Elective Mathematics Mock 2025

Question 1 of 50

Find ∫ (2x + 3) dx.

Question 2 of 50

The standard deviation of a set of data is 3. What is its variance?

Question 3 of 50

A body of mass 2 kg moves with velocity 5 m/s. Find its kinetic energy.

Question 4 of 50

Find the gradient of the line perpendicular to y = 2x + 5.

Question 5 of 50

Find the gradient of the curve y = x³ − 2x at x = 2.

Question 6 of 50

Evaluate ∫₀² 3x² dx.

Question 7 of 50

Events A and B are independent with P(A) = 0.5 and P(B) = 0.4. Find P(A ∩ B).

Question 8 of 50

Two forces of 3 N and 4 N act at right angles on a particle. Find the magnitude of their resultant.

Question 9 of 50

A binary operation is defined by a * b = a + b − ab. Find 2 * 3.

Question 10 of 50

Which binary operation on the real numbers is commutative?

Question 11 of 50

n(A) = 20, n(B) = 15 and n(A ∩ B) = 8. Find n(A ∪ B).

Question 12 of 50

How many subsets does a set with 4 elements have?

Question 13 of 50

Evaluate 8^(2/3).

Question 14 of 50

Solve 2^(x + 1) = 32.

Question 15 of 50

Evaluate log₂ 8 + log₂ 4.

Question 16 of 50

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

Question 17 of 50

Use the first two terms of the binomial expansion to estimate 1.02⁵.

Question 18 of 50

Solve x² − 5x + 4 < 0.

Question 19 of 50

Solve |x − 3| < 2.

Question 20 of 50

Find the centre and radius of x² + y² − 4x + 6y − 12 = 0.

Question 21 of 50

If a · b = ½|a||b|, what is the angle between a and b?

Question 22 of 50

The matrix (0 −1; 1 0) represents

Question 23 of 50

For 5 pairs of ranks, Σd² = 4. Using Spearman's formula, find the rank correlation coefficient.

Question 24 of 50

Evaluate log₄ 8.

Question 25 of 50

Differentiate x sin x with respect to x.

Question 26 of 50

Differentiate (2x + 1)³ with respect to x.

Question 27 of 50

A fair coin is tossed 3 times. What is the probability of exactly 2 heads?

Question 28 of 50

What is the focus of the parabola y² = 8x?

Question 29 of 50

What is the directrix of the parabola y² = 8x?

Question 30 of 50

What is the greatest value of 3 sin x + 4 cos x?

Question 31 of 50

What is the general solution of sin x = 0 (x in radians)?

Question 32 of 50

The volume formed when the region under y = f(x) from a to b is rotated about the x-axis is

Question 33 of 50

X follows a binomial distribution with n = 20 and p = 0.3. What is the variance of X?

Question 34 of 50

Express 1/((x − 1)(x + 1)) in partial fractions.

Question 35 of 50

Solve the equation 2^(2x) − 5(2^x) + 4 = 0.

Question 36 of 50

A curve has gradient 3x² − 4 and passes through (2, 1). Its equation is

Question 37 of 50

A committee of 4 is chosen from 5 men and 4 women. In how many ways can it contain exactly 2 women?

Question 38 of 50

A 4 kg mass on a smooth plane inclined at 30° is released. Its acceleration down the plane is (g = 10 m/s²)

Question 39 of 50

Three forces (2i + 3j), (−4i + j) and (ai + bj) are in equilibrium. Find a and b.

Question 40 of 50

Differentiate y = x²/(x + 1).

Question 41 of 50

Find ∫ x(x² + 1)³ dx.

Question 42 of 50

Find the area enclosed by y = x² and y = 2x.

Question 43 of 50

Find dy/dx if x² + y² = 25.

Question 44 of 50

In how many ways can 4 boys and 3 girls sit in a row if the girls must sit together?

Question 45 of 50

P(A) = 0.4, P(B) = 0.5 and P(A ∪ B) = 0.7. Find P(A | B).

Question 46 of 50

The probability that a student passes Maths is 0.7 and English 0.8, independently. Find the probability that exactly one subject is passed.

Question 47 of 50

A particle starts from rest with acceleration a = 6t m/s². Its displacement after 2 s is

Question 48 of 50

Two particles of masses 3 kg and 2 kg hang over a smooth pulley. The acceleration of the system is (g = 10 m/s²)

Question 49 of 50

A body projected at 20 m/s at 30° to the horizontal reaches a maximum height of (g = 10 m/s²)

Question 50 of 50

Find the coefficient of x⁴ in (1 − 2x)⁶.