GCSE Maths Non-Calculator Topics and Preparation

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Prepare skills, not predictions

What you need to know for a GCSE Maths non-calculator paper

A non-calculator paper tests whether you can carry out suitable mathematics by hand. The mathematical topic is not determined by the absence of a calculator: official specifications allow content to be assessed across the papers. The useful distinction is therefore between questions where exact, written or mental methods are efficient and those where a calculator would normally perform the arithmetic.

Exact method → visible working → check

Turn calculator actions into visible mathematics

For every calculation, choose a transformation that keeps the numbers manageable and leaves evidence an examiner can follow.

ReadWhat exact result is needed?fraction, surd, percentage, equation or measure

TransformUse a hand methodcommon denominator, factor, partition or rearrange

CheckEstimate or reverseconfirm size, sign and units

From problem to method

Typical problems you need to be able to solve

These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.

Calculate exactly

What the problem asks: Work with integers, decimals, fractions, percentages, powers or surds without decimal approximation.

How to solve it: Partition, use place value, find common denominators or simplify factors before calculating.

Manipulate algebra

What the problem asks: Expand, factorise, substitute, rearrange or solve while showing each change.

How to solve it: Keep equations balanced and make one meaningful transformation per line.

Use number relationships

What the problem asks: A ratio, proportional relationship, standard-form calculation or compound unit must be handled by hand.

How to solve it: Find one part or unit first, then scale using exact multiplication or division.

Use exact geometry

What the problem asks: A length, angle or area can be found from a known theorem or exact trig value.

How to solve it: Write the relationship first, substitute exact values and add units only to measured results.

Protect method marks

What the problem asks: The arithmetic may be difficult or a final slip is possible.

How to solve it: Show the setup, intermediate values and conclusion so a valid method remains visible.

A reliable routine

Routine for a non-calculator question

Use this routine for questions whose arithmetic must be completed without electronic calculation. It works by replacing one large opaque calculation with smaller exact steps that can be checked.

Write the relationship or operation before calculating.
Simplify first: cancel fractions, factor numbers or partition percentages.
Carry out one exact step per line.
Estimate the expected size and check signs and units.
State the final answer clearly and retain exact form unless rounding is requested.

Check: Do not revise from a predicted Paper 1 topic list. Use the specification and mixed practice because a topic seen on one paper can still be used or combined elsewhere.

Fully worked

Non-calculator preparation GCSE worked examples

Each solution explains the clue, why the method fits and how to check the result.

Example 1

Subtract fractions exactly

3 marks

Question

Work out $\frac34-\frac25$ .

The lowest common denominator is $20$ .

$\frac34=\frac{15}{20}$

$\frac25=\frac8{20}$

$\frac{15}{20}-\frac8{20}=\boxed{\frac7{20}}$

Example 2

Find a percentage by partitioning

2 marks

Question

Work out $15\%$ of $240$ .

$10\%\text{ of }240=24$

$5\%\text{ of }240=12$

$15\%\text{ of }240=24+12=\boxed{36}$

Example 3

Solve an equation visibly

3 marks

Question

Solve $3(2x-1)=21$ .

Expand the bracket.

$6x-3=21$

Add $3$ to both sides.

$6x=24$

Divide both sides by $6$ .

$\boxed{x=4}$

Example 4

Simplify a surd

Higher only2 marks

Question

Simplify $\sqrt{72}$ .

Use the largest square factor $36$ .

$\sqrt{72}=\sqrt{36\times2}$

$=6\sqrt2$

$\boxed{6\sqrt2}$

Example 5

Use exact trig values

2 marks

Question

Work out $4\sin30^\circ+2\cos60^\circ$ .

$4\left(\frac12\right)+2\left(\frac12\right)$

$=2+1$

$\boxed{3}$

12 original questions · total 33 marks

Non-calculator preparation GCSE exam-style questions

Try each question before opening its fully worked answer. The difficulty rises through the set.

Before you startAllow about 40 minutes · Do not use a calculator. Show the exact method, simplify before multiplying and check each answer by estimation or reversal where possible. · answers start collapsed

1

Subtract whole numbers

2 marks

Work out $704-286$ .

Show worked answer

$704-200=504$

$504-80=424$

$424-6=\boxed{418}$

2

Multiply using a useful factor

2 marks

Work out $36\times25$ .

Show worked answer

Since $25=100\div4$ ,

$36\times25=36\times100\div4$

$=3600\div4=\boxed{900}$

3

Add unlike fractions

3 marks

Work out $\frac56+\frac38$ . Give a mixed number.

Show worked answer

The lowest common denominator is $24$ .

$\frac56=\frac{20}{24},\qquad\frac38=\frac9{24}$

$\frac{20}{24}+\frac9{24}=\frac{29}{24}$

$\boxed{1\frac5{24}}$

4

Find a percentage

3 marks

Work out $18\%$ of $350$ .

Show worked answer

$10\%=35$

$8\%=4\times2\%=4\times7=28$

$18\%=35+28=\boxed{63}$

5

Share in a ratio

3 marks

Share £84 in the ratio $3:4$ .

Show worked answer

There are $7$ parts.

$84\div7=12$

$3\times12=36,\qquad4\times12=48$

$\boxed{£36\text{ and }£48}$

6

Solve with x on both sides

3 marks

Solve $5x-7=3x+13$ .

Show worked answer

Subtract $3x$ from both sides.

$2x-7=13$

Add $7$ .

$2x=20$

$\boxed{x=10}$

7

Expand two brackets

2 marks

Expand and simplify $(x+4)(x-2)$ .

Show worked answer

$x(x-2)+4(x-2)$

$=x^2-2x+4x-8$

$\boxed{x^2+2x-8}$

8

Calculate in standard form

3 marks

Work out $(3\times10^5)(4\times10^{-2})$ . Give the answer in standard form.

Show worked answer

Multiply the numbers and the powers separately.

$3\times4=12$

$10^5\times10^{-2}=10^3$

$12\times10^3=\boxed{1.2\times10^4}$

9

Use index laws

2 marks

Work out $2^5\times2^{-2}$ .

Show worked answer

Add the powers because the base is the same.

$2^5\times2^{-2}=2^{5-2}$

$=2^3=\boxed{8}$

10

Use Pythagoras exactly

3 marks

A right-angled triangle has shorter sides $6$ cm and $8$ cm. Find its hypotenuse.

Show worked answer

$c^2=6^2+8^2$

$c^2=36+64=100$

$c=\sqrt{100}$

$\boxed{c=10\text{ cm}}$

11

Use probability without replacement

Harder4 marks

A bag has $4$ red and $3$ blue counters. Two counters are taken without replacement. Find the probability both are red.

Show worked answer

The first red probability is $4/7$ . After taking one red, $3$ red counters remain out of $6$ .

$\frac47\times\frac36$

$=\frac{12}{42}$

$\boxed{\frac27}$

12

Estimate a calculation

3 marks

Estimate $\dfrac{19.8\times0.51}{4.9}$ .

Show worked answer

Round each number to one significant figure.

$19.8\approx20,\quad0.51\approx0.5,\quad4.9\approx5$

$\frac{20\times0.5}{5}=\frac{10}{5}$

$\boxed{2}$

Examiner-style feedback

Common non-calculator GCSE Maths mistakes

Revising a predicted topic list

A published or social-media list cannot guarantee paper content. Revise connected skills across the specification.

Doing all arithmetic mentally

Written partitioning, common denominators and algebra protect both accuracy and method marks.

Turning exact answers into decimals

Keep fractions, surds and π exact unless a question specifically requests a decimal accuracy.

Skipping a reasonableness check

A one-significant-figure estimate can expose a place-value or sign error before time runs out.

30-second recap

Choose, carry out, check

Translate the wording before you reach for a rule.

Any permitted content can be assessed.
Write the relationship before calculating.
Simplify and partition numbers.
Keep exact values and check the result.

Quick answers

Non-calculator preparation FAQ

Which topics are on GCSE Maths non-calculator papers?

There is no definitive topic-only list. Prepare across the specification and practise skills that require exact hand calculation.

Is Paper 1 always non-calculator?

For current Edexcel and AQA GCSE Maths, Paper 1 is non-calculator. For OCR, the second paper at each tier is non-calculator: J560/02 at Foundation and J560/05 at Higher.

Should I show working?

Yes. Visible setup and intermediate steps can earn method marks and make errors easier to find.

Should I convert fractions and surds to decimals?

No, unless a decimal approximation is requested. Exact form is normally preferable without a calculator.

Build connected skills

What to revise next

Exact arithmetic

Fractions

Use common denominators and exact operations confidently.

Revise fractions

Powers of ten

Standard form

Calculate with coefficients and index laws by hand.

Revise standard form

Special angles

Exact trig values

Use exact sine, cosine and tangent ratios.

Revise exact trig values

Content standards

Curriculum and rights review

Reviewed 5 September 2026 against current assessment structures and official specifications. It deliberately avoids predicting fixed paper topics. All practice questions are original.

Official specification references