JAMB Mathematics past questions and answers pdf for free reading 2024

1. If \( x \) represents the median and \( y \) the mode of the measurements 5, 9, 3, 5, 8, then \( (x, y) \) is:

**(A)** 5,8 **(B)** 6,5 **(C)** 5,5 **(D)** 7,5

2. Olu sold his bicycle to Ade at a profit of 10%. Ade sold it to Ola for #209 at a loss of 5%. How much did the bicycle cost Olu?

**(A)** #200 **(B)** #180 **(C)** #196 **(D)** #410

3. Evaluate \( 212_3 - 121_3 + 222_3 \)

**(A)** 313_3 **(B)** 1000_3 **(C)** 1020_3 **(D)** 1222_3

4. 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?

**(A)** 6:5 **(B)** 25:24 **(C)** 5:6 **(D)** 24:25

5. If \( \log_{10} 2 = 0.3010 \) and \( \log_{10} 3 = 0.4771 \), evaluate without using logarithm tables \( \log_{10} 4.5 \)

**(A)** 0.9542 **(B)** 0.6532 **(C)** 0.4771 **(D)** 0.3010

6. Four interior angles of a pentagon are \( (90 - x)^0 \), \( (90 + x)^0 \), \( (110 - 2x)^0 \) and \( (110 + 2x)^0 \), find the fifth interior angle.

**(A)** 110° **(B)** 120° **(C)** 130° **(D)** 140°

7. If \( a:B = 5:8 \) and \( x:y = 25:16 \), evaluate \( \frac{a}{x} \div \frac{b}{y} \)

**(A)** 125:128 **(B)** 3:5 **(C)** 3:4 **(D)** 2:5

8. If -8, \( m \), \( n \), 19 are in arithmetic progression, find \( (m, n) \)

**(A)** 1,10 **(B)** 2,10 **(C)** 3,13 **(D)** 4,16

9. Simplify \( \sqrt{160x^2} + \sqrt{71x^4} + \sqrt{100x^8} \)

**(A)** 9x² **(B)** 12√3x **(C)** 13x **(D)** √13x

10. Rationalize \( \frac{2\sqrt{3} + 3\sqrt{2}}{3\sqrt{2} - 2\sqrt{3}} \)

**(A)** 5 - 2√6 **(B)** 5 + 2√6 **(C)** 5√3 **(D)** 5√6 + 2

11. Find \( n \) if \( 34_n = 1001_{12} \)

**(A)** 5 **(B)** 6 **(C)** 7 **(D)** 8

12. Express \( \frac{5x - 12}{(x - 2)(x - 3)} \) in partial fractions.

**(A)** \( \frac{2}{x+2} - \frac{3}{x-3} \)

**(B)** \( \frac{2}{x-2} + \frac{3}{x-3} \)

**(C)** \( \frac{3}{x-3} - \frac{3}{x-2} \)

**(D)** \( \frac{5}{x-3} + \frac{4}{x-2} \)

13. Two variables \( x \) and \( y \) are such that \( \frac{dy}{dx} = 4x - 3 \) and \( y = 5 \) when \( x = 2 \). Find \( y \) in terms of \( x \).

**(A)** \( 2x^2 - 3x + 5 \)

**(B)** \( 2x^2 - 3x + 2 \)

**(C)** \( 2x^2 - 3x + 3 \)

**(D)** \( 3x^2 - 2x + 3 \)

14. Determine \( x + y \) if

\[

\begin{bmatrix} 2 & -3 \\ -1 & 4 \end{bmatrix}

\begin{bmatrix} x \\ y \end{bmatrix}

=

\begin{bmatrix} -1 \\ 8 \end{bmatrix}

\]

**(A)** 3 **(B)** 4 **(C)** 1 **(D)** 7

15. The angle of elevation of the top of a building from a measuring instrument placed on the ground is 30°. If the...

16. A number is selected at random between 10 and 20, both numbers inclusive. Find the probability that the number is an even number:

**(A)** 5/11 **(B)** 1/2 **(C)** 6/11 **(D)** 4/11

17. The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the progression if its sum to infinity is 8:

**(A)** 8/5 **(B)** 8/3 **(C)** 72/25 **(D)** 25/72

18. A straight line makes an angle of 30° with the positive x-axis and cuts the y-axis at \( y = 5 \). Find the equation of the line:

**(A)** \( \sqrt{3} y = x + 5\sqrt{3} \)

**(B)** \( \sqrt{3} y = -x + 5\sqrt{3} \)

**(C)** \( y = x + 5 \)

**(D)** \( \frac{1}{10} x + 5 \)

19. Evaluate \( \int \sin 3x \, dx \)

**(A)** \( \frac{2}{3} \cos 3x + C \)

**(B)** \( \frac{1}{3} \cos 3x + C \)

**(C)** \( -\frac{1}{3} \cos 3x + C \)

**(D)** \( -\frac{2}{3} \cos 3x + C \)

20. The probability that a student passes any examination is \( \frac{2}{3} \). If the student takes three examinations, what is the probability that he will not pass any of them?

**(A)** 2/3 **(B)** 4/9 **(C)** 8/27 **(D)** 1/27

21. How many three-digit numbers can be formed from 32564 without any digit being repeated?

**(A)** 12 **(B)** 10 **(C)** 120 **(D)** 60

22. Calculate the mean deviation of the set of numbers 7, 3, 14, 9, 7 and 8:

**(A)** 2 1/6 **(B)** 2 1/2 **(C)** 1 1/6 **(D)** 2 1/3

23. In a class of 40 students, 32 offer Mathematics, 24 offer Physics. How many offer both Mathematics and Physics?

**(A)** 20 **(B)** 16 **(C)** 8 **(D)** 4

24. If \( \frac{9^{2x-1}}{27^{x+1}} = 1 \), find the value of \( x \):

**(A)** 8 **(B)** 5 **(C)** 3 **(D)** 2

25. If

\[

\left| \frac{-4x}{2} \quad \frac{2}{1} \right| = \left| \frac{3}{4} \quad \frac{3x}{-5} \right|

\]

find the value of \( x \):

**(A)** 5 **(B)** 2 **(C)** -2 **(D)** 5

26. The length a person can jump is inversely proportional to his weight. If a 20 kg person can jump 1.5 m, find the constant of proportionality:

**(A)** 15 **(B)** 20 **(C)** 30 **(D)** 60

27. An arc of a circle subtends an angle of 30° on the circumference of a circle of radius 21 cm. Find the length of the arc:

**(A)** 11 cm **(B)** 22 cm **(C)** 44 cm **(D)** 88 cm

28. A triangle has vertices \( P(-1,6) \), \( Q(-3,-4) \), and \( R(1,-4) \). Find the midpoints of \( PQ \) and \( QR \) respectively:

**(A)** (0,-2) and (-1,-4)

**(B)** (-1,0) and (-1,-1)

**(C)** (-2,1) and (0,1)

**(D)** (-2,1) and (-1,-4)

29. What is the rate of change of the volume \( V \) of a hemisphere with respect to its radius \( r \) when \( r = 2 \)?

**(A)** 2π **(B)** 16π **(C)** 8π **(D)** 4π

30. What is the quotient when \( 6x^2 - 13x + 5 \) is divided by \( 2x - 1 \)?

**(A)** 3x + 5

**(B)** 3x - 5

**(C)** 5x - 3

**(D)** 5x + 3

31. If \( \sin \theta = -\frac{1}{2} \) for \( 0 < \theta < 360^\circ \), the values of \( \theta \) are:

**(A)** 30° and 150°

**(B)** 150° and 330°

**(C)** 210° and 330°

**(D)** 150° and 210°

32. For what value of \( n \) is \( \binom{n+1}{3} = 4 \binom{n}{3} \)?

**(A)** 6 **(B)** 5 **(C)** 4 **(D)** 3

33. A binary operation \( * \) on the set of rational numbers is defined as

\[

x * y = \frac{x^2 - y^2}{2xy}

\]

Find \( -5 * 3 \):

**(A)** -8/15 **(B)** 8/15 **(C)** 17/15 **(D)** -17/15

34. Find the value of

\[

\frac{\tan 60^\circ - \tan 30^\circ}{\tan 60^\circ + \tan 30^\circ}

\]

**(A)** \( \frac{4}{\sqrt{3}} \)

**(B)** \( \frac{2}{\sqrt{3}} \)

**(C)** \( \frac{1}{2} \)

**(D)** 1

35. The area of a square is \( 144cm^2 \). Find the length of the diagonal:

**(A)** 13 cm

**(B)** \( 12\sqrt{2} \) cm

**(C)** 12 cm

**(D)** \( 11\sqrt{3} \) cm

36. If \( \log_{x^{1/2}} 64 = 3 \), find the value of \( x \):

**(A)** 4

**(B)** 16

**(C)** 32

**(D)** 64

37. Factorize completely \( (4x + 3y)^2 - (3x - 2y)^2 \):

**(A)** \( (x + 5y)(7x + y) \)

**(B)** \( (x + 5y)(7x - y) \)

**(C)** \( (x - 5y)(7x + y) \)

**(D)** \( (x - 5y)(7x - y) \)

38. The fifth term of an A.P. is 24 and the eleventh term is 96. Find the first term:

**(A)** 12

**(B)** 4

**(C)** -12

**(D)** -24

39. Find the remainder when \( 2x^3 - 11x^2 + 8x - 1 \) is divided by \( x + 3 \):

**(A)** -871

**(B)** -781

**(C)** -187

**(D)** -178

40. The probabilities that a man and his wife live for 80 years are \( \frac{2}{3} \) and \( \frac{3}{5} \) respectively. Find the probability that only one of them will live up to 80 years:

**(A)** \( \frac{4}{15} \)

**(B)** \( \frac{7}{15} \)

**(C)** \( \frac{3}{15} \)

**(D)** \( \frac{1}{15} \)