Opening Maths Unlocked
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Opening Maths Unlocked
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GCSE MATHS REVISION
Non-calculator GCSE Maths questions test how confidently you can work with numbers, algebra and mathematical methods without relying on a calculator.
Success is not just about doing mental arithmetic quickly. You also need to choose efficient methods, show clear working, use exact values and check whether your answers are reasonable.
This guide covers the key non-calculator skills to practise, useful techniques and common mistakes to avoid.
Updated 3 October 2026
These short examples illustrate useful methods. Open the relevant Maths Unlocked lesson for fuller explanations and practice.
Recall times tables, number bonds, factors, multiples, squares, roots and powers of ten. For 25 × 16, use 25 × 4 = 100, then 100 × 4 = 400. Tip: look for a simpler equivalent calculation first.
Practise column addition and subtraction, long multiplication, division and decimal calculations. For 36 × 24: 36 × 20 = 720 and 36 × 4 = 144, so 720 + 144 = 864. Tip: write the method when mental calculation becomes unreliable.
Use equivalent fractions, simplification and common denominators for the four operations. ⅔ + ¼ = ⁸⁄₁₂ + ³⁄₁₂ = ¹¹⁄₁₂. Tip: simplify where possible and retain an exact fraction when needed.
Know ½ = 0.5 = 50%, ¼ = 0.25 = 25%, ⅕ = 0.2 = 20% and ¹⁄₁₀ = 0.1 = 10%. For 15% of £80, 10% is £8 and 5% is £4, giving £12. Tip: break awkward percentages into familiar parts.
Practise addition, subtraction, multiplication and division with signed numbers. −6 × (−4) = 24. Tip: identify the operation before applying a sign rule; subtracting a negative is different from multiplying two negatives.
Recall squares, cubes and their roots, integer powers, index laws and order of operations. 2³ × 2⁴ = 2⁷ = 128. Tip: for the same base, add the indices when multiplying; do not multiply the indices.
Estimate 19.8 × 4.9 using 20 × 5 = 100. The exact answer should be reasonably close to 100. Tip: estimate before or after calculating to spot a result with the wrong size.
Practise simplifying, expanding, factorising, solving equations and rearranging formulae; Higher students should also work with algebraic fractions. For 3x + 7 = 22, 3x = 15, so x = 5. Tip: substitute back to check.
Non-calculator questions often become easier when you recognise useful numerical relationships.
Break a number into parts: 18 × 7 = (10 × 7) + (8 × 7) = 126.
Rearrange a product: 16 × 25 = 4 × 4 × 25 = 400.
Rewrite fractions with a suitable common denominator, or simplify before calculating.
Check an answer using the opposite operation when appropriate.
Foundation students need accurate written and mental methods and the ability to apply them throughout the Foundation curriculum. These examples are useful priorities, not an exhaustive non-calculator syllabus.
Plan revision across the Foundation course.
View Foundation RevisionCheck the full Foundation curriculum.
View Foundation TopicsHigher students need the same calculation fluency alongside demanding algebra and exact methods. Practise retaining exact values instead of automatically converting to decimals. These examples may not all appear on a particular paper.
Plan revision across the Higher course.
View Higher RevisionCheck the full Higher curriculum.
View Higher TopicsWithout a calculator, fractions, surds, π and algebraic expressions can express answers exactly. Exact answers avoid rounding error. Read the question to decide whether an exact form or a specified approximation is required.
1 ÷ 3 = ⅓ exactly.
√50 = 5√2 exactly.
A circle with radius 4 cm has area 16π cm² exactly.
Check both the operation and the way you record your method.
Mistake: confusing subtraction with multiplication rules. Correction: identify the operation before applying its sign rule.
Mistake: adding numerators and denominators separately. Correction: use a common denominator first.
Mistake: misplacing the decimal point. Correction: estimate and check the size of your answer.
Mistake: adding before multiplying without brackets. Correction: follow the order of operations and read brackets carefully.
Mistake: replacing an exact fraction or surd with an approximation. Correction: retain exact form until approximation is requested.
Mistake: doing a lengthy calculation mentally and recording only a wrong result. Correction: write a suitable method and important steps.
Try these five short questions without a calculator. Question 5 is Higher-tier content; Foundation students may skip it or treat it as an extension. Answers only appear below.
Calculate ¾ + ⅖.
Calculate 3.6 ÷ 0.06.
Find 15% of 240.
Solve 3(2x − 5) = 27.
Simplify √72.
On non-calculator papers, written methods are especially useful for multi-step calculations. Appropriate working helps you track your steps and may allow an examiner to award method marks where the mark scheme provides them.
Write enough mathematics for your method to be followed, especially on questions worth several marks. Not every one-mark question requires written working, and method marks are not automatically available.
These 30-minute timings are flexible. Spend longer where a method needs more work.
Practise number facts, multiplication, division or fraction equivalences.
Choose a topic needing a written or exact method and revisit the explanation.
Attempt questions without a calculator or notes.
Mark your work, identify mistakes and decide what to practise next.
Non-calculator assessment involves mathematical reasoning as well as arithmetic. Prepare for both.
Complete calculations accurately without relying on shortcuts you find unreliable.
Revisit multiplication facts, common squares, roots and fraction equivalences.
Practise fractions, surds and π where appropriate to your tier.
Check the instructions and equipment rules for your examination.
Try mixed questions without a calculator, notes or worked examples.
Use the full lesson and practice questions for skills that need attention. You can choose to practise suitable questions without a calculator; the app does not automatically impose non-calculator conditions.
Revisit equivalences and calculations.
Open Number lessonPractise signed-number operations.
Open Number lessonCheck calculations by approximating.
Open Number lessonUse these published guides to plan your practice and strengthen skills across both tiers.
Prepare for the papers where calculators are allowed.
Read the companion guideSet out longer revision sessions.
View the planStrengthen your study approach.
Read the guideSample key skills to identify gaps.
Take the diagnostic