Elective Mathematics Mock 2026

Question 1 of 50

In how many ways can 3 books be arranged on a shelf?

Question 2 of 50

Express log₃ 81 as a whole number.

Question 3 of 50

If a = 3i + 4j, find |a|.

Question 4 of 50

Simplify sin²θ + cos²θ.

Question 5 of 50

Differentiate y = 3x² + 5x − 7 with respect to x.

Question 6 of 50

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

Question 7 of 50

Find ∫ 4x³ dx.

Question 8 of 50

Find the sum of the roots of 2x² − 7x + 3 = 0.

Question 9 of 50

Find the product of the roots of 2x² − 7x + 3 = 0.

Question 10 of 50

If f(x) = 3x − 2, find f⁻¹(x).

Question 11 of 50

Solve 3^(2x) = 27.

Question 12 of 50

Find the dot product of a = 2i + 3j and b = 4i − j.

Question 13 of 50

Evaluate ⁶C₂.

Question 14 of 50

Evaluate ⁵P₃.

Question 15 of 50

Express 135° in radians.

Question 16 of 50

Evaluate the limit of (x² − 4)/(x − 2) as x approaches 2.

Question 17 of 50

If f(x) = 2x + 1 and g(x) = x², find f(g(3)).

Question 18 of 50

For what values of k does x² + kx + 9 = 0 have equal roots?

Question 19 of 50

Find the remainder when x³ − 2x² + 4 is divided by (x − 2).

Question 20 of 50

Find the sum to infinity of the geometric series 8 + 4 + 2 + …

Question 21 of 50

Find the inverse of the matrix [[2, 1], [5, 3]].

Question 22 of 50

Find the coefficient of x² in the expansion of (1 + 2x)⁵.

Question 23 of 50

Find the centre of the circle x² + y² − 4x + 6y − 3 = 0.

Question 24 of 50

Find the radius of the circle x² + y² − 4x + 6y − 3 = 0.

Question 25 of 50

Differentiate y = sin 3x with respect to x.

Question 26 of 50

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

Question 27 of 50

Find the minimum value of y = x² − 6x + 10.

Question 28 of 50

Find the area between the curve y = 2x, the x-axis and the lines x = 0 and x = 3.

Question 29 of 50

Find the variance of 2, 4, 6, 8 and 10.

Question 30 of 50

A particle moves so that its displacement is s = t³ − 3t metres. Find its velocity at t = 2 s.

Question 31 of 50

Find the coefficient of x² in the expansion of (1 + 2x)⁴.

Question 32 of 50

Find the sum of the first 10 terms of the geometric sequence 1, 2, 4, 8, …

Question 33 of 50

Find the inverse of the matrix (2 1; 5 3).

Question 34 of 50

Evaluate the limit of (x² − 4)/(x − 2) as x → 2.

Question 35 of 50

Find the variance of 2, 4 and 6.

Question 36 of 50

Find dy/dx if y = x² eˣ.

Question 37 of 50

A bag has 4 red and 6 green balls. Two are picked one after the other without replacement. Find the probability that both are red.

Question 38 of 50

Find the remainder when x⁴ − 3x² + 2 is divided by x + 2.

Question 39 of 50

If log₂ y = 3 + log₂ x, express y in terms of x.

Question 40 of 50

If A = [[2, 1], [3, 4]], find A⁻¹.

Question 41 of 50

If f(x) = (2x + 1)/(x − 3), x ≠ 3, find f⁻¹(x).

Question 42 of 50

Solve 2 log₃ x − log₃(x − 2) = 2.

Question 43 of 50

Find the range of values of k for which x² + kx + 4 = 0 has no real roots.

Question 44 of 50

Find the term independent of x in (2x − 1/x)⁶.

Question 45 of 50

Find the angle between a = 2i + j and b = i + 3j.

Question 46 of 50

Use the binomial expansion to evaluate (1.02)⁵ to 3 decimal places.

Question 47 of 50

Find the equation of the tangent to the circle x² + y² = 25 at (3, 4).

Question 48 of 50

Express √3 sin θ + cos θ in the form R sin(θ + α).

Question 49 of 50

Find the acute angle between the lines y = 2x + 1 and y = −3x + 4.

Question 50 of 50

Solve cos 2x = cos x for 0° ≤ x ≤ 360°.