2011 Mathematics Jamb Past Questions CBT

1. Question

If 2q3₅ = 77₈, find q

4
0
1
2

2. Question

Simplify $ \normalsize \frac{3\frac{2}{3} \times \frac{5}{6} \times \frac{2}{3}}{\frac{11}{15} \times \frac{3}{4} \times \frac{2}{27}} $

$ \scriptsize 5 \frac{2}{3}$
30
$ \scriptsize 4 \frac{1}{3}$
50

3. Question

A man invested ₦5,000 for 9 months at 4%. What is the simple interest?

₦ 150
₦ 220
₦ 130
₦ 250

4. Question

If the numbers M, N, Q are in the ratio 5 : 4 : 3, find the value of $ \frac{2N\: – \:Q}{M}$

2
3
1
4

5. Question

Simplify $\; (\frac{16}{81})^{\frac{1}{4}} \div (\frac{9}{16})^{-\frac{1}{2}}$

$ \frac{2}{3}$
$ \frac{1}{2}$
$ \frac{8}{9}$
$ \frac{1}{3}$

6. Question

If log₃18 + log₃3 – log₃x = 3, Find x.

1
2
0
3

7. Question

Rationalize $\frac{2\: -\: \sqrt5}{3\: -\: \sqrt5}$

$ \frac{1 \: – \: \sqrt5}{2} $
$ \frac{1 \: – \: \sqrt5}{4} $
$ \frac{\sqrt5\: – \: 1}{4} $
$ \frac{1 \: + \: \sqrt5}{4} $

8. Question

Simplify $ \left(\scriptsize\sqrt{2} \:+\: \normalsize\frac{1}{\sqrt{3}})(\scriptsize\sqrt{2} \:- \:\normalsize \frac{1}{\sqrt{3}}\right)$

$ \frac{7}{3} $
$ \frac{5}{3} $
$ \frac{5}{2} $
$ \frac{3}{2} $

9. Question

From the Venn diagram above, the complement of the set P $\cap$ Q is given by

{a, b, d, e}
{b, d}
{a, e}
{c}

10. Question

Raial has 7 different posters to be hanged in her bedroom, living room and kitchen. Assuming she has plans to place at least a poster in each of the 3 rooms, how many choices does she have?

49
170
21
210

11. Question

Make R the subject of the formula if T = $\frac {KR^2 \: + \: M}{3}$

$ \sqrt{\frac{3T\:- \:K}{M}}$
$ \sqrt{\frac{3T\: +\: K}{M}}$
$ \sqrt{\frac{3T\:-\: M}{K}}$
$ \sqrt{\frac{3T\:-\: K}{M}}$

12. Question

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

2x – 1
x + 3
2x + 1
x – 3

13. Question

Factorize completely 9y² – 16x²

(3y – 2x)(3y + 4x)
(3y + 4x)(3y + 4x)
(3y + 2x)(3y – 4x)
(3y – 4x)(3y + 4x)

14. Question

Solve for x and y respectively in the simultaneous equations

-2x – 5y = 3
x + 3y = 0

-3, -9
9, -3
-9, 3
3, -9

15. Question

If x varies directly as square root of y and x = 81 when y = 9, Find x when y = $\scriptsize 1 \frac{7}{9}$

$\scriptsize 20 \frac{1}{4}$
27
$\scriptsize 2 \frac{1}{4}$
36

16. Question

T varies inversely as the cube of R. When R = 3, T = $ \frac{2}{81}$

Find T when R = 2

$ \frac{1}{18} $
$ \frac{1}{12} $
$ \frac{1}{24} $
$ \frac{1}{6} $

17. Question

Which of the following diagrams represents the solution of the inequalities:

y ≤ x − 2 and y ≥ x²− 4?

A
B
C
D

18. Question

Solve the Inequalities $- 6 (x + 3) \leq 4 (x - 2)$

x ≤ 2
x ≥ -1
x ≥ -2
x ≤ -1

19. Question

Solve the inequalities x²+ 2x > 15

x < -3 or x > 5
-5 < x < 3
x < 3 or x > 5
x > 3 or x < -5

20. Question

Find the sum of the first 18 terms of the series 3, 6, 9,…, 36

505
513
433
635

21. Question

The second term of a geometric series is 4 while the fourth term is 16.

Find the sum of the first five terms

60
62
54
64

22. Question

A binary operation ⊕ on real numbers is defined by x ⊕ y = xy + x + y for two real numbers x and y. Find the value of $ \scriptsize 3 \:\oplus \:- \normalsize \frac{2}{3} $

$ – \frac{1}{2} $
$ \frac{1}{3} $
-1
2

23. Question

If $\scriptsize \begin{vmatrix} 2 & 3 \\ 5 & 3x \end{vmatrix} = \begin{vmatrix} 4 & 1 \\ 3 & 2x \end{vmatrix} $

find the value of x.

-6
6
-12
12

24. Question

Evaluate $\scriptsize \begin{vmatrix} 4 & 2 & -1 \\ 2 & 3 & -1 \\ -1 & 1 & 3 \end{vmatrix} $

25
45
15
55

25. Question

The inverse of matrix N = $ \scriptsize \begin{vmatrix} 2 & 3 \\
1 & 4\end{vmatrix} $ is

$ \normalsize \frac{1}{5} \scriptsize \begin{vmatrix} 2 & 1 \\ 3 & 4\end{vmatrix}$
$ \normalsize \frac{1}{5} \scriptsize\begin{vmatrix} 4 & -3 \\ -1 & 2\end{vmatrix}$
$ \normalsize \frac{1}{5} \scriptsize \begin{vmatrix} 2 & -1 \\ -3 & 4\end{vmatrix}$
$ \normalsize \frac{1}{5} \scriptsize\begin{vmatrix} 4 & 3 \\ 1 & 2\end{vmatrix}$

26. Question

What is the size of each interior angle of a 12-sided regular polygon?

30º
150º
180º
120º

27. Question

A circle of perimeter 28 cm is opened to form a square. What is the maximum possible area of the square?

56 cm²
49 cm²
98 cm²
28 cm²

28. Question

A chord of circle of radius 7cm is 5cm from the centre of the circle. What is the length of the chord?

$ \scriptsize 4 \sqrt{6} \: cm $
$ \scriptsize 3 \sqrt{6} \: cm $
$ \scriptsize 6 \sqrt{6} \: cm $
$ \scriptsize 2 \sqrt{6} \: cm $

29. Question

A solid metal cube of side 3 cm is placed in a rectangular tank of dimensions 3, 4 and 5 cm. What volume of water can the tank now hold

48 cm³
33 cm³
60 cm³
27 cm³

30. Question

The perpendicular bisector of a line XY is the locus of a point

whose distance from X is always twice its distance from Y
whose distance from Y is always twice its distance from X
which moves on the line XY
which is equidistant from the points X and Y

31. Question

The midpoint of P(x, y) and Q(8, 6) is (5, 8). Find x and y

(2, 10)
(2, 8)
(2, 12)
(2, 6)

32. Question

Find the equation of a line perpendicular to line 2y = 5x + 4 which passes through (4, 2).

5y – 2x -18 = 0
5y + 2x – 18 = 0
5y – 2x + 18 = 0
5y + 2x – 2 = 0

33. Question

In a right-angled triangle, if tan θ = ³/₄

What is cos θ – sin θ?

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

34. Question

A man walks 100 m due West from a point X to Y, he then walks 100 m due North to a point Z. Find the bearing of X from Z

195º
135º
225º
45º

35. Question

The derivative of (2x + 1)(3x + 1) is

12x + 1
6x + 5
6x + 1
12x + 5

36. Question

Find the value of x at the minimum point of the curve y = x³ + x² – x + 1

$ \frac{1}{3} $
$- \frac{1}{3} $
1
-1

37. Question

Find the derivative of $ \frac{sin\: \theta}{cos \: \theta} $

sec² θ
tan θ cosec θ
cosec θ sec θ
cosec² θ

38. Question

Evaluate $ \scriptsize \int^{1}_{0} (3 \: -\: 2x)dx $

3
5
2
6

39. Question

Find $ \scriptsize \int cos\:4x\:dx$

$ \frac{3}{4} \scriptsize sin\:4x\: +\:k $
$ -\frac{1}{4} \scriptsize sin\:4x\: +\:k $
$ -\frac{3}{4} \scriptsize sin\:4x\: +\:k $
$ \frac{1}{4} \scriptsize sin\:4x\: +\:k $

40. Question

The pie chart shows the distribution of courses offered by students. What percentage of students offer English?

30%
25%
35%
20%

41. Question

The bar chart above shows the distribution of SS2 students in a school.

Find the total number of students

180
135
210
105

42. Question

The sum of four consecutive integers is 34. Find the least of these numbers

7
6
8
5

43. Question

$\scriptsize \begin{array}{c|c} No & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline Frequency & 1 & 4 & 3 & 8 & 2 & 5 \end{array} $

From the table above, find the median and range of the data respectively

(8, 5)
(3, 5)
(5, 8)
(5, 3)

44. Question

$\scriptsize \begin{array}{c|c} Class \:interval & 0-2 & 3-5 & 6-8 & 9-11 \\ \hline Frequency & 3 & 2 & 5 & 3 \end{array} $

Find the mode of the above distribution.

9
8
10
7

45. Question

$ \scriptsize \begin{array}{c|c}
Class Interval & 3 – 5 & 6 – 8 & 9 – 11 \\ \hline Frequency & 2 & 2 & 2 \end{array}$

Find the standard deviation of the above distribution

$ \scriptsize \sqrt{5} $
$ \scriptsize \sqrt{6} $
$ \scriptsize \sqrt{7} $
$ \scriptsize \sqrt{2} $

46. Question

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

6!
7!
5!
8!

47. Question

In how many ways can five people sit round a circular table?

24
60
12
120

48. Question

Find the probability that a number picked at random from the set(43, 44, 45, …, 60) is a prime number

$ \frac{2}{3} $
$ \frac{1}{3} $
$ \frac{2}{9} $
$ \frac{7}{9} $

49. Question

In a class of 60 students, 30 offer Physics and 40 offer Chemistry. If a student is picked at random from the class, what is the probability that the student offers both Physics and Chemistry?

$ \frac{1}{6} $
$ \frac{1}{4} $
$ \frac{1}{2} $
$ \frac{1}{3} $

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