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Number practice problems GCSE Maths, Topic 1

Written by STEM-Tutor's tutors · Updated October 2026 · 8 questions and 1 exam-style question

Fractions, percentages and reverse percentages, index laws, standard form, surds and bounds. Try each question before you look: use the hint if you are stuck, then reveal the worked solution one step at a time.

On this page
  1. Key equations
  2. Warm-up questions
  3. Exam-style questions
  4. Exam question practice
  5. Common mistakes
  6. Keep going

Key equations for number

% change = change ÷ original × 100percentage change
am × an = am+nindex laws
A × 10n, 1 ≤ A < 10standard form
√(ab) = √a × √bsimplifying surds

A formulae sheet is provided in the 2025, 2026 and 2027 GCSE Maths exams. Answers within 2.5% are marked correct, and you can type fractions such as 23/20. Every topic, Foundation and Higher, is in our GCSE Maths topic list.

Warm-up questions

Quick checks on the core ideas. If these feel easy, go straight to the exam-style questions.

Q1Warm-up
Work out 3/4 + 2/5. Give your answer as a fraction or decimal.

Hint

Use a common denominator of 20.

Worked solution
  1. 3/4 = 15/20 and 2/5 = 8/20.
  2. 15/20 + 8/20 = 23/20 (1.15).
Q2Warm-up
Work out 15% of 240.

Hint

10% is 24 and 5% is half of that.

Worked solution
  1. 10% = 24, 5% = 12.
  2. 15% = 24 + 12 = 36.
Q3Warm-up
Write 0.00056 in standard form.

Hint

Move the decimal point until the number is between 1 and 10.

Worked solution
  1. The point moves 4 places to the right to make 5.6.
  2. So 0.00056 = 5.6 × 10−4: B.

Exam-style questions

Questions at the level of the GCSE Maths exam. The ones marked Challenge combine more than one idea.

Q4Exam-style
A price rises from £80 to £92. Work out the percentage increase.
%

Hint

Divide the increase by the original price.

Worked solution
  1. Increase = 92 − 80 = 12.
  2. 12 ÷ 80 × 100 = 15%.
Q5Exam-style
Work out 23 × 25 ÷ 24.

Hint

Add the powers when multiplying, subtract when dividing.

Worked solution
  1. 23 + 5 − 4 = 24.
  2. = 16.
Q6Exam-style
After a 20% increase, a jacket costs £96. What was the price before the increase?
£

Hint

A 20% increase means multiplying by 1.2. Undo it.

Worked solution
  1. Original × 1.2 = 96.
  2. Original = 96 ÷ 1.2 = 80, so £80.
Q7Exam-styleHigher
Simplify √50 + √18, writing your answer as a√2. What is a?

Hint

Find square factors: 50 = 25 × 2 and 18 = 9 × 2.

Worked solution
  1. √50 = 5√2 and √18 = 3√2.
  2. 5√2 + 3√2 = 8√2, so a = 8.
Q8ChallengeHigher
A rectangle is 12 cm long and 5 cm wide, each measured to the nearest centimetre. Work out the upper bound of its area.
cm²

Hint

The upper bounds are half a unit above each measurement.

Worked solution
  1. Upper bounds: 12.5 cm and 5.5 cm.
  2. Upper bound of area = 12.5 × 5.5 = 68.75 cm².

Exam question practice

One original exam-style question in the style of a GCSE paper. Answer it in full, with working, before you open the mark scheme: most marks are for method, so show every step.

Exam-style question style · 5 points · about 6 minutes

Sam earns £1800 a month. He spends 1/3 of it on rent. He then spends 15% of what is left on travel.

  1. (a) How much does Sam spend on rent?
  2. (b) How much does Sam spend on travel?
  3. (c) What fraction of his earnings does Sam have left after rent and travel? Give it in its simplest form.

Write your full answer on paper first, then open the scoring guide and tick each point you earned.

Scoring guide and model answer

Part (a)

1800 ÷ 3 = £600.

Part (b)

What is left: 1800 − 600 = 1200. 15% of 1200 = £180.

Part (c)

1800 − 600 − 180 = 1020. 1020/1800 = 17/30.

Your mark: 0 of 5

Common mistakes in number

Keep going

Revise the ideas behind these questions:

Then try real exam questions: GCSE Maths past papers, with official scoring guidelines. · All GCSE Maths units