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Exam-Style Questions.

Problems adapted from questions set for previous Mathematics exams.


GCSE Higher

(a) Write 90 as a product of its prime factors.

(b) Find the lowest common multiple (LCM) of 76 and 90.


GCSE Higher

Find the highest common factor (HCF) of 60 and 96.


GCSE Higher

Without using a calculator:

(a) Express 68 as the product of its prime factors.

(b) Divide 68 by 5 giving your answer in decimal format.

(c) Multiply 13.06 by 2.1


GCSE Foundation

Write 250 as a product of powers of its prime factors.


GCSE Higher

Show that 206 can be written as the sum of a power of five and a square number.


GCSE Higher

The number, \(N\), can be written as the product of prime factors in index form as:

$$N = 3 × 5^3 × x^4$$

Work out \(5N^2\) as a product of prime factors in index form giving your answer in terms of \(x\).


GCSE Higher

Here is a list of five numbers.

$$57^{17} \quad 57^{61} \quad 57^{72} \quad 57^{83}$$

(a) Find the lowest common multiple of these five numbers.

(b) Find the highest common factor of these five numbers.

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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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