Core Mathematics Mock 2016

Question 1 of 50

If P(A) = 0.35, what is P(not A)?

Question 2 of 50

Two events that cannot happen at the same time are

Question 3 of 50

P = {1, 2, 3, 4, 5, 6} and Q = {2, 4, 6, 8}. Find P ∩ Q.

Question 4 of 50

U = {1, 2, …, 10} and A = {even numbers in U}. Find n(A′).

Question 5 of 50

Which property is shown by a × 1 = a?

Question 6 of 50

Solve 2x + 3 ≤ 11.

Question 7 of 50

Find the equation of the line through (0, 4) with gradient −2.

Question 8 of 50

Which line is parallel to y = 3x − 5?

Question 9 of 50

The point (k, 7) lies on the line y = 2x + 1. Find k.

Question 10 of 50

Express 1.25 as a fraction in lowest terms.

Question 11 of 50

What is the amplitude of y = 2 cos x?

Question 12 of 50

A letter is chosen at random from the word MATHEMATICS. What is the probability that it is M?

Question 13 of 50

In a class of 40, 25 study French, 18 study Music and 10 study both. How many study neither?

Question 14 of 50

If n(A) = 12, n(B) = 9 and n(A ∪ B) = 17, find n(A ∩ B).

Question 15 of 50

A = {letters of the word "BANANA"}. How many elements does A have?

Question 16 of 50

If A ⊂ B, then A ∩ B is equal to

Question 17 of 50

How many proper subsets does a set with 3 elements have?

Question 18 of 50

GH¢1,000 is invested at 10% per annum compound interest. What is the amount after 2 years?

Question 19 of 50

At what simple interest rate will GH¢800 earn GH¢240 in 3 years?

Question 20 of 50

How long will it take GH¢1,500 to earn GH¢450 at 6% simple interest?

Question 21 of 50

Find the simple interest on GH¢3,600 at 7½% per annum for 4 years.

Question 22 of 50

Make t the subject of v = u + at.

Question 23 of 50

Make r the subject of A = πr².

Question 24 of 50

Make x the subject of y = (x + 3)/2.

Question 25 of 50

Find the largest integer x that satisfies 3x − 2 < 10.

Question 26 of 50

What are the gradient and y-intercept of 3y = 6x − 9?

Question 27 of 50

Find the equation of the line through (1, 3) and (3, 7).

Question 28 of 50

Find the length of the line joining (−1, 2) and (5, 10).

Question 29 of 50

Where does the line 2x + 5y = 10 cut the x-axis?

Question 30 of 50

Simplify 3⁻² × 9.

Question 31 of 50

Evaluate 16^(3/4).

Question 32 of 50

Simplify log₃ 81.

Question 33 of 50

Evaluate (0.2)² ÷ 0.04.

Question 34 of 50

Find the next number in the sequence 1, 3, 7, 15, 31, …

Question 35 of 50

Which is the largest: 0.3, 1/3, 0.33 or 3/10?

Question 36 of 50

The mean of 10 numbers is 8. When one number is removed, the mean becomes 7. The number removed is

Question 37 of 50

A die is thrown twice. P(the same number both times) is

Question 38 of 50

In a set of 20 scores, the cumulative frequency up to 40 marks is 15. The percentage scoring above 40 is

Question 39 of 50

If a ∆ b = (a + b)/ab, find 2 ∆ 3.

Question 40 of 50

Factorise completely 2x³ − 18x.

Question 41 of 50

Simplify (2x + 3)² − (2x − 3)².

Question 42 of 50

f(x) = ax + b, f(1) = 5 and f(3) = 11. Find a and b.

Question 43 of 50

If p = (3, −1) and q = (−2, 5), find 3p + 2q.

Question 44 of 50

A rectangular field 120 m by 80 m is fenced with 3 rows of wire. The total wire length is

Question 45 of 50

Which set is closed under division?

Question 46 of 50

A trader sells two items for GH¢240 each, making a 20% profit on one and a 20% loss on the other. His overall result is

Question 47 of 50

A man spent 3/8 of his money and then 1/3 of the remainder. He had GH¢200 left. How much had he at first?

Question 48 of 50

The population of a town rose by 10% one year and fell by 10% the next. The net change is

Question 49 of 50

The sides of a right triangle are x, x + 7 and x + 8. Find x.

Question 50 of 50

The angles of a hexagon are 2x, 2x, 3x, 3x, 4x and 4x. The largest angle is