Subject knowledge test: Mathematics

The purpose of these questions is to help you identify areas of strength, and areas that need further development, in your knowledge and understanding of primary mathematics. Try and complete all the questions and then click on the submit button to get instant feedback. The feedback page includes the answers to these questions as well as links to printed resources that will support and deepen your understanding.

IMPORTANT - Before starting the test, make sure that you note the following protocols for answering questions:

If your answer is 109 type 10^9 (to get the 'to the power of' sign, ^, press SHIFT on your keyboard and type 6)
If your answer is 5.3 x 102 type 5.3*10^2 (to get the multiplication sign, *, press SHIFT on your keyboard and type 8)
If your answer is a3b2 type a^3*b^2
If your answer is 51/2 type 5 1/2 (with a space between the integer and the fraction)
Where a question requires you to use , take to have two decimal places.

Good luck!


Q1 Use a long division algorithm to solve:
A: 1768 ÷ 34
B: 1638 ÷ 63
C: 3335 ÷ 23
Q2 Convert the following to vulgar fractions:
A: 0.375
B: 0.28
C: 76%
Q3 A school basketball team scored 24 points in one game and 30 points in the next. What was their percentage increase in the points scored?
Answer: %
Q4 Write the number 0.0606 in standard form.
Q5 Find the highest common factor of a2b and a3b2.

Algebra - patterns and relationships

Q6 If a = 5, b = 15, c = 2, d = 3, de = 15 and df = 18 find:
A: e
B: 2d2e
Q7 Jess is doing a mathematics investigation and obtained the results 1, 2, 4, 8, 16, 32.
A: What would be the next term in this sequence?
B: What would be the nth term?
Q8 Solve the following equation:
= 3
x + 2
Answer: x =

Shape and space

Q9 If angle a = 95º, angle b = 110º and angle c = 105º, what does angle d equal?

Answer: d = º

Which of these shapes are congruent?

(tick relevant boxes)

A: B: C: D:
Q11 Answer yes or no if the following triangles have right angles.

A: AB = 3 BC = 4 AC = 5
B: XY = 4 YZ = 5 XZ = 6
Q12 Calculate the area of the sector marked in the circle.

Answer: cm2
Q13 Find the surface area (A) and volume (B) of the following cylinder, with radius 5 cm and length 10 cm.
A: Surface Area cm2
B: Volume cm3



The wages of 10 workers in a factory are £30K, £22K, £6K, £6K, £6K, £6K, £6K, £6K, £6K, £6K. Find:

A: the mode £ K
B: the mean £ K
C: the median £ K



A: A coin is flipped. What is the probability of achieving tails?

B: A fair die is rolled and a coin is flipped. What is the probability of achieving a 5 and tails?

Q16 A card is drawn from a pack of 52. What is the probability that the card is higher than a Jack (ace is high)?



James is following a recipe, which is written using metric units of measurement (give your answer to the nearest quarter of an inch, pint, or ounce)
A: The recipe suggests using a mixing bowl with a diameter of 30 cm. How many inches (approximately) should the diameter of the bowl be?

B: The recipe requires 1 litre of milk. How many pints must James use?

C: It also requires 500 g of flour. How many pounds and/or ounces are required?
pounds / ounces

Equations and graphs


This is the graph of y = 10x + 8.

A: What is the gradient of the line?

B: What is the y-intercept?

Reasoning and proof


Answer true or false. (x is a real number.)

A: 2(x + 4) = 2x + 8
B: 3(x - 3) = 3x - 6
C: x2 = -4