GCSE Maths non-calculator paper: tips and methods

• Percentages: 15% of 60 = 10% (6) + 5% (3) = 9.
• Fraction of an amount: $\tfrac{3}{8}$ of 64: divide by 8, multiply by 3: 24.
• Dividing by a decimal: $4.2 \div 0.6 = 42 \div 6 = 7$ (multiply both by 10).
• Squares and roots: know squares to 15² and cubes to 5³, and simplify surds: $\sqrt{48} = 4\sqrt{3}$.

Round each number to 1 significant figure, then calculate: $\dfrac{4.87 \times 21.3}{0.52} \approx \dfrac{5 \times 20}{0.5} = 200$. Show the rounded values; the marks are for the method. See significant figures.

Method marks (M) are awarded for correct steps even if the final answer is wrong. Set working out clearly, one step per line, and write formulas before substituting. An unsupported answer can get zero if it's wrong.

Practise without a calculator from the start of revision, not just before the exam. Our free GCSE Maths mock Paper 1 is non-calculator, timed and marked instantly. Use the fraction calculator and order of operations calculator only to check your working afterwards.

$47 \times 36$:

• $47 \times 6 = 282$
• $47 \times 30 = 1410$
• Add: $282 + 1410 = 1692$

Check by estimating: $50 \times 40 = 2000$, and the answer should be a bit less because both numbers were rounded up. 1692 fits. For decimals, ignore the point, multiply, then put it back: $4.7 \times 3.6$ has two decimal places in total, so it's $16.92$.

• Times tables to $12 \times 12$. Our times tables quiz has a 6-second mode.
• Square numbers to $15^2 = 225$ and cubes $2^3, 3^3, 4^3, 5^3$ and $10^3$.
• Primes to 50.
• Fraction, decimal and percentage equivalents: see fractions, decimals and percentages.
• Powers of 2 to $2^{10} = 1024$, useful for index questions.

Knowing these instantly frees up time for the harder parts of each question.

With AQA, the non-calculator paper is 80 marks in 90 minutes, a little more than a minute per mark. If a question worth 2 marks has taken five minutes, move on and come back. The paper gets harder as it goes, so bank the earlier marks carefully and leave time to check.

• Place value errors when multiplying or dividing decimals. Estimate first so you know roughly what the answer should be.
• Adding fractions without a common denominator. See how to simplify fractions and the LCM guide.
• Order of operations slips: $3 + 4 \times 2$ is 11, not 14. See BIDMAS.
• Negative numbers: $-3 - 5 = -8$, and a negative times a negative is positive.
• Leaving answers unsimplified when the question asks for the simplest form.