Elective Mathematics Mock 2021

Question 1 of 50

The normal distribution curve is

Question 2 of 50

Two forces of 6 N and 8 N act at right angles. Find their resultant.

Question 3 of 50

If f(x) = x² and g(x) = x + 1, find f(g(2)).

Question 4 of 50

Solve log₂ x = 5.

Question 5 of 50

Find the determinant of [[3, 2], [1, 4]].

Question 6 of 50

The magnitude of the vector 3i + 4j is

Question 7 of 50

The gradient of the line joining (1, 2) and (3, 8) is

Question 8 of 50

Differentiate y = 3x⁴.

Question 9 of 50

The derivative of sin x is

Question 10 of 50

In how many ways can 5 people be arranged in a row?

Question 11 of 50

A score of 70 comes from a normal distribution with mean 60 and standard deviation 5. What is its z-score?

Question 12 of 50

About what percentage of a normal distribution lies within one standard deviation of the mean?

Question 13 of 50

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

Question 14 of 50

What is the expected score when a fair six-sided die is thrown?

Question 15 of 50

Find the range of f(x) = x² + 1 for real x.

Question 16 of 50

If f(x) = 2x − 3, find f⁻¹(5).

Question 17 of 50

Find the remainder when 2x³ − x + 4 is divided by (x + 1).

Question 18 of 50

Find the product of (1 2; 3 4) and (2; 1).

Question 19 of 50

Find the 4th term of the expansion of (1 + x)⁵ in ascending powers of x.

Question 20 of 50

If p = 2i + 3j and q = i − j, find |p + q|.

Question 21 of 50

For which value of k is the matrix (2 k; 4 6) singular?

Question 22 of 50

Find the equation of the circle with centre (2, −1) and radius 3.

Question 23 of 50

Simplify (1 − cos²θ)/sin θ.

Question 24 of 50

Find the acute angle between the lines y = x and y = −x.

Question 25 of 50

Find dy/dx if y = (x² + 1)³.

Question 26 of 50

Find the gradient of y = x² − 4x at the point (1, −3).

Question 27 of 50

Evaluate the integral of (2x + 1) from 1 to 2.

Question 28 of 50

In how many ways can a committee of 3 be chosen from 6 people?

Question 29 of 50

If f(x) = 2x + 3, find f⁻¹(x).

Question 30 of 50

The remainder when x³ − 2x + 5 is divided by (x − 1) is

Question 31 of 50

The coefficient of x² in the expansion of (1 + x)⁵ is

Question 32 of 50

If a = 2i − j and b = i + 3j, find a · b.

Question 33 of 50

Express sin 2θ in terms of sin θ and cos θ.

Question 34 of 50

Two perpendicular lines have gradients m₁ and m₂. Then

Question 35 of 50

Find the x-coordinate of the stationary point of y = x² − 6x + 5.

Question 36 of 50

The scores of a test have mean 60 and SD 8. A score of 76 has a z-score of

Question 37 of 50

A discrete variable X takes values 1, 2, 3 with probabilities 0.2, 0.5, 0.3. Find E(X).

Question 38 of 50

Find the domain of f(x) = √(4 − x²).

Question 39 of 50

If f(x) = 3x + 2, find f⁻¹(11).

Question 40 of 50

Find the value of k for which the vectors 2i + kj and 3i − 6j are perpendicular.

Question 41 of 50

Evaluate ∫₁² (3x² − 2x) dx.

Question 42 of 50

P(A) = 0.6, P(B) = 0.5 and A, B independent. Find P(A ∪ B).

Question 43 of 50

For X ~ B(4, 1/2), find P(X ≥ 3).

Question 44 of 50

Express (5x + 1)/((x + 1)(x − 1)) in partial fractions.

Question 45 of 50

The coefficient of x² in (1 + x)(1 − 2x)⁵ is

Question 46 of 50

Find the centre and radius of x² + y² + 4x − 2y − 20 = 0.

Question 47 of 50

Given sin 3θ = 3 sin θ − 4 sin³θ, find sin 3θ when sin θ = 1/2.

Question 48 of 50

Find the equation of the normal to y = x² at (1, 1).

Question 49 of 50

If y = e^(2x) sin x, dy/dx is

Question 50 of 50

The number of ways to arrange the letters of ACCRA is