Elective Mathematics Mock 2023

Question 1 of 50

Differentiate 3x⁴ with respect to x.

Question 2 of 50

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

Question 3 of 50

The standard deviation of a data set is

Question 4 of 50

How many terms are there in the expansion of (a + b)⁷?

Question 5 of 50

Find the unit vector in the direction of 3i + 4j.

Question 6 of 50

Two non-zero vectors are perpendicular when

Question 7 of 50

What is the exact value of sin 120°?

Question 8 of 50

What is cos(−60°)?

Question 9 of 50

Solve 2 sin θ = 1 for 0° ≤ θ ≤ 180°.

Question 10 of 50

Convert 135° to radians.

Question 11 of 50

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

Question 12 of 50

Differentiate y = 1/x with respect to x.

Question 13 of 50

To estimate the mean of grouped data, each class is represented by its

Question 14 of 50

The mean of five numbers is 12. Four of them are 10, 14, 8 and 16. Find the fifth.

Question 15 of 50

Evaluate ⁶P₂.

Question 16 of 50

Evaluate ⁷C₃.

Question 17 of 50

Two fair coins are tossed. What is the probability of at least one head?

Question 18 of 50

What is the coefficient of the middle term in the expansion of (1 + x)⁶?

Question 19 of 50

Find 1 + 2 + 3 + … + 100.

Question 20 of 50

The directrix of y² = 12x is

Question 21 of 50

In triangle ABC, a = 5, b = 7 and C = 60°. Find c².

Question 22 of 50

The volume generated when y = x from 0 to 3 is rotated about the x-axis is

Question 23 of 50

The area between y = 4 − x² and the x-axis is

Question 24 of 50

A fair coin is tossed 4 times. P(exactly 2 heads) is

Question 25 of 50

Express (3x + 1)/((x − 1)(x + 2)) in partial fractions. The coefficient over (x − 1) is

Question 26 of 50

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

Question 27 of 50

Find the perpendicular distance from (1, 2) to the line 3x + 4y − 1 = 0.

Question 28 of 50

Differentiate y = x sin x.

Question 29 of 50

Find dy/dx if y = ln(3x).

Question 30 of 50

A body of mass 2 kg is acted on by forces (3i + 4j) N and (i − 2j) N. Its acceleration is

Question 31 of 50

If x ⊕ y = x + y − 2, find the identity element.

Question 32 of 50

If each value in a data set is increased by 5, the standard deviation

Question 33 of 50

How many terms of the AP 3, 7, 11, ... are needed to give a sum of 210?

Question 34 of 50

If x = −1 is a root of x³ + 2x² − x − 2 = 0, the other roots are

Question 35 of 50

For 6 pairs of ranks with Σd² = 14, Spearman's coefficient is

Question 36 of 50

The sum to infinity of a GP is 27 and the first term is 9. Find the common ratio.

Question 37 of 50

If α, β and γ are roots of x³ − 6x² + 11x − 6 = 0, find α + β + γ.

Question 38 of 50

The regression line of y on x passes through

Question 39 of 50

The mean of 10 numbers is 15. If each number is multiplied by 2 and then 3 is added, the new mean is

Question 40 of 50

The standard deviation of a data set is 4. If each value is multiplied by 3, the new standard deviation is

Question 41 of 50

How many ways can 6 people be seated around a round table?

Question 42 of 50

How many 4-digit even numbers can be formed from 1, 2, 3, 4, 5 without repetition?

Question 43 of 50

Expand (1 + x)^(1/2) up to the term in x².

Question 44 of 50

Solve (x − 1)/(x + 2) > 0.

Question 45 of 50

Find the sum of all multiples of 3 between 1 and 100.

Question 46 of 50

When f(x) is divided by (x − 1) the remainder is 3, and by (x + 1) it is −1. The remainder when divided by (x² − 1) is

Question 47 of 50

Find the equation of the circle with diameter joining (1, 2) and (5, 6).

Question 48 of 50

The locus of points P such that PA = 2PB, where A = (0, 0) and B = (3, 0), is a

Question 49 of 50

Solve log₂ x + log₂ (x − 2) = 3.

Question 50 of 50

Prove that (1 − cos 2θ)/sin 2θ equals