The specific skills, mental strategies and written methods you need to perform well on Paper 1 without a calculator.
Paper 1 of GCSE Maths is the non-calculator paper, and it genuinely tests a different set of skills from Papers 2 and 3. Students who revise only the mathematical content — without specifically practising non-calculator techniques — often find Paper 1 unexpectedly hard. This guide explains exactly what the non-calculator paper tests, and how to prepare for it.
The paper tests all the same topics as the calculator papers, but it's designed so that answers can be worked out without a calculator. This means questions tend to involve cleaner numbers, exact values, and methods that work through written arithmetic. Topics that are disproportionately represented on Paper 1 include:
Strong mental arithmetic is the foundation of a good non-calculator performance. These strategies reduce errors and speed up your working.
23 × 7: split as (20 × 7) + (3 × 7) = 140 + 21 = 161. Much easier than long multiplication for this type of question.
Find 3/8 of 480: first find 1/8 (480 ÷ 8 = 60), then multiply by 3 (60 × 3 = 180). Always find the unit fraction first.
Build up percentages from 10% and 1%. To find 35%: find 10% (÷10), multiply by 3 for 30%, find 5% (half of 10%), add them. This is faster and more reliable than trying to multiply by 0.35 in your head.
10% of any number = divide by 10. 1% = divide by 100. Build all other percentages from these two. This avoids the decimal multiplication errors that cause most non-calculator percentage mistakes.
Surprisingly many students arriving at GCSE have forgotten formal written methods because they've relied on calculators throughout KS3. Paper 1 requires you to perform these reliably.
To multiply 347 × 28: split into 347 × 20 and 347 × 8. Calculate each separately using column multiplication, then add. Always write out the calculation in full — trying to hold it in your head causes errors.
To divide 946 by 11: how many times does 11 go into 9? Zero. Into 94? Eight times (88). Remainder 6. Bring down the 6 to get 66. 11 into 66 = 6. Answer: 86. Write each step clearly — the method marks are in the working.
A specific question type on almost every non-calculator paper: "estimate the value of..." You must round each number to 1 significant figure before calculating, then show the simplified calculation.
Don't use original values — that's not estimating. Don't calculate the exact answer and then round it — that's also wrong. Round first, calculate second. The examiner wants to see the rounded values explicitly written before the calculation.
Non-calculator papers regularly ask for exact answers involving trigonometric values, π, and surds. These require memorisation — you cannot derive them under exam pressure without prior preparation.
Questions using exact values often ask something like: "A right-angled triangle has hypotenuse 8 cm and one angle of 30°. Find the exact length of the opposite side." Answer: 8 × sin 30° = 8 × 1/2 = 4 cm. The word "exact" is your signal to use the memorised value rather than a decimal approximation.
These appear consistently on non-calculator papers. Prime factorisation using a factor tree is the most reliable method.
To find the HCF of 60 and 84: 60 = 2² × 3 × 5. 84 = 2² × 3 × 7. HCF = product of shared prime factors = 2² × 3 = 12.
To find the LCM: take the highest power of every prime that appears in either factorisation. LCM = 2² × 3 × 5 × 7 = 420.
HCF = Highest Common Factor = the biggest number that divides into both. It's always smaller than or equal to both numbers. LCM = Lowest Common Multiple = the smallest number both divide into. It's always larger than or equal to both numbers. If your HCF is bigger than one of the numbers, or your LCM is smaller, you've made an error.
The single most important thing: practise past Paper 1s with no calculator at all. Don't keep one nearby "just in case". The discipline of working through calculations by hand is what builds the skill — you can't shortcut it.
Secondly, identify which topics give you the most calculator-dependency. If you find yourself completely stuck on a percentage question without a calculator, that's a gap to address. Practise those topics specifically in non-calculator conditions.
Thirdly, work on your written arithmetic speed. Timed practice matters here — the non-calculator paper has the same time allowance as the calculator papers, but written methods genuinely take longer. Students who are slow at arithmetic often run out of time on Paper 1 even when they know the maths.
AQA's Paper 1 past papers and mark schemes are available free on the AQA GCSE Mathematics assessment resources page. Edexcel's are on the Edexcel course materials page.
PaperPlus generates GCSE Maths questions across all topics — ideal for non-calculator practice when you want to build fluency without relying on a calculator. Free for AQA, Edexcel and OCR.
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