GCSE & IGCSE maths practice

Estimation questions and answers

To estimate a calculation, round every number to 1 significant figure, then work it out. It's a quick check on a calculator answer. Dividing by a number less than 1 makes the answer bigger, so keep the decimal sensible (0.48 ≈ 0.5).

15 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 10 Nov 2026.

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Where estimation comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: estimate answers and check calculations using approximation and estimation.
Cambridge IGCSE (0580)	Core and Extended: make estimates of numbers, quantities and lengths, and give approximations to calculations by rounding to 1 significant figure.

The method

Round each number to 1 significant figure.
Do the simpler calculation.
For square roots, use the nearest square number.
Overestimate or underestimate? Look at which way each number was rounded.

Estimation questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

Estimate $48.7 \times 3.1$ .

Question 2Warm-upFoundation

Estimate $612 \div 19.8$ .

Question 9Warm-upFoundation

Estimate $31.2 \times 9.8$ .

Question 10Warm-upFoundation

Estimate $398 \div 4.1$ .

Exam-style

Question 3Exam-styleFoundation

Estimate $(4.89 + 5.2) \times 3.97$ .

Question 4Exam-styleFoundation

Estimate $\sqrt{48.6}$ .

Question 5Exam-styleFoundation

Estimate $\dfrac{21.4 \times 5.9}{0.48}$ .

Question 6Exam-styleFoundation

The exact value of $48.7 \times 3.1$ is 150.97. Is the estimate 150 an overestimate or an underestimate?

Question 11Exam-styleFoundation

Estimate $6.1^2$ .

Question 12Exam-styleFoundation

Estimate $\dfrac{19.7 \times 0.52}{4.8}$ .

Question 13Exam-styleFoundation

Estimate $\sqrt{97.3}$ .

Question 14Exam-styleFoundation

A shop sells 39 notebooks at £2.95 each. Estimate the total cost.

Challenge

Question 7ChallengeFoundation

Estimate the area of a circle of radius 9.8 cm using $A = \pi r^2$ (take $\pi \approx 3$ ).

cm²

Question 8ChallengeFoundation

Estimate $\dfrac{812 \times 0.49}{2.1}$ .

Question 15ChallengeFoundation

Estimate $\dfrac{52.3 + 47.1}{0.198}$ .

Common mistakes

Rounding to the nearest whole number instead of 1 s.f.
Rounding 0.48 to 0 (it's 0.5).
Working out the exact answer instead of estimating.

Stuck on one of these?

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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