Elective Mathematics Mock 2019

Question 1 of 50

Evaluate ⁵P₂.

Question 2 of 50

If P(A) = 0.3, find P(not A).

Question 3 of 50

If n(A) = 12, n(B) = 9 and n(A ∩ B) = 4, find n(A ∪ B).

Question 4 of 50

Expand (1 + x)³.

Question 5 of 50

The common ratio of the GP 27, 9, 3, ... is

Question 6 of 50

The degree of the polynomial 4x⁵ − x² + 7 is

Question 7 of 50

Find the equation of the circle with centre (0, 0) and radius 5.

Question 8 of 50

The identity matrix of order 2 is

Question 9 of 50

The angle between vectors a and b with a · b = 0 is

Question 10 of 50

A correlation coefficient of −1 indicates

Question 11 of 50

A correlation coefficient close to 0 indicates

Question 12 of 50

Solve 2ˣ = 32.

Question 13 of 50

Simplify log₃ 27 + log₃ 3.

Question 14 of 50

sin²θ + cos²θ =

Question 15 of 50

How many ways can 3 people be chosen from 7?

Question 16 of 50

How many arrangements of the letters of the word BOOK are there?

Question 17 of 50

Find the sum of the first 10 terms of the AP 2, 5, 8, ...

Question 18 of 50

Find the sum to infinity of the GP 8, 4, 2, ...

Question 19 of 50

The sum of the roots of x² − 7x + 10 = 0 is

Question 20 of 50

The product of the roots of 2x² + 5x − 3 = 0 is

Question 21 of 50

The locus of points equidistant from two fixed points is

Question 22 of 50

Find the product [[1, 2], [0, 1]] × [[3], [4]].

Question 23 of 50

Spearman's coefficient uses the

Question 24 of 50

A line of best fit on a scatter graph should

Question 25 of 50

If Σd² = 0 for 5 pairs of ranks, Spearman's coefficient is

Question 26 of 50

Simplify log 8 ÷ log 2.

Question 27 of 50

Simplify 8^(2/3).

Question 28 of 50

Express log 12 in terms of log 2 and log 3.

Question 29 of 50

Solve log x + log 4 = log 20.

Question 30 of 50

1 + tan²θ =

Question 31 of 50

cos 2θ can be written as

Question 32 of 50

sin(A + B) =

Question 33 of 50

The minimum value of y = x² − 4x + 7 is

Question 34 of 50

If s = t³ − 3t, the velocity at t = 2 is

Question 35 of 50

A stationary point is a maximum if d²y/dx² is

Question 36 of 50

The image of the point (1, 2) under the matrix [[2, 0], [0, 3]] is

Question 37 of 50

Three coins are tossed. P(at least two heads) is

Question 38 of 50

If X ~ N(100, 225), the standard deviation is

Question 39 of 50

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

Question 40 of 50

The equation x³ − 7x + 6 = 0 has roots

Question 41 of 50

Find the length of the tangent from (7, 1) to the circle x² + y² = 25.

Question 42 of 50

Solve 2^x = 7, giving x to 2 decimal places (log 2 = 0.3010, log 7 = 0.8451).

Question 43 of 50

Simplify sin 2θ / (1 + cos 2θ).

Question 44 of 50

The truth value of (T → F) ∨ (F → T) is

Question 45 of 50

Use Cramer's rule: x + y = 3, 2x − y = 0. Then x =

Question 46 of 50

∫ x eˣ dx =

Question 47 of 50

The area between y = x³ and the x-axis from x = −1 to x = 1 is

Question 48 of 50

For a Poisson distribution with mean 2, P(X = 0) is

Question 49 of 50

Find the remainder when 3x³ − 2x² + x − 5 is divided by 3x − 2.

Question 50 of 50

Solve log₂(x + 1) + log₂(x − 1) = 3.