MATHS

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