Elective Mathematics Mock 2024

Question 1 of 50

Evaluate log₁₀ 100 − log₁₀ 10.

Question 2 of 50

Find the determinant of the matrix (3 2; 1 4).

Question 3 of 50

Find (1 2; 3 4) + (0 1; 1 0).

Question 4 of 50

Find the gradient of the line through (1, 2) and (3, 8).

Question 5 of 50

Find the midpoint of the line joining (2, 6) and (8, −2).

Question 6 of 50

Find |3i − 4j|.

Question 7 of 50

Simplify (√5 + √3)(√5 − √3).

Question 8 of 50

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

Question 9 of 50

What is the domain of f(x) = 1/(x − 3)?

Question 10 of 50

Find the inverse of f(x) = (x − 4)/2.

Question 11 of 50

A 2 × 3 matrix is multiplied by a 3 × 2 matrix. What is the order of the product?

Question 12 of 50

A square matrix has no inverse when

Question 13 of 50

What is the gradient of a line perpendicular to y = 2x + 1?

Question 14 of 50

Find the distance between (1, 1) and (4, 5).

Question 15 of 50

If a = 2i − j and b = 3i + 4j, find a · b.

Question 16 of 50

Find the distance from the point (3, 4) to the line 3x + 4y − 5 = 0.

Question 17 of 50

Find the area enclosed by y = 4 − x² and the x-axis.

Question 18 of 50

If s = 2t³ − 3t², find the acceleration at t = 2.

Question 19 of 50

P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.3. Are A and B independent?

Question 20 of 50

Find the mean deviation of 2, 4 and 6 about the mean.

Question 21 of 50

A particle is projected horizontally at 10 m/s from a height of 20 m. How far does it travel horizontally before landing? (g = 10 m/s²)

Question 22 of 50

A body of mass 4 kg moves with velocity (3i + 4j) m/s. What is its kinetic energy?

Question 23 of 50

The centre of the circle x² + y² − 4x + 6y − 3 = 0 is

Question 24 of 50

The variance of 2, 4, 6 is

Question 25 of 50

The coefficient of x³ in (1 + 2x)⁴ is

Question 26 of 50

The constant term in (x + 1/x)⁴ is

Question 27 of 50

Solve x² − 5x + 6 < 0.

Question 28 of 50

If (x − 2) is a factor of x³ − 3x² + kx − 2, find k.

Question 29 of 50

The radius of the circle x² + y² − 6x + 8y = 0 is

Question 30 of 50

The matrix [[0, −1], [1, 0]] represents a rotation of

Question 31 of 50

The equation of the tangent to y = x² at (1, 1) is

Question 32 of 50

A bag has 4 red and 6 green balls. Two are drawn without replacement. P(both red) is

Question 33 of 50

The inverse of [[2, 1], [1, 1]] is

Question 34 of 50

If det A = 4, then det(2A) for a 2 × 2 matrix A is

Question 35 of 50

The focus of the parabola y² = 8x is

Question 36 of 50

A binary operation is defined by a * b = ab/(a + b) for positive reals. Is * commutative?

Question 37 of 50

Simplify log₂ 8 + log₃ 9 − log₅ 125.

Question 38 of 50

If logₐ 2 = 0.3 and logₐ 3 = 0.48, find logₐ 12.

Question 39 of 50

f(x) = 2x + 1 and g(x) = (x − 1)/2. Show that f and g are

Question 40 of 50

If [[x, 2], [3, 4]] [[1], [2]] = [[7], [11]], find x.

Question 41 of 50

Find the point of intersection of y = 2x + 1 and x + y = 7.

Question 42 of 50

Find the scalar projection of a = 3i + 4j onto b = i.

Question 43 of 50

Find the length of an arc of radius 6 cm subtending 2 radians.

Question 44 of 50

Differentiate from first principles: the derivative of x² is found from lim (h→0) of

Question 45 of 50

Solve 9ˣ − 4(3ˣ) + 3 = 0.

Question 46 of 50

The 3rd and 7th terms of an AP are 10 and 30. Find the sum of the first 10 terms.

Question 47 of 50

The distance from (2, −1) to the line 4x − 3y + 4 = 0 is

Question 48 of 50

The points A(1, 2), B(3, 6), C(4, 8) are

Question 49 of 50

The area of a sector of radius 4 cm and angle π/4 is

Question 50 of 50

Evaluate lim (x→0) (sin 3x)/x.