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1.

Convert 726 to a number in base three. 

.
A.

2211

B.

2121

C.

1212

D.

1122


2.

Convert 2710 to another number in base three.

.
A.

10103

B.

11003

C.

10003

D.

10013


3.
3 girls share a number of apples in the ratio 5:3:2. If the highest share is 40 apples, find the smallest share.
.
A. 24
B. 16
C. 38
D. 36

4.

Evaluate 1.25 × 0.0250.05, correct to 1 decimal place.

.
A.

6.2

B.

6.3

C.

0.5

D.

0.6


5.

Calculate the time taken for N3,000 to earn N600 if invested at 8% simple interest.

.
A.

3 years

B.

312 years

C.

112 years

D.

212 years.


6.

Simplify 3-n91-n× 27n+1

.
A.

33

B.

35

C.

3

D.

32


7.

If log 104 = 0.6021, evaluate log10 412

.
A.

0.9021

B.

1.8063

C.

0.2007

D.

0.3011


8.

Simplify 5147-1215

.
A.

1/5

B.

1/9

C.

9

D.

5


9.

P, Q and R are subsets of the universal set U. The venn diagram showing the relationship (P Q) R is

.
A. a-image

.

B. b-image

.

C. c-image

.

D. d-image

.


10.

If P = { x : x is odd, -1 < x ≤ 20 } and Q = { y : y is prime, -2 < y ≤ 25 }, find P Q

.
A.

{3,5,11,13,17,19}

B.

{3,5,7,11,13,17,19}

C.

{2,3,5,7,11,13,17,19}

D.

{3,5,7,11,17,19}


11.

If S = t2-4t+4, find t in terms of S.

.
A.

S + 2

B.

S – 2

C.

S2 + 2

D.

S2 – 2


12.

if x – 4 is a factor of x2 – x – k, then k is

.
A.

12

B.

20

C.

2

D.

4


13.

The remainder when 6p2 - p2 - 47p + 30 is divided by p – 3 is

.
A.

42

B.

63

C.

18

D.

21


14.

P varies jointly as m and u, and varies inversely as q. Given that p=4, m=3 and u= 2 when q = 1, find the value of p when m = 6, u = 4 and q =  3/5.

.
A.

15

B.

10

C.

200/5

D.

120/5


15.

If r varies inversely as the square root of s and t, how does s vary with r and t?

.
A.

s varies inversely as r2 and t.

B.

s varies directly as r2 and t2 .

C.

s varies directly as r and t.

D.

s varies inversely as r and t2 .


16.
Evaluate 3(x + 2) > 6(x + 3)
.
A. x > −4
B. x < −4
C. x > 4
D. x < 4

17. q-image

The graph above is correctly represented by

.
A.

y = x2 – 3x + 2

B.

y = x2 – x – 1

C.

y = x2 + x – 2

D.

y = x2 – x – 2


18.

Solve for x: [x - 2] < 3

.
A.

−2 < x < 3

B.

−1 < x < 5

C.

x < 1

D.

x < 5


19.
If the sum of the first two terms of a G. P is 3, and the sum of the second and the third terms is −6, find the sum of the first term and the common ratio.
.
A. −3
B. −5
C. 5
D. −2

20.

The nth term of the progression 42,73,104,135... is

.
A.

3n+1n+1

B.

3n+1n-1

C.

3n-1n+1

D.

1-3nn+1


21.

If a binary operation ∗ is defined by x * y = x + 2y , find 2 * (3 * 4)

.
A.

16

B.

14

C.

26

D.

24


22.

If P = 5321 and Q = 4235, find 2P + Q.

.
A.

14877

B.

77814

C.

81477

D.

77148


23.

Find the inverse of 5364

.
A.

2-32-352

B.

232-3-52

C.

232-352

D.

2-32-3-52


24. q-image

In the diagram above, find the value of x.

.
A.

40º

B.

45º

C.

15º

D.

30º


25. q-image

The value of x in the figure above is

.
A.

100º

B.

70º

C.

130º

D.

110º


26.

If the angles of a quadrilateral are (3y + 10)º , (2y + 30)º , (y + 20)º and 4yº , find the value of y.

.
A.

42º

B.

66º

C.

12º

D.

30º


27.

A square tile has side 30cm. How many of these tiles will cover a rectangular floor of length 7.2m and width 4.2m?

.
A.

576

B.

720

C.

336

D.

420


28.

Find the length of a chord which subtends an angle 90º at the centre whose radius is 8cm.

.
A.

82cm

B.

83cm

C.

4 cm

D.

8 cm


29.

A chord of a circle subtends an angle 120º at the centre of a circle of diameter 43cm. Calculate the area of the major sector.

.
A.

16π cm2

B.

32π cm2

C.

4π cm2

D.

8π cm2


30.
The locus of the points which is equidistant from the line PQ forms a
.
A. pair of parallel lines to PQ
B. perpendicular line to PQ
C. circle centre P
D. circle centre Q.

31.

If the mid-point of the line PQ is (2, 3) and the point P is (−2, 1), find the coordinate of the point Q.

.
A.

(6, 3)

B.

(8, 6)

C.

(5, 6)

D.

(0, 4)


32.
Find the equation of the perpendicular bisector of the line joining P(2, −3) to Q(−5, 1).
.
A. 8y + 14x – 13 = 0
B. 8y + 14x + 13 = 0
C. 8y – 14x + 13 = 0
D. 8y – 14x – 13 = 0

33.

In triangle PQR, q = 8 cm, r = 6 cm and cos P =112 . Calculate the value of p.

.
A.

10 cm

B.

108cm

C.

9 cm

D.

92cm


34.

If tanθ = 34, find the value of sin θ + cos θ.

.
A.

125

B.

113

C.

123

D.

135


35.

If y = (2x + 2)3 , find dydx

.
A.

6(2x + 2)

B.

3(2x + 2)

C.

6(2x + 2)2

D.

3(2x + 2)2


36.

If y = x sin x, find dydx

.
A.

cos x – x sin x

B.

cos x + x sin x

C.

sin x + x sin x

D.

sin x – cos x.


37.

The radius of a circle is increasing at the rate of 0.02 cms-1 . Find the rate at which the area is increasing when the radius of the circle is 7cm.

.
A.

0.53 cm-2s-1

B.

0.35 cm-2s-1

C.

0.88 cm-2s-1

D.

0.75 cm-2s-1


38.

Integrate 1+xx3 dx

.
A.

x2-1x+k

B.

2x2-1x+k

C.

-12x2-1x+k

D.

-x22-1x+k


39.

Evaluate 0π2sin x dx

.
A.

−1

B.

−2

C.

2

D.

1


40. q-image

The bar chart above shows the allotment of time (in minutes) per week for selected subjects in a certain school. What is the total time allocated to the six subjects per week?

.
A.

720 mins.

B.

960 mins.

C.

200 mins.

D.

460 mins.


41. q-image

The pie chart above shows the statistical distribution of 80 students in five subjects in an examination. Calculate how many students offer Mathematics.

.
A.

40

B.

50

C.

12

D.

30


42.
Find the mean of t + 2, 2t – 4, 3t + 2 and 2t.
.
A. 2t
B. 2t + 1
C. t
D. t + 1

43.
The mean of seven numbers is 10. If six of the numbers are 2, 4, 8, 14, 16 and 18, find the mode.
.
A. 8
B. 14
C. 2
D. 6

44.
Age 20 25 30 35 40 45
No. of people 3 5 1 1 2 3

Calculate the median age of the frequency distribution in the table above.

.
A.

30

B.

35

C.

20

D.

25


45.

If the variance of 3 + x, 6, 4, x and 7 – x is 4 and the mean is 5, find the standard deviation.

.
A.

2

B.

3

C.

2

D.

3


46.
Score 3 4 5 6 7 8 9 10
Freq. 1 0 7 5 2 3 1 1

The table above shows the scores of 20 students in Further Mathematics test. What is the range of the distribution?

.
A.

6

B.

3

C.

10

D.

7


47.
In how many ways can a student select 2 subjects from 5 subjects?
.
A.

5!2!2!

B.

5!2!3!

C.

5!2!

D.

5!3!


48.

In how many ways can 3 seats be occupied if 5 people are willing to sit?

.
A.

20

B.

5

C.

120

D.

60


49.

What is the probability that an integer x (1 ≤ x ≤ 25) chosen at random is divisible by both 2 and 3?

.
A.

15

B.

125

C.

34

D.

125


50.

A basket contains 9 apples, 8 bananas and 7 oranges. A fruit is picked from the basket, find the probability that it is neither an apple nor an orange.

.
A.

18

B.

724

C.

23

D.

38


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