognition, getting African civil society on board, promoting good governance through peer reviews, developing regional infrastructure and also promoting agricultural activities. NEPAD PRIMARY OBJECTIVES • To eradicate poverty; • To place African countries, both individually and collectively, on a path of sustainable growth and development; • To halt the marginalisation of Africa in the globalisation process; • To accelerate the empowerment of women; • To fully integrate Africa into the global economy OTHER OBJECTIVES NEPAD provides an historic opportunity to overcome obstacles to development in Africa. Our contribution to the initiative is the creation of NEPAD Council, designed to encourage the imaginative effort that underlies the NEPAD and to lay a solid foundation for future cooperation and sustainable development. The case for action is compelling. Despite its great potential and human resources, Africa continues to face some of the world’s greatest challenges. The many initiatives designed to spur Africa’s development have failed to deliver sustained improvements to the lives of women, men and children throughout Africa. NEPAD Council offers something different. It is, first and foremost, a common vision shared by African professionals to support and promote the New Partnership for Africa’s Development. Together, we have an unprecedented opportunity to make progress on our common goals of eradicating extreme poverty and achieving sustainable development. NEPAD Council will support African leaders’ efforts to encourage public engagement in the NEPAD and will consult with NEPAD members on how we can best assist their efforts. NEPAD Council will be committed to mobilize and energize global action, marshal resources and expertise, and provide impetus in support of NEPAD’s objectives. As NEPAD’s partner, NEPAD Council will undertake mutually reinforcing actions to help Africa accelerate growth and make lasting gains against poverty. The Agenda of NEPAD Council will focus on a limited number of priority areas where, collectively and individually, we can add value. NEPAD Council will focus particular attention on enhanced-partnership countries. It will also work with countries that do not yet meet the standards of NEPAD but which are clearly committed to and working towards its implementation. The objectives of NEPAD Council include: 1. Support the new partnership for Africa’s Development 2. Support African leaders’ efforts to encourage public engagement in NEPAD strategies and projects 3. Assist the Steering Committee and NEPAD 4. Secretariat in the implementation of NEPAD projects 5. Collaborate with NEPAD to undertake mutually reinforcing actions to help accelerate growth and make long-lasting gains against poverty 6. Encourage Africans in the Diaspora to actively participate in all efforts aimed at developing Africa "NEPAD Council offers something different. It is, first and foremost, a common vision shared by African professionals to support and promote the New Partnership for Africa’s Development." CONCLUSION Our interest in NEPAD is a simple one. It is a call that NEPAD should be accepted on the ground that Africa requires a development blueprint. This acceptance should not be uncritical. NEPAD must not be regarded as a finished and closed document that cannot accommodate the high points other pan-African and national development blueprints. Our suggestions point out to one problem NEPAD is bound to face. NEPAD has wholesomely and uncritically adopted ‘neo-liberal democracy’ cum Keynesian free market political economy. But Africa requires more of a social democracy, especially those practiced in States that were challenged with the task of revamping their economies and putting themselves on the path of development. Germany is a good example in this light. No development is possible in Africa except majority of its people who are rural dwellers and have been historically disconnected from the State and indeed productions are reconnected to these institutions and functions. Today, the African productive class is one that is unemployed, a hawker and loafer in the city, or one who is seeking to escape to Europe, the United States of America or some other developed societies. NEPAD is the appreciation of the fact that undue ‘economism’ has failed to deliver in Africa for over 40 years. REFERENCES Adedeji and T. Shaw, eds., Economic Crisis in Africa: Perspectives on Development Problems and Potentials (Boulder, Colorado: Lynne Rienner Publishers) Adejumobi, Said. (2002): “Globalisation and Africa’s Development Agenda: From the WTO to NEPAD.” Proceedings of the 7th Annual Conference on the Challenges of Globalisation to Democratic Governance in Africa: What Role for the Civil Society And other Stakeholders? Addis Ababa: Development Policy Management Forum Agbu, Osita. (2002): “Nigeria and the NEPAD initiative.” Nigeria Forum: The Nigerian Institute of International Affairs (NIIA), vol. 23, Nos. 7-8. Bukarambe, Bukar. (2002): “Historical Overview of Africa’s Development Efforts: Problems and Prospects of NEPAD.” Nigerian Forum, ibid. Edward W. Blyden, (1995): “Africa and the African.” In Albert G. Mosley, ed., African Philosophy: Selected Readings, New Jersey: Prentice-Hall, Inc. Gambari, Ibrahim A. (2004): “The New Partnership for Africa’s Development: Challenges and Progress in Organizing International Support.” NIIA Lecture Series, No.85. Mosley, Albert G. ed. (1995): African Philosophy: Selected Readings, New Jersey:Prentice- Hall, Inc. Ogwu, Joy U. (2002): ‘Introduction.’ NIIA Lecture Series, No. 82. Ogwu, Joy U. (2004): “Partnership for human development in Africa.” NIIA Lecture Series, No. 85. Olukoshi, Adebayo O. (2004): “Governing the African Development Process: the Challenges of the New Partnership for Africa’s Development.” NIIA Lecture Series, No.82. Omoweh, Daniel A. (2002): “The New Partnership for Africa’s Development (NEPAD): A preliminary evaluative analysis, Nigerian Forum, NIIA, vol. 23, Nos. 7-8, July- August,2002.

social

Social responsibility Social responsibility is an ethical framework which suggests that an entity, be it an organization or individual, has an obligation to act for the benefit of society at large. Social responsibility is a duty every individual has to perform so as to maintain a balance between the economy and the ecosystems. A trade-off may[citation needed] exist between economic development, in the material sense, and the welfare of the society and environment. Social responsibility means sustaining the equilibrium between the two. It pertains not only to business organizations but also to everyone whose any action impacts the environment.[1] This responsibility can be passive, by avoiding engaging in socially harmful acts, or active, by performing activities that directly advance social goals. Businesses can use ethical decision making to secure their businesses by making decisions that allow for government agencies to minimize their involvement with the corporation.[2] For instance if a company follows the United States Environmental Protection Agency (EPA) guidelines for emissions on dangerous pollutants and even goes an extra step to get involved in the community and address those concerns that the public might have; they would be less likely to have the EPA investigate them for environmental concerns.[3] "A significant element of current thinking about privacy, however, stresses "self-regulation" rather than market or government mechanisms for protecting personal information".[4] According to some experts, most rules and regulations are formed due to public outcry, which threatens profit maximization and therefore the well-being of the shareholder, and that if there is not outcry there often will be limited regulation.[5] Critics argue that corporate social responsibility (CSR) distracts from the fundamental economic role of businesses; others argue that it is nothing more than superficial window-dressing; others argue that it is an attempt to pre-empt the role of governments as a watchdog over powerful corporations though there is no systematic evidence to support these criticisms. A significant number of studies have shown no negative influence on shareholder results from CSR but rather a slightly negative correlation with improved shareholder returns.[clarification needed][6] Contents • 1 Student social responsibility • 2 Corporate social responsibility • 3 Social Responsibility of Scientists and Engineers • 4 Emerging normative status of social responsibility • 5 See also • 6 Notes • 7 References • 8 Further reading Student social responsibility Student social responsibility is the responsibility of every student for his/her actions. It is morally binding on everyone to act in such a way that the people immediately around them are not adversely affected. It is a commitment everyone has towards the society – contributing towards social, cultural and ecological causes. SSR is based on an individual's ethics. Instead of giving importance only to those areas where one has material interests the individual supports issues for philanthropic reasons. It forms the base for CSR or Corporate Social Responsibility because if everyone in a business organization does his/her bit the bigger things automatically fall into place. The trends however show that big charitable organizations recorded high growth due to the SR efforts of individuals and not corporations or the government. ISR may be slightly impractical, especially in the modern competitive world, where everyone works for self-interest, but it will succeed if we take decisions based on what will benefit a large number of people and respect everyone's fundamental rights. As individuals we can make our small contributions to society by donating money to trustworthy NGO's, saving our resources by reducing our consumption, e.g. by switching off lights or computers when not in use. 2. Corporate social responsibility Corporate social responsibility or CSR has been defined by Lord Holme and Richard Watts in the World Business Council for Sustainable Development’s publication “Making Good Business Sense” as “…the continuing commitment by business to behave ethically and contribute to economic development while improving the quality of life of the workforce and their families as well as the local community and society at large.” CSR is one of the newest management strategies where companies try to create a positive impact on society while doing business. Evidence suggests that CSR taken on voluntarily by companies will be much more effective than CSR mandated by governments.[7] There is no clear-cut definition of what CSR comprises. Every company has different CSR objectives though the main motive is the same. All companies have a two-point agenda—to improve qualitatively (the management of people and processes) and quantitatively (the impact on society). The second is as important as the first and stake holders of every company are increasingly taking an interest in "the outer circle"-the activities of the company and how these are impacting the environment and society.[8] Social Responsibility of Scientists and Engineers One common view is that scientists and engineers are morally responsible for the negative consequences which result from the various applications of their knowledge and inventions.[9][10][11][12][13] After all, if scientists and engineers take personal pride in the many positive achievements of science and technology, why should they be allowed to escape responsibility for the negative consequences related to the use or abuse of scientific knowledge and technological innovations?[14] Furthermore, scientists and engineers have a collective responsibility for the choice and conduct of their work. Committees of scientists and engineers are often involved in the planning of governmental and corporate research programs, including those devoted to the development of military technologies and weaponry.[15][16] Many professional societies and national organizations, such as the National Academy of Science and the National Academy of Engineering in the United States, have ethical guidelines (see Engineering ethics and Research ethics for the conduct of scientific research and engineering).[17] Clearly, there is recognition that scientists and engineers, both individually and collectively, have a special and much greater responsibility than average citizens with respect to the generation and use of scientific knowledge. Unfortunately, it has been pointed out that the situation is not that simple and scientists and engineers should not be blamed for all the evils created by new scientific knowledge and technological innovations.[18] First, there is the common problem of fragmentation and diffusion of responsibility. Because of the intellectual and physical division of labor, the resulting fragmentation of knowledge, the high degree of specialization, and the complex and hierarchical decision-making process within corporations and government research laboratories, it is exceedingly difficult for individual scientists and engineers to control the applications of their innovations.[19] This fragmentation of both work and decision-making results in fragmented moral accountability, often to the point where "everybody involved was responsible but none could be held responsible."[20] Another problem is ignorance. The scientists and engineers cannot predict how their newly generated knowledge and technological innovations may be abused or misused for destructive purposes in the near or distant future. While the excuse of ignorance is somewhat acceptable for those scientists involved in very basic and fundamental research where potential applications cannot be even envisioned, the excuse of ignorance is much weaker for scientists and engineers involved in applied scientific research and technological innovation since the work objectives are well known. For example, most corporations conduct research on specific products or services that promise to yield the greatest possible profit for share-holders. Similarly, most of the research funded by governments is mission-oriented, such as protecting the environment, developing new drugs, or designing more lethal weapons. In all cases where the application of scientific knowledge and technological innovation is well known a priori, it is impossible for a scientist or engineer to escape responsibility for research and technological innovation that is morally dubious.[21] As John Forge writes in Moral Responsibility and the Ignorant Scientist: "Ignorance is not an excuse precisely because scientists can be blamed for being ignorant."[22] Another point of view is that responsibility falls on those who provide the funding for the research and technological developments, which in most cases are corporations and government agencies. Furthermore, because taxpayers provide indirectly the funds for government-sponsored research, they and the politicians that represent them, i.e., society at large, should be held accountable for the uses and abuses of science.[23] Compared to earlier times when scientists could often conduct their own research independently, today's experimental research requires expensive laboratories and instrumentation, making scientists dependent on those who pay for their studies. Emerging normative status of social responsibility Social responsibility as a non-binding, or soft law principle has received some normative status in relation to private and public corporations in the United Nations Educational, Scientific and Cultural Organization (UNESCO) Universal Declaration on Bioethics and Human Rights developed by the UNESCO International Bioethics Committee particularly in relation to child and maternal welfare.[24](Faunce and Nasu 2009) The International Organization for Standardizationrd will "encourage voluntary commitment to social responsibility and will lead to common guidance on concepts, definitions and methods of evaluation."[25] The standard describes itself as a guide for dialogue and language, not a constraining or certifiable management standard.[26] How Companies Can Become More Socially Responsible In a recent article I co-wrote with Milinda Martin, In the Future, Companies Will Only Survive if They Help Solve Big Social Problems, we predicted that “2015 will mark the beginning of a long-term transition of the role and purpose of the world’s largest public companies and the value chains they control” and suggested that “the new imperative for business leaders will be to embrace the idea that the viability of their businesses depends on solving the world’s most pressing societal issues.” The vision for the future we illustrated was based on input from corporate leaders who have observed that most of the ways in which businesses currently contribute to social change aren’t very effective for companies or communities. We suggested that in the years ahead leading businesses would abandon tokenistic corporate social responsibility, commit to bold social goals, and integrate social change in all aspects of their operations. In responding to comments from readers, I realized that we missed an opportunity to help corporations become more effective agents of social change by providing specific ideas for what they should start to do differently in 2015. So here are seven ideas to help executives move their businesses towards a more compelling long-term vision and improve their performance in 2015. 1. Pick a big issue, declare a clear goal, and mobilize your resources. Corporations become successful because they identify problems, allocate resources to uncover and deliver solutions, and are accountable for what happens. The role of business in social change should be no different. Tyson Foods, one of the world’s largest producers of meat and poultry, has a social goal of ending hunger. Through its KNOW Hunger program, Tyson donates to food banks and increases awareness of hunger issues on a large scale. At the end of 2010, Tyson had donated 78 million pounds of protein—enough to serve one meal to every American citizen. 2. Make more effort to engage the millennials in your workforce. Employees of this generation want to be rewarded in ways that go beyond compensation and expect their employers to support their interest in social change. These employees also want to apply what they know to issues that they’re passionate about. This means reduce or eliminating activities that have employees doing menial tasks that don’t contribute to measurable social outcomes. For more about this, refer to MSLGroup’s excellent report, The Future of Business Citizenship. 3. Engage your naysayers. Corporations that include the perspectives of advocacy organizations create opportunities to make meaningful changes. “Nestlé has been engaging much more systematically with stakeholders, even constructively critical ones, to ask them what they expect of us,” said Paul Bakus, that company’s president of corporate affairs, in a recent Forbes.com interview. “This has led to the development of 35 forward-looking commitments covering every area of our business—nutrition, water, rural development, sustainability, and compliance.” 4. Begin to allocate some of your company’s philanthropic giving to social purpose businesses and/or social enterprises. This will establish a base of social investment the results of which can be quantified while you preserve philanthropic commitments that are meaningful to employees and stakeholders. Based on 2013 figures from the Giving USA Foundation, reducing philanthropic contributions by approximately 50% of what they are today would create an annual pool of social finance capital of approximately $8 billion in the U.S. alone. Company More Socially Responsible for the Stakeholders Companies can be torn between two extremes in today's global marketplace. On the one hand, the desire to compete and succeed is the basis for all business activity. Businesses that do not compete do not survive. On the other hand, concerns over environmentalism, social welfare, charity and other humanitarian concerns are also important for businesses because businesses are also expected to be socially responsible on some level. Making your company more socially responsible for stakeholders is no simple task, but there are a few simple steps you can take to get yourself moving in the right direction. Step 1 Assess your current level of participation in social programs. You need to know where you are starting from if you are to determine how to be more socially responsible for your stakeholders. The misalignment of corporate competitiveness with corporate responsibility stems from one of three issues: inexperienced corporate staff, isolation of managers in charge of corporate responsibility from the rest of the business, and a limited or restricted budget. Step 2 Establish goals that are attainable. Taking baby steps to get started and build your corporate responsibility can get you moving in the right direction. Make sure that your goals can be measured to make sure you are moving forward in the right direction. Eliminate waste or take care of other "close to home" responsibilities first. Step 3 Provide detailed reports to your stakeholders to ensure that they know exactly what steps you are taking to improve your socially responsible activity. Use concurrent press releases and other announcements to increase awareness of your company's actions. This will provide the added advantage of creating a picture among the general public of your company as being socially responsible. Step 4 Obtain feedback from stakeholders in the company. Create a system of two-way communication between shareholders and the company when it comes to the cultivation of social responsibility. This method flies in the face of more traditional methods of corporate communication where the company simply tells shareholders about its actions. Instead, this gives the shareholders a stake in what the company does. Step 5 Prioritize your efforts. Take on the simplest tasks first so that you can accomplish them quickly. This will help build your reputation with the rest of the community and give your stakeholders an opportunity to get involved incrementally as you build towards bigger and more ambitious projects. Wade out into the water before jumping or diving in to immerse yourself.

Mathemat ics 1983-2004 JAMB QuestionsAndAnswers Mathematics 1983 1. If M represents the median and D the mode of the measurements 5, 9, 3, 5, 8 then (M,D) is A. (6,5) B. (5,8) C. (5,7) D. (5,5) E. (7,5) 2. A construction company is owned by two partners X and Yand it is agreed that their profit will be divided in the ratio 4:5. at the end of the year. Y received #5,000 more than x. what is the total profit of the company for the year? A. #20,000.00 B. P’0#25,000.00 C. #30,000.00 D. #15,000.003 E.#45,000.00 3. Given a regular hexagon, calculate each interior angle of the hexagon. A. 600 B. 300 C. 1200 D. 450 E. 1350 4. Solve the following equations 4x – 3 = 3x + y = 2y + 5x – 12 A. 4x=5, y= 2 B. x=2, y=5 C. x=-2, y=-5 D. x=5,y=-2 E. x=-5,y=-2 5. If x = 1 is root of the equation x3 – 2x2 – 5x + 6, find the other roots A. -3and2 B. –2 and2 C. 3and –2 D. 1and 3 E. –3and 1 6. If x is jointly proportional to the cube of y and the fourth power of z. In what ratio is x increased or decreased when y is halved and z is doubled? A. 4:1 increase B. 2:1increase C. 1:4 decrease D. 1: 1 nochange E. 3: 4 decrease 7. In the above figure PQR = 600, QPR= 900, PRS = 900, RPS = 450,QR= 8cm. DeterminePS A. 2Ö3cm B. 4Ö6cm C. 2Ö6cm D. 8Ö6cm E. 8cm 8. Given that cos z = L, where z is an acute angle find an expression for Co +Z - cosecz sec Z + tan z A. l - L B. L2-Ö1-L2 C. -L-Ö1-L 1+L L2+L-1 (C1+L) +Ö1-L2 D. ÖL-1. E. L-(L2-1) (L1+L2) +Ö1-L2 1+ Ö1 - L2+ Ö1 - L2 9. If 0.0000152 x 0.00042 =Ax108,where 1 £A< 10, findAand B. A. A= 9, B= 6`.38 B. A= 6.38, B = -9 C. A= 6.38, B = 9 D. A= 6.38, B = -1 E. A= 6.38, B= 1 10. If x + 2 and x – 1 are factors of the expressions lx + 2kx2 + 24, find the values of l and k A. l=-6,k=-9 B. l=-2,k= 1 C. l=-2,k=-1 D. l=0,k= 1 E. l=6,k= 0 11. Make T the subject of the equation av = 3 2V + T 1- V a 2T A. 3av/(1-v) B. 2v(1-v)2 - a2v2/2a2v2 - (1-V)2 C. 2v(1 - v)2 + a3v2/ 2a2v2 + (1 - v)2 D. 2v(1 - v)2 - a4v3/2a3v3 - (1 - v)3 E. 2v(1-v)3 - a4v3/2a3v3 + (1-v)3 12. In a class of 60 pupils, the statistical distribution of the number of pupils offering Biology, History, French, Geography andAdditionalMathematics is as shown in the pie chart above. Howmany pupils offerAdditional Mathematics? A. 15 B. 10 C. 18 D. 12 E. 28 13 The value of (0.303)3 – (0.02)3 is A. 0.019 B. 0.0019 C. 0.00019 D. 0.000019 E. 0.000035 14. y varies partly as the square of x and y partly as the inverse of the square root of x. write down the expression for y if y= 2 when x = 1 and y= 6 when x = 4 A. y = 10x2 + 52 B. y = x2 + 1 31 31Öx Öx C. y= x2 + 1 D. y= x2 + 1 E. y = 10 (x2 + 1 ) x 31 31Ö x 31( Öx) 15. Simplify (x – 7) / (x2 – 9) ( x2 – 3x)/( x2 - 49) A. x/(x-3)(x+7) B. (x+3)(x+7)/x C. x/(x-3)(x - 7) D. x/(x+3)(x+7) E. x/(x+4)(x+7) 16. The lengths of the sides of a right-angled triangle at (3x + 1)cm, (3x - 1)cmand x cm. A. 2 B. 6 C. 18 D. 12 E. 0 17. The scores of a set of a final year students in the first semester examination in a paper are 41,29,55,21,47,70,70,40,43,56,73,23,50,50. find themedian of the scores. A. 47 B. 481/2 C. 50 D. 48 E. 49 45O 60O S P 8 cm Q R (2x-24)O (3x-18)O (x+12)O (2x+12)O xO Geography Additional Mathematics Biology French History 18. Which of the following equations represents the above graph? A. y=1+2x+3x2 B. y=1–2x+3x2 C. y=1+2x3x2 D.y=1–2x–3x2 E.y=3x2+2x- 1 19. The above figure FGHKis a rhombus.What is the value of the angle x? A. 900 B. 300 C. 1500 D. 1200 E. 600 20. PQRS is a desk of dimensions 2mx0.8mwhich is inclined at 300 to the horizontal. Find the inclination of the diagonal PR to the horizontal. A. 23035’ B. 300 C. 15036’ D. 100 E. 10042’ 21. Find x if (x base 4)2 = 100 1000base 2 A. 6 B. 12 C. 100 D. 210 E. 110 22. Simplify log10a1/2 + 1/4log10a – 1/12log10a7 A. 1 B. 7/6log10a C. 0 D. 10 E. a 23. If w varies inversely as V and u varies directly as w3, find the relationship between u and V given that u = 1, when V = 2 A. u=8V3 B. u=2 V C. V=8/u2 D. V=8u2 E. U= 8/v3 24. Solve the simultaneous equations for x x2 + y – 8 = 0 y + 5x – 2 = 0 A. –28, 7 B. 6,-28 C. 6,-1 D. –1, 7 E. 3, 2 25. Find the missing value in the following table. A. -3 B. 3 C. –9 D. 13 E. 9 26. If O is the centre of the circle in the figure above. Find the value of x A. 50 B. 260 C. 100 D. 65 E. 130 27. Find the angle of the sectors representing each item in a pie chart of the following data. 6,10,14,16,26 A. 150,250,350,400,650, B.600,1000,1400,1600,2600 C. 60,100,140,160,260, D.300,500,700,800,1300 E. None of the above 28. The scores of 16 students in a Mathematics test are 65,65,55,60,60,65,60,70,75,70,65,70,60,65,65,70 What is the sum of the median and modal scores? A. 125 B. 130 C. 140 D. 150 E. 137.5 29. The letters of the wordMATRICULATION are cut and put into a box. One of the letter is drawn at randomfrom the box. Find the probability of drawing a vowel. A. 2/13 B. 5/13 C. 6/13 D. 8/13 E. 4/13 30. Correct each of the number 59.81789 and 0.0746829 to three significant figures andmultiply them, giving your answer to three significant figures. A. 4.46 B. 4.48 C. 4.47 D. 4.49 E. 4.50 31. If a rod of length 250cm is measured as 255cm longer in error, what is the percentage error in measurement? A. 55 B. 10 C. 5 D. 4 E. 2 32. If (2/3)m (3/4)n = 256/729, find thevalues ofm and n A. m=4,n= 2 B. m=-4,n=-2 C. m=-4,n= 2 D. m=4,n=-2 E. m=-2,n= 4 33. Without using tables find the numerical value of log749 + log7(1/7) A. 1 B. 2 C. 3 D. 7 E. 0 y x 12 9 6 3 -3 -6 -9 -12 -15 -3 -2 -1 3 2 1 30O H K G F x 30O 0-8 m 2 m P 0 Q R S 130O xO O x -2 -1 0 1 2 3 y = x - x + 3 3 3 3 9 27 O3 34. Factorize completely 81a4 – 16b4 A. (3a + 2b) (2a – 3b) (9a2 + 4b2) B. (3a - 2b) (2a – 3b) (4a2 - 9b2) C. (3a - 2b) (3a – 2b) (9a2 + 4b2) D. (3a - 2b) (2a – 3b) (9a2 + 4b2) E. (3a - 2b) (2a – 3b) (9a2 - 4b2) 35. One interior angle of a convex hexagon is 1700 and each of the remaining interior angles is equal to x0. find x A. 1200 B. 1100 C. 1050 D. 1020 E. 1000 36. PQRS is a cyclic quadrilateral in which PQ= PS. PT is a tangent to the circle and PQmakes and angle 500 with the tangent as shown in the figure below. What is the size of QRS? A. 500 B. 400 C. 1100 D. 800 E. 1000 37. A ship H leaves a port P and sails 30km due South. Then it sails 60km due west.What is the bearing of H fromP? A. 26034’ B. 243026’ C. 116034’ D. 63026’ E. 2400 38. In a sample survey of a university community the following table shows the percentage distribution of the number ofmembers per household. A. 4 B. 3 C. 5 D. 4.5 E. None 39. On a square paper of length 2.524375cm is inscribed a square diagram of length 0.524375. find the area of the paper no covered by the diagramcorrect to 3 significant figures. A. 6.00cm2 B. 6.10cm2 C. 6.cm2 D. 6.09cm2 E. 4.00cm2 40. If f(X) = 1 + x - 1 find f(1-x) x-1 x2-1 A. 1/x + 1/(x+2) B. x +1/(2x -1) C. -1/x - 1/(x-2) D. -1/x + 1/(x2-1) 41. In the figure belowfind PRQ A. 661/2 0 B. 621/2 0 C. 1250 D. 1050 E. 650 42. Simplify 27a9/8 A. 9a2/2 B. 9a3/2 C. 2/3a2 D. 2/3a2 E. 3a3/2 43. The farm yields of four crops on a piece of land in Ondo are represented on the pie chart above. What is the angle of the sector occupied by Okro in the chart? A. 911/2 0 B. 191/3 0 C. 331/3 0 D. 110 E. 910 44. In the figure above, PQR is a straight line. Find the values of x and y A. x = 22.50 and y = 33.750 B. x = 150 and y = 52.50 C. x = 22.50 and y = 45.00 D. x = 56.250 and y = 11.50 E. x = 18.0 and y = 56.50 45. PQR is the diameter of a semicircle RSP with centre at Qand radius of length 3.5cmc. ifQPT= QRT = 600. Find the perimeter of the figure (PTRS p = 22/7) A. 25cm B. 18ccm C. 36cm D. 29cm E. 255cm 50O S R Q T P No of members per household 1 2 3 4 5 6 7 8 Total 3 12 15 28 21 10 7 4 100 Number of households 235 o Q P R Yams 184.5 kg Rice 45.4 kg Okro 14.5 Beans kg 14.5 kg 45O yO (x+3y)O (3x+y)O Q R P 60O O 60O P R S T 46. In a trianglePQR,QR= 3cm, PR= 3cm, PQ= 3cmand PQR = 300. find angles P and R A. P = 600 and R = 900 B. P = 300 and R = 1200 C. P = 900 and R = 600 D. P = 600 and R = 600 E. P = 450 and R = 1050 47. In the above diagramif PS= SRand PQ//SR. what is the size of PQR? A. 250 B. 500 C. 550 D. 650 E. 750 48. Find the mean of the following 24.57,25.63,25.32,26.01,25.77 A. 25.12 B. 25.30 C. 25.26 D. 25.50q E. 25.73 49. In the figure above PT is a tangent to the circle with centreO. if PQT = 300. find the value of PTO A. 300 B. 150 C. 240 D. 120 E. 600 50 A man drove for 4hours at a certain speed, he then doubled his speed and drove for another 3 hours. Altogether he covered 600km. At what speed did he drive for the last 3 hours? A. 120km/hr B. 60km/hr C. 600/7km/hr D. 50km/hr E. 100km/hr. 1. Simplify (2/3 – 1/5) – 1/3 of 2/5 3 – 1/1/2 A. 1/7B. 7 C. 1/3 D. 3 E. 1/5 2. If 263 + 441 = 714, what number base has been used? A. 12 B. 11 C. 10 D. 9 E. 8 3. 0.00014323/1.940000 = k x 10nwhere 1 £ k < 10 and n is a whole number. The values ofK and are A. 7.381 and –11 B. 2.34 and 10 C. 3.87 and 2 D. 7.831 and –11 E. 5.41 and –2 4. P sold his bicycle toQ at a profit of 10%. Q sold it to R for #209 at a loss of 5%. Howmuch did the bicycle cost P? A. #200 B. #196 C. #180 D. #205 E. #150 5. If the price of oranges was raised by 1/2k per orange, the number of oranges customer can buy for #2.40 will be less by 16. What is the present price of an orange? A. 21/2k B. 31/2k C. 51/2k D. 20k E. 211/2k Mathematics 1984 6. A man invested a total of #50,000 in two companies. If these companies pay dividend of 6% and 8% respectively, how much did he invest at 8% if the total yield is #3.700? A. #15,000 B. #29,600 C. #21,400 D. #27,800 E. #35,000 7. Thirty boys and x girls sat for a test. The mean of the boys’ scores and that of the girls were respectively 6 and 8. find x if the total score was 468. A. 38 B. 24 C. 36 D. 22 E. 41 8. The cost of production of an article is made up as follows Labour #70 Power #15 Materials #30 Miscellaneous #5 Find the angle of the sector representing labour in a pie chart. A. 2100 B. 1050 C. 1750 D. 1500 E. 900 9. Bola chooses at random a number between 1 and 300. What is the probability that the number is divisible by 4? A. 1/3 B. ¼ C. 1/5 D. 4/300 E. 1/300 100O P Q 130O S R 30O 2xO xO xO Q T P O 10. Find without using logarithm tables, the value of Log327 – Log1/464 Log31/81 A. 7/4 B. –7/4 C. –3/2 D. 7/3 E. –1/4 11. A variable point P(x, y) traces a graph in a two dimensional plane. (0, -3) is one position of P. If x increases by 1 unit, y increases by 4 units. The equation of the graph is A. -3 = y+ 4/ x + 1 B. 4y= -3 + x C. y/x = -3/4 D. y+ 3 = 4x E. 4y= x + 3 12. Atrader in a countrywhere their currency ‘MONT’ (M) is in base five bought 103(5) oranges at M14(5) each. If he sold the oranges at M24(5) each, what will be his gain? A. M103(5) B. M1030(5) C. M102(5) D. M2002(5) E. M3032(5) 13. Rationalize (5Ö5 - 7Ö5)(/Ö7- Ö5 A. -2Ö35 B. 4Ö7 - 6Ö5 C. -Ö35 D. 4Ö7 - 8Ö5 E. Ö35 14. Simplify 3n – 3n – 1 33 x 3n – 27 x 3n – 1 A. 1 B. 0 C. 1/27 D. 3n – 3n – 1 E. 2/27 15. p varies directly as the square of q an inversely as r. if p = 36, when q = 3 and r = p, find pwhen q = 5 and r = 2 A. 72 B. 100 C. 90 D. 200 E. 125 16. Factorise 6x2 – 14x - 12 A. 2(x +3) (3x - 2) B. 6(x - 2) (x +1) C. 2(x - 3) (3x +2) D. 6(x+ 2) (x - 1) E. (3x +4) (2x+3) 17. A straight line y=mx meets the curve y = x2 – 12x + 40 in two distinct points. If one of them is (5,5), find the other A. (5,6) B. (8,8) C. (8,5) D. (7,7) E. (7,5) 18. The table belowis drawn for a graph y = x2 – 3x + 1 Fromx = -2 to x = 1, the graph crosses the x-axis in the range(s) A. -1 < x< 0 and 0 < x < 1 B. -2 < x < -1 and 0< x < 1 C. -2 < x < -1 and 0< x < 1 D. 0< x <1 E. 1< x < 2 19. In a racing competition.Musa covered a distance of 5xkm in the first hour and (x + 10)kmin the next hour. Hewas second toNgozi who covered a total distance of 118km in the two hours.Which of the following inequalities is correct? A. 0 < -x < 15 B. –3 < x < 3 C. 15 y A. (12, 9) B. (23,17) C. (17,11) D. (18,12) 12. In 1984, Ike was 24 years old and is father was 45 years old in what year was Ike exactly half his father’s age? A. 1982 B. 1981 C. 1979 D. 1978 13. Simplify ( 1 1 ) x -1/Ö3 (Ö5 + Ö3 - Ö5 - Ö3) A. Ö3/Ö5 B. –2/Ö3 C. –2 D. –1 14. Find n if Log24 + Log2Z – Log2n = -1 A. 10 B. 14 C. 27 D. 28 15. (91/3 x 27-1/2) / (3-1/6 x 3-2/3) A. 1/3 B. 1 C. 3 D. 9 16. If x varies directly as y3 and x = 2 when y = 1, find x when y = 5 A. 2 B. 10 C. 125 D. 250 17. Factorize completely. 3a+ 125ax3 A. (2a+ 5x2)(4 + 25ax) B. a(2+ 5x)(4 – 10x + 25ax2) C. (2a + 5x)(4 - 10ax +25ax2) D. a(2+ 5x)(4+ 10ax + 25ax2) 18. If y = x/(x – 3) + x/(x + 4) find ywhen x = -2 A. -3/5 B. 3/5 C. –7/5 D. 7/5 19. Find all the numbers x which satisfy the inequality 1/ 3(x + 1) – 1 > 1/5 (x + 4) A. x<11 B. x< -1 C. x> 6 D. x>11 20. Factorize x2 + 2a + ax+ 2x A. (x+ 2a)(x +1) B. (x+ 2a)(x - 1) C. (x2 - 1)(x + a) D. (x+ 2)(x +a) 21. Solve the equation 3x2 + 6x – 2 = 0 A. x= -1,±Ö3/3 B. x=-1,±Ö15/Ö3 C. x = -2, ±2Ö3/3 D. x= -2, ±2Ö15/3 22. Simplify. 1/ 5x +5 + 1/7x + 7 A. 12/35+7 B. 1/35(x+1) C. 12x/35(x+1) D. 12/35x+ 35 23. The curve y = -x2 + 3x + 4 intersects the coordinate axes at A. (4,0)(0,0)(-1,0) B. (-4,0)(0,4)(1,1) C. (0,0)(0,1)(1,0) D. (0,4)(4,0)(-1,0) 24. Factorize (4a + 3)2 – (3a - 2)2 A. (a + 1)(a + 5) B. (a - 5)(7a - 1) C. (a + 5)(7a + 1) D. a(7a + 1) 25. If 5(x + 2y) = 5 and 4(x + 3y) = 16, find 3(x +y) A. 0 B. 1 C. 3 D. 27 26. Simplify 1/ x - 2 + 1/ x + 2 + 2x / x2 - 4 A. 2x/ (x-2) (x+2) (x2 - 4) B.2x/x2 - 4 C. x/x2 - 4 D. 4x/ x2 - 4 27. Make r the subject of the formula S = 6/v - w/2 A. V = 6 = 12 B. v = 12 S2 w 252 - w C. v = 12 - 2s2 D. v = 12 w 2s2 + w 28. Find the values of x which satisfy the equation 16x – 5x 4x + 4 = 0 A. 1 and 4 B. –2 and 2 C. 0 and 1 D. 1 and 0 29. a/b –c/d = k, find the value of (3a2 – ac + c2)/(3b2 – bd + d2) in term of k A. 3k2 B. 3k – k2 C. 17k2/4 D. k2 30. At what point does the straight line y = 2x + 1 intersect the curve y = 2x2 + 5x – 1? A. (-2,-3) and (1/2, 2) B. (-1/2 0) and (2, 5) C. (1/2, 2) and (1, 3) D. (1, 3) and (2, 5) 31. A regular polygon on n sides has 1600 as the size each interior. Find n. A. 18 B. 16 C. 14 D. 12 32. If cos q = a/b, find 1 + tan2q A. b2/a2 B. a2/b2 C. (a2 + b2) / (b2 – a2) D. (2a2 + b2)/ (a2 + b2) 33. In the diagram below, PQ and RS are chords of a circle centre O which meet at T outside the circle. If TP = 24cm, TQ= 8cmand TS = 12cm, findTR. A. 16cm B. 14cm C. 12cm D. 8cm 34. The angle of elevation of the top of a vertical tower 50 metres high froma point Xon the ground is 300. From a point Y on the opposite side of the tower, the angle of elevation of the top of the tower is 600. find the distance between the points X and Y. A. 14.43m B. 57.73m C. 101.03m D. 115.47m 35. Agirl walk 45metres in the direction 0500 froma point Q to a point X. She then walks 24metres in the direction 1400 from X to a point Y. Howfar is she then from Q? A. 69m B. 57m C. 51m D. 21m 36. The figure is a solid with the trapezium PQRS as its uniform cross-section. Find its volume A. 102m3 B. 576m3 C. 816m3 D. 1056m3 37. PQ and PR are tangents from P to a circle centre O as shown in the figure above. IfQRP = 340. Find the angle markedx. A. 340 B. 560 C. 680 D. 1120 38. An arc of circle of radius 6cm is 8cmlong. Find the area of the sector. A. 51/3cm2 B. 24cm2 C. 36cm2 D. 48cm2 39. In XYZ above, determine the cosine of angle Z A. ¾ B. 29/36 C. 2/3 D. ½ 40. In the figure above PQT is isosceles. PQ = QT. SRQ = 350, TQ = 200 and PQR is a straight line. Calculate TSR. A. 200 B. 550 C. 75 D. 1400 41. Find the total surface are of a solid cone of radius 2 3cm and slanting side 4 3cm A. 8Ö3cm2 B. 24cm2 C. 15Ö3cm2 D. 36cm2 42. If U and V are two distinct fixed points and W is a variable point such that UWV is a straight angle.What is the locus of W? A. The perpendicular bisector ofUV B. A circle with UV as radius C. Aline parallel to the lineUV D. A circle with the line UV as the diameter 43. In the figure above, PQ//ST, RS//UV. If PQR = 350 and QRS= 650, find STV A. 300 B. 350 C. 550 D. 650 P O S R Q T S R 11 m 6 m 8 m 12 m Q P Q x T R O Y 4 3 6 X Z 35O 20O S Q T R 65O 35O P 48. The people in a citywith a population of 109million were grouped according to their ages. Use the diagrambelow to determine the number of people in the 15-29 years group. A. 29x104 B. 26x104 C. 16x104 D. 13x104 49. A man kept 6black, 5 brown and 7 purple shirts in a drawer.What is the probability of his picking a purple shirt with his eyes closed? A. 1/7 B. 11/18 C. 7/18 D. 7/11 50. The table belowgives the scores of a group of students in aMathematics test If the mode ism and the number of students who scored 4 or less is S.What is (s, m)? A. (27,4 ) B. (14, 4) C. (13, 4) D. (4, 4) 44. An open rectangular box externallymeasures 4m x 3m x 4m. find the total cost of painting the box externally if it costs #2.00 to paint one square metre. A. #96.00 B. #112.00 C. #136.00 D. #160.00 45. Of the nine hundred students admitted in a university in 1979, the following was the distribution by state Anambra 185 Imo 135 Kaduna 90 Kwara 110 Ondo 155 Oyo 225 In a pie chart drawn to represent this distribution, the angle subtended at the centre byAnambra is A. 500 B. 650 C. 740 D. 880 46. Find themedian of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119 A. 131 B. 125 C. 123 D. 120 47. Find the probability that a number selected at random from40 to 50 is a prime A. 3/11 B. 5/11 C. 3/10 D. 4/11 Mathematics 1987 24O 116O 104O 64O 52O 1. Convert 241 in base 5 to base 8 A. 718 B. 1078 C. 1768 D. 2418 2. Find the least length of a rod which can be cut into exactly equal strips, each of either 40cm or 48cm in length. A. 120cm B. 240ccm C. 360cm D. 480cm 3. Arectangular has lawn has an area of1815square yards. If its length is 50meters, find its width in metres. Given that 1meters equals 1.1yards A. 39.93 B. 35.00 C. 33.00 D. 30.00 4. Reduce each number to two significant figures and then evaluate (0.02174 x 1.2047) 0.023789 A. 0.8 B. 0.9 C. 1.1 D. 1.2 5. A train moves fromP toQ at an average speed of 90km/ hr and immediately returns from O to P through the same route and at an average speed of 45km/h. find the average speed for the centre journey. A. 5500km/hr B. 6000km/hr C. 67.50km/hr D. 7500km/hr 6. If the length of a square is increased by 20% while its width is decreased by20% to form a rectangle, what is the ratio of the area of the rectangle to the area of the square? A. 6.5 B. 25.24 C. 5.6 D. 24.25 7. Two brothers invested a total of #5,000.00 on a farm project. The farm yield was sold for # 15, 000.00 at the end of the season. If the profit was shared in the ratio 2:3, what is the difference in the amount of profit received by the brothers? A. #2,000.00 B. #4,000.00 C. #6,000.00 D. #10,000.00 8. Peter’s weeklywages are #20.00 for the first 20 weeks and #36.00 for the next 24 weeks. Find his average weekly wage for the remaining 8 weeks of the year. If his averageweekly wage for the whole year is #30.00 A. #37.00 B. #35.00 C. #30.00 D. #5.00 9. Aman invests a sumofmoney at 4% per annumsimple interest. After 3 years, the principal amounts to #7,000.00. find the sum invested A. #7,840.00 B. #6,250.00 C. #6,160.00 D. #5,833.33 10. By selling 20 oranges for #1.35 a trader makes a profit 8%. What is his percentage gain or loss if he sells the same 20 oranges for #1.10? A. 8% B. 10% C. 12% D. 15% 11. Four boys and ten girls can cut a field in 5 hours. If the boys work at 1/4 the rate of which the girls work, how many boys will be needed to cut the field in 3 hours? A. 180 B. 60 C. 25 D. 20 12. Evaluate without using tables. A. 625/8 B. 8/625 C. 1/8 D. 8 13. Instead of writing 35/6 as a decimal correct to 3 significant figures, a student wrote it correct to 3 places of decimals. Find his error in standard form A. 0.003 B. 3.0 x 10-3 C. 0.3x 102 D. 0.3 x 10-3 14. Simplifywithout using tables (Log26 – Log23)/(Log28- 2Log21/2) A. 1/5 B. ½ C. –1/2 D. Log23/Log27 15. Simplifywithout using tables 2Ö 14 x 3Ö21) / 7Ö24x 2Ö98) A. 3Ö14 B. 3Ö21 4 4 C. 3 Ö14 D. 3 Ö2 28 28 16. If p – 2/3 (1 – r2)/n2, find n when r = Ö1/3 and p = 1 A. 3/2 B. 3 C. 1/3 D. 2/3 17. If a =U2–3V2 and b = 2UV + V2 evaluate (2a - b) (a – b3 ), when u = 1 and v = -1 A. 9 B. 15 C. 27 D. 33 18. The formula Q = 15 + 0 5n gives the cost Q (in Naira) of feeding n people for a week. Find in kobo the extra cost of feeding one additional person. A. 350k B. 200k C. 150k D. 50k 19. If P varies inversely as V and V varies directly as R2, find the relationship between P and R given that R = 7 when P = 2 A. P= 98R2 B. PR2 = 98 C. P= 1/98R D. P= R2/98 20. Make y the subject of the formula Z = x2 + 1/y3 A. y = 1 B. y= 1 (z - x2) 3 (Z + x3) 1/3 C. y = 1 D. y = 1 (Z - x2) 1/3 3ÖZ - 3Ö x2 21. Find the values ofmwhichmake the following quadratic function a perfect square x2 + 2 (m+ 1) x +m+ 3 A. -1, 1 B. –1, 2 C. 1, -2 D. 2, -2 22. Factorize 62x+ 1 + 7(6x) - 5 A. {3(6x) – 5} {2(6x)} + 1} B. {3(6x) – 5} {2(6x)} - 1} C. {2(6x) – 5} {3(6x)}+ 1} D. {2(6x) – 5} {3(6x)} - 1} 23. Find two values of y which satisfy the simultaneous equations x + y = 5, x2 – 2y2 = 1 A. 12, -2 B. –12, 12 C. –12, 2 D. 2, -2 24. An (n - 2)2 sided figure has n diagonals find the number n of diagonals for a 25 sided figure A. 7 B. 8 C. 9 D. 10 25. A cubic function f(x) is specified by the graph show above. The values of the independent variable for which the function vanishes are A. -1, 0, 1 B. –1 < x < 1 C. x, - 1 D. x> 1 26. Solve the inequality x – 1 > 4(x + 2) A. x> -3 B. x< -3 C. 2< x <3 D. –3 < x < -2 f(x) -1 0 1 27. Simplify (x2 - y2) / (2x2+ xy-y2) A. x + - y B. x + y 2x + y 2x - y C. x - y D. x - y 2x - y 2x + y 28. The minimum value of y in the equation y = x2 – 6x + 8 is A. 8 B. 3 C. 0 D. –1 29. Find the sum of the first 21 terms of the progression – 10, -8, -6,…. A. 180 B. 190 C. 200 D. 210 30. Find the eleventh term of the progression 4, 8, 16,.. A. 213 B. 212 C. 211 D. 210 31. In the diagramabove, POQis a diameter, Ois the centre of the circle and TP is a tangent. Find the value of x. A. B. 400 C. 450 D. 500 32. In the diagram above, QR//TS, QR:TS = 2:3. find the ratio of the area of triangle PQR to the area of the trapeziumQRST A. 4:9 B. 4:5 C. 1:3 D. 2:3 33. Three angle s of a nonagon are equal and the sum of six other angles is 11100. Calculate the size of one of the equal triangles A. 2100 B. 1500 C. 1050 D. 500 34. In the figure above, XYZ = YTZ = 900, XT = 9cm and TZ = 16cm. Find YZ A. 25cm B. 20cm C. 16cm D. 9cm 35. Two chords QR and NP of a circle intersect inside the circle at X. ifRQP = 370,RQN= 490 andQPN= 350, find PRQ A. 350 B. 370 C. 490 D. 590 36. In the figure above, find the value of x. A. 1100 B. 1000 C. 900 D. 800 37. In the figure above, PQRS is a rectangle. If the shaded area is 72sq.cm find h A. 12cm B. 10cm C. 8cm D. 5cm 38. The sine, cosine and tangent of 2100 are respectively A. -1/2, 3/2, 3/3 B. 1/2, 3/2 3/3 C. 3/2, 3/3, 1 D. 3/2, 1/2 1 39. If tan q = (m2 – n2)/2mn, find sec q A. (m2+ n2)/(m2 – n2) B. (m2+ n2)/2mn C. mn/2(m2– n2) D. m2 n2/(m2 – n2) 30O Q x O R P T T Q R S P 9 cm 16 cm Y X T Z x x x y y P Q 3h S 2 cm 2 cm 2h R 2 cm 40. FromtwopointsXandY, 8mapart, and in linewith a pole, the angle of elevation of the top of the pole are 300 and 600 respectively. Find the height of the pole, assuming that X, Y and the foot of the pole are on the same horizontal plane. A. 4m B. 8Ö3/2m C. 4Ö3m D. 8Ö3m 41. A room is 12m long. 9m wide and 8m high. Find the cosine of the angle which a diagonal of the roommakes with the floor of the room A. 15/17 B. 8/17 C. 8/15 D. 12/17 42. What is the circumference of radius of the earth? A. R cos q B. 2p R cos q C. R sin q D. 2p R sin q 43. The base of a pyramid is a square of side 8cm. If its vertex is directly above the centre, find the height, given that the edge is 4.3cm A. 6cm B. 5cm C. 4cm D. 3cm 44. The figure above is an example of the construction of a A. perpendicular bisector to a given straight line B. perpendicular froma given point toa given line C. perpendicular to a line from a given point on that line D. given angle. 45. What is the locus of the mid-points of all chords of length 6cm within a circle of radius 5cmand with centre O. A. A circle of radius 4cm and with centre O B. The perpendicular bisector of the chords C. A straight line passing through center O D. A circle of radius 6cm and with centre O 46. Taking the period of daylight on a certain day to be from5.30a.mto 7.00p.m, calculate the period of daylight and of darkness on that day A. 187030’172030’ B. 1350225’ C. 202030’157030’ D. 1950165’ 47. The goals scored by40 football teams from three league divisions are recorded below What is the total number of goals scored by all the teams? A. 21 B. 40 C. 91 D. 96 48. The numbers 3,2,8,5,7,12,9 and 14 are themarks scored by a group by a group of students in a class test if P is themean and Q the median the P + Q is A. 18 B. 171/2 C. 16 D. 15 49. Beloware the scores of a group of students in a music test If CF(x) is the number of students with scores less than or equal to x, find CF(6) A. 40 B. 38 C. 33 D. 5 50. Find the probability of selecting a figure which is parallelogram from a square, a rectangle, a rhombus, a kite and a trapezium A. 3/5 B. 2/5 C. 4/5 D. 1/5 Mathematics 1988 Q P R X 1. Simplify (1 1 / (2¸ 1 of 32) 2 4 A. 3/256 B. 3/32 C. 6 D. 85 2. If x is the addition of the prime numbers between 1 and 6, and y the H. C.F of 6,9, 15, find the product of x and y A. 27 B. 30 C. 33 D. 90 3. A 5.0g of salts was weighed by Tunde as 5.1g. what is the percentage error? A. 20 B. 2 C. 2 D. 0.2 4. Find correct to one decimal place, 0.24633 /0.0306 A. 0.8 B. 1.8 C. 8.0 D. 8.1 5. Two sisters, Taiwo and Kehinde, own a store. The ratio ofTaiwo’s share toKehind’s is 11:9. later Kehinde sells 2/3 of her share to Taiwo for #720.00. Find the value of the store. A. #1,080.00 B. #2,400.00 C. #3,000.00 D. #3,600.00 6. A basket contains green, black and blue balls in the ratio 5:2:1. if there are 10 blue balls, find the corresponding new ratio when 10green and 10black balls are removed from the basket. A. 1:1;1 B. 4:2:1 C. 5:1:1 D. 4:1:1 7. A taxpayer is allowed 1/8th of his income tax free, and pays 20% on the remainder. If he pays #490. 00 tax, what is his income? A. #560.00 B. #2,450.00 C. #2,800.00 D. #3,920.00 8. Evaluate (8 1/3 x5 2/3) / 102/3 A. 2/5 B. 5/3 C. 2Ö5 D. 3Ö5 9. If Log102 = 0.3010 andLog103 = 0.4771, evaluate,without using logarithm tables log104.5 A. 0.3010 B. 0.4771 C. 0.6352 D. 0.9542 10. Findm such that (m¸ 3) (1 - Ö3 )2 = 6 - Ö3 = 6 - 2Ö3 A. 1 B. 2 C. 3 D. 4 11. The thickness of an 800-paged book is 18mm. Calculate the thickness of one leaf of the book giving your answer in metres and in standard form. A. 2.25x 10-4m B. 4.50x 10-4m C. 2.25x 10-5m D. 4.50x 10-5m 12. Simplify ( x+ 2) - (x - 2) ( x + 1) ( x +2) A. 3 B. 3x + 2 x + 1 (x+1) (x+2) C. 5x + 6 D. 2x2+5x + 2 (x + 1) (x + 2) (x + 1) (x + 2) 13. If 1/p = (a2 + 2ab + b2) (a - b) and 1/q = (a + b) (a2 - 2ab + b2) find p/q A. a + b B. 1 a - b a2 - b2 C. a - b D. a2 - b2 a + b 14. If x varies inversely as the cube root of y and x = 1 when y= 8 find ywhen x = 3 A. 1/3 B. 2/3 C. 8/27 D. 4/9 15. If a = -3, b = 2, c = 4, calculate (a3-b3-c1/2) (b-1-c) A. 37 B. –37/5 C. 37/5 D. –37 16. If g(y) = y – 3/11 + 11/ y2 – 9 what is g(y + 3)? A. y + 11 B. y + 11 11 y(y+6) 11 y(y+3) C. y + 30 + 11 D. y + 3 + 11 11 y(y+3) 11 y(y-6) 17. Factorize completely (x2 + x) 2 (2x + 2)2 A. (x+y)(x+2)(x-2) B. (x+y)2(x-2)2 C. (x+1)2(x+2)2 D. (x+1)2(x+2)2(x-2) 18. Simplify (x - y) (x1/3 - y1/2) A. x2 = xy + y2 B. x2/3 + x1/3+ y2/3 C. x2/3 - x1/3 y1/3 - y2/3 D. x2 - xy + y2 19. Solve the following equation for x x2 + 2x + 1 = o r2 r1 A. r2 B. 1/r2 C. –1/r2 D. 1/r 20. List the integral values of x which satisfy the inequality 1 < 5 < -2x < 7 A. -1,0,1,2 B. 0,1,2,3 C. -1,0,1,2,3, D. -1,0,2,3 21. Given value that 3x – 5y – 3 = 0 2y – 6x + 5 = 0 the value of (x, y) is A. (-1/8, 19/24) B. (8, 24/10) C. (-8, 24/19) D. (19/24, -1/8) 22. The solution of the quadratic equation bx2 + qx + b = 0 A -b±Öb2 - 4ac B -b± p2- 4pb 2a 2a C -q±Öq2 - 4bp D -q±Öp2 - 4bp 2p 2p 23. Simplify 1 + 1 (x2+5x+6) (x2 + 3x + 2) A. x + 3 B. 1 (x+1) (x+2) (x+1) x+2) x+3) C. 2 D. 4 (x+1) (x+3) (x+1) (x+3) 24. Evaluate (4a2 - 4ab2) (2a2 + 5ab - 7b2) A. a - b B. 2a + 7b 2a + b a - b C. 2a - 7b D. 2a - 7b a + b a - b Using the graph to answer questions 25 and 26 25. What is the solution of the equation x2 – x – 1 = 0? A. x=1.6andx=-0.6 B. x=-1.6andx=0.6 C. x=1.6andx=0.6 D. x=-1.6andx=-0.6 26. For what values of x is the curve y= (x2 + 3) / (x + 4) A. -3 < x< 0 B. –3 < x < 0 C. 0< x < 3 D. 0< x < 3 27. The solution of x2 – 2x – 1 0 are the points of intersection of two graphs. If one of the graphs is y= 2 + x – x2, find the second graph. A. y= 1 – x B. y= 1 + x C. y= x – 1 D. y= 3x + 3 28. If the sum of the 8th and 9th terms of an arithmetic progression is 72 and the 4th termis –6, find the common difference. A. 4 B. 8 C. 62/3 D. 91/3 29. If 7 and 189 are the first and fourth terms of a geometric progression respectively find the sum of the first three terms of the progression. A. 182 B. 91 C. 63 D. 28 30. In the figure above, PQRS is a circle. If chords QR and RS are equal, calculate the value of x A. 800 B. 600 C. 450 D. 400 31. In the figure above, PQ is parallel to ST andQRS = 400. find the value of x A. 55 B. 60 C. 65 D. 75 32. For which of the following exterior angles is a regular polygon possible? i 350 ii 180 iii. 1150 A. i and ii B. ii only C. ii and iii D. iii only 33. In the figure above, PS = 7cm and RY= 9cm. If the area of parallelogram PQRS is 56cm2, find the area of trapeziumPQTS. A. 56cm2 B. 112cm2 C. 120cm2 D. 1762 34. A quadrilateral of a circle of radius 6cm is cut away from each corner of a rectangle 25cm long and 18cm wide. Find the perimeter of the remaining figure A. 38cm B. (38+12p)cm C. (86-12p)cm D. (86-6p)cm 35. In the figure above STQ= SRP, PT =TQ = 6cm and QS = 5cm. Find SR. A. 47/5 B. 5 C. 37/5 D. 22/5 36. Four interior angles o f a pentagon are 900 – x0, 900 + x0, 100 – 2x0, 1100 + 2x0. find the fifth interior angle. A. 1100 B. 1200 C. 1300 D. 1400 y 4 3 2 1 -2 -1 -4 -3 -2 -1 0 1 2 1 y = I 120O 100O S P Q R T 40O S P Q T R 3xo xo P Q R 9cm 7cm S Y T P R T Q 5 6 6 S 37. In the figure above, PS = RS = QS and QSR = 500. find QPR. A. 250 B. 400 C. 500 D. 650 38. In the figure above, XR and YQ are tangents to the circleYZXP if ZXR = 450 andYZX= 550 find ZYQ. A. 1350 B. 1250 C. 1000 D. 900 39. From a point 14Ö3 metres away from a tree, a man discovers that the angle of elevation of the tree is 300. If the manmeasures this angle of elevation from a point 2meters above the ground how high is the tree? A. 12m B. 14m C. 14Ö3m D. 16m 40. Alero starts a 3km walk from P on a bearing 0230. she thenwalks 4kmon a bearing 1130 toQwhat is the bearing ofQ from P? A. 26052’ B. 5208’ C. 7608’ D. 900 41. If cot q = x/y, find cosec q A. 1/y(x2+y) B. (x/y) C. 1/y(x2+y) D. y/x 42. In triangle PQR, PQ= 1cm, QR = 2cm and PQR = 1200. Find the longest side of the triangle A. 3 B. 3 7/7 C. 3 7 D. 7 44. If a metal pipe 10cm long has an external diameter of 12cm and a thickness of 1cm, find the volume of the metal used in making the pipe. A. 120pcm3 B. 110pcm3 C. 60pcm3 D. 50pcm3 45. In the figure above, a solid consists of a hemisphere surmounted by a right circular cone with radius 3.0cm and height 6.0cm. find the volume of the solid. A. 18pcm3 B. 36pcm3 C. 54pcm3 D. 108pcm3 46. PQRis a triangle in which PQ= 10ccmandQPR = 600. S is a point equidistant from P and Q. also S is a point equidistant from PQ and PR. If U is the foot of the perpendicular from S on PR, find the length SUin cmto one decimal place. A. 2.7 B. 2.9 C. 3.1 D. 3.3 47. In a class of 150 students, the sector in a pie chart representing the students offering Physics has angle 120. How many students are offering Physics? A. 18 B. 15 C. 10 D. 5 48. If x and y represents the mean and the median respectively of the following set of numbers; 11, 12,13,14,15,16,17,18,19,21,. Find x/y correct to one decimal place. A. 1.6 B. 1.2 C. 1.1 D. 1.0 49. In the distribution above, the mode and the median respectively are A. 1.3 B. 1.2 C. 3.3 D. 0.2 50. If two dice are thrown together, what is the probability of obtaining at least a score of 10? A. 1/6 B. 1/12 C. 5/6 D. 11/12 50O P S R Q 60 cm 30 cm 45O 55O Y Q Z P R X 1. Which of the following is in descending order? A. 9/10,4/5,3/4,17/10 B. 4/5,9/10,3/4,17/20 C. 6/10,17/20,4/5,3/4 D. 4/5,9/10,17/10,3/4 2. Evaluate 2,700, 000 x 0.03 ¸18,000 A. 4.5x 100 B. 4.5x 101 C. 4.5x 102 D. 4.5x 103 3. The prime factors of 2,520 are A. 2,9,5, B. 2,9,7, C. 2,3,5,7, D. 2,3,7,9, 4. If 12e = X7 find x where e = 12 A. 20 B. 15 C. 14 D. 12 5. Simplify 3Ö64r -6)1/2 A. r B. 2r C. 1/2r D. 2/r 6. What is the difference between 0.007685 correct to three significant figures and 0.007685 correct to four places of decimal? A. 10-5 B. 7 x 10-4 C. 8 x 10-5 D. 10 -6 7. If a : b = 5: 8, x : y= 25 : 16, evaluate a/x : b/y A. 125:128 B. 3:5 C. 3:4 D. 2:5 8. Oke deposited #800.00 in the bank aat the rat of 121/2% simple interest. After some time the total amount was one and half times the principal. For how many years was the money left in the bank A. 2 B. 4 C. 51/2 D. 8 9. If the surface area of a sphere is increased by 44%. Find the percentage increase in its diameter. A. 44 B. 30 C. 22 D. 20 10. Simplify 4 - 1 (2-Ö3) A. 2Ö3 B. –2., Ö3 C. –2+ Ö3 D. 2, -Ö3 11. Find p in terms of q if Log3p + 3log3q = 3 A. (3)3 B. (q)1/3 (q) (3) C. (q)3 D. (3)1/3 (3) (q) 12. What are the values of y which satisfy the equation 9y – 4 ( 3y) + 3 = 0 A. -1 and 0 B. –1 and 1 C. 1 and 3 D. 0 and 1 13. Make R the subject of the formula S= Ö(2R +T ) (3RT) A. R = T B. T (TS2 - 1) 2(TS2 - 1) C R = T D. T (TS2 + 1) 2(TS2 + 1) 14. Find the value of the expression 32 - 64 81 when x = -3/4 81x3 xx2 16 A. 101/2 B. 101/6 C. 33/8 D. –131/2 15. The cost of dinner for a group of students is partly cconstant and partly varies directly as the number of students. If the cost is #74.00 when the number of students is 20, and #96.00when the number is 30, find the cost when there are 15 students. A. #68.50 B. #63.00 C. #60.00 D. #52.00 16. If f(x) = 2x2 + 5x + 3, find f(x + 1) A. 2x2– x B. 2x2 – x + 10 C. 4x2 +3x + 2 D. 4x2 +3x +12 17. Solve the positive number x such that 2(x3 – x2 – 2x) = 1 A. 4 B. 3 C. 2 D. 1 18. Simplify (32x - 4x2) (2x + 18) A. 2(x - 9) B. 2(9+ x ) C. 81– x2 D. –2(x - 9) 19. Factorize completely y3 – 4xy + xy3 – 4y A. (x + xy)(y+ 2)(y - 2) B. (y+ xy)(y + 2)(y - 2) C. y(1 + x)(y+ 2)(y - 2) D. y(1 - x)(y+ 2)(y - 2) 20. If one of x3 – 8-1 is x – 2–1 , the other factors is A. x2 + 2-1 x – 4-1 B. x2 - 2-1 x – 4-1 C. x2 + 2-1 x + 4-1 D. x2 + 2-1 x –4-1 21. Factorize 4a2 + 12ab – c2+ 9b2 A. 4a(a – 3b) + (3b - c)2 B. (2a + 3b – c )(2a + 3b + c) C. (2a – 3b -c)(2a –3b + c) D. 4a(a – 3b) + (3b +c)2 22. What are K and L respectively if ½ (3y – 4x)2 = (8x2 + kxy+ Ly2) A. -12, 9/2 B. –6, 9 C. 6, 9 D. 12, 9/2 Mathematics 1989 A. 1,10 B. 2,10 C. 3,13 D. 4,16 31. MNis a tagent to the given circle atM,MR andMQ are two chords. IfQMN is 600 andMNQ is 400, find RMQ A. 1200 B. 110 C. 600 D. 200 32. In the diagram above,HKis prallel toQR, PH= 4cmand HQ = 3cm.What is the ratio ofKR;PR? A. 7:3 B. 3:7 C. 3:4 D. 4:3 33. A regular polygon of (2k + 1) sides has 1400 as the size of each interior angel. Find K. A. 4 B. 41/2 C. 8 D. 81/2 34. If PST is a straight line and PQ = QS = SR in the above diagram, find y A. 240 B. 480 C. 720 D. 840 35. In the above diagramPQis parallel toRS and QS bisects PQR. If PQRis 600, find x A. 300 B. 400 C. 600 D. 1200 36. PQRS is a rhombus. If PR2 + QS2 = kPQ2. Determine k. A. 1 B. 2 C. 3 D. 4 23. Solve the pair of equation for x and y respectively 2x-1 – 3y-1 = 4 4x-1 + y-1 = 1 A. -1,2 B. 1,2 C. 2,1 D. 2,-1 24. What value ofQwillmake the expression 4x2 + 5x +Q a complete square? A. 25/16 B. 25/64 C. 5/8 D. 5/4 25. Find the range of values of r which satisfies the following inequality, where a, b and c are positive. r/a+r/b+r/c >1 A. r> abc B. r>abc bc + ac + ab C. r > 1/a + 1/b + 1/c D. r>1/abc 26. Express 1 - 1 (x + 1) (x - 2) A. -3 B. 3 (x +1)(2-x) (x+1)2-X) C. -1 D. 1 (x+1)(x-2) (x+1)(x-2) 27. Simplify x - (x+ 1 ) 1/2 (x + 1) (x + 1) 1/2 A. 1 B. - 1 x + 1 x+ 1 C. 1 D. 1 x x + 1 28. On the curve above, the points at which the gradient of the curve is equal to zero are A. c.d.f.i.l B. b.e.g.j.m C. a.b.c.d.f.i.j.l. D. c.d.f.h.i.l 29. The sum of the first two terms of a geometric progression is x and the sum of the last two terms is y. if there are n terms in all, then the common ratio is A. x/y B. y/x C. (x/y)1/2 D. (y/x)1/2 30. If –8, m,n, 19 in arithmetic progression, find (m, n) -1 a b c d e f g h i j k y l x m 1 2 3 4 5 6 R M N Q P H 3 cm 4 cm K Q R 24O P Q S T R R Q S P 60O 37. In DXYZ, Y= Z = 300 and XZ = 3cm find YZ A. Ö3/2cm B. 3Ö3/2cm C. 3Ö3cm D. 2Ö3cm 38. In DPQR, the bisector ofQPRmeets QRat S. the line PQ is produced to V and the bisector of VQS meets PS produced at T. if QPR = 460 and QST = 750, calculate QTS A. 410 B. 520 C. 640 D. 820 39. A. If PQR is a straight line with OS = = QR, calculate TPQ, ifQT//SRand TQS = 3y0. A. 620 B. 560 C. 202/3 0 D. 182/3 0 40. If x : y = 5:12 and z = 52cm, find the perimeter of the triangle. A. 68cm B. 84cm C. 100cm D. 120cm 41. The pilot of an aeroplane, flying 10km above the ground in the direction of a landmark, views the landmark to have angle of depression of350 and 550. find the distance between the two points of observation A. 10(sin 350 – sin 550) B. 10(cos 350 – cos 550) C. 10(tan 350 – tan 550) D. 10(cot 350 – cot 550) 42. A sin2x – 3 = 0, find x if0 < x < 900 A. 300 B. 450 C. 600 D. 900 43. A square tile has side 30cm. How many of these tiles cover a rectangular floor of length 7.2cm and width 4.2m? A. 336 B. 420 C. 576 D. 720 44. A cylindricalmetal pipe 1mlong has an outer diameter of 7.2cmand an inner diameter of 2.8cm. find the volume ofmetal used for the cylinder. A. 440pcm3 B. 1,100pcm3 C. 4,400pcm3 D. 11,000pcm3 45. OXYZWis a pyramid with a square base such that OX = OY = OZ = OW= 5cm and XY = XW= YZ =WZ = 6cm. Find the height OT. A. 2Ö5 B. 3 C. 4 D. Ö7 46. In preparing rice cutlets, a cook used 75g of rice, 40g of margarine, 105g ofmeat and 20g of bread crumbs. Find the angle of the sector which represents meat in a pie chart. A. 300 B. 600 C. 112.50 D. 157.50 47. In a class of 30 students, the marks scored in an examination are displayed in the following histogram. What percentage of the students scored more than 40% A. 14% B. 40% C. 452/3% D. 531/3% 48. In a family of 21 people, the average age is 14years. If the age of the grandfather is not counted, the average age drops to 12years. What is the age of the grandfather? A. 35years B. 40years C. 42years D. 54years 49. If n is the median andm is themode of the following set ofnumbers,2.4,2.1,1.6,2.6,2.6,3.7,2.,1,2.6, then (n,m) is A. (2.6,2.6) B. (2.5,2.6) C. (2.6,2.5) D. (2.5,2.1) 50. The numbers are chosen at random from three numbers 1,3,6. find the probability that the sum of the two is not odd. A. 2/3 B. ½ C. 1/3 D. 1/6 Q P yO 56O 3yO Y S R X R Z S T Y Z W T X O 20 40 60 80 100 Marks scored No . of students 10 8 6 4 2 0 1. Simplify (43/4 - 61/4) (41/5 of 1 1/4) A. -77/8 B. –2/7 C. –10/21 D. 10/21 2. The H.C.F. of a2bx + abx2 and a2b – b3 is A. b B. a + b C. a(a + b) D. abx (a2 – b2) 3. Correct 241.34 (3 x 10-3)2 to 4 significant figures A. 0.0014 B. 0.001448 C. 0.0022 D. 0.002172 4. At what rate would a sum of #100.00 deposited for 5 years raise an interest of #7.50? A. 11/2% B. 21/2% C. 15% D. 25% 5. Three children shared a basket of mangoes in such a way that the first child took ¼ of the mangoes and the second ¾ of the remainder. What fraction of the mangoes did the third child take? A. 3/16 B. 7/16 C. 9/16 D. 13/16 6. Simplify and express in standard form (0.00275 x 0.00640/( 0.025x0.08) A. 8.8 x 10-1 B. 8.8x 102 C. 8.8 x 10-3 D. 8.8x 103 7. Three brothers in a business deal share the profit at the end of contract. The first received 1/3 of the profit and the second 2/3 of the remainder. If the third received the remaining #12.000.00, how much profit did they share? A. #60,000.00 B. #54,000.00 C. #48,000.00 D. #42,000.00 8. Simplify Ö 160r2 + Ö (71r4+ Ö100r3 A. 9r2 B. 12 3r C. 13r D. 13r 9. Simplify Ö27 + 3/Ö3 A. 4Ö3 B. 4/Ö3 C. 3Ö3 D. 3Ö/4 10. Simplify 3Log69 + Log612 + Log664 – Log672 A. 5 B. 7776 C. Log631 D. (7776)6 11. Simplify (1 + 1 ) -1 x-1 y-1 A. x/y B. xy C. y/x D. (xy)-1 12. If a = 2, b = -2 and c = -1/2, evaluate (ab2 – bc2) (a2c - abc) A. 0 B. –28 C. –30 D. –34 13. Y varies inversely as x2 and X varies directly as Z2. find the relationship between Y and Z, if C is a constant. A. Z2y = C B. Y= CZ2 C. Y= CZ2 D. Y= C 14. Find the value of r in terms of p and q in the following equation P/2 = (r/(r+q) A. r = q B. pq2 2 - p2 2 - q2 C. r = p2q2 D. p 2 - pq q(2-p) 15. If f(x - 4) = x2 + 2x + 3, find f(2) A. 6 B. 11 C. 27 D. 51 16. Factorize 9(x + y)2 – 4(x - y)2 A. (x+y)(5x+y) B. (x+y)2 C. (x+5y)(5x+y) D. 5(x+y)2 17. If a2 + b2 = 16 and 2ab = 7 find all the possible values of (a – b ) A. 3, -3 B. 2, -2 C. 1, -1 D. 3, -1 18. Divide x3 – 2x2 – 5x + 6 by (x - 1) A. x2 – x –6 B. x2 – 5x + 6 C. x2 – 7x + 6 D. x2 – 5x - 6 19. If x + = 4, find the x2 + 1/x A. 16 B. 14 C. 12 D. 9 20. What must be added to 4x2 – 4 to make it a perfect square? A. -1/x2 B. 1/x2 C. 1 D. -1 21. Find the solution of the equation x – 8 Öx + 15 = 0 A. 3, 5 B. –3, -5 C. 9, 25 D. –9, 25 22. The lengths of the sides of a right-angled triangle are xcm. (3x-1)cmand(3x + 1)cm. Find x A. 5 B. 7 C. 8 D. 12 23. The perimeter of a rectangular lawn is 24m, if the area of the lawn is 35m2, howwide is the lawn? A. 5m B. 7m C. 12m D. 14m Mathematics 1990 25. Simplify x + y - x2 (x+y) (x-y) (x2 - y2) A. x2 B. y2 x2 - y2 x2 - y2 C. x D. y x2 - y2 x2 - y2 26. Given that x2+ y2 + z2= 194, calculate z ifx = 7 andÖ y = 3 A. Ö10 B. 8 C. 12.2 D. 13.4 27. Find the sum of the first twenty terms of the arithmetic progression Log a, Log a2, Log a3 A. log a20 B. log a21 C. log a200 D. log a210 24. A carpainter charges #40.00 per day for himself and #10.00 per day for his assistant. If a fleet of a cars were painted for #2,000.00 and the painter worked 10 days more than his assistant, how much did the assistant receive? A. #32.00 B. #320.00 28. Find the sum of the first 18 terms of the progression 3, 6,12……….. A. 3(217 - 1) B. 3(218 ) - 1 ) C. 3(218 + 1) D. 3(218 - 1) 29. What is the equation of the quadratic function represented by the graph above? A. y = x2 + x - 2 B. y= x2 – x –2 C. y= -x2 – x + 2 D. y= -x + x + 2 30. At what value of x is the function x2 + x + 1 minimum? A. -1 B. –1/2 C. ½ D. 1 31. In the diagram above, the area of PQRS is 73.5cm2 and its height is 10.5cm. find the length of PS ifQR is onethird of PS. A. 21cm B. 171/2cm C. 14cm D. 101/2cm 32. The angle of a sector of a circle, radius 10.5cm, is 480. calculate the perimeter of the sector A. 8.8cm B. 25.4cm C. 25.6cm D. 29.8cm 33. In the figure above PS = QS and QSR = 1000, find QPR A. 400 B. 500 C. 800 D. 1000 34. In triangleXYZandXQP,XP= 4cm,XQ= 5cmand PQ = QY= 3ccm. FindZY A. 8cm B. 6ccm C. 4cm D. 3cm 35. Find the length of a side of a rhombus whose diagonals are 6cm and 8cm. A. 8cm B. 5cm C. 4cm D. 3cm 36. Each of the interior angles of a regular polygon is 1400. how many sides has the polygon? A. 9 B. 8 C. 7 D. 5 37. In the figure above, PQRS is a circle. If PQT and SRT are straight lines, find the value of x. A. 590 B. 770 C. 1030 D. 1210 -1 0 2 y x P Q R S 100O P R Q S Q Z Y 3 cm 3 cm 5 c m 4 cm X P 0 0 P T S Q x R 81O 22O 38. In a regular pentagon, PQRST, PR intersects QS at O. calculateRQS. A. 360 B. 720 C. 1080 D. 1440 39. If cos q = 12/13, find 1 + cot2 q A. 169/25 B. 25/169 C. 169/144 D. 144/169 40. In the figure above, YXZ = 300,XYZ = 1050 and XY = 8cm.CalculateYZ. A. 162Öcm B. 8Ö2cm C. 4Ö2cm D. 2Ö2cm 41. In the figure above PQR is a semicircle. Calculate the area of the shaded region. A. 1252/7cm2 B. 1492/7cm2 C. 2431/7cm2 D. 2671/2cm2 42. A cylindrical pipe, made of metal is 3cm, thick if the internal radius of the pipe is 10cm. Find the volume of metal used in making 3m of the pipe A. 153pcm3 B. 207pcm3 C. 15,300pcm3 D. 20,700pcm3 43. If the height of two circular cylinders are in the ratio 2:3 and their base radii are in the ratio 9. what is the ratio of their volume A. 27:32 B. 27:23 C. 23:32 D. 21:27 44. Find the curved surface area of the frustrumin the figure. A. 16 10cm B. 20 10 C. 24 D. 45. The locus of a point which moves so that it is equidistant from two intersecting straight lines is the A. perpendicular bisector of the two lines B. angle bisector of the two lines C. bisector of the two lines D. line parallel to the two lines 46 4, 16, 30, 20, 10, 14 and 26 are represented on a pie chart. Find the sum of the angles of the sectors representing all numbers equal to or greater than 16. A. 480 B. 840 C. 920 D. 2760 47. The mean of ten positive numbers is 16. when another number is added, the mean becomes 18. find the eleventh number. A. 3 B. 16 C. 18 D. 30 48. Below are the scores of a group of students in a test. If the average score is 3.5, find the value of x. A. 1 B. 2 C. 3 D. 4 49. Two numbers are removed at randomfrom the numbers 1,2,3 and 4. what is the probability that the sum of the numbers removed is even? A. 2/3 B. ½ C. 1/3 D. ¼ 50. Find the probability that a number selected at random from 41 to 56 is amultiple of 9 A. 1/9 B. 2/15 C. 3/16 D. 7/8 X Y 8 cm Z T S P R Q O 11 cm 6 cm 8 cm 6 cm 6 cm 4 cm 1. Simplify 31/3 – 11/4x 2/3 + 12/5 A. 217/30 B. 39/10 C. 41/10 D. 4 11/36 2. If 2257 is the result of subtracting 4577 from7056 in base n, find n. A. 8 B. 9 C. 10 D. 11 3. Find correct to 3 decimal places ( 1 ¸ 1 0.05 5.005 - (0.05X2.05) A. 99.998 B. 98.999 C. 89.899 D. 9.998 4. Express 62/3 as a decimal correct to 3 significant figures. A. 20.6 B. 20.667 C. 20.67 D. 20.7 5. FactoryP produces 20,000 bags of cement per daywhile factory Q produces 15,000 bags per day. If P reduces production by 5% and Q increases production by 5% determine the effective loss in the number of bags produced per day by the two factories. A. 250 B. 750 C. 1000 D. 1250 6. Musa borrows #10.00 at 2% per month interest and repays #8.00 after 4 months. However much does he still owe? A. #10.80 B. #10.67 C. #2.80 C. #2.67 7. If 3 gallons of spirit containing 20%water are added to 5gallons of another spirit containing 15% water, what percentage of the mixture is water? A. 24/5% B. 167/8% C. 181/8% D. 187/8% 8. What is the product of 27/5 – (3)3 and (1/5)? A. 5 B. 3 C. 1 D. 1/25 9. Simplify 2log2/5 – log72/125 + log9 A. 1 – 4log 3 B. –1 + 2log3 C. –1 +5log2 D. 1-2log2 10. Rationalize (2Ö3 + 3Ö2)/(3Ö2 - 2Ö3) A. 5 - 2 6 B. 5 + 2 6 C. 5 3 D. 5 11. Simplify(1/3+ Ö5) – 1/3 - Ö5 A. -1/2 5 B. 1/2 5 C. –1/4 5 D. 0 12. Multiply (x2 –3x - + 1)2 by (x - a) A. x3 – (3 - a)x2+ (1 + 3a)x –1 B. x3 – (3 - a)x2 + 3ax – a C. x3 – (3 - a)x2 + (1 + 3a) – a D. x3+ (3 - a)x2 + (1 + 3a) - a 13. Evaluate (Xy2 - X2y) (x2 - xy) when x = -2 and y = 3 A. -3 B. –3/5 C. 3/5 D. 3 14. A car travels from Calabar to Enugu, a distant of pkm with an average speed of ukm per hour and continues to Benin, a distance of qkm, with an average speed of wkm per hour. Find its average speed from Calabar to Benin. A. (p+q)/(up+wq) B. u+w C. uw(p+q)/(wp+uq) D. (wp+uq)/(u+wq) 15. Ifw varies inversely as uv/u + v and is equal to 8 when u = 2 and v = 6, find a relationship between u, v, w. A. upw= 16(u + t) B. 16ur = 3w(u + t) C. upw= 12(u + t) D. 12upw= u + r 16. If g(x = x2 + 3x ) find g(x + 1) – g(x) A. (x+ 2) B. 2(x+2) C. (2x+1) D. (x+ 4) 17. Factorize m3 – m2 –m + 2 A. (m2 +1)(m- 2) B. (m+ 1)(m+ 1)(m+2) C. (m+ 1)(m+ 1)(m- 2) D. (m2 +2)(m- 1) 18. Factorize 1 – (a - b)2 A. (1 – a - b)(1 – a - b) B. (1– a +b)(1+ a - b) C. (1 – a + b)(1 – a + b) D. (1 – a - b)(1 + a - b) 19. Which of the following is a factor of rs + tr – pt –ps? A. (p - s) B. (s - p) C. (r - p) D. (r + p) 20. Find the two values of ywhich satisfy the simultaneous equation 3x + y = 8 x2 + xy = 6 A. -1 and 5 B. –5 and 1 C. 1 and 5 D. 1 and 1 21. Find the range of values of xwhich satisfy the inequality (x/2 + x/3 +x/4) < 1 A. x< 12/13B. x<13 C. x< 9 D. x< 13/12 22. Find the positive number n, such that thrice it s square is equal to twelve times the number. A. 1 B. 2 C. 3 D. 4 23. Solve the equation (x - 2)(x - 3) = 12 A. 2,3 B. 3,6 C. –1,6 D. 1,6 Mathematics 1991 24. Simplify (Ö1 + x + Ö x) (Ö 1 + X - Ö x) A. 1- 2x - 2Öx(1 + x) B. 1+2x+2Öx(1+x) C. Öx(1+x) D. 1+2x - 2Öx (1+x) 25. Evaluate x2(x2 - 1)1/2 – (x2 – 1)1/2 A. (x2 – 1)1/2 B. (x2 – 1) C. (x2 – 1)-1 D. (x2 – 1)-1/2 26. Find the gradient of the line passing through the points (-2,0) and (0, -4) A. 2 B. –4 C. –2 D. 4 27. At what value of x is the function y = x2 – 2x – 3 minimum? A. 1 B. –1 C. –4 D. 4 28. What is the nth termof the progression 27, 9,3,………..? A. 27(1/3)n – 1 B. 3n + 2 C. 27 + 18(n - 1) D. 27 + 6(n - 1) 29. Find the sumof the 20 termin an arithmetic progression whose first term is 7 and last term is 117 A. 2480 B. 1240 C. 620 D. 124 30. In the figure above, find the value of x A. 1300 B. 1100 C. 1000 D. 900 31. The angles of a quadrilateral are 5x – 30, 4x + 60, 60 – x and 3x + 61. find the smallest of these angles. A. 5x– 30 B. 4x+60 C. 60 – x D. 3x+61. 32. The area of a square is 144sqcm. Find the length of its diagonal A. 11Ö3cm B. 12cm C. 12Ö2cm D. 13cm 33. One angle of a rhombus is 600. the shorter of the two diagonals is 8cm long. Find the length of the longer one A. 8Ö3 B. 16/Ö3 C. 5Ö3 D. 10/Ö3 34. If the exterior angles of a pentagon are x0, (x + 5)0, (x + 10)0, (x + 15)0 and (x + 20)0, find x A. 1180 B. 720 C. 620 D. 360 use the figure below to answer questions 35 and 36 PMN and PQR are two secants of the circle MQTRN and PT is a tangent 35. If PM= 5cm, PN = 12cm and PQ = 4.8cm, calculate the respective lengths of PR and PT in centimeters. A. 7.3,5.9 B. 7.7,12.5 C. 12.5,7.7 D. 5.9,7.3 36. IfPNR = 1100 and PMQ= 550, findMPQ. A. 400 B. 300 C. 250 D. 150 37. In the figure above, find the value of y A. 280 B. 1220 C. 1500 D. 1520 38. In the figure above, PQ = PR = PS and SRTY= 680. find QPS. A. 1360 B. 1240 C. 1120 D. 680 39. Aflagstaff stands on the top of a vertical tower. Aman standing 60m away from the tower observes that the angles of elevation of the top and bottomof the flagstaff are 640 and 620 respectively. Find the length of a flagstaff. A. 60(tan 620 – tan 640) B. 60(cot 640 – cot 620) C. 60(cot 620 – cot 640) D. 60(tan 640 – tan 620) 110O P Q R T S 120O x T P R N M Q 152O 30O y P Q R S T 68O 40. Simplify cos2x (sec2x + sec2x tan2x) A. Tan x B. Tan x sec x C. Sec2 x D. Cosec2 x 41. If cos x = Öa/b, find cosec x. A. b B. b Ö b - a Ö a C. b D. Ö b - a Ö b - a a 42. From a point Z, 60m, north of X, a man walks 60Ö3m eastwards to another point Y. find the bearing of y from x. A. 0300 B. 0450 C. 0600 D. 0900 43. A surveyor walks 500m up a hill which slopes at an angle of 300. calculate the vertical height through which he rises A. 250m B. 500Ö3/3m C. 250Ö2m D. 250Ö3m 44. In the figure above, PQRS is a square of side 8cm.What is the area of UVW? A. 64sq.cm B. 54sq.cm C. 50sq.cm D. 10sq.cm 45. Find the total area of the surface of a solid cylinder whose base radius is 4cm and height is 5cm. A. 56pcm2 B. 72pcm2 C. 96pcm2 D. 192pcm2 46. Find the volume of the figure above. A. pa2/3 B. pa2y C. pa2/3(y + x) D. (1/3pa2 x + y) 47. 3% of a family’s income is spent on electricity. 9% on food. 20% on transport, 11% on education and 7% on extended family. The angles subtended at the centre of the pie chart under education and food are respectively A. 76.80 and 25.20 B. 10.80 and 224.60 C. 112.40 and 72.00 D. 39.60 and 212.40 Use the following information to answer question 48 and 49. Fifty boxes each of 50balls were inspected for the number which were defective. The following was the result 48. The mean and the median of the distribution are respectively A. 6.7,6 B. 6.7,6.5 C. 6,6.7 D. 6.5,6.7 49. Find the percentage of boxes containing at least 5 defective bolts each. A. 96 B. 94 C. 92 D. 90 50. A crate of soft drinks contains 10bottles of Coca-cola, 8 of Fanta and 6 of Sprite. If one bottle s selected at random, what is the probability that it is NOT a Coca cola bottle? A. 5/12 B. 1/3 C. ¾ D. 7/1 S P 8 cm 6 cm 2 cm 4 cm Q V W R x y a a No of defective per box 4 5 6 7 8 9 No . of boxes 2 7 17 10 8 6 1. Find n if 34n= 100112 A. 5 B. 6 C. 7 D. 8 2. The radius of a circle is given as 5cm subject to an error of 0.1cm. what is the percentage error in the area of the circle. A. 1/25 B. ¼ C. 4 D. 25 3. Evaluate Logban if b = 1/an A. n2 B. n C. 1/n D. 1/n 4. What is the value of x satisfying the equation 42y / 43x = 2? A. -2 B. –1/2 C. ½ D. 2 5. Simplify {(1.25 x 104) x (2.0 x 10-1) (6.25 x 105 A. 4.0 x 10-3 B. 5.0 x 10-2 C. 2.0 x 10-1 D. 5.0x 103 6. Simplify 5Ö18 - 3Ö72+ 4Ö50 A. 17Ö4 B. 4Ö17 C. 17Ö2 D. 12Ö4 7. If x = 3 - Ö3, find x2 + 36 / x2 A. 9 B. 18 C. 24 D. 27 8. If x = {all prime factors of 44} and y= {all prime factors of 60}, the elements of xÇyand xÇy respectively are. A. {2,4,3,5,11} and {4} B. {4,3,5,11} and {3,4} C. {2,5,11} and {2} D. {2,3,5,11} and {2} 9. IfU={0,2,3,6,7,8,9,10} is the universal set, E = {0,4,6,8,} and F = {x: x2 = 26 ,}, x is odd}. Find (ECF)’ wheremeans the complement of a set A. {0} B. U C. C D. f 10. Make l the subject of the formula s = ut + ½ at2 A. 1/a [u± Ö(u2-2as)] B. 1/a [-u± Ö(u2 - 2as] C. 1/a [u±Ö(u2 + 2as) D. 1/a [-u±Ö(u2 + 2as)] 11. Factorize 9p2 – q2 + 6pr – 9r2 A. (3p – 3q + r)(3p – q – 9r) B. (6p – 3q + 3r)(3p – q – 4r) C. (3p – q + 3r)(3p + q – 3r) D. (3p – q + 3r)(3p – q – 3r) 12. Solve the equation y - 11 y + 24 = 0 A. 8,3 B. 64,9 C. 6,4 D. 9,-8 13. A man invested a sum of #280.00 partly at 59% and partly at 4%. If the total interest is #12.80 per annum, find the amount invested at 5%. A. #14.00 B. #120.00 C. #140.00 D. #160.00 14. If x + 1 is a factor of x3 + 3x2 + kx +4, find the value of k A. 6 B. –6 C. 8 D. –8 15. Resolve (3/x2 + x – 2) into partial fractions A. 1 - 1 B. 1 1 x-1 x+2 x + 2 x - 1 C. 1 - 1 D. 1 1 x + 1 x - 2 x - 2 + x + 1 16. Find all values of x satisfying the inequality –11£ 43x £ 28 A. -5 £ x £ 18 B. 5 £ x £ 8 C. –8 £x £ 5 D. –5 < x £ 8 17. The sketch above is the curve of y = ax2 + bx + c. find a, b, and c respectively A. 1,0,-4 B. –2,2,-4 C. 0,1,-4 D. 2,-2,-4 18. Find the sum of the infinity of the following series. 3 + 2 + 4/3 + 8/9 + 16/27 + .. A. 1270 B. 190 C. 18 D. 9 19. What is the nth term of the sequence 2,6,12,20,…? A. 4n – 2 B. 2(3n - 1) C. n2 + n D. n2 + 3n +2 20. For an arithmetic sequence, the first term is 2 and the common difference is 3. find the sumof the fist 11 terms. Mathematics 1992 -3 -2 -1 1 2 3 4 3 2 -1 -2 -3 0 y x A. 157 B. 187 C. 197 D. 200 21. If the binary operation * is defined bym*n = mn + m + n for any real number m and n, find the identity element under this operation. A. e = 1 B. e = -1 C. e = -2 D. e = 0 Use thematrices belowtoanswer questions 22 and 23. 22. When PT is the transpose of P, calculate [PT]when x = 0, y= 1 and z = 2 A. 48 B. 24 C. –24 D. –48 23. PQ is equivalent to A PPT B. PP-T C. QP D. PP 24. In the figure above, TSP = 1050 and PRQ = 200, find PQR A. 1300 B. 1200 C. 750 D. 300 25. If the angles of a quadrilateral are (p + 10)0, (p + 20)0 and 4p0, find p A. 63 B. 40 C. 36 D. 28 26. In the figure above, PQR is a semicircle while PQ and QR are chords. QS is the perpendicular from Q to the diameter PR.What is the expression for QS? A. QS = PS.SR B. QS= Ö(PS.SR) C. QS= Ö2 Ö(PS.SR) D. QS= 1/Ö2Ö(PS.SR) 27. Determine the distance on the earth’s surface between two towns P(Lat. 600N, Long. 200E) and Q(Lat. 600N, Long 250W) A. 800p/9km B. 800Ö3p/9km C. 800pkm D. 800Ö3pkm 28. If in the diagram above, FG is parallel toKM, find the value of x A. 750 B. 950 C. 1050 D. 1250 29. X is a point due east of point Y on a coast Z is another point on the coast but 6.3km due south of Y. if the distance ZX is 12km, calculate the bearing of Z from X A. 2400 B. 2100 C. 15008 D. 600 30. The above diagram is a circle with centre O. find the area of the shaded portion. A. 9pcm2 B. 9(p -2)cm2 C. 18pcm2 3D. 36pcm2 31. The locus of a point which is equidistant from two given fixed points is the A. perpendicular bisector of the straight line joining them B. parallel line to the straight line joining them C. transverse to the straight line joining them D. angle bisector of 900 which the straight line joining them makes with the horizontal 32. What is the perpendicular distance of a point (2, 3 )from the line 2x – 4y + 3 = 0 A. Ö5/2 B. -Ö5/20 C. –5/Ö13 D. 0 33. Find the equation of the line through (5, 7) parallel to the line7x + 5y= 12 A. 5x+ 7y= 120 B. 7x + 5y= 70 C. x + y = 7 D. 15x + 17y= 90 34. Given that q is an acute angle and sin q = m/n, find cot q. A. n2 - m2 B. (n + m) (n - m) m m m C. D. n n2 - m2 n2 - m2 Q P S R 105O 20O U P Q R S T X 109O 109O F H G K M x O 6 cm 6 cm 35. In the figure above, ifXZ is 10cm, calculate RYin cm A. 10 B. 10(1 – 1/Ö3) C. 10(1 -Ö3) D. 10(1 - 1Ö2) 36. Evaluate lim (x-2) (x2+3x-2) x-->2 (x2-4) A. 0 B. 2 C. 3 D. 4 37. If y= x, find d2y/dx2 A. 2 cos x – x sin x B. sin x + x cos x C. sin x – x cos x D. x sin x – 2 cos x 38. Ice forms on a refrigerator ice-box at the rate of (4 – 0.6t)g per minute after t minute. If initially there are 2g of ice in the box, find the mass of ice formed in 5 minutes. A. 19.5 B. 17.0 C. 14.5 D. 12.5 39. Obtain a maximumvalue of the function f(x) = x3 – 12x + 11 A. -5 B. –2 C. 5 D. 27 40. A student blows a ballon and its volume increases at a rate of p (20 – t2)ccm3s-1 after t seconds. If the initial volume of 0cm3, find the volume of the balloon after 2 seconds. A. 37.00p B. 37.33p C. 40.00p D. 42.67p 41. Evaluate the integral p/4p/12 cos 2x dx A. -1/2 B. –1 C. ½ D. 1 42. A storekeeper checked his stock of five commodities and arrived at the following statistics. What angle will commodityHrepresent on a pie chart? A. 2160 B. 1080 C. 680 D. 540 43. If the mean of the above frequency distribution is 5.2, find y A. 6.0 B. 5.2 C. 5.0 D. 4.0 44. Find the mode and median respectively of the distribution above A. 2,1 B. 1,2 C. 1,5 D. 5,2 45. If the scores of 3students in a test are 5,6 and 7 find the standard deviation of their scores A. 2/3 B. 3/2Ö3 C. Ö 2/3 D. Ö3/2 46. Sample variance can be defined as S2 = 1/n n=1 (x1-x)2 and S2 = 1 nån=11 (x1-x) (n-1) Where n is the number of sample observations. There is no difference practically between the above definitions when A. n =35 B. n > 35 C. n < 35 D. n = 5 47. Two perfect dice are throw together. Determine the probability of obtaining a total score of 8 A. 1/12 B. 5/36 C. 1/8 D. 7/36 48. The probability of an event P is¾ while that of another Q is 1/6. if the probability of both P and Q is 1/12, what is the probability of either P or Q? A. 1/96 B. 1/8 C. 5/6 D. 11/12 49. Five people are to be arranged in a row for a group photograph. How many arrangements are there if a married couple in the group insist on sitting next to each other? A. 48 B. 24 C. 20 D. 10 50. A student has 5 courses to take from Mathematics and Physics. There are 4 courses in Mathematics and 3 in Physics which he can choose from at will. In howmany ways can he choose his courses so that he takes exactly two courses in Physics? A. 11 B. 12 C. 10 D. 7 30O 15O X Y Z 10 cm R Commodity Quantity F GHK M 215 113 108 216 68 2 4 6 8 xf 4 y 6 5 0 1 2 3 4 5 6 7 11 6 7 7 5 3 No . of children No . of families 1. Change 7110 to base 8 A. 1078 B. 1068 C. 718 D. 178 2. Evaluate 3524/0.05 correct to 3 significant figures. A. 705 B. 70000 C. 70480 D. 70500 3. If 9(x-1/2)= 3x2, find the value of x. A. ½ B. 1 C. 2 D. 3 4. Solve for y in the equation 10y, X5(2y-2) x 4(y-1)=1 A. ¾ B. 2/3 C. 1 D. 5/4 5. Simplify 1/3-2 – 1/3+2 A. 4 B. 2/3 C. 0 D. -4 6. If 2 log3 y+ log3 x2 = 4, then y is A. (4-log3 x2)/2 B. 4/log3 x2 C. 2/X D. ± 9/X 7. Solve without using tables log5 (62.5)-log5 (1/2) A. 3 B. 4 C. 5 D. 8 8. If #225.00 yields #27.00 in x years simple interest at the rate of 4%per annum, find x A. 3 B. 4 C. 12 D. 27 9. The shaded portion in the venn diagram above is A. XÇZ B. XcÇYÇZ C. XÇYcÇ Z D. XÇYÇZc 10. If x2 + 9 = x+ 1, solve for x A. 5 B. 4 C. 3 D. 1 11. Make x the subject of the relation 1+ax/1-ax = p/q A. p+q/a(p-q) B. p-q /a(p+q) C. p-q/apq D. pq/a(p-q) 12. Which of the following is a factor of 15 + 7x – 2x2? A. x-3 B. x+3 C. x-5 D. x+5 13. Evaluate (x+1/x+1)2 – (x-1/x-1) 2 A. 4x2 B. (2/x+2) 2 C. 4 D. 4(1+x) 14. Solve the following simultaneous equations for x. x2 + y – 5= 0 y – 7x + 3=0 A. -2, 4 B. 2, 4 C. -1, 8 D. 1, -8 15. Solve the following equation (3x-2)(5x-4)=(3x-2) 2 A. -3/2, 1 B. 1 C. 2/3, 1 D. 2/3, 4/5 16. The figure above represents the graphs of y= x (2-x) and y = (x-1) (x-3).What are the x-coordinates of p, q and r respectively? A. 1,3,2 B. 0,0,0 C. 0,2,3 D. 1,2,3 17. If the function f is defined by f(x+2)=2x2 + 7x – 5, find f(-1) A. -10 B. -8 C. 4 D. 10 18. Divide the expression x3 + 7x2 –x –7 by -1 +x2 A. –x3+7x2-x-7 B. –x3-7x+7 C. X-7 D. X+7 19. Simplify 1/p-1/q –p/q-q/p A. 1/p-q B. -1/p+q C. 1/pq D. 1/pq(p-q) 20. Solve the inequality y2-3y>18 A. -26 C. y>-3 or y>6 D. y<-3 or y<6 21 If x is negative, what is the range of values of x within which x+1/3 > 1/x+3 A. 3 2 is true A. x < ½ B. x < 0 or x > ½ C. 0 < x < ½ D. 1 < x < 2 x y 0 (3.0) (0.-27) above. A. 11.5 B. 12.5 C. 14.0 D. 14.5 48. A number is selected at random between 20 and 30 both numbers inclusive. Find the probability that the number is a prime A. 2/11 B. 5/11 C. 6/11 D. 8/11 1. Evaluate 1/3¸[5/7(9/10 – 1 + 3/4)] A. 28/39 B. 13/84 C. 39/28 D. 84/13 2. Evaluate (0.36x 5.4 x 0.63) (4.2 x 9.0 x 2.4) correct to 2 significant figures A. 0.013 B. 0.014 C. 0.13 D. 0.14 3. Evaluate Log5(0.04) (Log318 – Log32) A. 1 B. -1 C. 2/3 D. -2/3 4. Without using tables, solve the equation 8x-2 = 2/25 A. 4 B. 6 C. 8 D. 10 5 Simply Ö48 – 9/Ö3 + Ö75 A. 5Ö3 B. 6Ö3 C. 8Ö3 D. 18Ö3 6. Given that “2 = 1.414, find without using tables, the value of 1/”2 A. 0.141 B. 0.301 C. 0.667 D. 0.707 7. In a science class of 42 students, each offers at least one ofMathematics and Physics. If 22 students offer Physics and 28 students offer Mathematics, find how many students offer Physics only? A. 6 B. 8 C. 12 D. 14 8. Given that for setsA and B, in a universal set E, AÍ B then AÇ(AÇB)’ is A. A B. O/ C. B D. å 9. Solve for x if 25x + 3(5x) = 4 A. 1 or -4 B. 0 C. 1 D. -4 or 0 Mathematics 1994 49. Calculate the standard deviation of the following data. 7, 8, 9, 10, 11, 12, 13. A. 2 B. 4 C. 10 D. 11 50. The chances of three independent event X, Y, Z occurring are 1/2 , 2/3, ¼ respectively. What are the chances of y and z only occurring? A. 1/8 B. 1/24 C. 1/12 D. ¼ 26. The equation of the line in the graph above is A. 3y = 4x + 12 B. 3y = 3x + 12 C. 3y = -4x + 12 D. 3y = -4x + 9 27. In the diagram above, O is the centre of the circle. If SOQ is a diameter and 0 19. If the 6th term of an arithmetic progression is 11 and the first term is 1, find the common difference. A. 12/5 B. 5/3 C. -2 D. 2 20. Find the value of r if log10r + log10r2 + log10r4 + log10r8 + log10r16 + log10r32 = 63 A. 10-8 B. 100 C. 10 D. 102 21. Find the nth term of the sequence 3,6,10,15,21,….. A. n(n - 1/2) B. n(n + 1/2) C. (n + 1)(n + 2)/2 D. n(2n + 1) 22. A binary operation * is defined on the set of all positive integers by a*b= ab for all positive integers a,b. which of the following properties doesNOT hold? A. Closure B. Associativity. C. Identity. D. Inverse. 23. The multiplication table above has modulo 10 on the set S = {2,4,6,8}. Find the inverse of 2 A. 2 B. 4 C. 6 D. 8 24. Solve for x and y 1 1 x = 4 3 y 1 1 A. x = -3, y = 3 B. x = 8, y = 3 C. x = 3, y = -8 D. x = 8, y = -3 25. The determinant of the matrix (1 2 3) (4 5 6) is (2 0 -1) A. -67 B. -57 C. -3 D. 3 y x 0 -2 1 2 3 -2 -4 2x-y-2=0 30O 50O 38O R S Q P O 10 2 4 6 8 2 4 6 8 4 8 2 6 8 6 4 2 2 4 6 8 6 2 8 4 xO mod 50O 60O Q T P R 6 cm h 5 cm 7 cm p p p p 43. The gradesA1, A2, A3, C4 and F earned by students in a particular course are shown in the pie chart above.What percentage of the students obtained a C4 grade? A. 52.0 B. 43.2 C. 40.0 D. 12.0 44. The table above shows the frequency distribution of a data. If the mean is 43/14, find y. A. 1 B. 2 C. 3 D. 4 45. The mean of twelve positive numbers is 3. when another number is added, the mean becomes 5. find the thirteenth number. A. 29 B. 26 C. 25 D. 24 46. Find the mean deviation of the set of numbers 4, 5, 9 A 0 B. 2 C. 5 D. 6 47. Estimate the median of the frequency distribution above. A. 101/2 B. 111/2 C. 121/2 D. 13 48. Find the variance of the frequency distribution above A. 3/2 B. 9/4 C. 5/2 D. 3 49. The table above shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old? A. 27/40 B. 17/20 C. 33/40 D. 3/20 1-5 6-10 11-15 16-20 21-25 6 15 20 7 2 Class interval Frequency x 1 2 3 4 5 f 2 1 2 1 2 10 11 12 Number of pupils 6 27 7 Age in years In the diagram above, find h. A. 12/7cm B. 12/7V6cm C. 7/12cm D. 1/2V51cm 33. In the frustumof a cone shown above, the top diameter is twice the bottomdiameter. If the height of the frustum is h centimeters, find the height of the cone. A. 2h B. 2ph C. ph D. ph/2 34. What is the locus of a point P which moves on one side of a straight line XY, so that the angle XPY is always equal to 900 A. The perpendicular B. Aright-angledtriangle. bisector of XYX C. A circle D. A semi-circle. 35. If M(4,q) is the mid-point of the line joining L(p, -2) and N(q, p), find the values of p and q. A. p = 2, q = 4 B. p = 3, q = 1 C. p = 5, q = 3 D. p = 6, q = 2 36. 37. The angle of depression of a boat from the top of a cliff 10m high is 300. how far is the boat from the foot of the cliff? A. 5Ö3/3m B. 5Ö3m C. 10Ö3m D. 10Ö3/3m 38. What is the value of sin (-6900)? A. Ö3/2 B. -Ö3/2 C. -1/2 D. ½ 39. If y = 3t3 + 2t2 – 7t + 3, find dy/dt at t = -1 A. -1 B. 1 C. -2 D. 2 40. Find the point (x, y) on the Euclidean plane where the curve y = 2x2 – 2x + 3 has 2 as gradient. A. (1,3) B. (2,7) C. (0,3) D. (3,15) 41. Integrate (1 – x)/x3 with respect to x. A. (x – x2)/(x4 + k) B. 4/x4 – 3/x3 + k C. 1/x – 1/2x2 + k D. 1/3x3 – 1/2x + k 42. Evaluate 1 (2x + 1)2 dx -1 A. 32/3 B. 4 C. 41/3 D. 42/3 h y x (0,4) (0,0) (3,0) x 1 2 3 4 5 f y + 2 y - 1 2y + 3 y + 4 3y - 4 72O 64.8O 43.2O 144O A1 A2 F AC 3 4 50. In a survey, it was observed that 20 students read newspapers and 35 read novels. If 40 of the students read either newspaper or novels, what is the 1. Calculate 33105 - 14425 A. 13135 B. 21135 C. 43025 D. 11035 2. Convert 3.1415926 to 5 decimal places A. 3.14160 B. 3.14159 C. 0.31415 D. 3.14200 3. The length of a notebook 15cm, was measured as 16.8cm. calculate the percentage error to 2 significant figures. A. 12.00% B. 11.00% C. 10.71% D. 0.12% 4. A worker’s present salary is #24,000 per annum. His annual increment is 10%of his basic salary.What would be his annual salary at the beginning of the third year? A. #28,800 B. #29,040 C. #31,200 D.#31,944 5. Express the product of 0.0014 and 0.011 in standard form. A. 1.54 x 102 B. 1.54 x 10-3 C. 1.54 x 104 D. 1.54 x10-5 6. Evaluate (813/4 - 27 1/3) 3 x 23 A. 27 B. 1 C. 1/3 D. 1/8 7. Find the value of (16)3/2 + log100.0001 + log232 A. 0.065 B. 0.650 C. 6.500 D. 65.00 8. Simplify Ö12 - Ö3 Ö12+ Ö3 A. 1/3 B. 0 C. 9/15 D. 1 9. Four members of a school first eleven cricket team are also members of the first fourteen rugby team. How many boys play for at least one of the two teams? A. 25 B. 21 C. 16 D. 3 10. If S = (x : x2 = 9, x > 4), then S is equal to A. 0 B. {0} C. f D. {f} 11. If x – 1 and x + 1 are both factors of the equation x3 + px3 + qx + 6 = 0, evaluate p and q A. –6, -1 B. 6, 1 C. -1 D. 6, -6 12. Find a positive value of p if the equation 2x2 – px + p leaves a remainder 6 when added A. 1 B. 2 C. 3 D. 4 13. Find r in terms ofK, Q and S if s = 2rÖ (QpT+K) A. r2 - k B. r2 - k 2pr2Q Q 4pr2Q C. r2 - k D. r2 - k 2pr2Q 4pr2Q 14. The graph of f(x) = x2 - 5x + 6 crosses the x-axis at the points Mathematics 1995 probability of the students who read both newspapers and novel? A. 1/2 B. 2/3 C 3/8 D. 3/11 A. (-6, 0)(-1, 0) B. (-3,0)(-2, 0) C. (-6, 0)(1, 0) D. (2, 0)(3, 0) 15. Factorize completely the expression abx2 + 6y – 3ax –2byx A. (ax – 2y)(bx - 3) B. (bx + 3)(2y - ax) C. (bx + 3)(ax – 2y) D. (ax – 2y) (ax - b) 16. Solve the following inequality (x - 3)(x - 4) £0 A. 3£ x £ 4 B. 3 < x < 4 C. 3 £ x < 4 D. 3 < x £4 17. The 4th term of anA. P is 13cmwhile the 10th termis 31. find the 31st term. A. 175 B. 85 C. 64 D. 45 18. Simplify x2 - 1 x3 + 2x2 – x - 2 A. 1/x + 2 B. x – 1/x + 1 C. x – 1/x + 2 D. 1/x – 2 19. Express 5x –½ (x - 2)(x - 3) in partial fraction A. 2/x – 2 – 3/x –3 B. 2/x – 2 + 3/x – 3 C. 2/x – 3 – 3x –2 D. 5/x – 3 + 4/x – 2 20. Use the graph of the curve y = f(x) above to solve the inequality f(x) > 0. A. -1£ x £ 1, x >2 B. x £-1, 1, < x > 2 C. x£ -1, 1 £ x £2 D. x £ 2, -1 £ x £ 1 21. Which of the following binary operation is commutative in a set of integers? A. a*b = a + 2b B. a*b = a + b –ab C. a*b = a2 + b D. a*b = a(b + 1)/2 22. If a*b = +Öab, Evaluate 2*(12*27) A. 12 B. 9 C. 6 D. 2 23. Find the sum to infinity of the following sequence 1, 9/10, (9/10)2, (9/10)3 A. 1/10 B. 9/10 C. 10/9 D. 10 24. Find the value of K if 2, 1, 1 2, 1 k 1, 3 -1 = 23 A. 1 B. 2 C. 3 D. 4 y -1 0 1 2 x 25. If X = 1, 2 and Y = 2, 1 0, 3 4, 3 A. (10, 7) B. (2, 7) (12, 9) (1, 17) C. (10, 4) D. (4, 3) ( 4, 6) (10, 9) 26. Determine the value of x in the figure above A. 1340 B. 810 C. 530 D. 460 27. PT is a tangent to the circle TYZX, YT = YX and < PTX = 500. calculate 0. solve the inequality f(x)/g(x) < 1 A. x < - ¾ B. x > - 4/3 C. x > - 3/4 D. x > - 12 18. Find the range of values of x which satisfies the inequality 12x2< x + 1 A. -1/4 < x < 1/3 B. ¼ < x <1/3 C. -1/3 < x<1/4 D. -1/4 < x <-1/3 19. Sn is the sum of the first n terms of a series given by Sn = n2 – 1. find the nth term. A. 4n + 1 B. 4n – 1 C. 2n + 1 D. 2n – 1 20. The nth term of a sequence is given by 31-n. find the sum of the first three terms of the sequence. A. 13/9 B 1 C. 1/3 D. 1/9 21. Two binary operations * and Ä are defined as m*n = mn – n – 1 and m Ä n = mn + n – 2 for all real numbers m, n. find the values of 3Ä (4*5). A. 60 B. 57 C. 54 D. 42 22. If xy = x + y – xy, find x, when (x*2)+(x*3) = 68 A. 24 B. 22 C. -12 D. -21 23. Determines x + y if 2 -3 (x) = (-1) -1 4 (y) (8) A. 3 B. 4 C. 7 D. 12 24. Find the non-zero positive value of x which satisfies the equation x 1 0 1 x 1 = 0 0 1 x A. 2 B. 3 C. 2 D. 1 25. Each of the base angles of an isosceles triangle is 580 and all the vertices of the triangle lie on a circle. Determine the angle which the base of the triangle subtends at the centre of the circle. A. 1280 B. 1160 C. 640 D. 580 26. From the figure above, FK//GR and FH = GH,< RFK = 340 and < FGH = 470. calculate the angle marked x. A. 420 B. 520 C. 640 D. 720 27. The figure above shows circles of radii 3cm and 2cm with centres at X andYrespectively. The circles have a transverse common tangent of length 25cm. Calculate XY. A. 630 cm B. 626 cm C. 615 cm D. 600 cm 28. A chord of a circle diameter 42cm subtends an angle of 600 at the centre of the circle. Find the length of theminor arc. A. 22 cm B. 44 cm C. 110 cm D. 220 cm [ = 22/7] 29. An arc of a circle subtends an angle of 700 at the centre. If the radius of the circle is 6cm, calculate the area of the sector subtended by the given angle. A. 22 cm2 B. 44 cm2 C. 66 cm2 D. 88 cm2 30. Find the volume of the prism above. t = v 1 + 1 f g 34O 47O x G H R F K X Y 2 cm 25 cm 3 cm 5 cm 8 cm 10 cm 11 cm p A. 990 cm3 B. 880 cm3 C. 550 cm3 D. 495 cm3 31. A cone with the sector angle of 450 is cut out of a circle of radius r cm. find the base radius of the cone. A. r/16cm B. r/8cm C. r/4cm D. r/2cm 32. A point P moves so that it is equidistant from points L and M. if LM is 16cm, find the distance of P from LM when P is 10cm from L. A. 12cm B. 10cm C. 8cm D. 6cm 33. The angle between the positive horizontal axis and a given line is 1350. find the equation of the line if it passes through the point (2, 3). A. x – y = 1 B. x + y = 1 C. x + y = 5 D x – y = 5 34. Find the distance between the point Q(4, 3) and the point common to the lines 2x – y = 4 and x + y = 2 A. 3 10 B. 3 5 C. 26 D. 13 35. The angle of elevation of a building from a measuring instrument placed on the ground is 300. if the building is 40m high, how far is the instrument from the foot of the building? A. 20Ö3m B. 40Ö3m C. 20Ö3m D. 40Ö3m 36. In a triangle XYZ, if 1/4x A. x> - 1/6 B. x>0 C. 0 x2 A. x <-2 or x> 1 B. x >2 or x< -1 C. –1 < x> 2 D. –2 < x< 1 22. If a and b are the roots of the equation 3x2 + 5x – 2 = 0, find the value of 1/a + 1/b A. -5/2 B. –2/3 C. ½ D. 5/2 23. Find the minimum value of the function f(q ) = 2/3 – cosq for o £ q £ 2p. A. ½ B. 2/3 C. 1 D. 2 24. A frustum of a pyramid with square base has its upper and lower sections as squares of sizes 2m and 5m respectively and the distance between them 6m. find the height of the pyramid from which the frustum was obtained. A. 8.0m B. 8.4m C. 9.0m D. 10.0m 25. P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight line ST is on the locus of P and Ð VUS = 500, find Ð UST. A. 3100 B. 1300 C. 800 D. 500 -1 -1 1 2 3 -2 -2 -3 2 3 -3 0 1 -1-1 1 2 3 -2 -2 -3 2 3 -3 0 1 -1-1 1 2 3 -2 -2 -3 2 3 -3 0 1 -1-1 1 2 3 -2 -2 -3 2 3 -3 0 1 6. A man wishes to keep some money in a savings deposit at 25% compound interest so that after 3 years he can buy a car for #150,000. how much does he need to deposit now? A. #112,000.50. B. #96,000.00 C. #85,714.28 D. #76,800.00 7. If 31410 – 2567 = 340x, find x A. 2n + 1 B. 2n – 1 C. 4 D. ¼ 8. Audu bought an article for #50 000 and sold it to Femi at a loss of x%. Femi later sold the article to Oche at a profit of 40%. If Femi made a profit of #10,000, find the value of x. A. 60 B. 50 C. 40 D. 20 9. Simplify 3(2n + 1) – 4(2n -1 )/2(n + 1) – 2n A. 2n + 1 B. 2n - 1 C. 4 D. ¼ 10. If P3446 – 23P26 = 2PP26, find the value of digit P. A. 2 B. 3 C. 4 D. 5 11. Evaluate 5-3log52 x 22log23 A. 8 B. 11/8 C. 2/5 D. 1/8 12. A binary operation * is defined by a * b = ab. if a * 2 = 2 –a, find the possible values of a. A. 1, -1 B. 1, 2 C. 2, -2 D. 1, -2 13. The 3rd term of an A. P. is 4x – 2y and the 9th term is 10x - 8y . find the common difference. A. 19x - 17y B. 8x - 4y C. x – y D. 2x 14. Find the inverse of p under the binary operation * by p * q= p + q – pq, where p and q are real numbers and zero is the identity. A. p B. p – 1 C. p/p – 1 D. p/p+1 (a, b) 15. Amatrix P(a, b) is such that PT= p, where (c, d) PT is the transpose of P, if b = 1, then P is A. (0, 1) B. (0, 1) (1, 0) (-1, 0) C. (0, 1) D. (1, 1) (1, 1) (-1,0) 16. Evaluate (1/2 – ¼ + 1/8 – 1/16 +…….) -1 A. 2/3 B. 0 C. –2/3 D. –1 17. The solution of the simultaneous inequalities 2x – 2 £ y and 2y 2 £ x is represent by 26. A ship sails a distance of 50km in the direction S50E and then sails a distance of 50km in the direction N400E. find the bearing of the ship from its original position. A. S900E B. N400E C. S950E D. N850E 27. An equilateral triangle of side Ö3 cm is inscribed in a circle. Find the radius of the circle. A. 2/3cm B. 2cm C. 1cm D. 3cm 28. 3y = 4x – 1 and Ky = x + 3 are equations of two straight lines. If the two lines are perpendicular to each other, find K A. -4/3 B. –3/4 C. ¾ D. 4/3 29. In the diagram above, if Ð RPS = 500, Ð RPQ = 300 and PQ = QR, find the value of Ð PRS A. 800 B. 700 C. 600 D. 500 30. In the diagram above, EFGH is a circle center O. FH is a diameter and GE is a chord which meets FH at right angle at the point N. if NH = 8 cm and EG = 24 cm, calculate FH. A. 16cm B. 20cm C. 26cm D. 32cm 31. If P and Q are fixed points and X is a point which moves so that XP = XQ, the locus of X is A. astraight line B. acircle C. thebisector Ð PXQ D. theperpendicular bisector ofPQ 32. In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon. A. 87 B. 6 C. 4 D. 3 33. A predator moves in a circle of radius Ö2 centre (0, 0), while a preymoves along the line y = x. if 0£ x£ 2, at which point(s) will theymeet? A. (1, 1) only B. (1, 1) and (1, 2) 50O S P Q 30O R E O N H F G 34. If the diagram above is the graph of y=x2, the shaded area is A. 64squareunits B. 128/3squareunits C. 64/3squareunits D. 32squareunits 35. Find the value of p(cos2q – 1/sin2q) dq A. p B. p/0 C. -p/0 D. p 36. If y = 2y cos 2x – sin 2x, find dy/dx when x = ë/4 A. p B. – p C. p/2 D. – p/2 37. A bowl is designed by revolving completely the area enclosed by y = x2 – 1, y= 0, y = 3 and x ³ 0 around the y-axis. What is the volume of this bowl? A. 7 p cubicunits. B. 15 p/2 cubic units C. 8 p cubic units D. 17 p/2 cubic units. 38. If the volume of a hemisphere is increasing at a steady rate of 8 pm3s-1, at what rate is its radius changing when it is 6m? A. 2.50ms-1 B. 2.00ms-1 C. 0.25ms-1 D. 0.20ms-1 39. A function f(x) passes through the origin and its first derivative is 3x + 2. what is f(x) A. y = 3/2x2 + 2x B. y = 3/2 x2 + x C. y = 3 x2 + x/2 D. y = 3 x2 + 2x 40. The expression ax2 + bx + c equals 5 at x = 1. if its derivative is 2x + 1, what are the values of a, b, c, respectively? A. 1, 3, 1 B. 1, 2, 1 C. 2, 1, 1 D. 1, 1, 3 41. X and Y are two events. The probability of X and Y is 0.7 and the probability of X is 0.4. If X and Y are independent, find the probability of Y. A. 0.30 B. 0.50 C. 0.57 D. 1.80 42. If the mean of the numbers 0, x + 2, 3x + 6 and 4x + 8 is 4, find their mean deviation. A. 0 B. 2 C. 3 D. 4 43. In how many ways can the word MATHEMATICS be arranged? A. 11!/9! 2! B. 11!/9! 2! 2! C. 11!/2! 2! 2! D. 11!/2! 2! y y= 16 x The cumulative frequency curve above represents the ages of students in a school. Which are group do 70% of the students belong? A. 15.5 – 18.5 B. 15.5 – 19.5 C. 16.5 – 19.5 D. 17.5 – 20.5 47. The variance of x, 2x, 3x 4x and 5x is A. xÖ2 B. 2x2 C. x2 D. 3x 48. Find the sum of the range and the mode of the set of numbers 10, 5, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 10, 9, 7, 10, 6, 5 A. 16 B. 14 C. 12 D. 10 49. In how many ways can a delegation of 3 be chosen from among 5 men and 3 women, if at least one man at least one woman must be included? A. 15 B. 28 C. 30 D. 45 50. The table above shows the frequency distribution of the ages (in years) of pupils in a certain secondary school.What percentage of the total number of pupils is over 15 years but less than 21 years? A. 35% B. 45% C. 50% D. 60% Mathematics 2001 44. A dice is rolled 240 times and the result depicted in the table above. If a pie chart is constructed to represent the data, the angle corresponding to 4 is A. 100 B. 160 C. 400 D. 600 45. If U = {x : x is an integer and {1 £ x £ 20} E1 = {x : x is a multiple of 3} E2 = {x : x is a multiple of 4} And an integer is picked at random from U, find the probability that it is not in E2 A. ¾ B. 3/10 C. ¼ D. 1/20 46. No . Of Pupils 1. Find the principal which amounts to #5,000 at simple interest in 5 years at 2% per annum A. #5000 B. #4900 C. #4800 D. #4700 2. A car dealer bought a second-hand car for #250,000.00 and spent #70 000.00 refurbishing it. He then sold the car for #400 000.00. what is the percentage gain? A. 20% B. 25% C. 32% D. 60% 3. Evaluate 21.05347 – 1.6324 x 0.43, to 3 decimal places. A. 20.351 B. 20.352 C. 20.980 D. 20.981 4. Evaluate (0.14)2 x 0.275)/7(0.02) correct to 3 decimal places A. 0.033 B. 0.039 C. 0.308 D. 0.358 5. Given that p = 1 + Ö2 and q = 1 - Ö2, evaluate (p2 – q2)/2pq A. -2(2 + Ö2 ) B. 2(2 + Ö2) C. -2Ö2 D. 2Ö2 6. If y/2 = x, evaluate (x3/y3 + 1/2) + (1/2 – x2/y2) A. 5/16 B. 5/8 C. 5/4 D. 5/2 7. Simplify (3Ö64a3)-3 A. 8a B. 4a C. 1/4a D. 1/4a 8. Factorize 4x2 – 9y2 + 20x + 25 A. (2x – 3y)(2x + 3y) B. (2x+5)(2x–9y+5) C. (2x – 3y+ 5)(2x – 3y - 5) D. (2x – 3y)(2x + 3y+ 5) 9. If tow graphs y = px2 and y = 2x2 – 1 intersect at x = 2, find the value of p in terms of q A. (7 + q)/8 B. (8 – q)/2 C. (q – 8)/7 D. 7 / (q –1) 10. Solve the equations: m2 + n2 = 29;m + n = 7 A. (5, 2) and (5, 3) B. (5, 3) and (3, 5) C. (2, 3) and (3, 5) D. (2, 5) and (5, 2) 11. Divide a3x – 26a2x + 156ax – 216 by a2x – 24ax + 108 A. ax – 18 B. ax – 6 C. ax – 2 D. ax + 2 12. Find the integral values of x and y satisfying the inequality 3y + 5x £ 15, given that y > 0, y< 3 and x > 0. A. (1,1),(2,1),(1,3) B. (1,1),(1,2),(1,3) C. (1,1), (1, 2),(2, 1) D. (1,1), (3, 1),(2, 2) 13. Triangle SPT is the solution of the linear inequalities A. 2y – x – 2 £ 0, y + 2x + 2 £ 0,³0, x £ 0 B. 2y – x – 2 £ 0, y + 2x + 2 £ 0, £ 0 C. 2y – x – 2 £ 0, y + 2x + 2 £ 0, £ 0, x £ -1 D. -2y < x £ 2 £ 0, y + 2x + 2 £ 0, £ 0 14.. The sixth term of an arithmetic progression is half of its twelfth term. The first term is equal to A. half of the common difference B. double of the common difference C. the common difference D. zero 15. A man saves #100.00 in his first year of work and each year saves #20.00 more than in the preceding year. In how many years will he save #580.00 A. 20 years B. 29 years C. 58 years D. 100 years 16. An operation * is defined on the set of real numbers by a*b = a + b + 1. if the identity elements is -1, find the inverse of the element 2 under. A. -4 B. –2 C. 0 D. 4 17 The identity element with respect to the multiplication shown in the table above is A. k B. l C. m D. o 18. Given that matrix k = (2, 1) the matrix (3, 4) k2 + k + 1, where I is the 2 x 2 identity matrix, is A. (9, 8 ) B. (10, 7) (22, 23) (21, 24) C. (7, 2) D. (6, 3) (12, 21) (13, 20) 19. Evaluate -1 -1 -1 3 1 1 1 2 1 S -1 -2 -2 1 x y y+ x+ 2 2=0 2 2= 0 y-x- P T A. 4 B. –2 C. –4 D. –12 20. If P = 3 -3 4 then -2p is 5 0 6 1 2 1 A. -6, 4, -8 B -6, 4, -8 5, 0, 6 -10, 0, 6 7, 5, -1 -14, 5, -1 C. -6, -4, 2 D -6, 4, -8 -10, -2, -12 -10, 0, -12 -14, 10, 2 -14, 40, 2 21. Find the number of sides of a regular polygon whose interior angle is twice the exterior angle A. 2 B. 3 C. 6 D. 8 22. In the figure above, PQR is a straight line segment, PQ = QT. Triangle PQT is an isosceles triangle, < SRQ is 750 and < QPT = 250. calculate the value of < RST. A. 250 B. 450 C. 500 D. 550 23. A cylindrical tank has a capacity of 3080m3. what is the depth of the tank if the diameter of its base is 14m? A. 20m B. 22m C. 23m D. 25m 24. A sector of a circle of radius 7.2 cm which subtends an angle 3000 at the centre is used to form a cone. What is the radius of the base of the cone? A. 6cm B. 7cm C. 8cm D. 9cm 25. The chord ST of a circle is equal to the radius, r of the circle. Find the length of arc ST. A. pr/2 B. pr/3 C. pr/6 D. pr/12 26. A point P moves such that it is equidistant from the points Q and R. find QR when PR = 8cm and < PRQ = 300 A. 4cm B. 4Ö3cm C. 8cm D. 8Ö3cm 27. Find the locus of a point which moves such that its distance from the line y = 4 is a constant, k. A. y = 4 + k B. y = k – 4 C. y = k ± 4 D. y = 4 ± k 28. A straight line makes an angle of 300 with the positive x-axis and cuts the y-axis at y = 5. find the equation of the straight line. k l m k l m k l m k l m k l m x P Q T S 25 R O 75O A. Ö3y = x + 5yÖ3 B. Ö3y= -x + 5Ö3 C. y = x + 5 D. y = 1/10x + 5 29. P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius A. 3.5 units B. 6.5 units C. 7.0 units D. 13.0 units 30. Find the value of p if the line joining (p, 4) and (6, - 2) is perpendicular to the line joining (2, p) and (-1, 3) A. 0 B. 3 C. 4 D. 6 31. The bearing of P and Q from a common point N are 0200 and 3000 respectively. If P and Q are also equidistant from N, find the bearing of P from Q. A. 3200 B. 2800 C. 0700 D. 0400 32. Find the value of q in the diagram above. A. 300 B. 600 C. 1000 D. 1200 33. Differentiate (2x + 5)2(x - 4) with respect to x A. (2x+5)(6x - 11) B. (2x+5)(2x –13) C. 4(2x +5)(x - 4) D. 4(2x +5)(4x - 3) 34. If y = x sin x, find dy/dx when x = p/2 A. p/2 B. 1 C. –1 D. p/-2 35. If the gradient of the curve y = 2kx2 + x + 1 at x = 1 find k A. 1 B. 2 C. 3 D. 4 36. Find the rate of change of the volume V of a sphere with respect to its radius r when r = 1 A. 4p B. 8p C. 12p D. 24p 37. Find the dimensions of the rectangle of greatest area which has a fixed perimeter p. A. Squareofsidesp/4 B. Squareofsidesp/2 C. Squareof sides p D. Square of sides 2p 38. Evaluate 2(2x - 3)2/3 dx A. 2x – 3 + k B. 2(2x - 3) + k C. 6/5(2x - 3)5/3+ k D. 3/5(2x - 3)5/3+ k 39. Find the area bounded by the curves y = 4 – x2 A. 101/3 sq. units B. 102/3 sq. units C. 201/3 sq. units D. 202/3 sq. units 3t 0 t t 40. The bar chart above shows different colours of cars passing a particular point of a certain street in two minutes.What fraction of the total number of cars is yellow? A. 4/15 B. 1/5 C. 3/25 D. 2/25 41 The histogram above shows the distribution of passengers in taxis of a certain motor park. Howmany taxis havemore than 4 passenger? A. 14 B. 15 C. 16 D. 17 Using the table below to answer questions 42 and 43 42. Find the square of the mode A. 25 B. 49 C. 64 D. 121 43. The mean score is A. 11.0 B. 9.5 C. 8.7 D. 7.0 44. Find the range of 1/6, 1/3, 3/2, 2/3, 8/9 and 4/3 A. 4/3 B. 7/6 C. 5/6 D. ¾ 45. Find the variance of 2, 6, 8, 6, 2 and 6 A. Ö5 B. Ö6 C. 5 D. 6 46. No . of cars 87654321 Color of cars Yellow White Red Green Blue Black No . of taxis 876543210 No . of passengers 0.5 2.5 4.5 6.5 8.5 10.5 12.5 Score Frequency 4 7 8 11 13 8 3 5 2 7 2 1 50 40 30 20 10 0 Cumulative frequency Masses (Kg) 5.5 10.5 15.5 20.5 25.5 30.5 P Q Q Q The graph above shows the cumulative frequency of the distribution of masses of fertilizer for 48 workers in one institution. Which of the following gives the interquartile range? A. Q3 – Q1 B. Q3 – Q2 C. Q2 – Q1 D. ½ (Q3 – Q1) 47. Find the number of ways of selecting 8 subjects from 12 subjects for an examination. A. 498 B. 496 C. 495 D. 490 48. If 6Pr = 6, find the value of 6Pr+1 A. 15 B. 30 C. 33 D. 35 Colour No . of beads Blue Black Yellow White Brown 1 2 4 5 3 49. The distribution of colors of beads in a bowl is given above.What is the probability that a bead selected at random will be blue or white? A. 1/15 B. 1/3 C. 2/5 D. 7/15 50. Teams P and Q are involved in a game of football. What is the probability that the game ends in a draw? A. ¼ B. 1/3 C. ½ D. 2/3 1. A trader bought goats for #4 000 each. He sold them for #180 000 at a loss of 25%. How many goats did he buy? A. 36 B. 45 C. 50 D. 60 2. Simplify (Ö0.7 + Ö70)2 A. 217.7 B. 168.7 C. 84.7 D. 70.7 3. Evaluate (0.21 x 0.072 x 0.0054)/ (0.006 x 1.68 x 0.063) correct to four significant figures. A. 0.1286 B. 0.1285 C. 0.01286 D. 0.01285 4. In a school, 220 students offer Biology or Mathematics or both. 125 offer Biology and 110 Mathematics. How many offer Biology but not Mathematics? A. 125 B. 110 C. 95 D. 80 5. Simplify 52.4 – 5.7 – 3.45 – 1.75 A. 42.2 B. 42.1 C. 41.5 D. 41.4 6. Without using tables, evaluate (343)1/3 x (0.14)-1 x (25)1/2 A. 7 B. 8 C. 10 D. 12 7. In the diagram below are two concentric circles of radii r and R respectively with centre O. if r = 2/5 R, express the area of the shaded portion in terms of p and R. A. 9/25pR2 B. 5/9pR2 C. 21/25pR2 D 21/23pR2 Mathematics 2002 R O r 8. Find the value of & if the line 2y - &x + 4 = 0 is perpendicular to the line y+ 1/4x – 7 = 0 A. -8 B. –4 C. 4 D. 8 9. A bucket is 12cm in diameter at the top, 8cm in diameter at the bottom and 4cm deep. Calculates its volume. A. 144pcm3 B. 304pcm3/3 C. 72pcm3 D. 128pcm3/ 10. In the diagram below, XZ is the diameter of the circle XYZW, with centre O and radius 15/2cm. If XY = 12cm, find the area of the triangle XYZ. A. 75cm2 B. 54cm2 C. 45cm2 D. 27cm2 11. Find the coordinate of the midpoint of x and y intercepts of the line 2y = 4x - 8 A. (-1, -2) B. (1, 2) C. (2, 0) D. (1, -2) 12. A chord of a circle subtends an angle of 1200 at the centre of a circle of diameter 4Ö3cm. Calculate the area of the major sector. A. 32pcm2 B. 16pcm2 C. 8pcm2 D. 4pcm2 13. If tan q = 4/3, calculate sin2 q - cos2 q. A. 7/25 B. 9/25 C. 16/25 SD. 24/25 14. X O Z Y P R Q S T x 72O In the diagram above, PST is a straight line, PQ = QS = RS. If < RSRT = 720, find x. A. 720 B. 360 C. 240 D. 180 15. The locus of a point P which is equidistant from two given points S and T is A. a perpendicular to ST B. a line parallel to ST C. the angle bisector of PS and ST D. the perpendicular bisector ST 16. A solid hemisphere has radius 7cm. Find the total surface area. A. 462cm2 B. 400cm2 C. 308cm2 D. 66cm2 17. The angle PGR below is A. a scalene triangle B. an isosceles triangle C. an equilateral triangle D. an obtuse – angled triangle 18. The sum of the interior angles of a polygon is 20 right angles. How many sides does the polygon have? A. 10 B. 12 C. 20 D. 40 19. Find the equation of the set of points which are equidistant from the parallel lines x = 1 and x = 7 A. y = 4 B. y = 3 C. x = 3 D. x = 4 20. In the diagram below, a cylinder is surrounded by a hemispherical bowl. Calculate the volume of the solid. A. 216pcm3 B. 198pcm3 C. 180pcm3 D. 162pcm3 21. A hunter 1.6m tall, views a bird on top of a tree at an angle of 450. If the distance between the hunter and the tree is 10.4m, find the height of the tree. A. 8.8m B. 9.0m C. 10.4m D. 12.0m 22. Themean of a set of six numbers is 60. if the mean of the first five is 50, Find the sixth number in the set. A. 110 B. 105 C. 100 D. 95 23. The range of the data k + 2, k – 3, k + 4, k – 2, k, k – 5, k + 3, k – 1 and k + 6 is. A. 6 B. 8 C. 10 D. 11 24. The distribution above shows the number of days a group of 260 students were absent from school in a particular term. How many students were absent for at least four days in the term? A. 40 B. 120 C. 160 D. 210 25. The venn diagram below shows the number of students offering Music and History in a class of 80 students. If a student is picked at random from the class, what is the probability that he offers Music only? A. 0.13 B. 0.25 C. 0.38 D. 0.50 26. Find the mean of the data 7,-3,4,-2,5,-9,4,8,-6,12 A. 1 B. 2 C. 3 D. 4 27. The probability of a student passing any examination is 2/3. if the student takes three examination, what is the probability that he will not pass any of them? A. 1/27 B. 8/27 C. 4/9 D. 2/3 28. How many three-digit numbers can be formed from 32564 without digit being repeated? A. 10 B. 20 C. 60 D. 120 29. The acres for rice, principle, cassava, cocoa and palm oil, in a certain district are given respectively as 2,5,3, 11 and 9. what is the angle of the sector for cassava in a pie chart? A. 360 B. 600 C. 1080 D. 1800 30. Calculate the mean deviation of the set of numbers 7,3,14,9,7 and 8 A. 21/2 B. 21/3 C. 21/6 D. 11/6 31. Find the maximum value of y in the equation y = 1 – 2x – 3x2 A. 5/3 B. 4/3 C. 5/4 D. ¾ 32. If the 9th term of an A. P is five times the 5th term, find the relationship between a and d. 50O 128O Q P R 3cm 23cm Music History U80 20 30 -x x 40 -x A. a + 2d = 0 B. a + 3d = 0 C. 3a + 5d = 0 D. 2a + d = 0 33. The time taken to do a piece of work is inversely proportional to the number of men employed. If it takes 45men to do a piece of work in 5 days, how long will take 25 men? A. 5 days B. 9 days C. 12 days D. 15 days 34. The binary operation is defined on the set of integers p and q by p*q = pq + p + q. find 2 (3*4) A. 19 B. 38 C. 59 D. 67 35. If –2 is the solution of the equation 2x + 1 – 3c = 2c + 3x – 7, find the value of c. A. 1 B. 2 C. 3 D. 4 36. If N = 3 5 -4 6 -3 -5 -2 2 1, find /N/ A. 91 B. 65 C. 23 D. 17 37. Use the graph below to find the values of p and q if px + qy < 4 A. p = 1, q = 2 B. p = 2, q = 1 C. p = -1, q = 2 D. p = 2, q = -1 38. The inverse of the function f(x) = 3x + 4 is A. 1/3(x + 4) B. 1/4(x + 3) C. 1/5(x - 5) D. 1/3(x - 4) 39. Solve for x in the equation x3 – 5x2 - x + 5 = 0 A. 1, 1 or 5 B. –1, 1 or –5 C. 1, 1 or –5 D. 1, -1 or 5 40. If P = (2, 1) (-3 0) and I is a 2 x 2 unit matrix, evaluate p2 – 2p + 41 A. (2, 1) B. (1, 0) (4, 1) (0, 1) x y (-4,0) (0,2) C. (-3, 0) D. (9, 4) (0 -3) (12, 1) 41. Find the range of values of x for which x + 2/4 – 2x – 3/3 <4 A. x > -3 B. x < 4 C. x > -6 D. x < 8 42. If x varies directly as n and x = 9 when n = 9, find x when n = 17/9 A. 27 B. 17 C. 4 D. 3 43. The sum of infinity of the series 1 + 1/3 + 1/9 + 1/27 + ……………… is A. 3/2 B. 5/2 C. 10/3 D. 11/3 44. Make r the subject of the formula x/r + a = a/r A. a/(x – a) B. (a/x + a C. a2/(x – a) D. a2/(x + a) 45. If y = x2 – 1/x, find dy/dx A. 2x + x2 B. 2x – x2 C. 2x – 1/x2 D. 2x – 1/x2 46. Evaluate sin3xdx A. -2/3 cos 3x + c B. –1/3 cos 3x + c C. 1/3 cos 3x + c D. 2/3 cos 3x + c 47. A circle with a radius 5cm has its radius increasing at the rate of 0.2cms-1. what will be the corresponding increase in the area? A. 5p B. 4p C. 2p D. p 48. If dy/dx = 2x – 3 and y = 3 when x = 0, find y in terms of x. A. x2 – 3x B. x2 – 3x + 3 C. 2x2 – 3x D. x2 – 3x – 3 49. Find the derivative of y = sin2(5x) with respect to x A. 2 sin 5x cos 5x B. 5 sin 5x cos 5x C. 10 sin 5x cos 5x D. 15 sin 5x cos 5x 50. The slope of the tangent to the curve y = 3x2 – 2x + 5 at the point (1, 6) is A. 1 B. 4 C. 5 D. 61. Mathematics 2003 1. Simplify 1 – (21/3 x 11/4) + 3/5 A. -231/60 B. –27/15 C. –119/60 D. –11/15 2. A cinema hall contains a certain number of people. If 221/2% are children, 471/2% aremen and 84 are women, find the number of men in the hall. A. 133 B. 113 C. 63 D. 84 3. Simplify 2134 x 234 A. 132114 B. 103114 C. 103214 D. 122314 4. A woman buys 270 oranges for # 1800.00 and sells at 5 for #40.00. what is her profit? A. #630.00 B. #360.00 C. #1620.00 D. #2160.00 5. Simplify (Ö98 - Ö50) Ö32 A. ½ B. ¼ C. 1 D. 3 6. The sum of four numbers is 12145. what is the average expressed in base five? A. 411 B. 401 C. 141 D. 114 7. Evaluate logÖ24 + log1/216 – log432 A. -2.5 B. 5.5 C. –5.5 D. 2.5 8. Given: U = {Even numbers between 0 and 30} P = {Multiples of 6 between 0 and 30} Q = {Multiples of 4 between 0 and 30} Find (PUQ)c. A. {0,2, 6, 22, 26} B. {2,4, 14,18, 26} C. {2,10, 14, 22,26} D. {0,10, 14, 22,26} 9. In a class of 40 students, 32 offer Mathematics, 24 offer Physics and 4 offer neither Mathematics nor Physics. How many offer both Mathematics and Physics? A. 16 B. 4 C. 20 D. 8 10. Find (1/0.06 ¸ 1/0.042)-1, correct to two decimal places A. 4.42 B. 3.14 C. 1.53 D. 1.43 11. If 92x – 1/27x + 1 = 1, find the value of x. A. 2 B. 8 C. 5 D. 3 12. Factorize completely 4abx – 2axy – 12b2x +6bxy A. 2x(3b - a)(2b- y) B. 2x(a – 3b)(b - 2y) C. 2x(2b - a)(3b- y) D. 2x(a – 3b)(2b- y) 13. The sum of the first n terms of an arithmetic progression is 252. if the first term is –16 and the last term is 72, find the number of terms in the series. A. 7 B. 9 C. 6 D. 8 14. The graphs of the function y = x2 + 4 and a straight line PQ are drawn to solve the equation x2 – 3x + 2 = 0. what is the equation of PQ? A. y = 3x + 2 B. y = 3x – 4 C. y = 3x + 4 D. y = 3x – 2 15. A matrix P has an inverse P-1 = (1 -3) (0, 1) Find P. A. (1 3) B (1 -3) (0 1) (0 -1) C. (1 3) D. (-1 3) (0 -1) (0 -1) 16. Find the values of x and y respectively if 3x – 5y + 5 = 0 and 4x – 7y + 8 = 0 A. -4, -5 B. –5, -4 C. 5, 4 D. 4, 5 17. If –(x, 2) = (3, 3x) (4x, 1) (4, –5) find the value of x A. -2 B. –5 C. 2 D. 5 18. Find the range of values of x satisfying the inequalities 5 + x £ 8 and 13 + ³ 7. A. -6 £ x £ 3 B. -6 £ x £ -3 C. 3 £ x £ 6 D. –3 £ x £ 3 19. x varies directly as the product of U and V and inversely as their sum. If x = 3 when U = 3 and V = 1, what is the value of x if U = 3 and V = 3? A. 4 B. 9 C. 6 D. 3 20. Tr iangle OPQ above is the solution of the inequalities. A. x – 1 £ 0, y + x £ 0, y, - x £ 0 B. x + 1 ³ 0, y + x £ 0, y, - x ³ 0 C. y + x £ 0, y – x ³ 0, x – 1 ³ 0 D. x –1 £ 0, y – x ³ 0, y + x ³ 0 21. Three consecutive terms of a geometric progression are given as n – 2, n and n + 3. find the common ratio. A. 2/3 B. 3/2 C. ½ D. ¼ 22. The length a person can jump is inversely proportional to his weigth. If a 20kg person can jump 1.5 m, find the constant of proportionality. A. 30 B. 60 C. 15 D. 20 23. P y x + 1 = 0 y - x = 0 y + x = 0 x Q O M P N Q O 40O 42O In the diagram above, O is the centre of the circle, POM is a diameter and Ð MNQ = 420. calculate ÐQMP. A. 1380 B. 1320 C. 420 D. 480 24. The locus of a point P which moves on one side only of a straight line XY so that Ð XPY = 900 is. A. the perpendicular bisector of XY B. a circle C. a semicircle D. an arc of a circle through X,Y 25. In the diagram above, PQ is parallel to RS. What is the value of a + b + y? A. 1800 B. 900 C. 2000 D. 3600 26. Whicch of the following is the graph of sinq for -p £ o £ 3p 2 2 A. B. C. D. 27. In the diagram above, PQR is a straight line and PS is a tangent to the circle QRS with /PS/ = Ð/SR/ and SPR = 400. find ÐPSQ. A. 200 B. 100 C. 400 D. 300 28. If p/2 £ 2p, find the maximum value of f(q) = 4/6 + 2 cos q A. 1 B. ½ C. 4 D. 2/3 P R Q S 0 2 2 2 3 1 1 0 2 2 2 3 1 1 0 2 2 2 3 1 1 0 2 2 2 3 1 1 Q R P S O 40O 29. An aeroplane flies due north from airports P to Q and then flies due east to R. if Q is equidistant from P and R, find the bearing of P and R. A. 2700 B. 0900 C. 1350 D. 2250 30. Find the value of p, if the line ofwhich passes through (-1, -p) and (-2, 2) is parallel to the line 2y + 8x – 17 = 0. A. –2/7 B. 7/6 C. –6/7 D. 6/7 31. Find the equation of the locus of a point P(x, y) which is equidistant form Q(0,0) and R(2, 1). A. 2x + y = 5 B. 2x + 2y = 5 C. 4x + 2y = 5 D. 4x – 2y = 5 32. An arc of a circle subtends an angle of 300 on the circumference of a circle of a radius 21cm. Find the length of the arc A. 66cm B. 44cm C. 22cm D. 11cm 33. A trapezium has two parallel sides of length 5cm and 9cm. If the area is 121cm2, find the distance between the parallel sides. A. 7cm B. 3cm C. 4cm D. 6cm 34. XYZ is a circle centre O and radius 7cm. Find the area of the shaded region. A. 14cm2 B. 38cm2 C. 77cm2 D. 84cm2 35. A triangle has vertices P(-1, 6), Q(-3, -4) and R(1, - 4). Find the midpoints of PQ and QR respectively. A. (-1, 0)and (-1, -1) B. (-2, 1)and (-1, -4) C. (0, -1)and (-1, -4) D. (-2,1) and (0, 1) 36. Evaluate 3 2(x2 – 2x)dx A. 4/3 B. 1/3 C. 2 D. 4 37. If y = 3 sin (-4x), dy/ dx is A. -12cos (-4x) B. 12 sin (-4x) C. 12xcos (4x) D. –12x cos (-4x) 38. Determine the maximum value of y = 3x2 + 5x – 3 at A. 6 B. 0 C. 2. D. 4 39. Find the slope of the curve y = 2x2 + 5x – 3 at (1, 4). 7 cm Z Y X 45O A. 7 B. 9 C. 4 D. 6 40. The histogram above shows the ages of the victims of a pollution. How many people were involved in the pollution? A. 18 B. 21 C. 15 D. 20 41. Find the mean of the distribution above. A. 4 B. 3 C. 1 D. 2 42. The mean of the numbers 3, 6, 4, x and 7 is 5. find the standard deviation A. 2 B. 3 C. Ö3 D. Ö2 43. Abag contains 5 blsck ball and 3 red balls. Two balls are picked at random without replacement. What is the probability that a black and a red balls are picked? A. 5/14 B. 13/28 C. 3/14 D. 15/28 44. On a pie chart, there are four sectors of which three angles are 450, 900 and 1350. if the smallest sector represents #28.00, how much is the largest sector? Value Frequency 0 1 2 3 4 1 2 2 1 9 Number Frequency 1 2 3 4 5 6 12 20 x 21 x -1 28 A. #48.00 B. #96.00 C. #42.00 D. #84.00 45. The range of 4, 3, 11, 9, 6, 15, 19, 23, 27, 24, 21 and 16 is A. 23 B. 24 C. 21 D. 16 46. The result of tossing a fair die 120 times is summarized above. Find the value of x. A. 21 B. 19 C. 22 D. 20 47. If nP3 – 6 (nC4) = 0, find the value of n A. 6 B. 5 C. 8 D. 7 48. Two dice are thrown.What is the probability that the sum of the numbers is divisible by 3. A. ½ B. 1/3 C. ¼ D. 2/3 49. Find the number of committees of three that can be formed consisting of two men and one woman from four men and three women. A. 24 B. 18 C. 3 D. 6 50. By how much is the mean of 30, 56, 31, 55, 43 and 44 less than the median. A. 0.50 B. 0.75 C. 0.17 D. 0.33 Mathematics 2004 C. (0,0)and(1,1) D. (Ö2, Ö2)only 1 4 2 4 3 _ 1 3 x 4 y 3 4 4 Find x and y respectively in the subtraction above c arried out in base 5 A. 2, 4 B. 3, 2 C. 4, 2 D. 4, 3 2. Find p, if 4516 – p7 = 3056 A. 6117 B. 1427 C. 1167 D. 627 3. 1/10 x 2/3 + 1/4 ________________ 1/2 ¸ 3/5 - ¼ A 2/25 B. 19/60 C. 7/12 D. 19/35 4. A farmer planted 5000 grains of maize and harvested 5000 cobs, each bearing 500 grains.What is the ratio of the number of grains sowed to the number harvested? A. 1:500 B. 1:5000 C. 1:25000 D. 1:250000 5. Three teachers shared a packet of chalk. The first teacher got 2/5 of the chalk and the second teacher received 2/15 of the remainder.What fraction did the third teacher receive? A. 11/25 B. 12/25 C. 13/25 D. 8/15 6. Given that 3Ö42x, find the value of x A. 2 B. 3 C. 4 D. 6 7. Simplify 1/Ö3 + 2 in the form a + bÖ3 A. -2 - 3 B. –2+ 3 C. 2- 3 D. 2+ 3 8. If 6logx2 – 3logx3 = 3log50.2, find x. A. 3/8 B. ¾ C. 4/3 D. 8/3 9. The shaded region in the venn diagram above A. Pc Ç(QR)B. PÇQ C. Pc U(QÇR) D. PcÇ (QUR) 10. In a class of 40 students, each student offers at least one of Physics and Chemistry. If the number of students that offer Physics is three times the number that offer both subjects and the number that offers Chemistry is twice the number that offer Physics, find the number of students that offer Physics only. A. 25 B. 15 C. 10 D. 5 11. Find the values of x where the curve y = x3 + 2x2 – 5x – 6 crosses the x-axis. A. -2, -1 and 3 B. -2, 1 and –3 C. 2, -1 and –3 D. 2, 1 and 3 12. Find the remainder when 3x3 + 5x2 – 11x + is divided by x + 3 A. 4 B. 1 C. –1 D. –4 13. Factorize completely ac – 2bc – a2 + 4b2 A. (a – 2b)(c + a – 2b) B. (a – 2b)(c - a – 2b) C. (a – 2b)(c + a + 2b) D. (a – 2b)(c - a + 2b) 14. y is inversely proportional to x and y = 4 when x = 1/ 2 . find x when y = 10 A. 1/10 B. 1/5 C. 2 D. 10 15. The length L of a simple pendulum varies directly as the square of its period T. if a pendulum with period 4 secs is 64cm long, find the length of a pendulum whose period is 9 sec. A. 36cm B. 96ccm C. 144cm D. 324cm 16. The shaded area in the diagram above is represented by A. {(x, y) : y + 3x < 6} B. {(x, y) : y + 3x < - 6} C. {(x, y) : y - 3x < 6} D. {(x, y) : y - 3x < - 6} 17. What are the integral values of x which satisfy the inequality –1 < 3 – 2x £ 5? A. -2, 1, 0, -1 B. -1, 0, 1, 2 C. -1, 0, 1, D. 0, 1, 2 18. The nth terms of two sequences are Qn – 3.2n-2 and Um = 3.22m– 3. find the product of Q2 and U2 A. 3 B. 6 C. 12 D. 18 19. Given that the first and fourth terms of a G.P are 6 and 162 respectively, find the sum of the first three terms of the progression. A. 8 B. 27 C. 48 D. 78 20. Find the sum to infinity of the series ½, 1/6, 1/ 18,…………… A. 1 B. ¾ C. 2/3 D. 1/3+ 21. If the operation * on the set of integers is defined by p*q = “pq, find the value of 4*(8*32). A. 16 B. 8 C. 4 D. 3 22. The inverse of the matrix (2 1) (1 1) is A. (1 1) B. (1 -1) (-12) (1 2) C. (1 1) D. (1 -1) (1 2) (-1 2) 23. If P = 1 0 -1 3 4 5 -1 0 1 then /P/ is A. -8 B. 0 C. 4 D. 8 24. The sum of the interior angles of a pentagon is 6x + 6y. find y in terms of x P Q R y x A. y = 60 – x B. y = 90 – x C. y = 120 – x D. y = 150 – x 25. PQRSTV is a regular polygon of side 7cm inscribed in a circle. Find the circumference of the circle PQRSTV. A. 22cm B. 42cm C. 44cm D. 56cm 26. P, R and S lie on a circle centre O as shown above while Q lies outside the circle. Find ÐPSO. A. 350 B. 400 C. 450 D. 550 27. In the diagram above, PQ =4cm and TS = 6cm, if the area of parallelogram PQTU is 32cm2, find the area of the trapezium PQRU A. 24cm2 B. 48cm2 C. 60cm2 D. 72cm2 28. An arc of a circle of length 22cm subtends an angle of 3x0 at the centre of the circle. Find the value of x if the diameter of the circle is 14cm. A. 300 B. 600 C. 1200 D. 1800 29. Determine the locus of a point inside a square PQRS which is equidistant from PQ and QR A. Thediagonal PR. B. ThediagonalQS C. Side SR D. Theperpendicular bisector ofPQ. 30. The locus of a point which is 5cm from the line LM is a A. pair of lines on opposite sides of LM and parallel to it, each distances 5cm form LM B. line parallel to LM and 5cm from LM C. pair of parallel lines on one side of LM and parallel to LM D. line distance 10cm from LM and parallel to LM. 31. Find the value of a2 + b2 if a + b = and the distance between the points (1, a) ands (b, 1) is 3 units. A. 3 B. 5 C. 11 D. 14 32. Find the midpoint of the line joining P(-3, 5) and Q (5, -3). 35O 20O 4 cm A. (4, -4) B. (4, 4) C. (2, 2) D. (1,1) 33. Find the value of x in the figure above. A. 20Ö6 B. 15Ö6 C. 5Ö6 D. 3Ö6 34. The shadow of a pole 5Ö3 m high is 5m. find the angle of elevation of the sun. A. 300 B. 450 C. 600 D. 750 35. Find the derivative of (2 + 3x)(1 - x) with respect to x A. 6x – 1 B. 1 – 6x C. 6 D. –3 36. Find the derivative of the function y = 2x2(2x - 1) at the point x= -1 A. -6 B. –4 C. 16 D. 18 37. If y – 3 cos (x/3), find dy/dx when x = 3p/2 A. 2 B. 1 C. –1 D. –3 38. What is the rate of change of the volume v of hemisphere with respect to its radius r when r = 2? A. 2p B. 4p C. 8p D. 16p 39. Evaluate 3 1 (x2 - 1) dx A. 62/3 B. 2/3 C. -2/3 D. -62/3 40. The pie chart above shows the distribution of the crops harvested from a farmland in a year. If 3000 tonnes of millet is harvested, what amount of beans is harvested? A. 9000 tonnes B. 6000 tonnes C. 1500 tonnes D. 1200 tonnes 41. I. Rectangular bars of equal width II. The height of each rectangular bar is proportional to the frequency of the3 corresponding class interval. III. Rectangular bars have common 45O 60O 15 cm X 60O 150O Maize Millet Beans Others sides with no gaps in between. A histogram is described by A. I and II B. I and III C. I,II and III D. II and III® 42. The graph above shows the cumulative frequency curve of the distribution ofmarks in a class test.What percentage of the students scored more than 20 marks? A. 68% B. 28% C. 17% D. 8% 43. Themean age of a group of students is 15 years.When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages becomes 18 years. Find the number of students in the group. A. 7 B. 9 C. 15 D. 42 44. The weights of 10 pupils in a class are 15kg, 16kg, 17kg, 18kg, 16kg, 17kg, 17kg, 17kg, 18kg and 16kg. What is the range of this distribution? A. 1 B. 2 C. 3 D. 4 45. Find the mean deviation of 1, 2, 3 and 4 A. 1.0 B. 1.5 C. 2.0 D. 2.5 46. In how many ways can 2 students be selected from a group of 5 students in a debating competition? A. 10 ways. B. 15 ways. C. 20 ways D. 25 ways. 47. A committee of six is to be formed by a state governor from nine state commissioners and three members of the state house of assembly. In how many ways can the members of the committee be chosen so as to include one member of the house of assembly? A. 924 ways B. 840 ways C. 462 ways D. 378 ways 48. Some white balls were put in a basket containing twelve red balls and sixteen black balls. If the probability of picking a white ball from the basket is 3/7, how many white balls were introduced? A. 32 B. 28 C. 21 D. 12 49. An unbiased die is rolled 100 times and the outcome is tabulated as follows: What is the probability of obtaining 5? A. 1/6 B. 1/5 C. ¼ D. ½ 50. A container has 30 gold medals, 22 silver medals and 18 bronzemedals. If one medal is selected at random from the container, what is the probability that it is not a gold medal? A. 4/7 B. 3/7 C. 11/35 D. 9/35