Jamb 2024 Mathematics Likely Questions And Answers

 Mathematics  

JAMB 

Past Questions

Mathematics 2024 

1. If M represents the median and D the mode of the  measurements 5, 9, 3, 5, 8 then (M,D) is 
2. If x + 2 and x – 1 are factors ofthe expressions lx +  2kx2 + 24, find the values of l and k 
   
3. (6,5) B. (5,8) C. (5,7) A. l = -6, k = -9 B. l=-2,k=1 C. l=-2,k=-1 D. (5,5) E. (7,5) D. l = 0, k = 1 E. l = 6, k = 0 
   
4. A construction company is owned by two partners X  and Y and 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? 
5. #20,000.00 B. P’0#25,000.00 C. #30,000.00 
6. #15,000.003 E.#45,000.00 
7. Given a regular hexagon, calculate each interior angle  of the hexagon. 
8. 600 B. 300 C. 1200 D. 450 E. 1350
9. Solve the following equations  

4x – 3 = 3x + y = 2y+ 5x – 12 

11. Make T the subject of the equation 

 av = 3 2V + T  

1- V a 2T 

1. 3av/(1-v) B. 2v(1-v)2– a2v2/2a2v2-(1-V)2 C. 2v(1 – v)2 + a3v2/ 2a2v2 + (1 – v)2
2. 2v(1 – v)2– a4v3/2a3v3– (1 – v)3
3. 2v(1-v)3– a4v3/2a3v3 + (1-v)3

Additional  

Mathematics  

(2x-24)OBiology  

(3x-18)O 

xO 

Geography 

(2x+12)O 

1. 4x = 5, y=2 B. x=2, y=5 C. x=-2, y= -5  D. x = 5, y=-2 E. x = -5, y= -2 

(x+12)O French 

History 

5. If x = 1 is root of the equation 

x3 – 2x2 – 5x + 6, find the other roots 

1. -3and2 B. –2 and2 C. 3and–2 D. 1and3 E. –3and1 
2. 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? 
3. 4:1 increase B. 2:1 increase C. 1:4 decrease 
4. 1: 1 no change E. 3: 4 decrease 
5. P Q 

45O60O 

8 cm 

S R 

In the above figure PQR = 600, QPR = 900, PRS = 900,  RPS = 450, QR= 8cm. Determine PS 

1. 2√3cm B. 4√6cm C. 2√6cm 
2. 8√6cm E. 8cm 
3. Given that cos z = L, where z is an acute angle find an  expression for Co +Z – cosecz

sec Z + tan z 

1. l – L B. L2–√1−L2 C. -L-√1−L 

1+L L2+L-1 (C1+L) +√1−L2 

1. √L−1. E. L-(L2-1)

(L1+L2) +√1−L21+ √1 – L2+ √1 – L2 

9. If0.0000152 x 0.00042=Ax 108,where 

In a class of 60 pupils, the statistical distribution of the  number of pupils offering Biology, History, French,  Geography and Additional Mathematics is as shown in  the pie chart above. How many pupils offer Additional  Mathematics? 

1. 15 B. 10 C. 18 
2. 12 E. 28 

13 The value of(0.303)3 – (0.02)3is 

1. 0.019 B. 0.0019 C. 0.00019 
2. 0.000019 E. 0.000035 
3. 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 
4. y = 10x2 + 52 B. y = x2 + 1

31 31√x √x 

1. y= x2 + 1 D. y= x2 + 1 E. y = 10 (x2 + 1 ) x 31 31√ x 31( √x)  
2. 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) 
3. x/(x+3)(x+7) E. x/(x+4)(x+7) 
4. The lengths ofthe sides of a right-angled triangle at (3x + 1)cm, (3x – 1)cm and x cm. 
5. 2 B. 6 C. 18 
6. 12 E. 0 
7. 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. 
   

1 £ A < 10, find A and B. A. 47 B. 481/ C. 50 

6. 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 

2

1. 48 E. 49 
   

y 

x 

12 

9 

6 

3 

-3 -2 -1-33 2 1 -6 

-9 

-12 

-15 

1. –28,7 B. 6,-28 C. 6,-1 
2. –1, 7 E. 3,2 
3. Find the missing value in the following table. 

x -2	-1 0	1 2	3
y = x3O – x + 3	3 3	3 9	27

 

1. -3 B. 3 C. –9 D. 13 E. 9 
   

Which of the following equations represents the above  

graph? 

1. y=1+2x+3x2 B. y= 1–2x+3x2 C. y=1+ 2x3x2

D.y=1–2x–3x2 E.y=3x2+2x-1 

Hx 

G 

30O 

K F 

O 

xO 

130O 

If O is the centre of the circle in the figure above. Find  the value of x 

1. 50 B. 260 C. 100 D. 65 E. 130 

The above figure FGHK is a rhombus. What isthe value  of the anglex? 

1. 900 B. 300 C. 1500 D. 1200 E. 600
2. Find the angle of the sectors representing each item in a pie chart ofthe 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. Noneofthe above 
   

0-8 m 

P 

0 

S 

2 m 

R 

Q 

30O 

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 word MATRICULATION are cut and 
    

PQRS is a desk ofdimensions 2m x 0.8m which isinclined  at 300 to the horizontal. Find the inclination of the  diagonal PRto the horizontal. 

put into a box. One ofthe letter is drawn at random from  the box. Find the probability of drawing a vowel. 

1. 23035’ B. 300 C. 15036’ A. 2/13 B. 5/13 C. 6/13 D. 100 E. 10042’ D. 8/13 E. 4/13 
2. Find x if(x base 4)2 = 100 1000base 2 30. Correct each of the number 59.81789 and 0.0746829 to 
   
3. 6 B. 12 C. 100 D. 210 E. 110 

three significant figures and multiplythem, giving your  answer to three significantfigures. 

4. 4.46 B. 4.48 C. 4.47 
   
5. Simplify log a1/2 +1/4log10a – 1/12log10 D. 4.49 E. 4.50 

10 a7 

1. 1 B. 7/6log10a C. 0 
2. 10 E. a 31. If a rod oflength 250cm is measured as 255cm longer in error, what is the percentage error in measurement? 
3. If w varies inversely as V and u varies directly as w3, A. 55 B. 10 C. 5 find the relationship between u and V given that u = 1, D. 4 E. 2 

when V = 2 

32. u=8V3 B. u=2 V C. V = 8/u2 32. If(2/3)m (3/4)n = 256/729, find thevalues ofm and n D. V=8u2 E. U= 8/v3 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. Solve the simultaneous equations for x  
    

x2 + y – 8 = 0 y + 5x – 2 = 0 

33. Without using tables find the numerical value of log749 + log7(1/7) 
34. 1 B. 2 C. 3 
35. 7 E. 0 
36. Factorize completely 81a4 – 16b4
37. (3a + 2b) (2a – 3b) (9a2 + 4b2) 
38. (3a – 2b) (2a – 3b) (4a2– 9b2) 
39. (3a – 2b) (3a – 2b) (9a2 + 4b2) 
40. (3a – 2b) (2a – 3b) (9a2 + 4b2) 
41. (3a – 2b) (2a – 3b) (9a2– 4b2) 
42. One interior angle of a convex hexagon is 1700and  each of the remaining interior anglesis equal to x0. find  x 
43. 1200 B. 1100 C. 1050
44. In the figure below find PRQ 

235o 

R 

Q 

P 

1. 1020 E. 1000
2. PQRS is a cyclic quadrilateral in which PQ = PS. PT is a  tangent to the circle and PQ makes and angle 500 with  the tangent as shown in the figure below. What is the  

size ofQRS? 

R 

44. 661/0 B. 621/0 C. 1250 2 2 
45. 1050 E. 650

Simplify 27a9/8 

1. 9a2/2 B. 9a3/2 C. 2/3a2 D. 2/3a2 E. 3a3/2

Okro 

Beans 14.5 

Q 

S 

50O 

PT 

14.5 kgkg 

Yams 

184.5 kg 

Rice  45.4 kg 

1. 500 B. 400 C. 1100
2. 800 E. 1000
3. 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? 
4. 26034’ B. 243026’ C. 116034’ 
5. 63026’ E. 2400

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. 911/0 B. 191/0 C. 331/0 

2 3 3 

1. 110 E. 910

(x+3y)O 

38. In a sample survey of a university community the  following table shows the percentage distribution of  the number of members perhousehold. 

P 

R 

45O QyO 

 

No of members  per household 1 2	3 4	5 6		7 8 Total
Number of  households 3 12		15 28 21 10		7 4 100

 

1. 4 B. 3 C. 5 
2. 4.5 E. None 
3. On a square paper of length 2.524375cm is inscribed a  square diagram of length 0.524375. find the area ofthe  paper no covered by the diagram correct to 3 significant  figures. 
4. 6.00cm2 B. 6.10cm2 C. 6.cm2 D. 6.09cm2 E. 4.00cm2
5. If f(X) = 1 + x – 1 find f(1-x) 

x-1 x2-1 

(3x+y)O 

In the figure above, PQR is a straight line. Find the  values of x and y 

22. x = 22.50and y = 33.750
23. x = 150and y = 52.50
24. x = 22.50and y= 45.00
25. x = 56.250and y = 11.50
26. x = 18.0and y = 56.50
27. PQR is the diameter of a semicircle RSP with centre at  Q and radius oflength 3.5cmc. if QPT= QRT = 600. Find  the perimeter of the figure (PTRS p = 22/7) 

S 

1. 1/x + 1/(x+2) B. x +1/(2x -1) P R 60O O 60O
2. -1/x – 1/(x-2) D. -1/x + 1/(x2-1) 

T 

1. 25cm B. 18ccm C. 36cm 
2. 29cm E. 255 cm 
   
3. In a trianglePQR, QR= 3cm, PR= 3cm, PQ= 3cm and  PQR = 300. find angles P and R
4. P = 600and R= 900
5. P = 300and R= 1200
6. P = 900and R = 600
7. P = 600and R = 600
8. P = 450and R= 1050
9. Q 30O

O 

xO 

T 

47. xO 2xO
    

S 

130O 

R 

100O 

P 

In the figure above PT is a tangent to the circle with  centre O. if PQT = 300. find the value of PTO A. 300 B. 150 C. 240 D. 120 E. 600 

P Q 

In the above diagram if PS= SRand PQ//SR. what isthe  size ofPQR? 

1. 250 B. 500 C. 550 D. 650 E. 750
2. Find the mean of the following  24.57,25.63,25.32,26.01,25.77 
3. 25.12 B. 25.30 C. 25.26 D. 25.50q E. 25.73 

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? 

1. 120km/hr B. 60km/hr C. 600/7km/hr D. 50km/hr E. 100km/hr. 
2. Simplify (2/3 – 1/5) – 1/3 of2/5 3 – / 

1 

1/2 

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  

1. 1/7B. 7 C. 1/3 
2. 3 E. 1/5 
3. If 263 + 441 = 714, what number base has been used?  A. 12 B. 11 C. 10 
4. 9 E. 8 
5. 0.00014323/1.940000 = k x 10n where 1 £ k < 10 and n is  a whole number. The values of K and are 
6. 7.381 and –11 B………………….2.34 and10 
7. 3.87 and 2 D……………..7.831 and–11 E……………………….5.41 and–2 
8. P sold his bicycle to Q at a profit of 10%. Q sold it to R  for #209 at a loss of 5%. Howmuch did the bicycle cost  P? 

yield is#3.700? 

1. #15,000 B. #29,600 C. #21,400 D. #27,800 E. #35,000 
2. 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. 
3. 38 B. 24 C. 36 
4. 22 E. 41 
5. The cost of production of an article is made up as  follows Labour #70 Power #15 

Materials #30 

Miscellaneous #5 

1. #200 B. #196 C. #180 Find the angle of the sector representing labour in a pie D. #205 E. #150 chart. 
2. 2100 B. 1050 C. 1750
3. If the price of oranges was raised by 1/2k per orange, D. 1500 E. 900
   

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/ k B. 31/ k C. 51/ k 

9. Bola chooses at random a number between 1 and 300.  What is the probability that the number is divisible by 
   

2 2 2 4? D. 20k E. 211/ k2 A. 1/3 B. ¼ C. 1/5 D. 4/300 E. 1/300

10. Find without using logarithm tables, the value of  Log327 –Log1/464 

Log31/81 

1. 7/4 B. –7/4 C. –3/2 D. 7/3 E. –1/4 
2. 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 
3. -3 = y+ 4/ x + 1 B. 4y= -3 + x 
4. y/x = -3/4 D. y+ 3 = 4x 
5. 4y= x + 3 
6. A trader in a country where 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? 
7. In a racing competition. Musa covered a distance of 5xkm  in the first hour and (x + 10)km in the next hour. He was  second to Ngozi who covered a total distance of 118km  in the two hours. Which of the following inequalities is  correct? 
8. 0 < -x < 15 B. –3 < x < 3 
9. 15<x < 18 D. 0 < x < 15 
10. 0 < x < 18 
11. 2x + 3y = 1 and y = x – 2y = 11, find (x + y) A. 5 B. –3 C. 8 
12. 2 E. 2 
13. Tunde and Shola can do a piece of work in 18days.  Tunde can do it alone in x days, whilst Shola takes 15  days longer to do it alone. Which of the following  equations is satisfied by x? 
14. x2– 5x– 18 = 0 B. x2 – 20x+360 =0 
    
15. M103 (5) B. M1030(5) C. M102(5) C. x2-21x–270=0 D. 2x2+42x–190=0 
    
16. M2002(5)
17. Rationalize 
18. M3032(5) (5√5 – 7√5)(/√7- √5 
19. 3x2–31x+150=0 
20. Iffx) = 2(x – 3)2 + 3(x – 3) – 4 and g(y) = √5 + y,find g(f(3))  and g{f(4)} 
    
21. -2√35 B. 4√7 – 6√5 C. –√35 A. 3 and 4 B. –3 and 4 
    

Simplify 

4√7 – 8√5 E. √35 C. E. 

3n – 3n – 1 

–3 and –4 0 and √5 

1. 3 and –4 
   

33 x 3n – 27 x 3n– 1 23. The quadratic equation whose roots are 1 – 13 and 1 + 

1. 1 B. 0 C. 1/27  D. 3n – 3n – 1 E. 2/27 

13 is 

1. x2+(1-√13)x+1+√13=0 B. x2+(1-√13)x+1-√13=0 
   
2. p varies directly as the square of q an inversely as r. if C. x2+2x+12=0 D. x2 –2x+12=0 p = 36, when q = 3 and r = p, find p when q = 5 and r = 2 E. x2–2x–12=0 
3. 72 B. 100 C. 90 
4. 200 E. 125 24. Find a factor which is common to all three binomial expressions 
5. Factorise 6x2 – 14x – 12 4a2 – 9b2, a3 + 27b3, (4a + 6b)2 A. 2(x + 3) (3x – 2) B. 6(x – 2) (x + 1) A. 4a + 6b B. 4a – 6b C. 2(x – 3) (3x + 2) D. 6(x + 2) (x – 1) C. 2a + 3b D. 2a – 3b E. (3x + 4) (2x + 3) E. none
   
7. 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 

5 cm 

P 

1. (5,6) B. (8,8) C. (8,5) Q D. (7,7) E. (7,5) 
2. The table below is drawn for a graph y = x2 – 3x + 1 

11 cm 

S 

R 4 cmT 

 

x -3 1	-2 -1	0 1	2	3
y=x2– 3x + 1 1	-1 3	1 -1	3	1

 

 

What is the volume of the regular three dimensional  

From x = -2 to x = 1, the graph crossesthe x-axis in the  range(s) 

1. -1 < x< 0 and 0 < x < 1 
2. -2 < x < -1 and 0 < x < 1 
3. -2 < x < -1 and 0 < x < 1 

figure drawn above? 

1. 160cm3 B. 48cm3 C. 96cm3 D. 120cm3 E. 40cm3
2. If(x – 2) and (x + 1) are factors ofthe expression x3 + px2
   
3. 0 < x < 1 E. 1 < x < 2 + qx + 1, what isthe sum of p and q? A. 0 B. –3 C. 3 
4. –17/3 E. –2/3 
   
6. A cone is formed by bending a sector of a circle having  an angle of 2100. Find the radius of the base of the cone  if the diameter of the circle is base of the cone if the  diameter ofthe circle is 12cm 
7. 7.00cm B. 1.75cm C. Ö21cm 
8. 3.50cm E. 2Ö21cm 

r r 60O 

X  

r 

60O60Or 

120 

3 cm 

Find the area ofthe shaded portion ofthe semi – circular  figure above. 

1. r2/4(4p – 3 3) B. r2/4(2p + 3 3) C. 1/2r2p D. 1/8r 3
   

Y 

5 cm 

Z 

1. P 

r2/8(4p + 3 3) 44O 

Using XYZ in the figure above find XYZ A. 290 B. 31020’ C. 310 D. 31018’ E. 590 

r 

20O 

Q 

29. The sides of a triangle are (x + 4)cm, x cm and (x- 4) cm S respectively. If the cosine of the largest angle is 1/5,  

find the value of x 

y 

1. 24cm B. 20cm C. 28cm 
2. 88/7ccm E. 0cm R In the figure above QRS is a line, PSQ = 350 SPR = 300
   
3. If a = 2x/1 – x and b = 1 + x / 1 – x 

and O is the centre of the circle find OQP 

then a2 – b2in thesimplest form is A. 350 B. 300 C. 1300 

A.3x+1/(x-1)  

1. 3x2+1/(1-x)2 E.5x2-2x-1/(1-x)2 ( x-1)
2. 3x2-1/(x-1)2
3. 5x2-1/(1-x)2

If pq + 1 express t 

250 

= q2and in terms 

t = 1/p – of q 

650 1/pq 

Simplifty (1 + 1 ) (x+2) 

1/p – q 

1. 1/ q – 1 
   

( x+1) C. E. 

1/q + 1 1/ 1- q 

1. 1 + q 
2. C. 

(x2– 1)(x + 2) x2– (x + 2) 

x2(x + 2)/x + 1 

2x(x + 2) 37. The cumulative frequency function of the data below 

1. 2x(x + 2)/x + 1 is given by the frequency y = cf(x). what is cf(5)? 
   
2. Q 

P R 

Scores(n)  3 

4 

5 

6 

7 

Frequency(f)  30 

32 

30 

35 

20 

V 

1. 30 B. 35 C. 55 
2. 62 E. 92 

W S38. In the figure determine the angle marked y A. 660 B. 1100 C. 260 

1. 700 E. 440

TP 

In the figure above PQRSTW is a regular hexagon. QS  

intersects RT at V. calculate TVS. 

44O 

1. 600 B. 900 C. 1200r D. 300 E. 80020O
2. Find the integral values of x which satisfy the S

Q 

inequalities –3 < 2 –5x < 12 

1. -2, -1 B. –2, 2 C. –1, 0 
2. 0,1 E. 1,2 y

R 

39. A right circular cone has a base radiusr cm and a vertical  2y0. the height of the cone is 
40. r tan y0cm B. r sin y0cm 
41. r cot y0cm D. r cos y0cm 
42. Bar Chart 10 

8 

y 

c

1. r cosec y0cm 

n

e

u

q

e

40. Two fair dice are rolled. What is the probability that  

r

F

both show up the same number of point? 

1. 1/36 B. 7/36 C. ½ 
2. 1/3 E. 1/6 
3. The larger value of y for which (y – 1)2 = 4y – 7 is 

6 

4 

2 

0 

0-9 10-19 20-29 30-39 40-49 50-59 Marks 

43. 2 B. 4 C. 6 D. 7 E. 8 

y 

The bar chart above shows the mark distribution in a  class test. Find the number of students in the class. A. 9 B. 2 C. 60 D. 30 E. 34 

S T 

135O 

P 

x 

O R Q 

Find the x coordinates of the points of intersection of the two equations in the graph above. 

In the figure above, O is the centre of circle PQRS and  PS//RT. If PRT = 1350, then PSQ is 

1. 671/0 B. 450 C. 900 2 
2. 333/0 E. 221/0

4 2 

47. 1,1 B. 0,-4 C. 4,9 47. XYZ is a triangle and XW is perpendicular toYZ at W. D. 0,0 E. 0,4 if XZ = 5cm and WZ = 4cm, calculate XY. A. 5√3cm B. 3√5cm C. 3Ö3cm 
48. If sin q = x/y and 00 < q < 900 D. 5cm E. 6cm then find 1/ tan q 

x/√(y2 – x2) 

√y2 –n2B. x/y 

X 

√y2−x2 D. (√y2 – x2)/(√y2 – x2)

45. √y2 – x2/y

P 

6 cm 

R 

Q 8 cm 

S T 

12 cm 

In the figure aboveTSP =PRQ, QR= 8cm. PR= 6cm and  ST = 12cm. Find the length SP 

1. 4cm B. 16cm C. 9cm D. 14cm E. Impossible insufficient data 

5 cm 

4 cm 

Y Z 

10 cm 

48. Measurements of the diameters in centimeters of 20  copper spheres are distributed as shown below 

Class boundary in cm frequency  

3.35-3.45 3 

3.45-3.55 6 

3.55-3.65 7 

3.65-3.75 4 

What is the mean diameter of the copper sphere?  A. 3.40cm B. 3.58cm C. 3.56cm  D. 3.62cm E. 3.63cm 

Use the instruction belowto answer question49 and 50 49. What is the obtuse angle formed when the point U is joined to Q? 

TU

1. 750 B. 1540 C. 1200 D. 1050 E. 1250
2. What isthe acute angle formed when the point V joined  to Q? 
   

V R S A. 600 B. 300 C. 450 D. 900 E. 150 

P 

O 

Mathematics 1985 

1. Arrange the following numbers in ascending order of A. 3/2 B. 2/3 C. 2 magnitude 6/7,13/15,0.865 D. 3 E. 18 A. 6/7 <0.865 < 13/15 
   
2. 6/7 <13/15 < 0.865 
3. 13/15< 6/7 <0.865 
4. 13/15< 0.865< 6/7 
5. 0.865< 6/7 < 13/15 
6. A sum of money was invested at 8% per annum simple  interest. If after 4years the money amounts to #330.00,  find the amount originally invested. 
7. Without using tables, evaluate Log24 + Log42 – Log255  A. ½ B. 1/5 C.0 
8. 5 E. 2 
9. John gives one third of his money to Janet who has  #105.00. He then finds that his money is reduced to  one-fourth of what Janet now has. Find how much  money John hadat first. 
   
10. D. 

#180.00 #200.00 

1. E. 

#165.00 #250.00 

150. #150.00 A. D. 

#45.00 B. #58.00 E. 

#48.00 C. #60.00 

#52.00 

3. In the equation below, solve for x if all the numbers are in  base 2? 11/x=1000/(x+101) 
4. Find x ifLog9x= 1.5  
5. 72.0 B. 27.0 C. 36.0 
   
6. 101 B. 11 C. 110 D. 3.5 E. 24.5 D. 111 E. 10
7. Write h in terms of a =b(1 – ch)
   
8. List all integers satisfying the inequality -2 < 2x – 6 < 4 

(1-dh) 

1. 2,3,4,5 B. 2,3,4 C. 2,5 A h = (a – b) B. h = (a + b ) D. 3,4,5 E. 4,5 (ad- bc) (ad – bc)
   
2. Find correct to tow decimal places 100+ 1/100+ 3/1000+ 27/10000 
3. 100.02 B. 1000.02 
4. h = (ad – bc) D. h = (1 – b) ( a – b ) (d – bc) 
   
5. 100.22 D. 100.01 E. h = (b – a) 
6. 100.51 (ad – bc) 
7. Simplify 1/2 + 1 12. 221/ % of theNigerian Naira is equal to 171/ % of a foreign 2 10 1 currency M. what isthe conversion rate of the M to the 2 + ————- Naira? 

1 A. 1M =15/ N B. 1M = 211 

57 57/ N 

2 – ————– C. 1M =118/ N D. 1M = 381 

57 /4N 

4 +1/5 E. 1M = 3843/4N 

1. ¾ B. –1/3 C. 169/190 
2. 13/15 E. 121/ 13. Find the values of p for which the equation x2 – (p – 2)x 169+ 2p + 1 = 0 has equal roots 
3. If three number p,q,r are in the ratio 6:4:5 find the value A. (0,12) B. (1,2) C. (21,0) of (3q – q)/(4q + r) D. (4,5) E. (3,4) 
   
4. If ex= 1 + x + x2/12+ x3/1.2.3+….. find1/e1/2 A. 1 – x + x2– x2 +… B. 1 + x + x2 + x2

2 123 24 3 2 1.22 23.3 

1. 1 + x +x2– x2+… D. 1 – x + x2– x2 +  2 1.23 24. 3 2 1.22 23.3 
2. 1+ x3 +x3– x4+  

1.2 12.4 12.63 

5. (4√3+ 4√2) (4√3 – 4√2) (3√ + √2) is equal to 
6. Iff(x – 2) = 4x2 + x + 7 find f(1) 
7. 12 B. 27 C. 7 
8. 46 E. 17 
9. In DXYZ,XY= 13cm,YZ= 9cm,XZ= 11cmandXYZ=  q0. find cos q0
10. 4/39 
11. 43/39 
12. 209/286 
    
13. C. 

0 B. 4√3+ 4√2  (4√2- 4√3)(√3+ √2) 

1. 1/6 E. 43/78 
   
2. √3 + √2 E. 1 
3. In a restaurant, the cost of providing a particular type  of food is partly constant and partly inversely  proportional to the number of people. If the cost per  head for 100people is 30k and the cost for 40 people is  60k, find the cost for 50people 
4. 15k B. 45k C. 20k D. 50k E. 40k 
5. The factors of 9 – (x2 – 3x – 1)2are  
6. -(x -4)(x+ 1)(x- 1)(x -2) 
7. (x- 4)(x- 1)(x -1)(x +2) 
8. -(x-2)(x+ 1)(x+ 2)(x+4) 
9. (x- 4)(x -3)(x- 2)(x+1) 
10. (x- 2)(x+ 2)(x-1)(x +1) 
11. If 32y – 6(3y) = 27 find y 
12. 3 B. –1 C. 2 
13. –3 E. 1 
14. Factorize abx2 + 8y – 4bx –2axy 
15. (ax – 4) (bx – 2y) B. (ax + b) (x – 8y) C. (ax – 2y) (by– 4) D. (abx – 4) (x – 2y) E. (bx – 4) (ax – 2y)
16. At what real value of x do the curves whose equations  are y = x3 + x and y = x2 + 1 intersect? 
17. -2 B. 2 C. –1 
18. 0 E. 1 
19. If the quadrilateral function 3x2 – 7x + R is a perfect  square find R 
20. 49/24 B. 49/3 C. 49/6 D. 49/12 E. 49/36 
21. Solve the following equation  

2/(2r – 1) – 5/3 = 1/ (r + 2) 

1. (-1, 5/2) B. (-1, -5/2) 
2. (5/2, 1) D. (2, 1) 
3. (1, 2) 
4. Solve for (x,y) in the equations 

2x + y = 4: x2 + xy = -12 

1. (6,-8); (-2,8) B. (3, -4); (-1, 4) C. (8, -4);(-1, 4) D. (-8, 6);(8, -2) E. (-4, 3);(4,-1) 
2. Solve the simultaneous equations  

2x – 3y+ 10 = 10x – 6y = 5 

1. x = 21/ , y = 31/ B. x = 31/ , y = 21/ 2 3 2 3 
2. x = 21/ , y = 3 D. x = 31/ , y =21/ 4 2 5 
3. x = 21/ , y = 21/ 

2 3 

27. Find the missing value in the table below 

x -2	-1 0	1 2	3
y = x2O – x + 3	3 3	3 9	27

 

1. -32 B. –14 C. 40 
2. 22 E. 37 
3. Find the number of goals scored by a football team in  20matches is shown below 

No . of goals 0 1 2 3 4 5 

No . of matches 3 5 7 4 1 0 

What are the values of the mean and the mode  

respectively? 

1. (1.75, 5) B. (1.75, 2) 
2. (1.75, 1) D. (2,2) 
3. (2,1) 
4. If the hypotenuse of a right angle isosceles triangle is  2, what is the length of each of the other sides? 
5. √2 B. 1/√2 C. 2√2 

2 

1. 1 E. -1 
2. If two fair coins are tossed, what is the probability of  getting at least one head? 
3. ¼ B. ½ C. 1 
4. 2/3 E. ¾ 
5. The ratio ofthe length of two similar rectangular blocks  is 2:3, if the volume of the larger block is 351cm3, then  the volume of the other blockis 
6. 234.00cm3 B. 526.50cm3
7. 166.00cm3 D. 729.75cm3
8. 104.00cm3
9. The bearing of bird on a tree from a hunter on the  ground is N720E. what is the bearing ofthe hunter from  the bird? 
10. S180W B. S720W 
11. S720Eq D. S270E 
12. S270W 
    

33.X 39. A solid sphere ofradius 4cm has mass of 64kg. What will  be the mass of a shell of the same metal whose internal  

25 

15 

8 

and external radii are 2cm and 3cm respectively? A. 5kg B. 16kg C. 19kg D. 25kg E. 48kg 

Y Z40. S 

K 

In D XYZ above, XKZ = 900, XK = 15cm, XZ cm and YK = 8cm. Find the area of the D XYZ. 

1. 180sq.cm B. 210sq.cm 

145O 

R 

1. 160sq.cm D. 320sq.cm P Q
2. 390sq.cm 

O 

34. Without using tables. Calculate the value of 1 + sec230? 
35. 21/ B. 2 C. 11/ 

3 

3

1. ¾ E. 3/7 

In the figure above POQ is the diameter of the circle  

35. What isthe probability that a number chosen at random 

PQRS. If PSR = 1450, find x0 

from the integers between 1 and 10 inclusive is either a A. 250 B. 350 C. 450 prime or a multiple of 3? D. 550 E. 250 A. 7/10 B. 3/5 C. 4/5  

1. ½ E. 3/10 
2. Find the area of a regular hexagon inscribed in a circle  of radius8cm. 
3. 16√3cm2 B. 96√3cm2
4. 192.3cm2 D. 16cm2
5. 32cm2
6. N 

M 

K 

L 

37.X 

I 

J 

G 

H 

In the figure above GHIJKLMN is a cube of side a. find  

the length of HN 

1. 3√a B. 3a C. 3a2
2. a√2 E. a√3 

M 

42. PQRS is a trapezium of area 14cm2in which PQ//RS, if  

PQ = 4cm and SR = 3cm, find the area of DSQRin cm2 

N 

86O 

122O Q 

7. 7.0 B. 6.0 C. 5.2 

P 

5. 5.0 E. 4.1 

Y 

In the figure above, MNOP is a cyclic quadrilateral,  MN and PQ are produced to meet at X and NQ and MP  are produced to meet at Y. if MNQ = 860and NQP= 1220,  find (x0,y0) 

1. (280,,360) B. (360,280) 
2. (430,,610) D. (610,430) 
3. (360,430) 
4. If cosq = √3/2 and 0 is less than 900, calculate cot (90 – q) / sin2q 
5. 4√3/3 B. 4√3 
6. √3/2 D. 1/√3  
7. 2/√3 

Q 

0O

0O 

S P R 

In the figure PQ isthe tangent from P to the circle QRS  with SRasitsdiameter. IfPQR= q0, which ofthefollowing  relationship 00iscorrect.? 

1. q0 + f = 900 B. f0 = 900– 200 C. q0 = f0 D. f0 =200 E. q0 + 2f0 = 1200
2. A bag contains 4 white balls and 6 red balls. Two Redballs  are taken from the bag without replacement. What is  the probability that they are both red? 
3. 1/3 B. 2/9 C. 2/15 
4. In a class of 120students, 18 of them scored an A grade in  Mathematics. If the section representing the A grade  students on a pie chart has angle Z0at the centre of the  circle, what isZ? 
   
5. 1/5 E. 3/5 A. 15 B. 28 C. 50 D. 52 E. 54 
6. How many 2 2cm diameter discs can be cut out of a  

sheet of cardboard 218 2p3/4cm long and p1/2cm wide?  

50. 49 B. 219 C. 217p3/4( 2p + 2) 
    
51. 210p3/4(1 + 2) E. 

29( 2 + 1) 

80O 

46. Two points X and Y both on latitude 600S have  longitudes 1470E and 1530W respectively. Find to the  nearest kilometre the distance between X and Y  measured along the parallel oflatitudes(Take 2 R= 4 x  104km, where R isthe radius of the earth). 
47. 28.850km B. 16.667km 
48. 8.333km D. 6.667km  
49. 3.333km 

120O3 

3

In the figure above the area of the shaded segment is A. 3p B. 9 3/4 

1. 3(p – 3 3/4) D. 3( 3 – p)/4
2. p + 9 3/4 

40O 

20OxO

In the figure above find the angle x 

1. 1000 B. 1200 C. 600 D. 1100 E. 1400
2. If a (x+1) – (x +1) =bx 

( x-2 ) ( n+2) 

Find a simplest form 

1. x2 – 1 B. x2 + 1 C. x2+ 4 D. 1 E. x2– 4 
   
2. Evaluate 

(212)3 – (121)3 + (222)3 

Mathematics 1986 

5. Find the reciprocal of 2/3

1/2 + 1/3 

1. (313)3 B. (1000)3
2. (1020)3 D. (1222)3 A. 4/5 B. 5/4 C. 2/5 D. 6/7 
3. If Musa scored 75 in Biology instead of 57, his 
   

average mark in four subjects would have been 60.  what was his total mark? 

1. 282 B. 240 C. 222 D. 210 
2. Three boys shared some oranges. The first receive 1/3  ofthe oranges, the second received 2/3 ofthe remainder,  if the third boy received the remaining 12 oranges. How  many oranges did they share? 
3. 60 B. 54 
   
4. Divide the L.C.M. of 48, 64 and 80 by their H.C.F C. 48 D. 42 A. 20 B. 30 
5. 48 D. 60 7. If P = 18, Q = 21, R= -6 and S = -4 calculate (P – Q) + S2 A. -11/216 B. 11/216 
6. Find the smallest number by which 252 can be C. –43/115 D. 41/116 multiplied to obtain a perfect square 
7. 2 B. 3 
8. 5 D. 7 
   
9. Simplify 0.03 x 4 x 0.00064

0.48 x 0.012 

3. 3.6x 102 B. 36×102
4. 3.6x 103 D. 3.6 x104
5. Udoh deposited #150 00 in the bank. At the end of 5  years the simple interest on the principal was #55 00.  At what rate per annum was the interest paid? 
6. Factorize x2 + 2a + ax + 2x 
7. (x+ 2a)(x +1) B. (x+ 2a)(x -1) C. (x2– 1)(x + a) D. (x+ 2)(x +a) 
8. Solve the equation 3x2 + 6x – 2 = 0 
9. x= -1,±√3/3 B. x = -1,±√15/√3  C. x =-2, ±2√3/3 D. x= -2, ±2√15/3 
   
10. 11% B. 71/ % 22. Simplify. 1/ 5x +5 + 1/7x + 7 3 
11. 5% D. 31/ % A. 12/35+7 B. 1/35(x+1) 2 
    
12. A number of pencils were shared out among Bisi, Sola  and Tunde in the ratio 2:3:5 respectively. If Bisi got 5,  how many were shared out? 
13. 15 B. 25 
14. 12x/35(x+1) D. 12/35x +35 
15. The curve y = -x2 + 3x + 4 intersectsthe coordinate axes  at 
    
16. 30 D. 50 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) 
17. The ages of Tosan and Isa differ by 6 and the product  
    

of their ages is 187. write their ages in the form (x, y),  where x >y 

24. Factorize (4a + 3)2 – (3a – 2)2
25. (a + 1)(a+ 5) B. (a – 5)(7a – 1) 
    
26. (12, 9) B. (23, 17) C. (a + 5)(7a + 1) D. a(7a + 1) C. (17, 11) D. (18, 12) 
27. If 5(x + 2y) = 5 and 4(x + 3y) = 16, find 3(x +y)
    
28. In 1984, Ike was 24 years old and isfather was 45 years  old in what year wasIke exactly half his father’s age? A. 1982 B. 1981 
29. 0 B. 1 C. 3 D. 27 
    
30. 1979 D. 1978 26. Simplify 1/ x – 2 + 1/ x + 2 + 2x / x2– 4
    
31. Simplify ( 1 1 ) x -1/√3 (√5 + √3 − √5 − √3) 
32. √3/√5 B. –2/√3 C. –2 D. –1 
33. Find n if Log 4 + Log Z – Log n = -1 
34. 2x/ (x-2) (x+2) (x2– 4) B.2x/x2– 4 C. x/x2– 4 D. 4x/ x2– 4 
35. Make r the subject of the formula  S = 6/v – w/2 
36. V = 6 = 12 B. v =12
    

2 A. 10 2 2 B. 14 S2 w 252-w 

1. 27 D. 28 
2. (91/3 x 27-1/2)/ (3-1/6 x 3-2/3) 
3. 1/3 B. 1 
4. 3 D. 9 
5. If x varies directly as y3and x = 2 when y = 1, find x  when y = 5 
6. 2 B. 10 
7. 125 D. 250 
8. Factorize completely. 

3a + 125ax3 

1. (2a+ 5x2)(4+ 25ax) 
2. a(2+ 5x)(4 – 10x + 25ax2) 
3. (2a + 5x)(4 – 10ax + 25ax2) 
4. a(2+ 5x)(4+ 10ax+ 25ax2) 
5. If y = x/(x – 3) + x/(x + 4) find ywhen x = -2 A. -3/5 B. 3/5 
6. –7/5 D. 7/5 
7. Find all the numbers x which satisfy the inequality 1/  3(x + 1) – 1> 1/5 (x+ 4) 
8. x<11 B. x< -1 
9. x>6 D. x>11 
10. v = 12 – 2s2 D. v = 12

w 2s2 + w 

28. Find the values of x which satisfy theequation 16x – 5x 4x + 4 = 0 
29. 1 and 4 B. –2 and 2 
30. 0 and 1 D. 1 and 0 
31. a/b –c/d = k, find the value of 

(3a2 – ac + c2)/(3b2 – bd + d2) in term of k 

1. 3k2 B. 3k –k2
2. 17k2/4 D. k2
3. At what point doesthe straight line y = 2x + 1 intersect  the curve y = 2x2 + 5x – 1? 
4. (-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) 
5. A regular polygon on n sides has 1600as the size each  interior. Find n. 
6. 18 B. 16 
7. 14 D. 12 
8. If cos q = a/b, find 1 +tan2q 
9. b2/a2 B. a2/b2
10. (a2 + b2) / (b2 – a2) D. (2a2 + b2)/ (a2 + b2)
11. 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. 

PQT OR 

S 

1. 16cm B. 14cm 
2. An arc of circle ofradius 6cm is 8cm long. Find the area of  the sector. 
3. 51/ cm2 B. 24cm2

3 

1. 36cm2 D. 48cm2

39.X 

4 3 

1. 12cm D. 8cm Y Z 6 
   
2. The angle of elevation of the top of a vertical tower 50  metres high from a point X on 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. 40. 
3. 14.43m B. 57.73m 
4. 101.03m D. 115.47m

In XYZ above, determine the cosine of angle Z  A. ¾ B. 29/36 C. 2/3 D. ½ 

T 

S 

35. A girl walk 45 metresin the direction 0500from a point Q  to a point X. She then walks 24metres in the direction  1400from X to a point Y. How far isshe then from Q? 

20O 

Q 

35OR 

1. 69m B. 57m C. 51m D. 21m 

In the figure above PQT isisosceles. PQ = QT. SRQ = 350, TQ = 200and PQR is a straight line. Calculate  TSR. 

36. S A. 200 B. 550 C. 75 D. 1400
    

6 m 

P 

12 m 

8 m Q 

11 m R 

41. Find the total surface are of a solid cone ofradius 2 3cm and slanting side 4 3cm 
42. 8√3cm2 B. 24cm2
43. 15√3cm2 D. 36cm2
44. 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? 
45. The perpendicular bisector ofUV 
    

The figure is a solid with the trapezium PQRS as its  

uniform cross-section. Find its volume 

1. 102m3 B. 576m3
2. 816m3 D. 1056m3

Q 

TP 

O x 

1. A circle with UV asradius 
2. A line parallel to the line UV 
3. A circle with the line UV asthe diameter 

65O 

R 

PQ and PR are tangents from P to a circle centre O as  shown in the figure above. If QRP = 340. Find the angle  markedx. 

35O

1. 340 B. 560In the figure above, PQ//ST, RS//UV. If PQR = 350and C. 680 D. 1120 QRS = 650, find STV 
2. 300 B. 350
3. 550 D. 650
   
4. An open rectangular box externally measures 4m x 3m x  4m. find the total cost of painting the box externally ifit  costs #2.00 to paint onesquare metre. 
5. #96.00 B. #112.00 
6. #136.00 D. #160.00 
7. 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 by Anambra is 

1. 500 B. 650
2. 740 D. 880
3. The people in a city with a population of 109 million were  grouped according to their ages. Use the diagram below  to determine the number of people in the 15-29 years  group. 

24O 

52O116O 

64O 

104O 

1. 29 x 104 B. 26 x 104
   
2. Find the median of the numbers 89, 141, 130, 161, 120, C. 16 x 104 D. 13 x 104 131, 131, 100, 108 and 119
3. 131 B. 125 49. A man kept 6black, 5 brown and 7 purple shirts in a C. 123 D. 120 drawer. What is the probability of his picking a purple shirt with his eyes closed? 
4. Find the probability that a number selected at random A. 1/7 B. 11/18 from 40 to 50 is a prime C. 7/18 D. 7/11 A. 3/11 B. 5/11 
5. 3/10 D. 4/11 50. The table below givesthe scores of a group ofstudents in a Mathematics test 

Ifthe mode is m and the number ofstudents who scored  

4 or less is S. What is (s, m)? 

1. (27,4 ) B. (14, 4) 
2. (13, 4) D. (4, 4) 

Mathematics 1987 

1. Convert 241 in base 5 to base 8  
2. 718 B. 1078
3. 1768 D. 2418
4. Find the least length of a rod which can be cut into  exactly equal strips, each of either 40cm or 48cm in  length. 
5. 120cm B. 240ccm 
6. 360cm D. 480cm 
7. A rectangular haslawn has an area of 1815square yards.  Ifitslength is 50meters, find its width in metres. Given  that 1meters equals1.1yards 
8. 39.93 B. 35.00 
9. 33.00 D. 30.00 
10. Reduce each number to two significant figures and then  evaluate (0.02174 x1.2047)

0.023789 

1. 0.8 B. 0.9 
2. 1.1 D. 1.2 
3. A train movesfrom P to Q 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. 
4. 5500km/hr B. 60 00km/hr  
5. 67.50km/hr D. 75 00km/hr 
6. If the length of a square is increased by 20% while its  width is decreased by 20% to form a rectangle, what is  the ratio of the area of the rectangle to the area of the  square? 
7. 6.5 B. 25.24 
8. 5.6 D. 24.25 
9. 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? 
10. #2,000.00 B. #4,000.00 
11. #6,000.00 D. #10,000.00 
12. Peter’s weekly wages 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 average weekly wage for the whole year is #30.00  A. #37.00 B. #35.00 
13. #30.00 D. #5.00 
14. A man invests a sum of money at 4% per annum simple  interest. After 3 years, the principal amounts to  #7,000.00. find the sum invested 
15. #7,840.00 B. #6,250.00 
16. #6,160.00 D. #5,833.33
17. 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 20oranges for #1.10? 
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. 
19. 350k B. 200k 
20. 150k D. 50k 
21. 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 
22. P = 98R2 B. PR2 = 98  
23. P = 1/98R D. P =R2/98 
24. Make y the subject of the formula  

Z = x2 + 1/y3 

1. y = 1 B. y= 1

(z – x2)3(Z + x3)1/ 

3 

1. y= 1 D. y = 1

(Z – x2) 1/3√Ζ −3√ x2 

3 

21. Find the values ofm which make the following quadratic  function a perfect square 

x2 + 2 (m + 1) x + m + 3 

1. -1,1 B. –1, 2 
   
2. 8% B. 10% C. 1, -2 D. 2, -2 C. 12% D. 15% 
3. Factorize 62x+ 1 + 7(6x) – 5 
   
4. 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 
5. 25 D. 20 
6. Evaluate without using tables. 
7. {3(6x) – 5} {2(6x)} + 1} 
8. {3(6x) – 5} {2(6x)} – 1} 
9. {2(6x) – 5} {3(6x)}+ 1} 
10. {2(6x) – 5} {3(6x)} – 1} 
11. Find two values of y which satisfy the simultaneous  equations x + y = 5, x2 – 2y2 = 1 
    
12. 625/8 B. 8/625 A. 12, -2 B. –12, 12 C. 1/8 D. 8 C. –12, 2 D. 2, -2 
    
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 
14. 0.003 B. 3.0 x 10-3
15. 0.3 x 102 D. 0.3 x 10-3
16. Simplifywithout using tables 

(Log26 – Log23)/(Log28- 2Log21/2) 

1. 1/5 B. ½ 
2. –1/2 D. Log23/Log27 
3. Simplify without using tables  

2√ 14 x 3√21) / 7√24x 2√98) 

1. 3√14 B. 3√21

4 4 

1. 3√14 D. 3√2

28 28 

16. If p – 2/3 (1 – r2)/n2, find n when r = Ö1/3 and p = 1 A. 3/2 B. 3 
17. 1/3 D. 2/3 
18. If a =U2–3V2and b = 2UV + V2evaluate (2a – b) (a – b3),  when u = 1 and v = -1 
19. 9 B. 15 
20. 27 D. 33 
21. An (n – 2)2sided figure has n diagonalsfind the number  n ofdiagonals for a 25 sided figure 
22. 7 B. 8 
23. 9 D. 10 

f(x) 

-1 0 1 

A cubic function f(x) is specified by the graph show  above. The values ofthe independent variable for which  the function vanishes are 

1. -1, 0, 1 B. –1 < x < 1 
2. x, – 1 D. x > 1 
3. Solve the inequality x – 1 > 4(x + 2) 
4. x> -3 B. x< -3  
5. 2 < x < 3 D. –3 < x < -2 
   
6. Simplify(x2– y2)/ (2x2+ xy-y2) A. x + – y B. x +y 

Y 

34.  

2x 

+ y 

2x – y 

1. x – y  2x – y 

x – y 

2x + y 

The minimum value of y in the equation  y = x2 – 6x + 8 is 

1. 8 B. 3 C. 0 D. –1

9 cm 16 cm 

X Z T 

29. Find the sum of the first 21 terms of the progression – 10, -8,-6,…. 

In the figure above, XYZ = YTZ = 900, XT = 9cm and  TZ = 16cm. Find YZ 

1. 180 B. 190 A. 25cm B. 20cm C. 200 D. 210 C. 16cm D. 9cm 
   
2. Find the eleventh term of the progression 4, 8, 16,..  A. 213 B. 212
3. 211 D. 210
4. Q

x 

35. Two chords QR and NP of a circle intersect inside the  circle at X. ifRQP = 370, RQN = 490and QPN = 350, find  PRQ 
36. 350 B. 370
37. 490 D. 590
    

RT O 30O36. P 

In the diagram above, POQ is a diameter, O isthe centre  of the circle and TP is a tangent. Find the value of x.  

yy 

x

x 

x 

1. B. 400In the figure above, find the value of x. C. 450 D. 500 A. 1100 B. 1000 C. 900 D. 800
   

P 

Q R 

T S 

In the diagram above, QR//TS, QR:TS = 2:3. find the  ratio of the area of triangle PQR to the area of the  trapezium QRST 

1. 4:9 B. 4:5 
2. 1:3 D. 2:3 
3. Q2hR 

2 cm 

3h 

P S 

2 cm 2 cm 

In the figure above, PQRS is a rectangle. If the shaded  area is 72sq.cm find h 

1. 12cm B. 10cm 
2. 8cm D. 5cm 
3. The sine, cosine and tangent of 2100are respectively 
   
4. Three angle s of a nonagon are equal and the sum ofsix  other angles is 11100. Calculate the size of one of the  equal triangles 
5. -1/2, 3/2, 3/3 B. 1/2, 3/2 3/3 
   
6. 2100 B. 1500 C. 3/2, 3/3, 1 D. 3/2, 1/2 1 C. 1050 D. 500
7. Iftan q = (m2 – n2)/2mn, find sec q 
8. (m2+n2)/(m2 – n2) B. (m2+n2)/2mn  
9. mn/2(m2–n2) D. m2 n2/(m2 – n2)
   
10. From two points X and Y,8m apart, and in line with a pole,  the angle of elevation of the top of the pole are 300and  600respectively. Find the height of the pole, assuming  that X, Y and the foot of the pole are on the same  horizontal plane. 
11. 4m B. 8√3/2m 
12. 4√3m D. 8√3m 
13. A room is 12m long. 9m wide and 8m high. Find the  cosine of the angle which a diagonal ofthe room makes  with the floor of theroom 
14. 15/17 B. 8/17 
15. 8/15 D. 12/17 
16. What is the circumference of radius of the earth? A. R cos q B. 2p R cos q 
17. Rsin q D. 2p R sin q 
18. 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 
19. 6cm B. 5cm 
20. 4cm D. 3cm 

44.P 

Q R 

X 

45. What isthe locus ofthe mid-points of all chords oflength  6cm within a circle ofradius 5cm and 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  from 5.30a.m to 7.00p.m, calculate the period of daylight  and of darkness on that day 
47. 187030’172030’ B. 1350225’ 
48. 202030’157030’ D. 1950165’ 
49. The goals scored by 40 football teams from three league  divisions are recorded below 

What is the total number of goals scored by all the teams? 

1. 21 B. 40 
2. 91 D. 96 
3. The numbers 3,2,8,5,7,12,9 and 14 are the marksscored  by a group by a group of students in a class test if P is  the mean and Q the median the P + Q is 
4. 18 B. 171/2
5. 16 D. 15 
6. Below are 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) 

1. 40 B. 38 
2. 33 D. 5 
3. Find the probability of selecting a figure which is  parallelogram from a square, a rectangle, a rhombus, a  kite and a trapezium 
   

The figure above is an example of the construction of a A. 3/5 B. 2/5 A. perpendicular bisector to a given straight line C. 4/5 D. 1/5 B. perpendicularfroma givenpointtoa givenline 

1. perpendicular to a line from a given point on 

that line 

1. given angle. 

Mathematics 1988 

1. Simplify (1 1 / (2÷ 1 of32)
   

2 4 

1. 3/256 B. 3/32 
2. 6 D. 85 
3. 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 
4. 27 B. 30 
5. 33 D. 90 
6. A 5.0g of salts was weighed by Tunde as 5.1g. what is  the percentage error? 
7. 20 B. 2 
8. 2 D. 0.2 
9. Find correct to one decimal place,  

0.24633/0.0306 

1. 0.8 B. 1.8 
2. 8.0 D. 8.1
3. Two sisters, Taiwo and Kehinde, own a store. The ratio  ofTaiwo’sshare to Kehind’sis 11:9. later Kehinde sells  2/3 of her share to Taiwo for #720.00. Find the value of  the store. 
4. #1,080.00 B. #2,400.00 
5. #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. 
7. 1:1;1 B. 4:2:1 
8. 5:1:1 D. 4:1:1 
9. 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 hisincome? 
10. #560.00 B. #2,450.00 
11. #2,800.00 D. #3,920.00 
12. Evaluate (8 1/3 x 52/3) / 102/3
13. 2/5 B. 5/3 
14. 2√5 D. 3√5 
15. If Log102 = 0.3010 and Log103 = 0.4771, evaluate, without  using logarithm tableslog104.5 
16. If g(y) = y – 3/11 + 11/ y2 – 9 what is g(y + 3)?  
17. y + 11 B. y + 11 

11 y(y+6) 11 y(y+3) 

1. y + 30 + 11 D. y + 3 + 11 11 y(y+3) 11 y(y-6) 
2. Factorize completely (x2 + x) 2(2x + 2)2
3. (x+y)(x+2)(x-2) B. (x+ y)2(x-2)2
4. (x+1)2(x+2)2 D. (x+1)2(x+2)2(x-2) 
5. Simplify (x – y)

(x1/3 – y1/2) 

1. x2 = xy + y2 B. x2/3 + x1/3 +y2/3
2. x2/3– x1/3 y1/3– y2/3 D. x2– xy + y2
3. Solve the following equation for x 

x2 + 2x + 1 = o 

r2r1 

1. r2 B. 1/r2
2. –1/r2 D. 1/r 
3. List the integral values of x which satisfy the inequality  1 < 5< -2x < 7 
4. 0.3010 C. 0.6352 
5. 0.4771 A. -1,0,1,2 B. 0,1,2,3 D. 0.9542 C. -1,0,1,2,3, D. -1,0,2,3 
6. Find m such that (m ¸3) (1 – √3 )2 = 6 – √3 = 6 – 2√3 A. 1 B. 2 
7. 3 D. 4 
8. 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. 
9. 2.25x 10-4m B. 4.50x 10-4m  C. 2.25x 10-5m D. 4.50×10-5m 
10. Simplify ( x + 2) – (x -2) 

( x + 1) ( x +2) 

1. 3 B. 3x + 2

x + 1 (x+1) (x+2) 

1. 5x+ 6 D. 2×2+5x +2  (x + 1) (x + 2) (x + 1) (x +2) 
2. If 1/p = (a2+ 2ab + b2) 

(a – b) and  

1/q = (a + b) 

(a2– 2ab + b2) find p/q 

1. a + b B. 1 

a – b a2– b2 

1. a – b D. a2– b2

a + b 

14. If x varies inversely asthe cube root of y and x = 1 when  y = 8 find y when x = 3 
15. 1/3 B. 2/3 
16. 8/27 D. 4/9 
17. If a = -3, b = 2, c = 4, calculate (a3–b3–c1/2) (b-1-c) 
18. Given value that 3x – 5y – 3 = 0 2y – 6x + 5 = 0 

the value of (x, y) is 

1. (-1/8, 19/24) B. (8,24/10) 
2. (-8, 24/19) D. (19/24, -1/8) 
3. The solution of the quadratic equation  bx2 + qx + b = 0 

A -b±√b2− 4ac B -b± p2−4pb 2a 2a 

C -q±√q2– 4bp D -q±√p2– 4bp 

2p 2p 

23. Simplify 1 + 1

(x2+5x+6) (x2 + 3x + 2) 

1. 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) 

1. a – b B. 2a + 7b 

2a + b a – b 

1. 2a- 7b D. 2a – 7b

a + b a – b 

1. 37 B. C. 37/5 D.

–37/5 

–37 

Using the graph to answer questions 25 and 26 31. S T 

y 

4 

3 

2 

1 

P 

xo 

Q 

3xo 

40O 

R 

-4 -3 -2 -1 0 1 2 1 -2 

-1 

25. What is the solution of the equation  

x2 – x – 1 = 0? 

1. x=1.6andx=-0.6 B. x= -1.6andx=0.6  C. x=1.6andx=0.6 D. x= -1.6andx=-0.6 

In the figure above, PQ is parallel to ST and QRS = 400.  find the value of x 

1. 55 B. 60 
2. 65 D. 75 
3. For which of the following exterior angles is a regular  polygon possible? 

i 350ii 180iii. 1150 

1. i and ii B. ii only 
2. ii and iii D. iii only 
4. For what values of x is the curve  

y= (x2 + 3)/ (x + 4) 

1. -3 < x< 0 B. –3 < x < 0 
2. 0 < x < 3 D. 0 < x < 3 
3. The solution of x2 – 2x – 1 0 are the points ofintersection  of two graphs. If one of the graphs is y= 2 + x – x2, find  the second graph. 
4. y = 1 – x B. y = 1 + x 
5. y = x – 1 D. y= 3x + 3 
6. If the sum of the 8th and 9th terms of an arithmetic  progression is 72 and the 4thterm is –6, find the common  difference. 
7. 4 B. 8 

Q R 9cm Y T 

P 7cm S 

In the figure above, PS = 7cm and RY= 9cm. Ifthe area  of parallelogram PQRS is 56cm2, find the area of  trapeziumPQTS. 

1. 56cm2 B. 112cm2 C. 120cm2 D.1762
   
2. 62/ D. 91/ 34. A quadrilateral of a circle of radius 6cm is cut away  
   

3 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. 
30. 182 B. 91 
31. 63 D. 28 

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 

Q 

P 

120O 

100ORT 

S 

In the figure above, PQRS is a circle. If chords QR and  RS are equal, calculate the value of x 

In the figure above STQ = SRP, PT = TQ = 6cm and QS = 5cm. Find SR. 

1. 47/5 B. 5 
2. 37/5 D. 22/5 
3. Four interior angles o f a pentagon are 900 – x0, 900 + x0,  100 – 2x0, 1100 + 2x0. find the fifth interior angle. 
4. 1100 B. 1200
   
5. 800 B. 600 C. 1300 D. 1400 C. 450 D. 400
6. 45. 

50O 

60 cm 

30 cm

In the figure above, PS = RS = QS and QSR = 500. find  

QPR. 

1. 250 B. 400
2. 500 D. 650In the figure above, a solid consists of a hemisphere  surmounted by a right circular cone with radius 3.0cm 
   
3. Z

55O 

Y 

P 

Q 

R 

45O  X 

and height 6.0cm. find the volume of the solid. 

1. 18pcm3 B. 36pcm3
2. 54pcm3 D. 108pcm3
3. PQRis a triangle in which PQ= 10ccm and QPR= 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 SU in cm to  one decimalplace. 
4. 2.7 B. 2.9 
5. 3.1 D. 3.3 
6. In a class of 150 students, the sector in a pie chart 
   

In the figure above, XR and YQ are tangents to the  circle YZXP if ZXR = 450and YZX = 550find ZYQ. 

representing the students offering Physics has angle 120. How many students are offering Physics? 

1. 1350 B. 1250 A. 18 B. 15 C. 1000 D. 900 C. 10 D. 5 
   
2. From a point 14√3 metres away from a tree, a man  discovers that the angle of elevation of the tree is 300.  If the man measuresthis angle of elevation from a point  2meters above the ground how high is the tree? 
3. 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. 
   
4. 12m B. 14m A. 1.6 B. 1.2 C. 14√3m D. 16m C. 1.1 D. 1.0 
   
5. Alero starts a 3km walk from P on a bearing 0230. she  

then walks 4km on a bearing 1130to Q what isthe bearing  of Q fromP? 

1. 26052’ B. 5208’ 
2. 7608’ D. 900
3. If cot q = x/y, find cosec q 

In the distribution above, the mode and the median  respectively are 

1. 1.3 B. 1.2 C. 3.3 D. 0.2 
2. 1/y(x2+y) 
3. (x/y)
4. If two dice are thrown together, what isthe probability  
5. 1/y(x2+y) D. y/x 
6. In triangle PQR, PQ = 1cm, QR = 2cm and PQR = 1200.  Find the longest side of thetriangle 
7. 3 B. 3 7/7
8. 3 7 D. 7 
9. 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. 
10. 120pcm3 B. 110pcm3
11. 60pcm3 D. 50pcm3

of obtaining at least a score of 10? A. 1/6 B. 1/12 C. 5/6 D. 11/12 

Mathematics 1989 

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. Evaluate2,700, 000x 0.03 ¸18,000 
3. 4.5x 100 B. 4.5 x 101
4. 4.5x 102 D. 4.5 x 103
5. The prime factors of2,520 are 
6. 2,9,5, B. 2,9,7, 
7. 2,3,5,7, D. 2,3,7,9, 
8. Make R the subject of the formula  S = √(2R +Τ ) 

(3RT) 

1. 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 

4. If 12 = X find x where e = 12 A. 101/ B. 101/ e 7 2 6 A. 20 B. 15 C. 33/ D. –131/2
   
5. 14 D. 12
6. Simplify 3√64r -6)1/2
7. r B. 2r 
8. 1/2r D. 2/r 
9. What is the difference between 0.007685 correct to three  significant figures and 0.007685 correct to four places  of decimal? 
10. 10-5 B. 7 x 10-4
11. 8 x 10-5 D. 10 -6
12. If a : b = 5: 8, x : y= 25 : 16, evaluate a/x : b/y  A. 125:128 B. 3:5 
13. 3:4 D. 2:5 
14. 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 
15. 2 B. 4 
16. 51/ D. 8 

2 

9. If the surface area of a sphere is increased by 44%.  Find the percentage increase in its diameter. 
10. 44 B. 30 
11. 22 D. 20 
12. Simplify 4 – 1

(2-√3) 

2. 2√3 B…………………….2.,√3 
3. –2 + √3 D. 2,-√3 
4. Find p in terms of q if Log p + 3log q = 3 

3 3 

1. (3)3 B. (q)1/3

(q) (3) 

1. (q)3 D. (3)1/3

(3) (q) 

12. What are the values of y which satisfy the equation  9y – 4 ( 3y) + 3 = 0 

8 

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 #96.00 when the number is 30, find  the cost when there are 15 students. 
16. #68.50 B. #63.00 
17. #60.00 D. #52.00 
18. Iff(x) = 2x2+ 5x + 3,find f(x + 1) 
19. 2x2 – x B. 2x2 – x + 10 C. 4x2 + 3x + 2 D. 4x2+3x+12 
20. Solve the positive number x suchthat 

2(x3 – x2 – 2x) = 1 

1. 4 B. 3 
2. 2 D. 1 
3. Simplify (32x – 4x2)

(2x +18) 

1. 2(x-9) B. 2(9+ x ) 
2. 81– x2 D. –2(x -9) 
3. Factorize completely y3 – 4xy+ xy3 – 4y A. (x + xy)(y+ 2)(y – 2) 
4. (y+ xy)(y+ 2)(y – 2) 
5. y(1 + x)(y+ 2)(y – 2) 
6. y(1 – x)(y+ 2)(y – 2) 
7. If one of x3 – 8-1is 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
8. Factorize 4a2 + 12ab – c2+9b2
9. 4a(a – 3b) + (3b – c)2
10. (2a + 3b – c )(2a + 3b + c) 
11. (2a – 3b -c)(2a –3b + c) 
12. 4a(a – 3b) + (3b +c)2
13. What are K and L respectively if ½ (3y – 4x)2 = (8x2 +  kxy +Ly2) 
14. -12,9/2 B. –6, 9 
    
15. -1 and 0 B. –1 and 1 C. 6, 9 D. 12, 9/2 C. 1 and 3 D. 0 and 1 
    
16. Solve the pair of equation for x and y respectively  2x-1 – 3y-1 = 4 

4x-1 + y-1 = 1 

1. -1,2 B. 1,2 
3. 2,1 D. 2,-1 
4. What value of Q will make the expression 4x2 + 5x + Q a  complete square? 
5. 25/16 B. 25/64 
6. 5/8 D. 5/4 
7. 1,10 B. 2,10 C. 3,13 D. 4,16 

M 

N 

Q 

R 

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 

MN is a tagent to the given circle at M, MR and MQ are  two chords. If QMN is 600and MNQ is 400, find RMQ 

1. r> abc

bc + ac + ab 

1. r>abc A. 1200 B. 110 C. 600 D. 200
   
2. r > 1/a + 1/b+ 1/c D. r>1/abc 
4. Express 1 – 1

(x + 1) (x – 2) 

1. -3 B. 3

(x +1)(2-x) (x+1)2-X) 

1. -1 D. 1

(x+1)(x-2) (x+1)(x-2) 

27. Simplify x – (x+ 1 ) 1/2

(x + 1) (x + 1) 1/2 

P 

H K 

Q R 

In the diagram above,HKis prallel toQR, PH= 4cm and  HQ = 3cm. What isthe ratio of KR;PR? 

1. 7:3 B. 3:7 
2. 3:4 D. 4:3 
3. 1 B. – 1 x + 1 x+1 
4. 1 D. 1 x x + 1 
5. A regular polygon of (2k + 1) sides has 1400as the size  of each interior angel. Find K. 
6. 4 B. 41/ 

2 

1. 8 D. 81/ 

2 

y 

b 

a g 

S 

T 

c k d 

h 

f l 

m 

x 

24O 

P R Q 

-1 1 2 3 i 4 5 6 

ej 

On the curve above, the points at which the gradient of  the curve is equal to zeroare 35. A. c.d.f.i.l B. b.e.g.j.m 

1. a.b.c.d.f.i.j.l. D. c.d.f.h.i.l 
2. The sum ofthe first two terms of a geometric progression  is x and the sum of the last two terms is y. if there are n  termsin all, then the common ratio is 
3. x/y B. y/x 
4. (x/y)1/2 D. (y/x)1/2

If PST is a straight line and PQ = QS = SR in the above  diagram, find y 

1. 240 B. 480
2. 720 D. 840

S 

P 

R 60O

Q 

In the abovediagram PQ is parallel toRSand QS bisects  PQR.If PQRis 600,find x 

30. If –8, m,n, 19 in arithmetic progression, find (m, n) A. 300 B. 400 C. 600 D. 1200
31. PQRS is a rhombus. If PR2 + QS2 = kPQ2. Determine k. 
32. 1 B. 2 
33. 3 D. 4
    
34. In DXYZ, Y = Z = 300and XZ= 3cm find YZ A. √3/2cm B. 3√3/2cm 
35. 3√3cm D. 2√3cm 
36. In DPQR, the bisector of QPR meets QRat S. the line PQ  is produced to V and the bisector of VQS meets PS  produced at T. if QPR = 460and QST = 750, calculate  QTS 
37. 410 B. 520
38. 640 D. 820
39. O 

X 

T 

YZ 

W 

39. Y

S 

3yO 

yO56O 

P R Q 

1. If PQR is a straight line with OS = = QR,  calculate TPQ, if QT//SRand TQS = 3y0. 
2. 620 B. 560
3. 202/0 D. 182/0

OXYZW is a pyramid with a square base such that OX = OY = OZ = OW = 5cm and XY = XW = YZ = WZ = 6cm. Find the height OT. 

1. 2√5 B. 3 
2. 4 D. √7 
3. In preparing rice cutlets, a cook used 75g of rice, 40g of  margarine, 105g of meat and 20g of bread crumbs. Find  the angle of the sector which represents meat in a pie  chart. 
4. 300 B. 600
5. 112.50 D. 157.50
6. In a class of 30 students, the marks scored in an 

3 

40. R 

3examination are displayed in the following histogram. 

s 

t

X S

10 

n

e

Z 

d

u

t

8 

s

 

f

o

 

.

 

6 

o

N

T 

If x : y = 5:12 and z = 52cm, find the perimeter of the  triangle. 

1. 68cm B. 84cm 
2. 100cm D. 120cm 
3. The pilot of an aeroplane, flying 10km above the ground  in the direction of a landmark, views the landmark to  have angle of depression of 350and 550. find the distance  between the two points of observation 
4. 10(sin 350 – sin550) 
5. 10(cos 350 – cos 550) 
6. 10(tan 350 –tan 550) 
7. 10(cot 350 – cot550) 
8. A sin2x – 3 = 0, find x if0 < x < 900
9. 300 B. 450
10. 600 D. 900
11. A square tile has side 30cm. How many of these tiles  cover a rectangular floor of length 7.2cm and width  4.2m? 

4 

2 

020 40 60 80 100 

Marksscored 

What percentage of the students scored more than  40% 

1. 14% B. 40% 
2. 452/ % D. 531/ % 

3 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? 
49. 35years B. 40years 
50. 42years D. 54years 
51. If n is the median and m isthe mode 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 
    
52. 336 B. 420 A. (2.6,2.6) B. (2.5,2.6) C. 576 D. 720 C. (2.6,2.5) D. (2.5,2.1) 
    
53. A cylindrical metal pipe 1m long has an outer diameter  of7.2cm and an inner diameter of2.8cm.find the volume  of metal used for the cylinder. 
54. The numbers are chosen at random from three numbers  1,3,6. find the probability that the sum of the two is not  odd. 
    
55. 440pcm3 B. 1,100pcm3 A. 2/3 B. ½ C. 4,400pcm3 D. 11,000pcm3 C. 1/3 D. 1/6
    
56. Simplify (43/4– 61/4)  (41/5 of 11/4) 

Mathematics 1990 

12. If a = 2, b = -2 and c = -1/2,  

evaluate (ab2 – bc2) (a2c – abc)  

1. 0 B. 28 
   
2. -77/ B. –2/7 8 
3. –10/21 D. 10/21 2. The H.C.F. of a2bx + abx2and a2b – b3is 
4. –30 D. 34 
5. Y varies inversely as x2and X varies directly as Z2. find  the relationship between Y and Z, if C is a constant. 
   
6. b B. a + b A. Z2y = C B. Y=CZ2 C. a(a + b) D. abx (a2 – b2) C. Y = CZ2 D. Y= C 
   
7. Correct 241.34 (3 x 10-3)2to 4 significant figures A. 0.0014 B. 0.001448 
8. 0.0022 D. 0.002172 
9. At what rate would a sum of #100.00 deposited for 5  yearsraise an interest of #7.50? 
10. 11/ % B. 21/ % 

2 2 

1. 15% D. 25% 
2. 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? 
3. Find the value of r in terms of p and q in the following  equation 

P/2 = (r/(r+q) 

1. r = q B. pq2

2 – p2 2 – q2 

1. r = p2q2 D. p

2 – pq q(2-p) 

15. Iff(x – 4) = x2+ 2x + 3,find f(2)  
16. 6 B. 11 
17. 27 D. 51 
18. Factorize 9(x + y)2 – 4(x – y)2
    
19. 3/16 B. 7/16 A. (x+ y) (5x+ y) B. (x+ y)2 C. 9/16 D. 13/16 C. (x+ 5y) (5x+ y) D. 5(x+y)2
    
20. Simplify and express in standard form (0.00275x 0.00640/( 0.025x 0.08) 
21. If a2 + b2 = 16 and 2ab = 7 find all the possible values of  (a – b ) 
    
22. 8.8 x 10-1 B. 8.8 x 102 A. 3, -3 B. 2, -2 C. 8.8 x 10-3 D. 8.8 x 103 C. 1, -1 D. 3, -1
    
23. 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? 
24. #60,000.00 B. #54,000.00 
25. #48,000.00 D. #42,000.00 
26. Simplify√ 160r2+ √ (71r4 + √100r3
27. Divide x3 – 2x2 – 5x + 6 by(x – 1) 
28. x2 –x –6 B. x2 – 5x + 6  C. x2 –7x + 6 D. x2 – 5x – 6 19. Ifx + = 4, find the x2 + 1/x 
29. 16 B. 14 
30. 12 D. 9 
31. What must be added to 4x2 – 4 to make it a perfect  square? 
32. -1/x2 B. 1/x2
    
33. 9r2 B. C. 13r D. 
34. Simplify√27 + 3/√3 

12 3r  13r 

1. 1 D. -1 
2. Find the solution of the equation  x – 8 √x+ 15 = 0 
   
3. 4√3 B. 4/√3 A. 3, 5 B. –3, -5 C. 3√3 D. 3√/4 C. 9, 25 D. –9, 25 
   
4. Simplify 3Log69 + Log612 + Log664 – Log672  A. 5 B. 7776 C. Log 31 D. (7776)6 6 
5. Simplify (1 + 1 ) -1

x-1 y-1 

1. x/y B. xy 
2. The lengths of the sides of a right-angled triangle are  xcm.(3x-1)cmand (3x+ 1)cm.Find x 
3. 5 B. 7 
4. 8 D. 12 
5. The perimeter of a rectangular lawn is 24m, ifthe area of  the lawn is 35m2, how wide isthe lawn? 
   
6. y/x D. (xy)-1 A. 5m B. 7m C. 12m D. 14m 
   
7. Simplify x + y – x2

(x+y) (x-y) (x2– y2) 

1. x2 B. y2

x2– y2 x2– y2 

1. x D. y

x2– y2 x2– y2 

26. Given that x2 + y2 + z2 = 194, calculate z if x = 7 and√ y = 3 A. √10 B. 8 
27. 12.2 D. 13.4 
28. Find the sum of the first twenty terms of the arithmetic  progression Log a, Log a2, Log a3
29. log a20 B. log a21
30. log a200 D. log a210
31. The angle of a sector of a circle, radius 10.5cm, is 480.  calculate the perimeter of the sector 
32. 8.8cm B. 25.4cm 
33. 25.6cm D. 29.8cm 

100O 

In the figure above PS = QS and QSR = 1000, find QPR A. 400 B. 500 

24. A carpainter charges #40.00 per day for himself and C. 800 D. 1000 #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 34. 

more than his assistant, how much did the assistant 

receive? 

32. #32.00 B. #320.00 
33. Find the sum of the first 18 terms of the progression 3,  

6,12……….. 

1. 3(217– 1) B. 3(218 )- 1 ) 
2. 3(218 + 1) D. 3(218– 1) 
   

y 

-1 0 2 x 

What is the equation of the quadratic function  represented by the graph above? 

In triangleXYZand XQP,XP= 4cm,XQ= 5cmand PQ=  QY= 3ccm. FindZY 

1. 8cm B. 6ccm 
2. 4cm D. 3cm 
3. Find the length of a side of a rhombus whose diagonals  are 6cm and 8cm. 
4. 8cm B. 5cm 
5. 4cm D. 3cm 
   
6. C. 

y = x2 + x – 2  y = -x2 – x + 2  

1. D. 

y= x2 – x –2  y= -x + x + 2 

36. Each of the interior angles of a regular polygon is 1400.  how many sides has the polygon? 
    

At what 

value of x isthe 

functionx2 

+ x + 1 minimum? 

1. 9 B. 8 
   
2. -1 B. –1/2 C. 7 D. 5 C. ½ D. 1 
3. S

QR 

R 

81O 

P S 

In the diagram above, the area of PQRS is 73.5cm2and  its height is 10.5cm. find the length of PS if QR is one third ofPS. 

Px22OT Q 

In the figure above, PQRS is a circle. If PQT and SRT  are straight lines, find the value of x. 

1. 21cm B. 171/ cm A. 590 B. 770 2 
2. 14cm D. 101/ cm C. 1030 D. 12102 
   
4. In a regular pentagon, PQRST, PR intersects QS at O.  calculateRQS. 
5. 360 B. 720
6. 1080 D. 1440
7. If cos q = 12/13, find 1 + cot2 q 
8. 169/25 B. 25/169 
9. 169/144 D. 144/169 

4 cm 

6 cm 

6 cm 

Find the curved surface area of the frustrum in the figure. 

X A. B. 

16 10cm 

1. 24 D. 

20 10 

8 cm 

Y Z 

In the figure above, YXZ = 300, XYZ = 1050and XY =  8cm. CalculateYZ. 

1. 162√cm B. 8√2cm 
2. 4√2cm D. 2√2cm 

In the figure above PQR is a semicircle. Calculate the  area of the shaded region. 

1. 1252/ cm2 B. 1492/ cm2
2. 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 
3. angle bisector of the two lines 
4. bisector of the two lines 
5. line parallel to the two lines 

46 4, 16, 30, 20, 10, 14 and 26 are represented on a piechart.  Find the sum of the angles of the sectors representing all numbers equal to or greater than 16.  

1. 480 B. 840
2. 920 D. 2760
3. The mean of ten positive numbers is 16. when another  number is added, the mean becomes 18. find the  eleventh number. 
4. 3 B. 16 
5. 18 D. 30 
6. Below are the scores of a group of students in a test.

If the average score is 3.5, find the value of x. 

1. 1 B. 2 
2. 3 D. 4 
3. Twonumbers are removed at random from the numbers  1,2,3 and 4. what is the probability that the sum of the  
   

numbers removed is even? 7 C. 2431/ cm27 

1. 2671/ cm2 A. 2/3 B. ½ 
   

7 2 

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 
43. 1/3 D. ¼ 
44. Find the probability that a number selected at random  from 41 to 56 is a multiple of 9 
    
45. 153πcm3 B. 207πcm3 A. 1/9 B. 2/15 C. 15,300πcm3 D. 20,700πcm3 C. 3/16 D. 7/8 
46. Ifthe height oftwo circular cylinders are in the ratio 2:3  

and their base radii are in the ratio 9. what is the ratio of  

their volume 

1. 27:32 B. 27:23 
2. 23:32 D. 21:27

Mathematics 1991 

1. Simplify 31/ – 11/ x 2/ + 12/ 13. Evaluate (Xy2– X2y) 3 4 3 5
   
2. 217/30 B. 39/10
3. 41/10 D. 411/36
4. If 2257 isthe result ofsubtracting 4577 from 7056 in base  n, find n. 
5. 8 B. 9 
6. 10 D. 11 
7. Find correct to 3 decimal places 

( 1 ÷ 1 

0.05 5.005 – (0.05X2.05) 

99. 99.998 B. 98.999 

(x2– xy) 

when x = -2 and y = 3 

1. -3 B. –3/5 
2. 3/5 D. 3 
3. 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. 
4. (p+q)/(up+wq) B. u+w 
   
5. 89.899 D. 9.998 C. uw(p+q)/(wp+uq) D. (wp+uq)/(u+wq) 
   
6. Express 62/3 as a decimal correct to 3 significant figures.  A. 20.6 B. 20.667 
7. 20.67 D. 20.7 
8. FactoryP produces 20,000 bags of cement per day while  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 twofactories. 
9. If w 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 
10. If g(x = x2 + 3x ) find g(x + 1) – g(x) 
11. (x+ 2) B. 2(x+2) 
12. (2x+1) D. (x+ 4) 
    
13. 250 B. 750 17. Factorize m3 – m2 – m + 2 C. 1000 D. 1250 A. (m2+1)(m -2) B. (m+ 1)(m+ 1)(m+2) 
    
14. Musa borrows #10.00 at 2% per month interest and  repays #8.00 after 4 months. However much does he  still owe? 
15. #10.80 B. #10.67 18. 
16. (m+ 1)(m+ 1)(m-2) D. (m2+2)(m -1) 

Factorize 1 – (a – b)2 

2. #2.80 C. #2.67 A. C. 
3. If 3 gallons ofspirit containing 20% water are added to  

(1 – a – b)(1 – a – b) B. (1 – a + b)(1 – a + b) D. 

(1– a +b)(1+ a -b) (1 – a – b)(1 + a – b) 

5gallons of another spirit containing 15% water, what  percentage ofthe mixture is water? 

1. 24/ % B. 167/ % 5 8 
2. 181/ % D. 187/ % 
3. Which of the following is a factor of rs + tr – pt –ps? A. (p – s) B. (s – p) 
4. (r – p) D. (r +p) 
   

8 820. Find the two values of y which satisfy the simultaneous 8. What is the product of 27/5 – (3)3and (1/5)? equation 3x + y = 8 

1. 5 B. 3 x2 + xy = 6 
2. 1 D. 1/25 A. -1 and 5 B. –5 and 1 C. 1 and 5 D. 1 and 1 
3. Simplify2log2/5 – log72/125 + log9 
   
4. 1 – 4log 3 B. –1 +2log3  C. –1 +5log2 D. 1-2log2 
5. Find the range of values of x which satisfy the inequality  (x/2+ x/3+x/4)< 1 
6. Rationalize (2√3 + 3√2)/(3√2 – 2√3) A. x < 12/13B. x < 13 A. 5 – 2 6 B. 5 + 2 6 C. x < 9 D. x < 13/12 C. 5 3 D. 5 
7. Find the positive number n, such that thrice it 
8. Simplify(1/3 + √5) – 1/3 – √5 is equal to twelve times the number. A. -1/2 5 B. 1/2 5 A. 1 B. 2 C. –1/4 5 D. 0 C. 3 D. 4 
9. Multiply (x2 –3x – + 1)2 by (x – a) 23. Solve the equation (x – 2)(x – 3) = 12 A. x3 – (3 – a)x2 + (1 + 3a)x –1 A. 2,3 B. 3,6 B. x3 – (3 – a)x2 + 3ax – a C. –1,6 D. 1,6 C. x3 – (3 – a)x2 + (1 + 3a) – a 
10. x3+ (3 – a)x2+ (1 + 3a)- a

s square 

24. Simplify (√1 + x +√ x) (√ 1 + X – √ x) 
25. If the exterior angles of a pentagon are x0, (x + 5)0, (x +  10)0,(x + 15)0and (x+ 20)0,find x 
    
26. 1- 2x – 2√x(1 + x) B. 1 +2x +2√x(1+x) A. 1180 B. 720 C. √x(1+x) D. 1 + 2x – 2√x (1+x) C. 620 D. 360
    
27. Evaluate x2(x2– 1)1/2 – (x2 – 1)1/2 A. (x2 –1)1/2B. (x2 –1) 
28. (x2 – 1)-1 D. (x2 –1)-1/2

use the figure below to answer questions 35 and 36 T 

26. Find the gradient of the line passing through the points  (-2,0) and (0,-4) 
27. 2 B. 4 
28. –2 D. 4 
29. At what value of x is the function y = x2 – 2x – 3  

P 

Q 

R 

M 

N 

minimum? 

A.1 

B.1 

C.4 

D.4 

28. What isthe nth term ofthe progression 27, 9,3,…………. ? A. 27(1/3)n– 1 B. 3n +2
29. 27 +18(n – 1) D. 27 + 6(n – 1) 
30. Find the sumofthe 20 term in an arithmetic progression  whose first term is 7 and last term is 117 

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 PRand PT in centimeters. 
36. 7.3,5.9 B. 7.7,12.5 
37. 12.5,7.7 D. 5.9,7.336. 

If PNR = 1100and PMQ = 550, find MPQ.  

1. 400 B. 300
2. 250 D. 150

152O

1. 2480 B. 1240 30O C. 620 D. 124
   
2. P Q

110O 

x 

120O 

T S 

In the figure above, find the value of x A. 1300 B. 1100 C. 1000 D. 900 

R 

y 

In the figure above, find the value of y  A. 280 B. 1220 C. 1500 D. 1520 

P 

S 

31. The angles of a quadrilateral are 5x – 30, 4x + 60, 60 – x 

68O 

and 3x + A. 

2. find the smallest oft 5x– 30 B. 60– x D. 

hese angles. 4x + 60 

3x + 61. 

Q R 

In the figure above, PQ =  QPS. 

T 

PR = PS and SRTY= 680. find 

32. The area of a square is 144sqcm. Find the length of its A. 1360 B. 1240 diagonal C. 1120 D. 680 A. 11√3cm B. 12cm 
33. 12√2cm D. 13cm 39. A flagstaff stands on the top of a vertical tower. A man standing 60m away from the tower observes that the 
34. One angle of a rhombus is 600. the shorter of the two angles of elevation ofthe top and bottom of the flagstaff diagonals is 8cm long. Find the length of the longer are 640and 620respectively. Find the length of a flagstaff. 
    

one 

1. 8√3 B. 16/√3 C. 5√3 D. 10/√3 
2. 60(tan 620 – tan 640) B. 60(cot 640 – cot 620) C. 60(cot 620 – cot 640) D. 60(tan 640 – tan620)
   
3. Simplify cos2x (sec2x + sec2x tan2x) 
4. Tan x B. Tan x secx 
5. Sec2 x D. Cosec2 x 
6. If cos x = √a/b, find cosec x. 
7. b B. b 

√ b – a √ a 

1. b D. √ b – a 

√ b – a a 

42. From a point Z, 60m, north of X, a man walks 60Ö3m  eastwardsto another point Y.find the bearing of y from  x. 
43. 0300 B. 0450
44. 0600 D. 0900
45. A surveyor walks 500m up a hill which slopes at an  angle of 300. calculate the vertical height through which  he rises 
46. 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. 76.80and 25.20 B. 10.80and 224.60
47. 112.40and 72.00 D. 39.60and212.40

Use the following information to answer question 48  and49. 

No of defective 

per box 4 5 6 7 8 9 

No . of boxes 2

7 17 10 8 6

 

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 
    
49. 250m B. 500Ö3/3m A. 6.7,6 B. 6.7,6.5 C. 250Ö2m D. 250Ö3m C. 6,6.7 D. 6.5,6.7 

44.P 4 cm Q49. Find the percentage of boxes containing at least 5  defective bolts each. 

1. 96 B. 94 
   

8 cm S 

6 cm 

V 

W 2 cm R 

1. 92 D. 90 
2. A crate of soft drinks contains 10bottles ofCoca-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? 
3. 5/12 B. 1/3 
   

In the figure above, PQRS is a square ofside 8cm. What  is the area of UVW? 

1. 64sq.cm B. 54sq.cm 
2. 50sq.cm D. 10sq.cm 
3. Find the total area of the surface of a solid cylinder  whose base radius is 4cm and height is 5cm. 
4. 56pcm2 B. 72pcm2
5. 96pcm2 D. 192pcm2

x 

a 

y 

a 

Find the volume of the figure above. 

1. pa2/3 B. pa2y 
2. pa2/3(y + x) D. (1/3pa2x + y) 
3. ¾ D. 7/1
4. Find n if 34n= 100112
5. 5 B. 6 C. 7 D. 8 

Mathematics 1992 

11. Factorize 9p2 – q2 + 6pr – 9r2
12. (3p – 3q + r)(3p – q – 9r) 
13. (6p – 3q + 3r)(3p – q – 4r) 
14. (3p – q + 3r)(3p + q – 3r) 
15. (3p – q + 3r)(3p – q – 3r) 
    
16. The radius of a circle is given as 5cm subject to an error  of 0.1cm. what isthe percentage error in the area ofthe  circle. 
17. 1/25 B. ¼ 
18. 4 D. 25 
19. Evaluate Log anif b = 1/an

b 

1. n2 B. n 
2. 1/n D. 1/n 
3. What is the value of x satisfying the equation 42y / 43x = 2? 
4. -2 B. –1/2 
5. ½ D. 2 
6. Simplify {(1.25 x 104) x (2.0 x 10-1)

(6.25 x 105 

4. 4.0x 10-3B……………….5.0 x10-2
5. 2.0x 10-1D…………..5.0x 103
6. Simplify5√18- 3√72+4√50 
7. 17√4 B. 4√17 
8. 17√2 D. 12√4 
9. Solve the equation y – 11 y + 24 = 0  
10. 8,3 B. 64,9 
11. 6,4 D. 9,-8 
12. 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%. 
13. #14.00 B. #120.00 
14. #140.00 D. #160.00 
15. If x + 1 is a factor of x3 + 3x2 + kx +4, find the value of k  A. 6 B. 6 
16. 8 D. 8 
17. Resolve (3/x2 + x – 2) into partial fractions  A. 1 – 1 B. 1 1

x-1 x+2 x + 2 x – 1  

1. 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 
17. –8 ≤x ≤ 5 D. –5 < x ≤8 
    
18. If x = 3 – √3, find x2 + 36 / x2 A. 9 B. 18 C. 24 D. 27 

y 4 

3 

2 

x 

8. If x = {all prime factors of 44} and 

y= {all prime factors of 60}, the elements of x∩yand  xÇy respectivelyare. 

1. {2,4,3,5,11} and {4} 

-3 -2 -1 0 1 -1 

-2 

-3

2 3 

1. {4,3,5,11} and {3,4} 
2. {2,5,11} and{2} 
3. {2,3,5,11} and{2} 
4. IfU = {0,2,3,6,7,8,9,10}isthe universalset, E = {0,4,6,8,}  and F = {x: x2 = 26,}, x is odd}. Find (ECF)’ wheremeans  the complement of aset 

The sketch above isthe curve of y = ax2 + bx + c. find a,  b, and c respectively 

1. 1,0,-4 B. –2,2,-4 
2. 0,1,-4 D. 2,-2,-4 
3. Find the sum of the infinity of the following series. 3 +  2 + 4/3 + 8/9 + 16/27 + .. 
4. 1270 B. 190 
   
5. {0} B. U C. 18 D. 9 C. C D. f 
6. What isthe nth term ofthe sequence 2,6,12,20,…? 
   
7. Make l the subject of the formula  

s = ut + ½ at2 

1. 1/a [u± √(u2−2as)] B. 1/a [-u± √(u2– 2as] C. 1/a [u±√(u2+ 2as) D. 1/a [-u±√(u2+ 2as)] 
2. 4n – 2 B. 2(3n – 1) 
3. n2 + n D. n2 + 3n +2 
4. For an arithmetic sequence, the first term is 2 and the  common difference is 3. find the sum ofthe fist 11 terms. 
   
5. 157 B. 187 28. F C. 197 D. 200 
6. If the binary operation * is defined bym*n = mn + m + n  for any real number m and n, find the identity element  

H 

x 

109O 

109O 

K 

under this operation. 

1. e = 1 B. e = -1 
2. e = -2 D. e = 0 

Use the matrices below to answer questions 22 and 23. 

22. When PTisthe transpose of P, calculate [PT] when x = 0,  y = 1 and z = 2 
23. 48 B. 24 
24. –24 D. 48 
25. PQ is equivalent to 

A PPT B. PP-T 

1. QP D. PP 
2. UP Q 

X 

G M 

If in the diagram above, FG is parallel to KM, find the  value of x 

1. 750 B. 950
2. 1050 D. 1250
3. 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
4. 15008 D. 600

6 cm 

105O 

TS 

20O 

R 

O 6 cm 

In the figure above, TSP = 1050and PRQ = 200, find  

PQR 

1. 1300 B. 1200 The above diagram is a circle with centre O. find the C. 750 D. 300area of the shaded portion. 
   
2. If the angles of a quadrilateral are (p + 10)0, (p + 20)0and 4p0, find p 
3. C. 

9πcm2 18πcm2 

3D. 

9(π -2)cm2 36πcm2 

31. 63 B. 40 31. The locus of a point which is equidistant from two C. 36 D. 28 given fixed points is theA. perpendicular bisector of the straight line  
    

Q 

joining them 

1. 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 
   

P R 32. What isthe perpendicular distance of a point (2, 3 )from Sthe line 2x – 4y + 3 = 0 

1. √5/2 B. –√5/20 
   

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? 

1. QS =PS.SR 
2. QS =√(PS.SR) 
3. QS= √2 √(PS.SR) 
4. QS =1/√2√(PS.SR) 
5. –5/√13 D. 0 
6. Find the equation of the line through (5, 7) parallel to  the line7x + 5y= 12 
7. 5x+ 7y= 120 B. 7x + 5y = 70  C. x + y= 7 D. 15x+ 17y= 90 
8. Given that q is an acute angle and sin q = m/n, find cot q. 
   
9. Determine the distance on the earth’s surface between  two towns P(Lat. 600N, Long. 200E) and Q(Lat. 600N,  Long 250W) 
10. 800p/9km B. 800Ö3p/9km 
11. n2– m2 B. m 

m 

(n + m) (n – m) m 

1. 800pkm D. 800Ö3pkm 
2. D. n2 – m2 

n 

n2 – m2 

35. Y 43. 

R 

15O 

30O 

X Z 

10 cm 

x 2	4	6	8
f 4	y	6	5

 

If the mean of the above frequency distribution is 5.2,  find y 

6. 6.0 B. 5.2 
7. 5.0 D. 4.0 

In the figure above, if XZ is 10cm, calculate RYin cm 

45. 10 B. 10(1 – 1/Ö3) 
46. 10(1 – Ö3) D. 10(1 – 1Ö2) 
47. Evaluate lim (x-2) (x2+3x-2)

No . of children 0	1 2	3 4	5	6
No . of families 7	11 6	7 7	5	3

 

Find the mode and median respectively of the 

x–>2 (x2-4) distribution above 

1. 0 B. 2 A. 2,1 B. 1,2 C. 3 D. 4 C. 1,5 D. 5,2 
   
2. If y = x, find d2y/dx2
3. 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 
4. 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 
5. If the scores of 3studentsin a test are 5,6 and 7 find the  standard deviation of their scores 
6. 2/3 B. 3/2√3 
7. √ 2/3 D. √3/2 
8. Sample variance can be defined as 
   

ofice in the box,find the mass ofice formed in 5minutes. S2 = 1/n n=1 (x1-x)2and 

19. 19.5 B. 17.0 S = 1n∑ (x −x) 
20. 14.5 D. 12.52(n-1)n=11 1

Where n is the number of sample observations. There  

39. Obtain a maximum value of the function f(x) = x3 – 12x + 11 

is no difference practically between the above  definitions when 

1. -5 B. –2 A. n =35 B. n > 35 C. 5 D. 27 C. n < 35 D. n = 5
   
2. A student blows a ballon and its volume increases at a  rate of p (20 – t2)ccm3s-1after t seconds. If the initial  volume of 0cm3, find the volume of the balloon after 2  seconds. 
3. 37.00π B. 37.33π 
4. 40.00π D. 42.67π 
5. Evaluate the integral π/4π/12 cos 2xdx 
6. Two perfect dice are throw together. Determine the  probability of obtaining a total score of 8 
7. 1/12 B. 5/36 
8. 1/8 D. 7/36 
9. The probability of an event P is ¾ 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? 
   
10. -1/2 B. –1 A. 1/96 B. 1/8 C. ½ D. 1 C. 5/6 D. 11/12 
    
11. A storekeeper checked his stock of five commodities  and arrived at the followingstatistics. 
12. 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  
    

Commodity F  

G  

H  

K  

M 

Quantity 215 

113 

108 

216 

68 

each other? 

1. 48 B. 24 
2. 20 D. 10 
3. 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 how many  
   

What angle will commodityH represent on a pie chart?  A. 2160 B. 1080 

ways can he choose his courses so that he takes exactly  two courses in Physics? 

1. 680 D. 540 A. 11 B. 12 C. 10 D. 7 
   
2. Change 7110

Mathematics 1993 

to base 8 12. Which of the following is a factor of  

1078 B.1068 

15 + 7x – 2x2? 

1. 718 D. 178
2. Evaluate 3524/0.05 correct to 3 significant figures. A. 705 B. 70000 13. C. 70480 D. 70500 
3. If 9(x-1/2)= 3x2, find the value of x. 
4. ½ B. 1 
5. x-3 B. x+3 C. x-5 D. x+5 

Evaluate 

(x+1/x+1)2 – (x-1/x-1) 2 

1. 4x2 B. (2/x+2) 2 C. 4 D. 4(1+x) 
2. 2 D. 3 
3. Solve the following simultaneous equations for x.  x2 + y – 5= 0 
   
4. Solve for y in the equation 10y, X5(2y-2) x 4(y-1)=1  

y – 7x 

+ 3=0 

1. ¾ B. 2/ 3 

-2, 4 

1. 2, 4 
   
2. 1 D. 5/ 4 
3. Simplify 1/3-2 – 1/3+2 
4. 4 B. 2
5. / 0 D. 3 
6. -1, 8 D. 1, -8 
7. Solve the following equation (3x-2)(5x-4)=(3x-2) 2
8. –3/ , 1 B. 1 
9. If 2 log3 y+ log = 4, then y is x2 3 

-4 2 

1. 2/ , 1 D. 2/ , 4/5 

3 3 

16. (4-log x2)/2 B. 4/log x2 16. Q 30O C. 2/3
    

3 

X 

1. ±9/ 

X 

7. Solve without using tables 

O 

xO 

log5(62.5)-log5(1/2) T 

1. 3 B. 4 
2. 5 D. 8 
3. If #225.00 yields #27.00 in x years simple interest  at the rate of 4%per annum, findx 

xO 2xO 

P 

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? 

1. 3 B. 4 A. 1,3,2 B. 0,0,0 C. 12 D. 27 C. 0,2,3 D. 1,2,3 
2. If the function f is defined by 
3. f(x+2)=2x2 + 7x – 5, find f(-1) 
   

X Y 

Z 

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 
11. 5 B. 4 
12. 3 D. 1 
13. Make x the subject of the relation  

1+ax/1-ax = p/q 

1. p+q/a(p-q) B. p-q /a(p+q) C. p-q/apq D. pq/a(p-q)
2. -10 B. -8 
3. 4 D. 10 
4. Divide the expression 

x3 + 7x2 –x –7 by -1 +x2 

1. –x3+7x2-x-7 B. –x3-7x+7 C. X-7 D. X+7 
2. Simplify 

1/p-1/q –p/q-q/p 

1. 1/p-q B. -1/p+q C. 1/pq D. 1/pq(p-q) 
2. Solve the inequality 

y2-3y>18 

1. -2<y<6 B. y<-3 or y>6 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 

1. 3<x<4 B. -4<x<-3 C. -2<x<-1 D. -3<x<0 
   

22 Aman’s initial salary is #540.00 a month and increases  after each period of six months by #36.00 a month.  Find his salary in the eighth month of the third year. A. #828.00 B. #756.00 

720. #720.00 D. #684.00 

Q 

O 

960 

P 

diaRam 

23. cle If k+  

1, 2k-1,3k+1 

etric progressiare three co  

nsecutive terms of a  

In the  

OQ a dabove. O is the centre of  gr 

the cir  

geom 

common ratio.  

on, find the 

possible values of the 

and P ORQ.  

iameter. If POR = 960, find 

the val 

ue of 

1. 0,8 B -1, 5/3 
2. 840 B. 480
   
3. 2, 3 D. 1, -1 C. 450 D. 420
   
4. A binary operation * is defined on a set of real  numbers by x*y = xy for all real values of x and y, if  x*2 = x, find the possible values of x 
5. 0, 1 B. 1, 2 
6. 2, 2 D. 0,2 

25 

Q P 340 

730 R 

S 

t diagram above, QT he P// 

P Q In730and RS = RT. Find SRTST; PQR. = 340, QRS= A. 680 B. 1020 

1. 1070 D. 1410

T R31. P T U 

U V 

S 

PQRST is a regular pentagon and PQVU is a  rectangle with U and V lying on TS and SR  respectively as shown in the diagram above. Calculate  TUV 

S 

Q

500 

xR 

50. 180 B. 540In the figure above, PT is a tangent to the circle at u C. 900 D. 1080and QU//RS. If TUR=350and SRU = 50.0find x.A. 950 B. 850
    
51. A regular polygon has 1500as the size of each interior  angle. How many sides has the polygon? 
52. 500 D. 350
    
53. 12 C. 9 
54. 10 D. 8 

P 

27. Calculate the length, in cm, of the arc of the circle of  

diameter 8cm which subtends an angle of 221/0 

2 

1. 2 π B. ππ Q R C. 2/ π D. /23 cm S 

3 

In the diagram above, QPS = SPR, PR= 9cm, PQ= 

28. 4cm and QS=3cm. Find SR. 
    
29. 33/ 
30. 22/ 

T 

P 

S 

O 

1. 63/ 

4 

8 

1. 43/ Q

8 

3 

33. The three sides of an isosceles triangle are of lengths 

x+3, 2x+3, 2x-3 respectively. Calculate x. A. 0 B. 1 

R C. 3 D. 6 

In the diagram above, PQRS is a circle with O as  centre and PQ//RT if RTS = 320, find PSQ A. 320 B. 450 C. 580 D. 900 

S 

O 

Q 

T 

In the figure above, the line segment ST is tangent to  the two circles at S and T. O and Q are the centres of  the circles with OS = 5cm, QT = 2cm and OQ =  14cm. Find ST. 

1. 7″3 B. 12cm C. “87cm D. 7cm 

P X Q 

	U

 

T V 

SYR 

In the figure above, the area of the square PQRS is  100cm2. If the ratio of the area of the square TUYS to  the area of the square XQVU is 1:16, find YR A. 6cm B. 7cm C. 8cm D. 9cm 

42 Quantities in the proportions 1,4,6,7 are to be  represented in a pie chart. Calculate the angle of the  sector with proportion 7 

1. 200 B. 800
2. 1200 D. 1400

The bar chart above shows the distribution of marks  in a class test. How many students took the test? A. 15 B. 20 

1. 25 D. 50 
2. The following marks were obtained by twenty  students in an examination 
   
3. Find the radius of a sphere whose surface area is 154cm2(π =22/7) 
4. 7.00cm B. 3.50cm 
5. 3.00cm D. 1.75cm 
6. Find the area of the sector of a circle with radius 3m,  if the angle of the sector is 600
7. 4.0m2 B. 4.1m2
9. 4.7m2 D. 5.0m2
10. The angle between latitudes 300S and 130N is  A. 170 B. 330
11. 430 D. 530
12. If sin θ= cos 0, find 0 between 00and 3600.  A. 450,2250 B. 1350,3150

53 30 70 84 59 43 90 20 78 48 

44 60 81 73 50 37 67 68 64 52 

Find the number of students who scored at least  50marks 

1. 6 B. 10 C. 13 D. 14 

 

Estimate the mode of the frequency distribution  above. 

13. 13.2g B. 15.0g C. 16.8g D. 17.5g 
14. 450,3150 D. 1350,2250 40. 
15. The mean of the ages of ten secondary school pupils  is 16 but when the age of their teacher is added to it,  the mean becomes 19. Find the age of the teacher. A. 27 B. 35 
16. 38 D. 49 
    

300 

450 

47 

P H 

5 m 

Q 

From the figure above, calculate TH in centimeters. A. 5/(√3+1) B. 5/√3-1 

1. 5/√3 D. √3/5 
2. If two angles of a triangle are 300each and the longest side is 10cm, calculate the length of each of the other  sides. 
3. 5cm B. 4cm 
4. 3√3cm D. 10√3/5cm 

1 – 5 2 

6 – 10 4 

11 – 15 5 

16 – 20 2 

21 – 25 3 

26 – 30 2 

31 – 35 1 

36 – 40 1

Find the median of the observations in the table 

above. 

11. 11.5 B. 12.5 
12. 14.0 D. 14.5 
13. A number is selected at random between 20 and 30  both numbers inclusive. Find the probability that the  number is a prime 
14. Calculate the standard deviation of the following  data. 

7, 8, 9, 10, 11, 12, 13. 

1. 2 B. 4 
2. 10 D. 11 
3. The chances of three independent event X, Y, Z 
4. 2/ C. 6/ 
5. 5/ 
6. 8/occurring are 1/ , 2/ , ¼ respectively. What are the  

11 

11 

2 3 

11 

chances of y and z only occurring? 

11 

1. 1/ B. 1/ 
   

8 

24 

1. 1/ D. ¼ 

12 

Mathematics 1994 

1. Evaluate1/ ÷[5/ (9/ – 1 + 3/ )]10. Simplify[(2m – u)2 – (m – 2u)2] 
   

3 

1. 28/ 39 
2. 39/ 

7 10 4 

1. 13/ 
2. 84/(5m2 – 5u2) 84 
   

28 

1. ¾ B. 2/5 

13 

1. 2m – u/5m + u D. m – 2u/m + 5u 
   
2. Evaluate (0.36x 5.4 x 0.63) (4.2 x 9.0 x 2.4) correct to 2 significant figures 
3. 0.013 B. 0.014 C. 0.13 D. 0.14 
4. Evaluate Log5(0.04)

(Log318 – Log32) 

1. 1 B. -1 
2. Factorize 

a2x – b2y – b2x + a2y 

1. (a – b)(x+ y) B. (y- x)(a – b)(a+ b) C. (x – y)(a- b)(a+ b) D. (x+ y)(a- b)(a+ b) 
2. Find the values of p and q such that (x – 1) and (x – 3) are factors of px3 + qx2 + 11x – 6 
   
3. 2/ D. –2/ A. -1,-6 B. 1,-6
   

3 3 

4. Without using tables, solve the equation 

8x-2 = 2/ 13. 

25 

1. 4 B. 6 
2. 8 D. 10 
3. 1,6 D. 6,-1 y 
   

Simply  

5 3 

1. 5√3√48 –9/√+ √75 
2. 6√3 
3. 8√3 D. 18√3
4. Given that “2 = 1.414, find without using tables, the  

0 (3.0) (0.-27) 

x 

value of 1/ The equation of the graph above is 

”2 

1. 0.141 B. 0.301 A. y = (x – 3)3 B. y = (x + 3)3 C. 0.667 D. 0.707 C. y = x3 – 27 D. y = -x3 + 27 
   
2. In a science class of 42 students, each offers at least  one of Mathematics and Physics. If 22 students offer 
3. If a = 1, b = 3, solve for x in the equation a/a – x = b/x – b 
   

Physics and 28 students offer Mathematics, find how  many students offer Physics only? 

1. 4/ C. 3/ 
2. 2/ 

3 3 

2 

1. 6 B. 8 
2. ¾ 
3. 12 D. 14 
4. Given that for sets A and B, in a universal set E, A⊆ B then 

A∩(A∩B)’ is 

1. A B. O/ 
2. Solve for r in the following equation 

1/(r – 1) + 2/(r + 1) = 3/r 

1. 3 B. 4 
2. 5 D. 6 
3. Find P if x – 3/(1 – x)(x + 2) = P/(1 – x) + Q/(x + 2) 
   
4. B D. ∑ 
5. –2/ 
6. –5/ 
7. Solve for x if 25x + 3(5x) = 4 
8. 5/ 

3 3 D. 2/ 

3 3 

1. 1 or -4 B. 0 C. 1 D. -4 or 0 
2. Find the range of values of x for which 1/x > 2 is  true 
3. x < ½ B. x < 0 or x > ½ C. 0 < x < ½ D. 1 < x < 2 
   
4. 26. 

y 

50O 

-4 -2 

2x-y-2=0

x 

-20 1 2 3 

30O

Find the inequality which represents the shaded  

portion in the diagram 

1. 2x – y – 2 £ 0 B. 2x – y – 2 ³ 0  
2. 2x – y – 2 < 0 D. 2x – y – 2 > 0 
4. If the 6th term of an arithmetic progression is 11 and  the first term is 1, find the common difference. 

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 

Q 

R 

1. 12/ C. -2 
2. 5/ 

5 3 D. 2 

38O O 

20. Find the value of r if log r + log r2 + log r4 + log r8 + log r16 + log10 10

SP 

10 10 

r32 = 6310 10 

1. 10-8 B. 100
2. 10 D. 102
3. Find the nth term of the sequence 

3,6,10,15,21,….. 

1. n(n – 1/2) B. n(n + 1/2) 
2. (n + 1)(n + 2)/2 D. n(2n + 1) 
3. 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 followingproperties doesNOT hold? 
4. Closure B. Associativity. C. Identity. D. Inverse. 

Ox mod 10 2 4 6 8 

2 4 8 2 6 

4 8 6 4 2 

6 2 4 6 8 

In the diagram above, O is the centre of the circle. If  SOQ is a diameter and <PRS is 380, what is the value  of <PSQ? 

1. 1480 B. 1040
2. 800 D. 520
3. If three angles of a quadrilateral are (3y – x – z)0, 3x0,  (2z – 2y – x)0, find the fourth angle in terms of x, y, and  z. 
4. (360 – x – y – z)0 B. (360 + x + y – z)0 C. (180 – x + y + z)0 D. (180 + x + y + z)0
5. An open rectangular box is made of wood 2cm thick. If  the internal dimensions ofthe box are 50cm long, 36cm  wide and 20cm deep, the volume of wood in the box is A. 11520cm3 B. 36000cm3
6. 38200cm3 D. 47520cm3
7. Calculate the perimeter in cm, of a sector of a circle of  radius 8cm and angle 450
   

8 6 2 8 4 

The multiplication table above has modulo 10 on the  set S = {2,4,6,8}. Find the inverse of 2 31.3 

1. 2 π 
2. 16 + 2 π 

R 

1. 8 + 2π D. 16+ 16 π 
3. 2 B. 4 

1 

. 

1. 6 D. 8 

Solve for x and y 

1 1 x = 4 

3 y 1 1

1. x = -3, y = 3 B. x = 8, y = 3  C. x = 3, y = -8 D. x = 8, y = -3 

60O 

50O 

Q T 

P 

In the diagram above, PTS is a tangent to the circle  TQR at T. calculate < RTS. 

1. 1200 B. 700
   
2. The determinant of the matrix C. 600 D. 400 (1 2 3) 

(4 5 6) is 32. 

(2 0 -1) 6 cm h 5 cm A. -67 B. -57

1. -3 D. 3 7 cm
   

In the diagram above, find h. 

1. 12/ cm B. 12/ V6cm 7 7
2. 7/ cm D. 1/ V51cm 43. 12 2 

h 

In the frustum of a cone shown above, the top diameter 

CA3 

4 

43.2O 64.8O 

F72O A2 

144O 

A1 

The grades A1, 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? 

is twice the bottom diameter. If the height of the frustum A. 52.0 B. 43.2 

is h centimeters, find the height of the cone. 

1. 2h B. 2πh 
2. πh D. πh/2 44. 
3. 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
4. The perpendicular B. Aright-angled triangle.  

bisector of XYX 

1. A circle D. A semi-circle. 
2. If M(4,q) is the mid-point of the line joining L(p, -2)  
3. 40.0 D. 12.0 

x	1	2 3 4 5
f	2	1 2 1 2

 

The table above shows the frequency distribution  of a data. If the mean is 43/14, find y. 

1. 1 B. 2 
2. 3 D. 4 

and N(q, p), find the values of p and q. 

1. p = 2, q = 4 B. p = 3, q = 1  C. p = 5, q = 3 D. p = 6, q = 2 
2. y

(0,4) 

(3,0) 

45. The mean of twelve positive numbers is 3. when  another number is added, the mean becomes 5. find  the thirteenth number. 
46. 29 B. 26 
47. 25 D. 24 
48. Find the mean deviation of the set of numbers 4, 5, 9  A 0 B. 2 
49. 5 D. 6 
    

(0,0) 

Class interval Frequency

1-5  6

6-10  15

11-15  20

16-20  7

21-25 2

 

x 

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? 

Estimate the median of the frequency distribution  above. 

1. 5√3/ m B. 5√3m 
2. 101/ 
3. 111/ 
   

2 2 

3 

1. 10√3m D. 10√3/ m 3 
2. What is the value of sin (-6900)? 
3. 121/ 

2 

49. 13 
    
50. √3/2 B. –√3/2 C. -1/2 D. ½ 
51. If y = 3t3 + 2t2 – 7t + 3, find dy/ at t = -1 dt 

x	1	2	3 4		5
f	y + 2	y – 1	2y + 3	y + 4	3y – 4

1. -1 B. 1 Find the variance of the frequency distribution above C. -2 D. 2 A. 3/ B. 9/ 2 4 
2. 5/ D. 3 
   
3. Find the point (x, y) on the Euclidean plane where the curve y = 2x2 – 2x + 3 has 2 as gradient. 
5. (1,3) B. (2,7) 
6. (0,3) D. (3,15) 
7. Integrate (1 – x)/x3 with respect to x. 

2 

Age in years 10 Number of pupils 6 

11 27 

12 7 

1. (x – x2)/(x4 + k) B. 4/x4 – 3/x3 + k  C. 1/x – 1/2x2 + k D. 1/3x3 – 1/2x + k 
2. Evaluate 1(2x + 1)2 dx 

-1 

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/ 

1. 33/B. 17/ 

40 20 

1. 3/ 
   
2. 32/ 3 
3. 41/ 
4. 4 D. 42/ 

40 20 

3 3

50. In a survey, it was observed that 20 students read  newspapers and 35 read novels. If 40 of the students 

probability of the students who read both newspapers  and novel? 

read either newspaper or novels, what is the A. 1/ 2 

C3/ 

8 

Mathematics 1995 

1. 2/ D. 3/ 

3 

11

1. Calculate 3310 -1442 A. (-6,0)(-1, 0) B. (-3,0)(-2,0) 5 5 C. (-6,0)(1,0) D.(2, 0)(3, 0) A. 13135 B. 21135 C. 43025 D. 11035
   
2. Convert 3.1415926 to 5 decimal places 
3. 3.14160 B. 3.14159 C. 0.31415 D. 3.14200 
4. The length of a notebook 15cm, was measured as  16.8cm. calculate the percentage error to 2 significant  figures. 
5. 12.00% B. 11.00% C. 10.71% D. 0.12% 
6. 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 ofthe third year?  A. #28,800 B. #29,040 C. #31,200 D.#31,944 
7. Express the product of 0.0014 and 0.011 in standard  form. 
8. 1.54 x 102 B. 1.54 x 10-3 C. 1.54 x 104 D. 1.54 x 10-5
9. Evaluate (813/4– 27 1/3) 

3 x 23 

1. 27 B. 1 C. 1/3 D. 1/8 
2. Factorize completely the expression 

abx2 + 6y – 3ax –2byx 

1. (ax – 2y)(bx – 3) B. (bx + 3)(2y – ax) 
2. (bx + 3)(ax – 2y) D. (ax – 2y) (ax – b) 
3. Solve the following inequality (x – 3)(x – 4) ≤0 A. 3≤ x ≤ 4 B. 3 < x < 4 
4. 3 ≤ x < 4 D. 3 < x ≤4 
5. The 4th term of an A. P is 13cm while the 10th term is 31.  find the 31st term. 
6. 175 B. 85 
7. 64 D. 45 
8. Simplify x2 – 1

x3 + 2x2 – x – 2 

1. 1/x + 2 B. x – 1/x + 1  
2. x – 1/x + 2 D. 1/x – 2 
3. Express 5x – ½ (x – 2)(x – 3) in partial fraction A. 2/x – 2 – 3/x – 3 B. 2/x – 2 + 3/x – 3 
   
4. Find the value of (16)3/2 + log 0.0001 + log 32 C. 2/x – 3 – 3x –2 D. 5/x – 3 + 4/x – 2 10 2 
   
5. 0.065 B. 0.650 C. 6.500 D. 65.00 
7. Simplify√12 – √3

√12 + √3 

1. 1/3 B. 0 C. 9/15 D. 1 
2. 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? 
3. 25 B. 21 C. 16 D. 3 

y 

-1 0 1 2 x 

Use the graph of the curve y = f(x) above to solve the  inequality f(x) > 0. 

1. -1≤ x ≤ 1, x > 2 B. x ≤-1, 1, < x > 2 C. x≤ -1, 1 ≤ x ≤ 2 D. x ≤ 2, -1 ≤ x ≤ 1 
2. If S = (x : x2 = 9, x > 4), then S is equal to  A. 0 B. {0} C. f D. {f} 
3. If x – 1 and x + 1 are both factors of the equation x3 +  px3 + qx + 6 = 0, evaluate p and q 
4. –6, -1 B. 6, 1 C. -1 D. 6, -6 

12.12. 

Find a positive value of p if the equation 2x2 – px + p  leaves a remainder 6 when added 

1. 1 B. 2 C. 3 D. 4 
2. Find r in terms of K, Q and S ifs = 2r√ (QπΤ+Κ) A. r2– k B. r2– k  

2πr2Q Q 4πr2Q 

1. r2– k D. r2– k  

2πr2Q 4πr2Q 

14. The graph of f(x) = x2– 5x + 6 crosses the x-axis at the  points 
15. Which of the following binary operation is commutative  in a set ofintegers? 
16. a*b = a + 2b B. a*b = a + b –ab  C. a*b = a2 + b D. a*b = a(b + 1)/2 
17. If a*b = +√ab, Evaluate 2*(12*27)  
18. 12 B. 9 
19. 6 D. 2 
20. Find the sum to infinity of thefollowing sequence  1, 9/10, (9/10)2,(9/10)3
21. 1/10 B. 9/10 
22. 10/9 D. 10 
23. Find the value of K if 2, 1, 1 

2, 1 k 

1, 3 -1 = 23 

1. 1 B. 2 
   
2. If X = 1, 2 and Y = 2, 1 0, 3 4, 3 
3. (10, 7) B. (2, 7) (12, 9) (1, 17) 
4. (10, 4) D. (4, 3) 

12 cm 

14 cm 

( 4, 6) (10, 9) In the diagram above, the base diameters is 14cm while  the height is 12cm. Calculate the total surface area if  

26.  

81Ox 53O 

the cylinder has both a base and a top (p = 22/7) A. 836cm2 B. 528cm2 

Determine the value of x in the figureabove  A. 1340 B. 810 C. 530 D. 460 

35. 308cm2 Q 

30O 

1. 154cm2
   

Z 

XY 

P T 

PT is a tangent to the circle TYZX, YT = YX and <  PTX = 500. calculate <TZY 

1. 500 B. 650 C. 850 D. 1300

P 10 cm R 

In the diagram above, find PQ if the area of triangle  PQR is 35ccm2 

1. 97cm B. 10cm 
2. 14cm D. 17cm 
3. A schoolboy lying on the ground 30m away from the  foot of a water tank lower observes that the angle of  elevation of the top of the tank is 600. Calculate the  height ofthe water tank. 
4. 60m B. 30.3m 
5. 20.3m D. 10.3m 
   
6. In a triangle XYZ, <YXZ = 440?and <XYZ = 1120.  calculate the acute angle between the internal triangle  of <XYZ and<XZY. 
7. 420 B. 560
8. 680 D. 780
9. Find the distance between two towns P(450N, 300N) and  
10. QRS is a triangle with QS = 12m, <RQS = 300and <QRS = 450, calculate the length of RS.  
11. 18√2m B. 12√2m 
12. 6√2m D. 3√2m 
13. Which of the following is a sketch of y = 3 sin x? 3 
    

Q(150S, 300W) ifthe radius of the earth is 7 000km. 

1. 1 100 B. 2 200

3 3 

1. 11 000

3 

30. Two perpendicular lines PQ and QRintersect at (1, -1). If  the equation of PQ is x – 2y + 4 = 0, find the equation of  

0 

2 2 

 3  

3 0 

2 2 

3 

0 

2 2 

 3  

1. 3

0 

2 2 

 3  

2. x – 2y + 1 = 0 B. 2x + y – 3 – 0  C. x – 2y – 3 = 0 D. 2x + y – 1 = 0 
3. P is on the locus of a point equidistant form two given  points X and Y. UV is a straight line through Y parallel to the locus. If < PYU is 400find <XPY 
4. 1000 B. 800
5. 500 D. 400

117O 

38. The derivative of cosec x is 
39. tan x cosec x B. – cot x cosec x C. tan x sec x D. –cot x sec x 
40. For what value of x is the tangent o the curve y = x2 – 4x + 3 parallel to the x – axis? 
41. 3 B. 2 
42. 1 D. 0 
43. Two variables x and y are such that dy/dx = 4x – 3 and y 
    

m 

n 

xO 

k 

= 5 when x = 2. find y in terms of x 

1. 2x2 – 3x+ 5 B. 2x2 – 3x+ 3 C. 2x2 – 3x D. 4 
   

In the diagram above, k, m, and n are parallel lines.  What is the value of the angle marked x? A. 370 B. 630 

1. 1170 D. 1530
2. Find the area bounded by the curve y = 3x2 – 2x + 1, the  coordinates x = 1 and y = 3 and the x-axis 
3. 24 9. B. 22 47 C. 21 D. 20 
5. The variance of the scores 1,2,3,4,5 is  
6. 1.2 B. 1.4C. 2.0 D. 3.0 

Age in years 13	14	15	16	17
No . of students 3	10	30	42	15

The frequency distribution above shows the ages of  studentsin a secondaryschool. In a pie chart constructed  to represent the data, the angle corresponding to the 15  years-old is 

1. 270 B. 300 C. 540 D. 1080

Economics History 

150O 90 O 

French 

1. R. K. 

The pie chart above shows the distribution of students  in a secondary school class. If 30 students offered  French, how many offered C.R.K? 

1. 25 B. 15 C. 10 D. 8 

Use the table below to answer questions 47 and 48 

Class   Interval	Frequency	Class   Boudaries
1.5-1.9  2.0-2.4  2.5-2.9  3.0-3.4  3.5-3.9  4.0-4.4  4.5-4.9	2  1  4  15  10  5  3	1.45-1.95  1.95-2.45  2.45-2.95  2.95-3.45  3.45-3.95  3.95-4.45  4.45-4.95

 

Class 

Mid-point 

1.7 

2.2 

2.7 

3.2 

3.7 

4.2 

4.7 

47. find the mode of the distribution 
48. 3.2 B. 3.4 C. 3.7 D. 4.2 
49. The median of the distributionis 
    
50. The mean and the range of the set of numbers  0.20,1.00,0.90,1.40,0.80,0.80,1.20,and 1.10 

are m and r respectively. Find m + r  

1. 1.11 B. 1.65 C. 1.85 D. 2.45 
2. 4.0 B. 3.5 C. 3.2 D. 3.0 
3. Let P be a probability function on set S, where S =  (a1,a2,a3,a4) find P(a1) if P(a2) = P(a3) = 1/6 and P(a4)1/5  A. 7/10 B 2/3 C. 1/3 D. 3/10 
   

Class 1 – 3		4 – 6 7 – 9
Frequency 5	8	5

 

Find the standard deviation of the data using the table  above 

A .5 B. √6 C. 5/3 D. √5 

50. A die has four of its faces coloured while and the  remaining two coloured black . What is the probability  that when the die is thrown two consecutive times, the  top face will be white in both cases? 
51. 2/3 B. 1/9 C. 4/9 D. 1/36 
    
52. If (1PO3) = 115 , find P A. 010B. 1 

4 

1. 2 D. 3 

Mathematics 1997 

1. 19 + 4″15/11 B. 19 + 4″15/19 
2. 19 + 2″15/11 D. 19 + 2″15/19
3. Find the simple interest rate per cent per annum at  
4. Evaluate 64.7642 – 35.2362correct to 3 significant  figures 
5. 2960 B 2950 
6. 2860 D. 2850 
7. Find the value of (0.006) 3 + (0.004) 3in standard form. A. 2.8 X 10-9 B 2.8 X 10-8
8. 2.8 X 10-7 D. 2.8 X 10-6
9. Given that loga2 = 0.693 and loga3 = 1.097, find loga13.5 
10. 1.404 B. 1.790 
11. 2.598 D. 2.790 
12. Simplify log 96 – 2log 6 

which #1000 accumulates to #1240 in 3 years. 

1. 6% B. 8% 
2. 10% D. 12% 

9 If U = {S,P,L,E,N,D,O,U,R}  

X = {S,P,E,N,D} 

Y = {P,N,O,U,R} 

Find X∩(Y’UZ). 

1. {P,O,U,R} B. {S,P,D,R} 
2. {P,N,D} D. {N,D,U} 
3. A survey of 100 students in an institution shows that  80 students speak Hausa and 20 students Igbo, while  only 9 students speaks both languages. How many 
   

A.2 2students neither Hausa nor Igbo? 

2 – log23 B. 3 – log23 

1. log23 – 3 D. log23 – 2 
2. If 8x/2= [23/8][43/4], find x 
3. 3/8 B. ¾ 
4. 4/5 D. 5/4 
5. Simplify (2√3+3√5)/(3√5 – 2√3) 
6. 0 B. 9 
7. 11 D. 20 
8. If the function (x) = x3 + 2x2 + qx – 6 is divisible by x +  1, find q. 
9. -5 B. -2 
10. 2 D. 5 
    
11. Solve the simultaneous equations 

2 –3/ = 2, 4/ + 3/ = 10 24. Find the non-zero positive value of x which satisfies 

/x 

y x y 

1. x = 3/ , y = ½ B. x = ½, y = 3/ the equation 
   

2 

2 

1. x = –1/ , y = –3/ D. x = ½, y = –3/ 
   

2 

2 

2 

x  

1 0 

13. Find the minimum value of x2 – 3x + 2 for all real x 1 = 0 
    

values of x.  

1 

1. –1/1 x 
   

4 

1. –1/ 2 

0 

1. ¼ D. ½ 
2. Make f the subject of the formula t = 

 v 

1+1 f g 

1. 2 B. 3 

2 

1. D. 1 
2. Each of the base angles of an isosceles triangle is  580and all the vertices of the triangle lie on a  
   
3. gv – t2/gt2 B. gt2/gv – t2
4. v/t1/2 – 1/g D. gv/t2 – g 
5. What value of g will make the expression 4x2 – 18xy – g a perfect square? 
7. 9 B. 9y2/4 
8. 81y2 D. 81y2/4 
9. Find the value of K if 5+2r/ expressed in partial fraction is /r-2 +(r+1)(r-2)

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 

F K 34O 

x 

47O 

G 

K L 

/r+1, where K and L are constants. R 

1. 3 B. 2 
2. 1 D. -1 
3. Let f(x) = 2x + 4 and g(x) = 6x + 7 where g(x) > 0. 

H 

From the figure above, FK//GR and FH = GH,< RFK = 340and < FGH = 470. calculate the angle marked x. 

solve the inequality f(x)/ g(x) < 1 A. 420 B. 520 

1. x < – ¾ B. x > – 4/3 
2. x > – 3/4 D. x > – 12 
3. Find the range of values of x which satisfies the  

inequality 12x2< x + 1 

1. -1/4 < x < 1/3 B. ¼ < x <1/3 
2. -1/3 < x<1/4 D. -1/4 < x <-1/3 
3. Sn is the sum of the first n terms of a series given by  S = n2 – 1. find the nth term. 

n 

1. 4n + 1 B. 4n – 1 
2. 2n + 1 D. 2n – 1 
3. The nth term of a sequence is given by 31-n. find the  sum of the first three terms of the sequence. 
4. 13/ 
5. 1/B 1
6. 640 D. 720

25 cm 

3 cm

X2 cm 

Y 

The figure above shows circles of radii 3cm and 2cm  with centres at X and Y respectively. The circles have  a transverse common tangent of length 25cm.  Calculate XY. 

1. 630 cm B. 626 cm C. 615 cm D. 600 cm 
   
2. 1/ 28. A chord of a circle diameter 42cm subtends an angle 0 9 

3 9 of 60 at the centre of the circle. Find the length of 

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). 
22. 60 B. 57 
23. 54 D. 42 
24. If xy = x + y – xy, find x, 

when (x*2)+(x*3) = 68 

1. 24 B. 22 
2. -12 D. -21 

the minor arc. 

1. 22 cm B. 44 cm 
2. 110 cm D. 220 cm  

[π = 22/7] 

29. An arc of a circle subtends an angle of 700at 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
30. 66 cm2 D. 88 cm2
31.  
32. Determines x + y if 5 cm 8 cm 

11 cm 

= (-1) 

(8) 

3 

2 

-1 

-3 4 

(x) 

(y) 

10 cm 

4

Find the volume of the prism above. 

1. 7 

12 

1. 990 cm3 B. 880cm3
2. 550 cm3 D. 495cm3
3. A cone with the sector angle of 450is cut out of a  circle of radius r cm. find the base radius of the  cone. 
4. Integrate 1/x + cos x with respect to x. A. -1/x2+ sin x+ k B. 1nx+sin x+k C. 1nx– sin x+k D. -1/x2 – sin x +k 
5. If y = x(x4 + x2 + 1), evaluate 1 dyx -1 
   
6. r/16cm B. r/8cm A. 11/12 B. 11/16 C. r/4cm D. r/2cm C. 5/6 E. 0 
   
7. 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. 

1. 12cm B. 10cm 

Housing 

69O Basic 

60O

1. 8cm D. 6cm 
2. The angle between the positive horizontal axis and  

Transport 

50O 

61O Others 

a given line is 1350. find the equation of the line if  it passes through the point (2, 3). 

1. x – y = 1 B. x + y = 1 
2. x + y = 5 D x – y = 5 
3. Find the distance between the point Q(4, 3) and the  point common to the lines 2x – y = 4 and x + y = 2 3 10 

Meal 

The pie chart above shows the income of a civil  servant in a month. If his monthly income is #6000,  find his monthly basic salary. 

1. #2000 B. #2600 C. #3100 D. #3450 
   
2. B. 

3 5 

44. D.44.
    

26 

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? 

1. 20√3m B. 40√3m 
2. 20√3m D. 40√3m 
3. In a triangle XYZ, if <XYZ is 600, XY = 3cm and  YZ = 4cm, calculate the length of the side XZ. 

In an examination, the result of a certain school is as  shown in the histogram above. How many candidates  did the school present? 

1. “23cm B. “13cm A. 12 B. 16 C. 2″5cm D. 2″3cm C. 18 D. 19 
   

37.X 

Age 20	25	30 35	40	45
No . of students 3	5	1 1	2	3

 

2 cm 

5 cm

Z 

150O 

Find the median age of the frequency distribution in  the table above 

1. 20 B. 25 
   

Y E 

In the figure above, XYZ is a triangle with XY =  5cm, XZ = 2cm and XZ is produced to E making the  angle YZE = 1500. if the angle XYZ = è, calculate the  value of the sin è. 

1. 3/5 B. ½ 
2. 2/5 D. 1/5 
3. Differentiate 6x3-5x2+1

3x2 

1. 30 D. 35 

46 The following are the scores of ten students in a test  of 20 marks; 15,16,17,13,16,8,5,16,19,17. what is the  modal score? 

1. 13 B. 15 
2. 16 D. 19 
3. Find the standard deviation of the following data – 5,-4,-3,-2,-1,0,1,2,3,4,5 
   
4. 2 + 2/3x3 B. 2 + 1/6x A. 2 B. 3 C. 2-2/3x3 D. 2-1/6x C. √10 D. √11
   
5. d/dx cos(3x2 – 2x) is equal to 
6. -sin(6x- 2) B. -sin(3x2 –2x) C. (6x- 2)sin(3x2 – 2x) D. (6x – 2) sin (3x2 – 2x) 
7. Find the gradient of the curve y = 2 √x – 1/x at the  point x= 1 
8. 0 B. 1 C. 2 D. 3 
9. Find the difference between the range and the variance  of the following set of numbers 4,9,6,3,2,8,10,5,6,7  where d2 = 60. 
10. 2 B. 3 
11. 4 D. 6 
12. In a basket of fruits, there are 6 grapes, 11 bananas  and 13 oranges. If one fruit is chosen at random,  what is the probability that the fruit is either a grape  or a banana? 
13. 17/30 B. 11/30  
14. 6/30 D. 5/30 
15. A number is selected at random between 10 and 20,  both numbers inclusive. Find the probability that the  numbers is an even number. 
16. 5/11 B. ½ 
17. 6/11 D. 7/10 
    

Mathematics 1998 

1. If 10112 + X7, = 2510, solve for X In the venn diagram above, the shaded region is A. 14 B. 20 A. (PÇQ)ÈR B. (PÇQ)ÇR C. 24 D. 25 C. (PÇQ’)ÇR D. (PÇQ’)ÇR 
   
2. Evaluate [1/0.03 ÷ 1/0.024] -1, correct to 2 decimal  places 
3. 3.76 B. 1.25 
4. When the expression pm2 + qm + 1 is divided by (m – 1), it has a remainder 2 and when divided by (m + 1) the remainder is 4. find p and q respectively 
   
5. 0.94 D. 0.75 A. 2, -1 B. -1, 2 C. 3, -2 D. -2, 3 
6. If b3 = a-3and c 1/3 = a1/2b, express in terms of  
   

aA. a-1/2 B. a1/2 

1. a3/2 D. a 2/3
2. Given that Log (y – 1) + Log (1/2x) = 1 andLog 4 4 2 

1) + log2x = 2, solve for x and y respectively 

(y + 

11. Factorize r2 – r (2p + q) + 2pq 
12. (r – 2q)(2r – p) B. (r – q)(r + p) C. (r – q)(r – 2p) D. (2r – q)(r + p) 
13. Solve the equation x – (x – 2) – 1 = 0
    
14. 2, 3 B. 3, 2 A. 3/2 B. 2/3 C. -2, -3 D. -3, -2 C. 4/9 D. 9/4 
    
15. Find the value of K if K/”3 + “2 = “3 – 2 A. 3 B. 2 
16. “3 D. “2 
17. A market woman sells oils in cylindrical tins 10cm  deep and 6cm diameter at #15.00 each. If she bought  a full cylindrical jug 18cm deep and 10cm in diameter  for #50.00, how much did she make by selling all  the oil? 
18. #62.50 B. #35.00 
19. #31.00 D. #25.00 
20. A man is paid r naira per hour for normal work and  double rate for overtime. If he does a 35-hour week  which includes q hours of overtime, what is his  weekly earning in naira? 
21. r(35 + q) B. q(35r – q) 
22. q(35r + r) D. r(35r – q) 
23. Given the universal set U = {1,2,3,4,5,6,} and the  sets P = {1,2,3,4,} Q = {3,4,5} and R = {2,4,6}.Find  PÈ(QÈR). 
24. Find the range of values of m for which the roots of  the equation 3x2 – 3mx + (m2 – m – 3) = 0 
25. -1<m<7 B. -2<m<6 
26. -3<m<9 D. -4<m<8 
27. Make a/x the subject of the formula 

x + a/x – a = m 

1. m – 1/m + 1 B. 1 + m/1 – m  C. 1-m/1 + m D. m + 1/m – 1 
2. Divide 2x3 + 11x2 + 17x + 6 by 2x + 1 A. x2 + 5x + 6 B. 2x2 + 5x + 6  C. 2x2 – 5x + 6 D. x2 – 5x + 6 
3. Express in partial fractions 

 11x + 2 

6x2 – x – 1 

1. 1/3x– 1 + 3/2x+ 1 B. 3/3x+ 1 – 1/2x– 1  C. 3/3x– 1 – 1/2x+ 1 D. 1/3x+ 1 +3/2x-1 
2. If x is a positive real number, find the range of values  for which 
   
3. C. 

{4} 

{1,2,3,5,6} 

{1,2,3,4} 

{1,2,3,4,5,6} A. x> – 1/6 

1/3x + ½ > 1/4x 

1. x>0 
   
2. 0<x<4 D. 0<x<1/6 
4. y

(0, 3) 

P Q 

(2, 0) 

x 

The shaded area above represents 

1. x≥0, 3y + 2x≥ 6 B. x≥ 0, y≥3, 3x + 2y≥ 6  

R 

1. x≥2,y≥ 0,3x+2y≤6 D. x≥ 0,y≥ 0,3x+2y≥6
   
2. If p + 1, 2p – 10 ,1 – 4p2are the consecutive terms of  an arithmetic progression, find the possible values  of p. 

In the diagram above, PQ//ST and ÐPQR = 1200, ÐRST = 1300. find the angle marked x. 

1. 500 B. 650
   
2. -4, 2 B. –2, 4/11 C. 700 D. 800 C. –11/4, 2 D. 5, -3 
   
3. The sum of the first three terms of a geometric  progression is half its sum to infinity. Find the  positive common ration of the progression. 
4. ¼ B. ½ 

27.P Q

1. 1/3″3 D. 1/3″2T 10cm S 8cm R 
   

Ox	p q	r s
P  q  r   s	r  p   q  p  r r  q s	p  r  s  r  r r  r q

 

In the figure above, PQST is a parallelogram and TSR  is a straight line. If the area of ∠QRS is 20cm2, find  the area of the trapezium PQRT. 

1. 35cm2 B. 65cm2 C. 70cm2 D. 140cm2 X 

32O 

The identity element with respect to the multiplication  shown in the table above is 

Y 40O 

R 

1. p B. qT Q C. r D. s 

TQ is tangent to circle XYTR. ∠YXT = 320, 

22. The binary operation * is defined by x*y = xy – y – x  for all real values x and y x*3 = 2 * x, find x. 

∠RTQ = 400. find ∠YTR. 

1. 1080 B. 1210
   
2. -1 B. 0 C. 1400 D. 1480 C. 1 D. 5 
3. A chord of a circle radius Ö3cm subtends an angle of  
   
4. The determinant of matrix 

in terms of x is 

1. -3x2– 17 B. 
2. 3x2 + 17 D. 
3. Let I= 1 0. P= 2 3 Q= u, 4 + u 0 1 4 5 -2v, v 

x, 1, 0 1-x, 2, 3 1, 1+ x, 4 

-3x2 + 9x – 1  3x2 – 9x + 5 

600 on the circumference of the circle. Find the length  of the chord. 

1. √3/2 cm B. 3/2 cm 
2. √3 cm D. 3 cm 
3. A cylindrical drum of diameter 56 cm contains 123.2  litres of oil when full. Find the height of the drumin  centimeters. 
4. 12.5 B. 25.0 

be 2 x 2 matrices such that PQ=1. find (u,v)  A. (-5/2, -1) B. (-5/2, 3/2) C. (–5/6,1) D. (5/2, 2/3) 

T 

S 30O 

35O 

R 

45. 45.0 D. 50.0 
46. The locus of all points at a distance 8 cm from a  point N passes through point T and S. if S is  

equidistant from T and N , find the area of triangle  STN. 

1. 4√3 cm2 B. 16√3 cm2
2. 32cm2 D. 64 cm2
   

P32. If the distance between the points (x, 3) and (-x, 2) Qis 5. find x 

6. 6.0 B. 2.5 
7. 6 D. 3
   

In the diagram above, PR is a diameter of the circle  PQRS. PST and QRT are straight lined. Find Ð QSR.  A. 200 

1. 250
2. 300
3. 350

R 

x 

120O 

33 The midpoint of the segment of the line y = 4x + 3  which lies between the x-axis and the y-axisis A. (-3/2, 3/2) B. (-2/3, 3/2) C. (3/8, 3/2) D. (-3/8, 3/2) 

34. Solve the equation 

cos x + sin x = 1/cos x – sinx  

for values of x such that 0 ≤ x < 2π 

1. π/2, 3π/2 B. π/3, 2π/3  
   

P 

Q 

130O 

ST 

1. 0, π/3 D. 0, π 

R 

15 

P10 8 

1. 2/3 B. 1 C. K + 1 D. (K +1)2
   

30O 

Q 

45. Find the positive value of x if the standard deviation  

T 

of the numbers 1, x +1, 2x + 1 is √6 

In the diagram above, QTR is a straight line and∠ PQT = 300. find the sine of ∠PTR. 

1. 8/15 B. 2/3 
2. ¾ D. 15/16 
3. For what value of x does 6 sin (2x – 25)0attain its  maximum value in the range 00 ≤x ≤1800? 
4. 1 B. 2 
5. 3 D. 4 
6. A bag contains 16red balls and 20blue balls only. How  many white balls must be added to the bag so that the probability of randomly picking a red ball is equal  to 2/5? 
   
7. 121
8. /A. 4 B. 20
9. / 571/ B. 321

2 2 

1471/ 

2 2 

48. 24 D. 40 
    
49. From the top of a vertical mast 150m high, two  

huts on the same ground level are observed. One  

o 

due east and the other due west of the mast. Their  

angles of depression are 600and 450respectively.  

Find the distance between the huts. 

120O

h 

1. 150 (1 + √3)m B. 50 (3 + √3)m C. 150√3m D. 50/√3m 
2. If y = 243 (4x + 5)-2, find dy/dx when x = 1 A. -8/3 B. 3/8 
3. 9/8 D. –8/9 

The pie chart above shows the monthly expenditure  of a public servant. The monthly expenditure on  housing is twice that of school fees. How much does  the worker spend on housing if his monthly income is  #7.200? 

A #1000 B. #2000 

Differentiate x/cos x with respect to x. 

1. 1 + x sec x tan x B. 1 + sec2x C. cos x + x tan x D. secx + x secx tan x 
2. #3000 D. #4000 48. 
   
3. Evaluate π (sec2x – tan2x)dx 

2 

1. π/2 B. π – 2 
2. π/3 D. π + 2 
3. Find the equation of the curve which passes  through the point (2, 5) and whose gradient at any  point is given by 6x – 5 
4. 6x2 – 5x + 5 B. 6x2 + 5x + 5 C. 3x2 – 5x – 5 D. 3x2 – 5x + 3 
5. If m and n are the mean and median respectively of  the set of numbers 2,3,9,7,6,7,8,5 and m + 2n to the  nearest whole number. 
6. 19 B. 18 
7. 13 D. 12 

The bar chart above shows the distribution of marks  scored by 60 pupils in a test in which the maximum  score was 10. if the pass mark was 5, what percentage  of the pupils failed the test? 

59. 59.4% B. 50.0% 
60. 41.7% D. 25.0% 
61. In a recent zonal championship games involving  10teams, teams X and Y were given Probabilities 2/  5 and 1/3 respectively of wining the gold in the  
    

Average hourly  earnings (N) 

No . of workers 

5 – 9	10 – 14 15 – 19 20 – 24
17	32 25	24

 

football event. What is the probability that either team  will win the gold? 

1. 2/15 B. 7/15 
   

Estimate the mode of the above frequency  

distribution. 

12. 12.2 B. 12.7 
13. 12.9 D. 13.4 
14. Find the variance of the numbers K, K + 1, K + 2. 
15. 11/15 D. 13/15 
16. If x, y can take values from the set {1,2,3,4,}, find the probability that the product of x and y is not  greater than 6. 
17. 5/8 B. 5/16 
18. ½ D. 3/8
19. If (a2b3c)/a-1b4c5

Mathematics 1999 

12. The first term of a geometrical progression is twice  

What is the value of P + 2q?  

1. 5/2 B. –5/4 

its common ratio. Find the sum of the first two terms  of the progression if its sum to infinity is 8 

1. –25/4 D. –10 A. 8/5 B. 8/3 C. 72/25 D. 56/9 
2. Find the value of x if √2/(x + √2) = 1/(x – √2)  
   
3. 3√2 + 4 B. 3√2 – 4 
4. 3 – 2√2 D. 4 + 2√2 
5. A trader bought 100 oranges at 5 for #1.20,20 oranges  got spoilt and the remaining were sold at 4 for #1.50.  find the percentage gain or loss 
6. 30% gain B. 25% gain 
7. 30% loss D. 25% loss 
8. If U = {1, 2, 3, 4, 5, 6}, P = {3, 4, 5}, Q = {2, 4, 6} and R = {1, 2, 3 4}, list elements of (PÈQ’ÇR). 
9. {1, 2, 3, 4, 5, 6} B. {1,2, 3, 4} 
10. {1} D. Æ 
11. Divide 24346 by 426
12. Tope bought x oranges at #5.00 each and some  mangoes at #4.00 each. If she bought twice as many  mangoes as oranges and spent at least #and at most  #, find the range of the value ofx 
13. 4 ≤ x ≤ 5 B. 5 ≤ x ≤ 8 
14. 5 ≤ x ≤ 10 D. 8 ≤ x ≤ 10 
15. If m*n = m/n – n/m, for m,n E R, evaluate –3 *4  A. -25/12 B. –7/12 
16. 7/12 D. 25/12 
17. Find the matrix T if ST = I where S = (-1, 1) (1, -2) 

and I is the identity matrix. 

1. (-2, 1) B. (-2, -1) 
   
2. 236 C. 526
3. 356 D. 556

(-1, 1) (-1, -1)C. (-1, -1) D. (-1, -1) 

6. If 2 x (Y3) = 3 (Y3) , find the value of Y (01, -1) (0, 1) 

9 9 5 9 

1. 4 B. 3 
   
2. 2 D. 1 
3. Simplify √(0.0023 x 750)/(0.00345) x 1.25  A. 15 B. 20 
4. 40 D. 75 
5. If log 10 = x, evaluate log 5 in terms ofx. 8 8 
6. Divide 4x3 – 3x + 1 by 2x – 1 
7. 2x2 – x + 1 B. 2x2 – x – 1  C. 2x2 + x + 1 D. 2x2 + x – 1 
8. Three consecutive positive integers k, l and m are  such that l2 = 3(k + m). find the value of m. 
9. 4 B. 5 
   
10. 1/ x B. x –1/4 C. 6 D. 7 2 
    
11. x –1/ D. x –1/ 

3 2 

19. A group of market women sell at least one of yam,  plantain and maize. 12 of them sell maize, 10 sell  yam and 14 sell plantain. 5 sell plantain and maize, 4  sell yam and maize, 2 sell yam and plantain only  while 3 sell all the three items. How many women  are in the group? 
20. 25 B. 19 
21. 18 D. 17 

y 

45O 

-1 0 1x 

The shaded portion in the graph above is represented  by 

1. y+ x – x3 0, y – x £ 0 B. y – + x3³ 0, y– x £ 0 C. y+ x – x3 £ 0, y+ x ³ 0 D. y – x + x3 £ 0, y+ x £ 0 
2. Given that Q = (6, 0) and Q + P = (7, 2) (4, 5) (6, 8) 

evaluate /Q + 2P/ 

1. 90 B. 96 
2. 102 D. 120 
3. A binary operation * is defined by a*b = ab + b for  any real number a and b. if the identity element is  zero, find the inverse of 2 under this operation A. 2/3 B. ½ 
4. –1/2 D. 56/9 
5. Factorize completely 

x2 + 2xy + y2 + 3x + 3y – 18 

1. (x + y+ 6)(x+ y- 3) B. (x – y- 6)(x – y+ 3)  C. (x – y+ 6)(x – y – 3) 
2. The sum of two members is twice their difference. If  the difference of the numbers is P, find the larger of  the two numbers. 
3. p/2 B. 3p/2 
4. 5p/2 D. 3p 
5. Express 1/x3– 1 
6. B. 
7. D. 
8. In MNO, MN = 6 units, MO = 4 units and NO – 12  units. If the bisector of angle M meets NO at P,  calculate NP. 
9. From the Point P, the bearings of two points Q and R  are N670W and N230E respectively. If the bearing of R  from Q is N680E and PQ = 150m, calculate PR. 
   
10. 4.8 units B. 7.2 units A. 120m B. 140m C. 8.0 units D. 18.0 units C. 150m D. 160m 
    
12. Find the equation of the locus of a point P(x, y )such  that PV = PW, where V = (1, 1) and W = (3, 5) 
13. 2x + 2y = 9 B. 2x + 3y = 8  
14. 2x + y = 9 D. x + 2y = 8 

PTxQ S 110O

3 cm 

4 cm 

6 cm 

Find the value of l in the frustum above. 

R 

In the figure above, PQRS is a circle with ST//RQ. Find  the value of x if PT = PS 

1. 700 B. 550
2. 400 D. 350
3. E 
   
4. 5cm B. 6cm C. 7cm D. 8cm 

F H

34O 

42O 

X 

G 

2m 

120cm 

Y 1cm Z 

In the diagrams above, EFGH is a cyclic quadrilateral  in which EH//FG and FH are chords. If ∠FHG = 420 and ∠ΕFH = 340, calculate ∠HEG 

1. 340 B. 420
2. 520 D. 760
   

Find the length XZ in the triangle above 33. If the maximum value of y = 1+ hx – 3x2is 13, find h. A. √7m B. √6m A. 13 B. 12 C. √5m D. √3m C. 11 D. 10 

26. Find a positive value of a if the coordinate of the  centre of a circle x2 + y2 – 2ax + 4y – a = 0 is (a, -2)  and the radius is 4units 
27. Evaluate 1 A. -31/ 

–2 

(x – 1) 2 

1. 7 
   
2. 1 B. 2 C.3

9 D. 11 

1. 3 D. 4 
   
2. A man 1.7m tall observes a bird on top of a tree at an  angle of 300. if the distance between the man’s head  and the bird is 25m, what is the height of the tree? A. 26.7m B. 14.2m 
3. (1.7 +25√3m)/3 D. (1.7 +25√2m)/2 
4. Evaluate π/4 (x -1)2dx 
5. √2 + 1 B. √2 – 1 C. –√2 – 1 D. 1 – √2 
6. Find the area bounded by the curve 
   

T 

O 

9 

P 

x 

6 

y = x(2 – x), the x-axis, x = 0 and x = 2 

1. 4 squnits B. 2squnits 
2. 11/ sq units D. 1/3sq units 

2 

37. If y = 3x2(x3 + 1)1/2find dy/dx 
38. 6x(x3+1)+ 3x2/2(x3+1)1/2 B. 12x(x3+1)+3x2/2(x3+1)1/2
    

Z 

In the figure above, TZ is tangent to the circle QPZ.  Find x if TZ = 6 units and PQ = 9 units. 

1. 3 B. 4 
2. 5 D. 6 
3. Find the tangent ofthe acute angle between the lines 2x + y =3 and 3x – 2y = 5 
4. -7/4 B. 7/8 
5. 7/4 D. 7/2

C.(15x4+6x)/6x2(x3+1)1/2 D. 12x(x3+1) +9x4/2(x3+1)1/2 

38. Find the volume of solid generated when the area  enclosed by y = 0, y = 2x and 3 is rotated about the x – axis. 
39. 81πcubic units B. 36πcubic units C. 18πcubic units D. 9π cubicunits 
40. What is the derivative oft2sin (3t – 5) with respectsto the  variable? 
41. 6t cos (3t- 5) B. 2dtsin (3t- 5)– 3t2cos(3t- 5)  
42. 2tsin(3t-5)+3t2cos(3t-5) 
43. 2tsin(3t- 5)+ t2cos3t 
44. Find the value of x for which the function y = x3 – x has  a minimum value. 
46. –√3 B. –√3/2 
47. √3/3 D. √3 
48. Three boys play a game a luck in which their respective  chances of wining are ½, 1/3 and ¼. What is the probability that one and only of the boys wins the game?  A. 1/24 B. 1/12 

The grades of 36 students in a class test are as shown  in the pie chart above. How many students had  excellent? 

1. 7 B. 8 
2. 9 D. 12 

No of students 2			2 11 10 16		51 40	10 25		15 20
Marks	0 1 2		3	4 5	6	7 8		9 10

 

The marks scored by students in a test are given in the  above. Find themedian. 

1. 7 B. 6 
2. 5 D. 4 
3. 11/24 D. 23/24 
4. A number is selected at random from 0 to 20. what is  the probability that the number is an odd prime? 
5. A student calculated the mean of 5 numbers as 45, 3.  while rechecking his working, he discovered that his  total was short by 20.5. what is the correct mean of the  5 numbers? 
   
6. 8/21 B. 1/3 A. 24.8 B. 41.2 C. 2/7 D. 5/21 C. 49.4 D. 65.8 
7. If 6C /6P/ = 1/6, find the valueof r. 49. The sectorial allocations to various ministriesin a state r r 
   
8. 1 B. 3 
9. 5 D. 6 
10. If the standard deviation of the set of numbers 3, 6, x,  7, 5, is √2, find the least possible value of x. 
11. 2 B. 3 
12. 4 D. 6 

budget are as follows: 

Agriculture – #25 000000.00 

Education – #20 000 000 .00 Women affairs – #35 000 000.00  Commerce and 

Industries – #20 000000.00 

In a pie chart to represent this information the  corresponding angle to agriculture is 

45. How many two digit numbers can be formed from the A. 250 B. 450 digits 0, 1, 2, if a digit can be repeated and no number C. 500 D. 900 may begin with 0 
46. 4 B. 12 50. The mean offour numbers is 5 and the mean deviation C. 16 D. 20 is 3. find the fourth number if the mean deviation of the first three numbers is 2. 
47. A. 6 B. 10 C. 11 D. 17 

Mathematics 2000 

1. Let P = {1,2,u,v,w,x} 

R = {2,3,u,v,w,5,6,y} 

and R = (2,3,4,v,x,y)  

Determine (P – Q) ∩ R. 

1. {1, x} B. {x, y} 
2. {x} D. φ
3. If the population of a town was 240000 in January  1998 and it increased by 2% each year, what would  be the population of the town in January 2000? A. 480 000 B. 249 696 
4. 249 600 D. 244 800 
5. If 2√3 – √2/√3 + 2√2 = m + n√6, 

Find the values of m and n respectively  

1. 1, -2 B. –2, 1 
2. –2/5, 1 D. 2, 3/5 
3. In a youth club with 94 members, 60 like modern  music and 50 like like traditional music. The number  of members who like both traditional and modern  music is three times who do not like any type of  music. How many members like only one type of  music? 
4. 8 B. 24 
5. 62 D. 86 
6. Evaluate (2.813 x 10-3) x 1.063

5.637 x 10-2 

reducing each number to two significant figures and  leaving your answers in two significant figures. 

1. 0.056 B. 0.055 
2. 0.054 D. 0.54 
   
3. 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 

3 

1. 2 B. 1 

0 

3 

2 

1 

-3 -2 -1–0 1 2 3 1 

he need to deposit now? -3 -2 -1 -1 

1 2 3 

-2 

1. #112,000.50. B. #96,000.00 C. #85,714.28 D. #76,800.00 
2. If 31410 – 2567 = 340x, find x 

-2 

-3 

1. 32 

-3 

3 

2 

1 

1. 2n + 1 B. 2n – 1
2. 4 D. ¼ 
3. 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  

1 

-3 -2 -1 0 1 2 3 -1 

-2 

-3 

-3 -2 -1–0 1 2 3 1 -2 

-3 

#10,000, find the value ofx. 18. Find the values of t for which the determinant of the A. 60 B. 50 matrix (t -4 0 0 ) C. 40 D. 20 (-1 t+t 1 ) is zero ( 3 4 t-2) 

9. Simplify 3(2n + 1) – 4(2n -1)/2(n + 1) – 2n
   
10. 2n + 1 B. 2n – 1
11. 4 D. ¼ 
12. If P3446 – 23P26 = 2PP26, find the value of digit P. A. 2 B. 3 
13. 0, 2, 3 B. –4, 2, 3 
14. –4, -2, -3 D. 4, -2, 3 
15. If (x – 1), (x + 1) and (x – 2) are factors of the  polynomial ax3 + bx2 + cx – 1, find a, b, c, respectively 
    
16. 4 D. 5 A. -1/2, 1, ½ B. ½, 1, ½ C. ½, 1, -1/2 D. ½, -1, ½ 

Evaluate 5-3log52 x 22log23

20. 8 B. 11/ 20. A trader realizes 10x –x2naira profit from the saleof 8 
    
21. 2/5 D. 1/8 
22. A binary operation * is defined by a * b = ab. if a * 2 = 2 –a, find the possible values of a.  
23. 1, -1 B. 1, 2 
24. 2, -2 D. 1, -2 
25. The 3rd term of an A. P. is 4x – 2y and the 9th term is  10x – 8y . find the common difference. 
26. 19x – 17y B. 8x – 4y 
27. x – y D. 2x 
28. 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. 
29. p B. p – 1 
30. p/p – 1 D. p/p+1 

(a, b) 

15. A matrix P(a, b) is such that PT= p, where (c, d) 

PTis the transpose of P, if b = 1, then P is  

1. (0, 1) B. (0, 1) 

(1, 0) (-1, 0) 

x bags of corn. How many bags will give him the  maximum profit? 

1. 4 B. 5 
2. 6 D. 7 
3. Solve the inequality 2 – x > x2
4. x <-2 or x> 1 B. x >2 or x< -1  C. –1 <x>2 D. –2< x< 1 
5. If a and b are the roots of the equation 3x2 + 5x – 2 =  0, find the value of 1/α + 1/β 
6. -5/2 B. –2/3 
7. ½ D. 5/2 
8. Find the minimum value of the function f(θ ) = 2/3 – cosθ for ο ≤ θ ≤ 2π. 
9. ½ B. 2/3 
10. 1 D. 2 
11. 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. 
    
12. (0, 1) D. (1, 1) A. 8.0m B. 8.4m (1, 1) (-1,0) C. 9.0m D. 10.0m 
    
13. Evaluate (1/2 – ¼ + 1/8 – 1/16 + …….) -1  A. 2/3 B. 0 
14. –2/3 D. 1 
15. 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 ∠ VUS = 500, find ∠ UST. 
    
16. The solution of the simultaneous inequalities 2x – 2 A. 3100 B. 1300 £ y and 2y 2 £ x is represent by C. 800 D. 500
    
17. 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. 
18. S900E B. N400E 
19. S950E D. N850E 
20. An equilateral triangle of side √3 cm is inscribed in  a circle. Find the radius of the circle. 
21. 2/3cm B. 2cm 
22. y 

x 

y= 16

1. 1cm D. 3cm 
2. 3y = 4x – 1 and Ky = x + 3 are equations of two  straight lines. If the two lines are perpendicular to each other, find K 
3. -4/3 B. –3/4 

If the diagram above is the graph of y=x2, the shaded  area is 

1. 64squareunits B. 128/3squareunits C. 64/3squareunits D. 32squareunits 
   
2. ¾ SD. 4/3 35. Find the value of π(cos2θ – 1/sin2θ) dθ A. π B. π/ 

50OC. –π/0 29. 

0 

1. π 
   

P 30O R  

Q 

In the diagram above, if ∠ RPS = 500, ∠ RPQ = 300 and PQ = QR, find the value of ∠ PRS 

1. 800
2. 600 FB. 700
3. 500
4. O 

EN G 

H 

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. 

1. 16cm B. 20cm 
2. 26cm D. 32cm 
3. If P and Q are fixed points and X is a point which  moves so that XP = XQ, the locus of X is 
4. astraightline B. acircle 
5. thebisector ∠ PXQ D. theperpendicular bisector of PQ 
6. In a regular polygon, each interior angle doubles its  corresponding exterior angle. Find the number of  sides of the polygon. 
7. 87 B. 6 
8. 4 D. 3 
9. A predator moves in a circle of radius √2 centre (0,  0), while a prey moves along the line y = x. if 0≤ x≤ 2, at which point(s) will they meet? 
10. If y = 2y cos 2x – sin 2x, find dy/dx when x = ë/4 A. π B. – π 
11. π/2 D. – π/2 
12. 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? 
13. 7 πcubicunits. B. 15 π/2cubic units C. 8 πcubic units D. 17 π/2cubic units. 
14. If the volume of a hemisphere is increasing at a steady  rate of 8 πm3s-1, at what rate is its radius changing  when it is 6m? 
15. 2.50ms-1 B. 2.00ms-1 
16. 0.25ms-1 D. 0.20ms-1 
17. A function f(x) passes through the origin and its first  derivative is 3x + 2. what is f(x) 
18. y = 3/2x2 + 2x B. y = 3/2 x2 + x  C. y = 3 x2 + x/2 D. y = 3 x2 + 2x
19. 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? 
20. 1, 3, 1 B. 1, 2, 1 
21. 2, 1, 1 D. 1, 1, 3 
22. 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. 
23. 0.30 B. 0.50 
24. 0.57 D. 1.80 
25. If the mean of the numbers 0, x + 2, 3x + 6 and 4x +  8 is 4, find their mean deviation. 
26. 0 B. 2 
27. 3 D. 4 
28. In how many ways can the word MATHEMATICS  be arranged? 
    
29. (1, 1) only B. (1, 1) and (1, 2) A. 11!/9! 2! B. 11!/9! 2! 2! C. 11!/2! 2! 2! D. 11!/2! 2!
    

 

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 

1. 400 D. 600

The cumulative frequency curve above represents  the ages of students in a school. Which are group  do 70% of the students belong? 

15. 15.5 – 18.5 B. 15.5 –19.5 
16. 16.5 – 19.5 D. 17.5 – 20.5 
17. The variance of x, 2x, 3x 4x and 5x is A. x√2 B. 2x2
18. x2 D. 3x 
19. Find the sum of the range and the mode of the set of 
    
20. 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 

1. ¾ B. 3/10 
2. ¼ D. 1/20 

numbers 10, 5, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 10, 9, 7, 10, 6, 5 

1. 16 B. 14 
2. 12 D. 10 
3. 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? 
4. 15 B. 28 
5. 30 D. 45 

No . Of  Pupils

 

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? 

1. 35% B. 45% 
2. 50% D. 60% 
   

Mathematics 2001 

1. Find the principal which amounts to #5,000 at simple  interest in 5 years at 2% per annum 
2. #5000 B. #4900 
3. #4800 D. #4700 
4. 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? 
5. 20% B. 25% 
6. 32% D. 60% 
7. Evaluate 21.05347 – 1.6324 x 0.43, to 3 decimal  places. 
8. 20.351 B. 20.352 
9. 20.980 D. 20.981 
10. Evaluate (0.14)2 x 0.275)/7(0.02) correct to 3 decimal  places 
11. 0.033 B. 0.039 
12. 0.308 D. 0.358 
13. Given that p = 1 + √2 and q = 1 – √2, evaluate (p2 – q2)/2pq 
14. -2(2 + √2 ) B. 2(2 + √2) 
15. -2√2 D. 2√2
16. If y/2 = x, evaluate 

(x3/y3 + 1/2) + (1/2 – x2/y2) 

1. 5/16 B. 5/8 
2. 5/4 D. 5/2 
3. Simplify (3√64a3)-3
4. 8a B. 4a 
5. 1/4a D. 1/4a 
6. Factorize 4x2 – 9y2 + 20x + 25 
7. (2x – 3y)(2x+ 3y) B. (2x+ 5)(2x–9y+5)  C. (2x– 3y+ 5)(2x– 3y- 5) 
8. (2x– 3y)(2x+ 3y+ 5) 
9. If tow graphs y = px2and y = 2x2 – 1 intersect at x =  2, find the value of p in terms of q 
10. (7 + q)/8 B. (8 – q)/2 
11. (q – 8)/7 D. 7 / (q –1) 
12. 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) 
13. Divide a3x – 26a2x + 156ax – 216  

bya2x – 24ax + 108 

1. ax – 18 B. ax – 6 A. 4 B. –2 C. ax – 2 D. ax + 2 C. –4 D. –12 
2. Find the integral values of x and y satisfying the 20. If P = 3 -3 4 then -2p is inequality 3y + 5x £ 15, given that y > 0, y< 3 and 5 0 6 x > 0. 1 2 1 A. (1, 1), (2, 1),(1, 3) B. (1, 1), (1, 2),(1, 3) 
3. (1,1),(1,2),(2,1) D. (1, 1), (3, 1), (2, 2) A. -6, 4, -8 B -6, 4, -8 
   

y5, 0, 6 

7, 5, -1 

-10, 0, 6 -14, 5, -1 

-2P 1T 

xC. -6, -4, 2 D -6, 4, -8 

S -1 

-2 

-10, -2, -12 -14, 10, 2 

-10, 0, -12 -14, 40, 2 

Triangle SPT is the solution of the linear inequalities  A. 2y – x – 2 ≤ 0, y + 2x + 2 ≤ 0,≥0, x ≤ 0 

1. 2y – x – 2 ≤ 0, y + 2x + 2 ≤ 0, ≤ 0 
2. 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 

21. Find the number of sides of a regular polygon whose  interior angle is twice the exterior angle 
22. 2 B. 3 
23. 6 D. 8 

S 

T 

1. half of the common difference 

25OQ 

75O 

1. double of the common difference P R
   
2. the common difference D. zero 
3. 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 
4. 20 years B. 29 years 
5. 58 years D. 100 years 
6. 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 2under. 
7. -4 B. 2 
8. 0 D. 4 

In the figure above, PQR is a straight line segment,  PQ = QT. Triangle PQT is an isosceles triangle, <  SRQ is 750and < QPT = 250. calculate the value of <  RST. 

1. 250 B. 450
2. 500 D. 550
3. A cylindrical tank has a capacity of 3080m3. what is  the depth of the tank if the diameter of its base is 14m? 
4. 20m B. 22m 
5. 23m D. 25m 

17 

x k	l	m
k l	m	k
l m	k	l
m k	l	m

 

The identity element with respect to the  multiplication shown in the table above is A. k B. l 

1. m D. o 
2. A sector of a circle of radius 7.2 cm which subtends  an angle 3000at the centre is used to form a cone.  What is the radius of the base of the cone? 
3. 6cm B. 7cm 
4. 8cm D. 9cm
5. The chord ST of a circle is equal to the radius, r of  the circle. Find the length of arcST. 
6. πr/2 B. πr/3 
7. πr/6 D. πr/12 
8. A point P moves such that it is equidistant from the  
9. 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) 

1. (7, 2) D. (6, 3) 

(12, 21) (13, 20) 

19. Evaluate -1 -1 -1  

3 1 1 

1 2 1 

points Q and R. find QR when PR = 8cm and < PRQ = 300 

1. 4cm B. 4√3cm 
2. 8cm D. 8√3cm 
3. Find the locus of a point which moves such that its  distance from the line y = 4 is a constant, k. 
4. y = 4 + k B. y = k – 4 
5. y = k ± 4 D. y = 4 ± k 
6. 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. 
   
8. √3y = x + 5y√3 B. √3y = -x + 5√3 
9. y = x + 5 D. y = 1/10x + 5 
10. P(-6, 1) and Q(6, 6) are the two ends of the diameter  of a given circle. Calculate the radius 
11. 3.5 units B. 6.5 units 
12. 7.0 units D. 13.0 units 

No . of cars 87654321 w 

o

l

l

e

e 

t

i

h

d e

R

n e

e

r

e 

u

l

B

k c

a

l

W

Y

G

Color of cars B

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) 
31. 0 B. 3 
32. 4 D. 6 
33. The bearing of P and Q from a common point N are  0200and 3000respectively. If P and Q are also  41 

equidistant from N, find the bearing of P from Q. 

1. 3200 B. 2800
2. 0700 D. 0400

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? 

1. 4/15 B. 1/5 
2. 3/25 D. 2/25 

No . of taxis 876 

54 

3 

t0t 

21 

0 

5 

.

0

5 .

2

5 .

4

5 .

6

5 .

8

5 .

0

5 .

2

No . of passengers 

1

1

3t 

Find the value of q in the diagram above. A. 300 B. 600 C. 1000 D. 1200 

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) 

The histogram above shows the distribution of  passengers in taxis of a certain motor park. How many  taxis have more than 4passenger? 

1. 14 B. 15 
2. 16 D. 17 

Using the table below to answer questions 42 and 43 

34. If y = x sin x, find dy/dx when x = π/2  

Score 

Frequency 

4 7 3 5 

8 11 13 8 2 7 2 1 

42. π/2 B. 1 42. Find the square of the mode 
    
43. –1 D. π/-2 
44. If the gradient of the curve 

y = 2kx2 + x + 1 at x = 1 find k 

1. 1 B. 2 
2. 3 D. 4 
3. Find the rate of change of the volume V of a sphere  with respect to its radius r when r = 1 
4. 4π B. 8π 
5. 12π D. 24π
6. Find the dimensions of the rectangle of greatest area  which has a fixed perimeter p. 
7. Squareofsidesp/4 B. Squareofsidesp/2 C. Squareof sidesp D. Squareofsides2p 
8. Evaluate 2(2x – 3)2/3 dx 
9. 2x – 3 + k B. 2(2x – 3) + k C. 6/5(2x – 3)5/3 + k D. 3/5(2x – 3)5/3+ k 
10. Find the area bounded by the curves  
11. 25 B. 49 
12. 64 D. 121 
13. The mean score is 
14. 11.0 B. 9.5 
15. 8.7 D. 7.0 
16. Find the range of 1/6, 1/3, 3/2, 2/3, 8/9 and 4/3  A. 4/3 B. 7/6 
17. 5/6 D. ¾ 
18. Find the variance of 2, 6, 8, 6, 2 and 6  A. √5 B. √6 
19. 5 D. 6 

46.Cumulative 

frequency 50 

40 

30P 

20 

10 

0 

Q Q Q 

y = 4 – x2 

5 

5 

5 

5 

5 

5 

1. 101/ sq. units B. 102/ sq. units 

.

.

.

.

.

.

5

Masses (Kg) 

0

5

0

5

0

1

1

2

2

3

3 3 

1. 201/ sq. units D. 202/ sq.units 

3 3 

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? 

1. Q3– Q1 B. Q3 – Q2
2. Q2 – Q1 D. ½ (Q3 – Q1) 
3. Find the number of ways of selecting 8 subjects from  12 subjects for an examination. 
4. 498 B. 496 

Colour Blue	Black Yellow		White Brown
No . of beads 1	2 4	5	3

 

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? 

1. 1/15 B. 1/3 
2. 2/5 D. 7/15 
3. 495 D. 490 
4. If 6P = 6, find the value of 6P r r+1 
5. 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 
   
6. 15 B. 30 C. ½ D. 2/3 C. 33 D. 35 

Mathematics 2002 

1. A trader bought goats for #4 000 each. He sold them  for #180 000 at a loss of 25%. How many goats did 
2. Find the value of & if the line 2y – &x + 4 = 0 is  perpendicular to the line y + 1/ x – 7 = 
   

4 

he buy? 0 

1. 36 B. 45 A. -8 B. –4 C. 50 D. 60 C. 4 D. 8 
2. Simplify (√0.7 + √70)29. A bucket is 12cm in diameter at the top, 8cm in A. 217.7 B. 168.7 diameter at the bottom and 4cm deep. Calculates its 
   

Evaluate 

84.7 D. 70.7 volume. 

1. 144πcm3 B. 304πcm3/3  
2. 72πcm3 D. 128πcm3/
   

(0.21 x 0.072 x 0.0054)/ (0.006 x 1.68 x 0.063) 

correct to four significant figures. 

11. 0.1286 B. 0.1285 
12. 0.01286 D. 0.01285 
13. In a school, 220 students offer Biology or  Mathematics or both. 125 offer Biology and 110  Mathematics. How many offer Biology but not  Mathematics? 
14. 125 B. 110 
15. 95 D. 80 
16. Simplify 52.4 – 5.7 – 3.45 – 1.75 

O 

X Z 

Y 

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. 

1. 75cm2 B. 54cm2 C. 45cm2 D. 27cm2
2. 42.2 B. 42.1 
3. 41.5 D. 41.4 
4. Without using tables, evaluate 

(343)1/3 x (0.14)-1 x (25)1/2 

1. 7 B. 8 
2. 10 D. 12 

O r 

In the diagram below are two concentric circles of  radii r and R respectively with centre O. if r = 2/5 R,  

11. Find the coordinate of the midpoint of x and y  intercepts of the line 2y = 4x – 8 
12. (-1, -2) B. (1, 2) 
13. (2, 0) D. (1, -2) 
14. A chord of a circle subtends an angle of 1200at the  centre of a circle of diameter 4Ö3cm. Calculate the  area of the major sector. 
15. 32πcm2 B. 16πcm2
16. 8πcm2 D. 4πcm2
17. If tan q = 4/3, calculate sin2 θ – cos2 θ.  A. 7/25 B. 9/25 
18. 16/25 SD. 24/25 

P 

express the area of the shaded portion in terms of π 

and R. 

1. 9/ πR2 B. 5/ πR2

25 9πR 23 

x 

Q 

R S 

1. 21/ πR2 D 21/2T 
   

25 

72O 

In the diagram above, PST is a straight line, PQ = QS  = RS. If < RSRT = 720, find x. 

1. 720 B. 360
2. 240 D. 180
3. The range of the data k + 2, k – 3, k + 4, k – 2, k, k – 5,  k + 3, k – 1 andk + 6 is. 
4. 6 B. 8 
5. 10 D. 11 
7. The locus of a point P which is equidistant from two  given points S and T is 
8. a perpendicular to ST 
9. a line parallel to ST 
10. the angle bisector of PS and ST 
11. the perpendicular bisector ST 

 

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? 

16. A solid hemisphere has radius 7cm. Find the total A. 40 B. 120 surface area. C. 160 D. 210A. 462cm2 B. 400cm2
    
18. 308cm2 D. 66cm2 Q 

50O 

R 

Music 

30 -x 

History U80 

x 40 -x 

20 

P

128O 

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  

The angle PGR below is 

1. a scalene triangle 
2. an isosceles triangle 
3. an equilateral triangle 
4. an obtuse – angled triangle 
5. The sum of the interior angles of a polygon is 20  right angles. How many sides does the polygon have?  A. 10 B. 12 
6. 20 D. 40 
7. 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 
8. x = 3 D. x = 4 

class, what is the probability that he offers Music  only? 

1. 0.13 B. 0.25 
2. 0.38 D. 0.50 
3. Find the mean of the data 7,-3,4,-2,5,-9,4,8,-6,12 A. 1 B. 2 
4. 3 D. 4 
5. 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 
6. 4/9 D. 2/3 
7. How many three-digit numbers can be formed from  
   

3cm  

23cm 

In the diagram below, a cylinder is surrounded by a  hemispherical bowl. Calculate the volume of the 

32564 without digit being repeated? 

1. 10 B. 20 
2. 60 D. 120 
3. The acres for rice, principle, cassava, cocoa and palm  oil, in a certain district are given respectively as2,5,3,  11 and 9. what is the angle of the sector for cassava  in a pie chart? 
   

solid. A. 360 B. 600 A. 216πcm3 B. 198πcm3 C. 1080 D. 1800 C. 180πcm3 D. 162πcm3 

30. Calculate the mean deviation of the set of numbers  
    
31. 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. 
32. 8.8m B. 9.0m 

7,3,14,9,7 and 8 A. 21/ 

2 

1. 21/ 

6 

1. 21/ 3 
2. 11/ 6 
   
3. 10.4m D. 12.0m 
4. The mean 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 
5. 100 D. 95 
6. Find the maximum value of y in the equation y = 1 – 2x – 3x2
7. 5/3 B. 4/3 
8. 5/4 D. ¾ 
9. If the 9th term of an A. P is five times the 5th term,  find the relationship between a and d. 
   
10. a + 2d = 0 B. a + 3d = 0  C. 3a + 5d = 0 D. 2a + d = 0 
11. (-3,0) (0 -3) 
12. (9, 4) (12, 1) 
    
13. 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? 
14. 5 days B. 9 days 
15. Find the range of values of x for which  x + 2/4 – 2x – 3/3 <4 
16. x > -3 B. x < 4 C. x > -6 D. x < 8 

n 

42. 12 days D. 15 days 42. If x varies directly as when n = 17/9 

and x = 9 when n = 9, find x 

34. The binary operation is defined on the set of integers  p and q by p*q = pq + p + q. find 2 (3*4) 
35. 19 B. 38 
36. 27 B. 
37. 4 D. 
38. The sum of infinity of the series 

17 3 

1. 59 D. 67 
2. If –2 is the solution of the equation 2x + 1 – 3c = 2c + 3x – 7, find the value of c. 

1 + 1/3 + 1/9 + 1/27 + ……………………..is A. 3/2 B. 5/2 C. 10/3 D. 11/3 

44. 1 B. 2 44. Make r the subject of the formula C. 3 D. 4 x/r + a = a/r 
45. a/(x – a) B. (a/x + a 
46. If N = 3 5 -4 C. a2/(x – a) D. a2/(x + a) 6 -3 -5 

-2 2 1, find /N/ 45. If y = x2 – 1/x, find dy/dx 

1. 91 B. 65 C. 23 D. 17 
2. 2x + x2 C. 2x – 1/x2
3. D. 

2x – x2 2x – 1/x2 

37. Use the graph below to find the values of p and q if 46. Evaluate sin3xdx 
    

px + qy < 4 

(-4,0) 

y 

(0,2) 

x 

1. -2/3 cos 3x + c B. –1/3 cos 3x + c C. 1/3 cos 3x + c D. 2/3 cos 3x + c 
2. 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? 
   
3. p = 1, q = 2 B. p = 2, q = 1  C. p = -1, q = 2 D. p = 2, q = -1 
4. 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) 
5. Solve for x in the equation  

x3 – 5x2– x + 5 = 0 

1. 5p B. 4p 
2. 2p D. p 
3. If dy/dx = 2x – 3 and y = 3 when x = 0, find y in terms of x. 
4. x2 – 3x B. x2 – 3x + 3 C. 2x2 – 3x D. x2 – 3x – 3 
5. Find the derivative of y = sin2(5x) with respect to x 
   
6. 1, 1 or 5 B. –1, 1 or –5 A. 2 sin 5x cos 5x B. 5 sin 5x cos 5x C. 1, 1 or –5 D. 1, -1 or 5 C. 10 sin 5x cos 5x D. 15 sin 5x cos 5x 
   
7. If P = (2, 1) 

(-3 0) and I is a 2 x 2 unit matrix, evaluate  

p2 – 2p + 41 

1. (2, 1) B. (1, 0) 

(4, 1) (0, 1) 

50. The slope of the tangent to the curve y = 3x2 – 2x + 5  at the point (1, 6) is 
51. 1 B. 4 
52. 5 D. 61. 
    

Mathematics 2003 

1. Simplify 1 – (21/ x 11/ ) + 3/ A. 133 B. 113 
   

3 

4 5 

1. -231/ B. –27/ C. 63 D. 84 
   

60 

1. –119/ 

15 

3. –11/3. Simplify 2134x 234
   

60 15 

2. A cinema hall contains a certain number of people. A. 132114B. 103114 If 221/ % are children, 471/ % are men and 84 are C. 103214 D. 122314

2 2 

women, find the number of men in the hall. 

4. A woman buys 270 oranges for # 1800.00 and sells  at 5 for #40.00. what is her profit? 
5. #630.00 B. #360.00 
6. #1620.00 D. #2160.00 
7. Simplify (√98 – √50)

√32 

1. ½ B. ¼ 
2. 1 D. 3 
3. The sum of four numbers is 12145. what is the  average expressed in base five? 
4. 411 B. 401 
5. 141 D. 114 
6. Evaluate log√24 + log1/216 – log432 
7. -2.5 B. 5.5 
8. –5.5 D. 2.5 
9. 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. 

1. {0,2,6,22,26} B. {2,4, 14,18,26} C. {2,10,14,22,26} D. {0,10,14,22,26} 
2. 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? 
3. 16 B. 4 
4. (1 3) B (1 -3) 

(0 1) (0 -1) 

1. (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 
17. -4, -5 B. –5, -4 
18. 5, 4 D. 4, 5 
19. If –(x, 2) = (3, 3x) 

(4x, 1) (4, –5) find the value of x 

1. -2 B. –5 
2. 2 D. 5 
3. Find the range of values of x satisfying the  inequalities 5 + x ≤ 8 and 13 + ³ 7. 
4. -6 ≤ x ≤ 3 B. -6 ≤ x ≤ -3 
5. 3 ≤ x ≤ 6 D. –3 ≤ x ≤ 3 
6. 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? 
7. 4 B. 9 
8. 6 D. 3 

y 

P 

0 

 

=

 

1

 

+

 

x

1. 20 D. 8 
2. Find (1/0.06 ÷ 1/0.042)-1, correct to two decimal  

places 

4. 4.42 B. 3.14 

x 

O 

Q 

12. 1.53 D. 1.43 

If 92x – 1/27x + 1 = 1, find the value of x. A. 2 B. 8 C. 5 D. 3 

Triangle OPQ above is the solution of the  inequalities. 

1. x – 1 ≤ 0, y + x ≤ 0, y, – x ≤ 0 B. x + 1 ≥ 0, y + x ≤ 0, y, – x ≥ 0 C. y + x ≤ 0, y – x ≥ 0, x – 1 ≥ 0 D. x –1 ≤ 0, y – x ≥ 0, y + x ≥ 0 
   
2. Factorize completely 

4abx – 2axy – 12b2x +6bxy 

22. 2x(3b- a)(2b- y) B. 2x(a– 3b)(b- 2y) 
23. 2x(2b- a)(3b- y) D. 2x(a– 3b)(2b- y) 
24. The sum of the first n terms of an arithmetic  progression is 252. if the first term is –16 and the  

Three consecutive terms of a geometric progression  are given as n – 2, n and n + 3. find the common  ratio. 

1. 2/3 B. 3/2 
2. ½ D. ¼ 

last term is 72, find the number of terms in the series. A. 7 B. 9 

1. 6 D. 8 
2. 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? 
3. y = 3x + 2 B. y = 3x – 4 
4. 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.  
5. 30 B. 60 
6. 15 D. 20 

NP 

O 

1. y = 3x + 4 D. y = 3x – 2 42O40O
   
2. A matrix P has an inverse P-1 = (1 -3) (0, 1) Find P. 

MQ 

In the diagram above, O is the centre of the circle,  POM is a diameter and ∠ MNQ = 420. calculate ∠QMP. 

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 andR. 
    
30. 1380 B. 1320 A. 2700 B. 0900 C. 420 D. 480 C. 1350 D. 2250
    
31. The locus of a point P which moves on one side only  of a straight line XY so that ∠ XPY = 900is. 
32. the perpendicular bisector of XY 
33. a circle C. a semicircle D. an arc of a circle through X,Y 
34. P R 

Q S 

In the diagram above, PQ is parallel to RS. What is  the value of α + β + y? 

1. 1800 B. 900
2. 2000 D. 3600
3. Whicch of the following is the graph of sinθ for –π ≤ ο ≤ 3π

2 2 

1 

30. Find the value of p, if the line of which passes through  (-1, -p) and (-2, 2) is parallel to the line 2y + 8x – 17 = 0. 
31. –2/7 B. 7/6 
32. –6/7 D. 6/7 
33. Find the equation of the locus of a pointP(x, y) which  is equidistant form Q(0,0) and R(2, 1). 
34. 2x + y = 5 B. 2x + 2y = 5 C. 4x + 2y = 5 D. 4x – 2y = 5 
35. 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 
36. 66cm B. 44cm 
37. 22cm D. 11cm 
38. A trapezium has two parallel sides of length 5cm and  9cm. If the area is 121cm2, find the distance between  the parallel sides. 
39. 7cm B. 3cm 
40. 4cm D. 6cm 

45O Z 

34.  

1 

1. B. 
   

0 

2 

1 

1 

0 

3 

2 2 3 

0 

2 12 

1 

03 

3  2 

X7 cm 

Y 

XYZ is a circle centre O and radius 7cm. Find the  area of the shaded region. 

2 12 

Q 

40O 

2 

R 

O 

2 1 2 2 

1. 14cm2 B. 38cm2
2. 77cm2 D. 84cm2
3. 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) 
   

P S 

In the diagram above, PQR is a straight line and PS is  a tangent to the circle QRS with /PS/ = ∠/SR/ and  

36. Evaluate 3(x2 – 2x)dx 

2 

1. 4/3 B. 1/3 C. 2 D. 4 

If y = 3 sin (-4x), dy/ dx is 

SPR = 400. find ∠PSQ. 37. A. 200 B. 100 

1. 400 D. 300
2. -12 cos (-4x) B. 12 sin (-4x) C. 12x cos (4x) D. –12x cos (-4x)
3. If π/ ≤ 2π, find the maximum value of f(θ) = 4/6 + 2  2 

cos θ 

1. 1 B. ½ 
2. 4 D. 2/3 
3. Determine the maximum value of  y = 3x2 + 5x – 3 at 
4. 6 B. 0 C. 2. D. 4 
5. Find the slope of the curve  y = 2x2+ 5x – 3 at (1, 4). 
   
6. 7 B. 9 A. #48.00 B. #96.00 C. 4 D. 6 C. #42.00 D. #84.00 
7. 45. The range of 4, 3, 11, 9, 6, 15, 19, 23, 27, 24, 21 and 16 is 
8. 23 B. 24 
9. 21 D. 16 
   

The histogram above shows the ages of the victims of  a pollution. How many people were involved in the  pollution? 

1. 18 B. 21 
2. 15 D. 20 

Number 1	2	3 4	5	6
Frequency 12	20	x 21	x -1	28

 

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 nP – 6 (nC ) = 0, find the value of n 
    
48. 4

3 

4 

 

1	2	3
2	2	1 B. D.

 

Find the mean of the distribution above. Value 0 4 

1. 6 B. 5 C. 8 D. 7 
   
2. 4 3 A. ½ B. 1/3 
   

Frequency 1 9 

48. Two dice are thrown. What is the probability that the  
    
49. 1 2 C. ¼ D. 2/3 sum of the numbers is divisible by 3. 
    
50. The mean of the numbers 3, 6, 4, x and 7 is 5. find  the standard deviation 
51. 2 B. 3 
52. Find the number of committees of three that can be formed  consisting of two men and one woman from four men  and three women. 
    
53. √3 D. √2 A. 24 B. 18 C. 3 D. 6 
54. A bag 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? 

50. By how much is the mean of 30, 56, 31, 55, 43 and  44 less than the median. 
    
51. 5/14 B. 13/28 A. 0.50 B. 0.75 C. 3/14 D. 15/28 C. 0.17 D. 0.33
52. On a pie chart, there are four sectors of which three angles  

are 450, 900and 1350. if the smallest sector represents  

#28.00, how much is the largest sector? 

Mathematics 2004 

A / 

1. (0,0)and(1,1) D. (√2,√2)only 225 
2. 19/ 60 
3. 7/ 

12 

1 4 2 4 3 

1. 19/ 35 
   

_ 

1 3 x 4 

y 3 4 4 

Find x and y respectively in the subtraction above c  arried out in base 5 

1. 2, 4 B. 3, 2 
2. 4, 2 D. 4, 3 
3. 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? 
4. 1:500 B. 1:5000 
5. 1:25000 D. 1:250000 
6. 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? 
   
7. Find p, if 4516– p7 = 3056 A. 11/ B. 12/ 

25 25 

1. 6117 B. 1427C. 13/ D. 8/ 
   
2. 1167 D. 627

25 15 

3. 1/ x 2/ + 1/ 6. Given that 3√42x, find the value of x 
   

10 3 

4 

1. 2 B. 3 
   

1/ ÷3/ –¼ C. 4 D. 6 2 5 

7. Simplify 1/√3 + 2 in the form a + b√3  A. -2 – 3 B. –2+ 3 
8. 2- 3 D. 2+ 3 
9. If 6log 2 – 3log 3 = 3log 0.2, find x. 

x x 5 

1. 3/8 B. ¾ 
2. 4/3 D. 8/3 

P Q 

R 

The shaded region in the venn diagram above 

1. Pc ∩(QR)B. P∩Q 
2. Pc U(Q∩R) D. Pc∩ (QUR) 
3. In a class of 40 students, each student offers at least  

y 

x 

The shaded area in the diagram above is represented  by 

1. {(x, y) : y + 3x < 6} 
2. {(x, y) : y + 3x < – 6} 
3. {(x, y) : y – 3x < 6} 
4. {(x, y) : y – 3x < – 6} 
5. What are the integral values of x which satisfy the  inequality –1 < 3 – 2x ≤ 5? 
6. -2, 1, 0, -1 B. -1, 0, 1, 2 
7. -1, 0, 1, D. 0, 1, 2 
8. The nth terms of two sequences are Q – 3.2n-2and n 

one of Physics and Chemistry. If the number ofU = 3.22m – 

. find the product of Q2 and U2 

3 

m 

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. 

1. 25 B. 15 
2. 10 D. 5 
3. Find the values of x where the curve 

y = x3 + 2x2 – 5x – 6 crosses the x-axis. 

1. -2, -1 and 3 B. -2, 1 and –3 C. 2, -1 and –3 D. 2, 1 and 3 
2. Find the remainder when 

3x3 + 5x2 – 11x + is divided by x + 3 

1. 4 B. 1 
2. –1 D. 4 
3. Factorize completely ac – 2bc – a2 + 4b2 A. (a – 2b)(c + a – 2b) 
4. (a – 2b)(c – a – 2b) 
5. (a – 2b)(c + a + 2b) 
6. (a – 2b)(c – a + 2b) 
7. y is inversely proportional to x and y = 4 when x = 1/  2 . find x when y = 10 
8. 1/10 B. 1/5 
9. 2 D. 10 
10. 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. 
11. 36cm B. 96ccm 
12. 144cm D. 324cm 
13. 3 B. 6 
14. 12 D. 18 
15. 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. 
16. 8 B. 27 
17. 48 D. 78
18. Find the sum to infinity of the series ½, 1/6, 1/  18,…………… 
19. 1 B. ¾ 
20. 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). 
22. 16 B. 8 
23. 4 D. 3 
24. The inverse ofthe matrix (2 1) 

(1 1) 

is 

1. (1 1) B. (1 -1) 

(-1 2) (1 2) 

1. (1 1) D. (1 -1) 

(1 2) (-1 2) 

23. If P = 1 0 -1 

3 4 5 

-1 0 1 then /P/ is 

1. -8 B. 0 
2. 4 D. 8 
3. The sum of the interior angles of a pentagon is 6x +  6y. find y in terms of x 
   
4. y = 60 – x B. y = 90 – x A. (4, -4) B. (4, 4) C. y = 120 – x D. y = 150 – x C. (2, 2) D. (1,1) 
   
5. PQRSTV is a regular polygon of side 7cm inscribed in  

a circle. Find the circumference of the circle PQRSTV. A. 22cm B. 42cm 

1. 44cm D. 56cm 

15 cm X 45O60O

20O 

35O 

Find the value of x in the figure above. 

1. 20√6 B. 15√6 
2. 5√6 D. 3√6 
3. The shadow of a pole 5√3 m high is 5m. find the  

angle of elevation of the sun. 

1. 300 B. 450
   

P, R and S lie on a circle centre O as shown above 

while Q lies outside the circle. Find ÐPSO.C. 600 D. 750 A. 350 B. 40035. Find the derivative of (2 + 3x)(1 – x) with respect to

4504 cm D.

550x 

1. 6x – 1 B. 1 – 6x 
2. 6 D. 3 
3. Find the derivative of the function  

y = 2x2(2x – 1) at the point x= -1 

1. -6 B. 4 
2. 16 D. 18 

In the diagram above, PQ =4cm and TS = 6cm, if the  

37. If y – 3 cos (x/ ), find dy/ 

when x = 3π/ 

area of parallelogram PQTU is 32cm2, find the area 

A.2 

3 dx 2 B.1 

of the trapezium PQRU 

1. 24cm2 B. 48cm2
2. 60cm2 D. 72cm2
3. An arc of a circle of length 22cm subtends an angle  of 3x0at the centre of the circle. Find the value of x  if the diameter of the circle is14cm. 

which is equidistant from PQ and QR 

1. Thediagonal PR. B. ThediagonalQS C. Side SR 
2. –1 D. 3 
3. What is the rate of change of the volume v of  hemisphere with respect to its radius r when r = 2?  A. 2π B. 4π 
4. 8π D. 16π 
   
6. TheperpendicularbisectorofPQ. 
7. 62/ 
8. 2/ 
   
9. 300 B. 600 C. 1200 D. 1800
10. –2/ 

3 3 D. -62/ 

3 3 

39. Evaluate 3(x2– 1) dx 
    

Determine the locus of a point i 

1 

nside a square PQRS 

h 60O 

30. The locus of a point which is 5cm from the line LM  is a 
31. pair of lines on opposite sides of LM and  parallel to it, each distances 5cm form LM 

M 

150O 

l 

1. line parallel to LM and 5cm from LM C. pair of parallel lines on one side of LM and  parallel to LM 
2. line distance 10cm from LM and  

parallel to LM. 

31. Find the value of α2 + β2 if a + b = and the distance  between the points (1, α) ands (β, 1) is 3 units. A. 3 B. 5 
32. 11 D. 14 
33. Find the midpoint of the line joining P(-3, 5) and Q  (5, -3). 

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? 

1. 9000 tonnes B. 6000 tonnes C. 1500 tonnes D. 1200 tonnes 
2. I. Rectangular bars of equal width 
3. The height of each rectangular bar  

is proportional to the frequency of 

the3 corresponding class interval. 

III. Rectangular bars have common 

sides with no gaps in between. 

A histogram is described by 

1. I and II B. I and III 
2. I,II and III D. II and III® 

The graph above shows the cumulative frequency  curve of the distribution of marks in a class test. What  percentage of the students scored more than 20  marks? 

1. 68% B. 28% 
2. 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. 
3. 20 ways D. 25 ways. 
4. 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? 
5. 924 ways B. 840 ways 
6. 462 ways D. 378 ways 
7. 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? 
   
8. 17% D. 8% A. 32 B. 28 
   
9. The mean 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. 
10. 7 B. 9 
11. 15 D. 42 
12. The weights of 10 pupils in a class are 15kg, 16kg,  17kg, 18kg, 16kg, 17kg, 17kg, 17kg, 18kg and 16kg. 
13. 21 D. 12
14. An unbiased die is rolled 100 times and the outcome  is tabulated as follows: 

5	5	5	7	8

 

What is the probability of obtaining 5? 

What is the range of this distribution? A. 1 B. 2 A. 1 

1. / B. 1/ 

6 5 

1. 3 D. 4 
2. Find the mean deviation of 1, 2, 3 and 4 A. 1.0 B. 1.5 C. 2.0 D. 2.5 

¼ D. ½ 

50. A container has 30 gold medals, 22 silver medals and  18 bronze medals. If one medal is selected at random  from the container, what is the probability that it is  not a gold medal? 
51. 4/ B. 3/ 
    

7 

7 

1. 11/ D. 9/ 
   

35 

35