2012 Mathematics Jamb Past Questions CBT

1. Question

Convert 72₆ to a number in base three

2211
2121
1212
1122

2. Question

Simplify $ \frac{2\frac{2}{3} \: \times \: 1 \frac{1}{2}}{4 \frac{4}{5}} $

$ \scriptsize 1 \frac{1}{4} $
$ \scriptsize 1 \frac{1}{6} $
$ \frac{5}{6} $
$ \frac{4}{5} $

3. Question

A man earns ₦3,500 per month out of which he spends 15% on his children’s education If he spends an additional ₦1,950 on food, how much does he have left?

₦525
₦1025
₦1950
₦2975

4. Question

If $ \scriptsize 27^{x\:+\:2} \: \div\: 9^{x\:+\:1} = 3^{2x} $

find x

3
4
5
6

5. Question

If $ \scriptsize \log_3x^2 = \: 8 $

What is x

$ \frac{1}{3} $
$ \frac{1}{9} $
$ \frac{1}{27} $
$ \frac{1}{81} $

6. Question

Simplify $ \scriptsize \left(\sqrt{6} \: +\: 2 \right)^2 \: -\: \left(\sqrt{6} \: -\: 2 \right)^2 $

$ \scriptsize 2 \sqrt{6} $
$ \scriptsize 4 \sqrt{6} $
$ \scriptsize 8 \sqrt{6} $
$ \scriptsize16 \sqrt{6} $

7. Question

If P is a set of all prime factors of 30 and Q is a set of all factors of 10 less than 10, find P $\cap$ Q.

{3}
{2,3}
{2,3,5}
{1,2}

8. Question

In a class of 46 students, 22 play football and 26 play volleyball. If 3 students play both games how many play neither?

1
2
3
4

9. Question

Make n the subject of the formula if w = $ \frac {v(2 \: + \: cn)}{1 \: – \: cn} $

$ \frac{1}{c} \left( \frac{w \; – \; 2v}{v \; + \; w} \right) $
$ \frac{1}{c} \left( \frac{w \; – \; 2v}{v \; – \; w} \right) $
$ \frac{1}{c} \left( \frac{w \; + \; 2v}{v \; – \; w} \right) $
$ \frac {1}{c} \left( \frac{w \; + \; 2v}{v \; + \; w} \right) $

10. Question

Find the remainder when 2x³ – 11x² + 8x – 1 is divided by x + 3

-871
-781
-187
-178

11. Question

Solve for x and y in the equations below

x² – y² = 4
x + y = 2

x = 0, y = -2
x = 0, y = 2
x = 2, y = 0
x = -2, y = 0

12. Question

If y varies directly as $ \scriptsize \sqrt{n}$ and y = 4 when n = 4.

Find y when n = $ \scriptsize 1 \frac{7}{9} $

$ \scriptsize \sqrt{17} $
$ \frac{2}{3} $
$ \frac{8}{3} $
$ \frac{4}{3} $

13. Question

U is inversely proportional to the cube of V and U = 81 when V = 2.

Find U when V = 3.

24
27
32
36

14. Question

The value of y for which $ \normalsize \frac{1}{5} \scriptsize y \: + \: \normalsize\frac{1}{5} \: < \: \frac{1}{2}\scriptsize y \: +\: \normalsize \frac{2}{5} $

y > ²/₃
y < ²/₃
y > – ²/₃
y < - ²/₃

15. Question

Find the range of values of m which satisfy (m – 3)(m – 4) < 0

2 < m < 5
-3 < m < 4
3 < m < 4
-4 < m < 3

16. Question

The shaded region above is represented by the equation

y ≤ 4x+2
y ≥ 4x+2
y ≤ -4x+4
y ≤ 4x+4

17. Question

The nth term of a sequence is n²– 6n – 4. Find the sum of the 3rd and 4th terms.

24
23
-24
-25

18. Question

The sum to infinity of a geometric progression is – ¹/₁₀ and the first term is – ¹/₈

Find the common ratio of the progression.

$ – \frac{1}{5} $
$ – \frac{1}{4} $
$ – \frac{1}{3} $
$ – \frac{1}{2} $

19. Question

The binary operation * is defined on the set of integers such that p*q = pq + p – q. Find 2*(3*4).

11
13
15
22

20. Question

The binary operation on the set of real numbers is defined by m*n = ^mn/₂ for all m, n ∈ R.

If the identity element is 2, find the inverse of -5

$ -\frac{4}{5}$
$ -\frac{2}{5}$
4
5

21. Question

If $ \scriptsize \begin{vmatrix} 5 & 3 \\ x & 2 \end{vmatrix} $

Find the value of x

3
4
5
7

22. Question

Given that I₃ is a unit matrix of order 3, find |I₃|⎸

-1
0
1
2

23. Question

In the diagram above. QR//TU, ∠PQR = 80°and ∠PSU = 95°. Calculate ∠SUT.

15°
25°
30°
80°

24. Question

The angles of a polygon are given by x, 2x, 3x and 5x respectively. Find the value of x.

24
30°
33°
36°

25. Question

In the diagram above, PQR is a circle centre O. If ∠QPR is x°, find ∠QRP.

x°
(90 – x)°
(90 + x)°
(180-x)°

26. Question

Find the area of the trapezium above.

91 cm ²
78 cm²
60 cm²
19 cm²

27. Question

A circular arc subtends angle 150° at the centre of a circle of radius 12 cm. Calculate the area of the sector of the arc.

30 π cm²
60 π cm²
120 π cm²
150 π cm²

28. Question

Calculate the volume of a cuboid of length 0.76 cm, breadth 2.6 cm and height 0.82 cm.

3.92 cm³
2.13 cm³
1.97 cm³
1.62 cm³

29. Question

The locus of a point equidistant from the intersection of lines 3x – 7y + 7 = 0 and 4x – 6y +1 = 0 is a

line parallel to 7x + 13y + 8 = 0
circle
semicircle
bisector of the line 7x + 13y + 8 = 0

30. Question

The gradient of the straight line joining the points P(5, -7) and Q(-2, -3) is

$ \frac{1}{2} $
$ \frac{2}{5} $
$- \frac{4}{7} $
$- \frac{2}{3} $

31. Question

The distance between the points (4, 3) and the intersection of y =2x + 4 and y = 7 – x is

$ \scriptsize \sqrt{13} $
$ \scriptsize 3\sqrt{2} $
$ \scriptsize \sqrt{26} $
$ \scriptsize 10 \sqrt{5} $

32. Question

Find the equation of the line through the points (-2, 1) and $ \left(- \frac{1}{2}\scriptsize, \: 4\right) $

y = 2x – 3
y = 2x + 5
y = 3x – 2
y = 2x + 1

33. Question

If angle θ is 135°, evaluate cos θ.

$ \frac{1}{2} $
$ \frac{\sqrt{2}}{2} $
$- \frac{\sqrt{2}}{2} $
$- \frac{1}{2} $

34. Question

A man stands on a tree 150 cm high and sees a boat at an angle of depression of 74°. Find the distance of the boat from the base of the tree.

52 cm
43 cm
40 cm
15 cm

35. Question

If y = $ \scriptsize x^2 \: -\: \normalsize \frac{1}{x}$

Find $ \frac{dy}{dx} $

$ \scriptsize2 x \: -\: \normalsize \frac{1}{x^2}$
2x + x²
2x – x²
$ \scriptsize2 x \: + \: \normalsize \frac{1}{x^2}$

36. Question

Find $ \frac{dy}{dx} $

If y = cos x

sin x
–sin x
tan x
–tan x

37. Question

Evaluate $ \scriptsize \int^2_1(x^2\: -\: 4x)dx $

$\frac{11}{3} $
$\frac{3}{11} $
$- \frac{3}{11} $
$-\frac{11}{3} $

38. Question

Evaluate $\scriptsize \int^{\frac{\pi}{4}}_0 sec^2 \theta d \theta $

1
2
3
4

39. Question

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

12
9
8
7

40. Question

The mean of seven numbers is 96. If an eighth number is added, the mean becomes 112. Find the eighth number.

126
180
216
224

41. Question

Find the median of 2, 3, 7, 3, 4, 5, 8, 9, 9, 4, 5, 3, 4, 2, 4 and 5.

9
8
7
4

42. Question

Find the range of 4, 9, 6, 3, 2, 8, 10 and 11.

11
9
8
4

43. Question

Find the standard deviation of 2, 3, 8, 10 and 12.

3.9
4.9
5.9
6.9

44. Question

Evaluate ⁿ⁺¹C_n-2

If n =15

3630
3360
1120
560

45. Question

In how many ways can the letters of the word TOTALITY be arranged?

6720
6270
6207
6027

46. Question

The probability that a student passes a Physics test is $ \frac{2}{3} $

If he takes three Physics tests, what is the probability that he passes two of the tests?

$ \frac{6}{9} $
$ \frac{2}{27} $
$ \frac{4}{27} $
$ \frac{4}{9} $

47. Question

The probabilities that a man and his wife live for 80 years are ²/₃ and ³/₅ respectively.

Find the probability that at least one of them will live up to 80 years.

$ \frac{2}{15} $
$ \frac{3}{15} $
$ \frac{7}{15} $
$ \frac{13}{15} $

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