Mathematics exam tips

Exam technique for Mathematics

AQA GCSE Maths rewards clear working, use of correct notation, and efficient technique. Marks come from method as well as answers, so showing every step is non-negotiable. Time pressure is real—90 minutes for 80 marks means just over 1 minute per mark.

Paper-by-Paper Strategy

Paper 1 (Non-Calculator)

90 minutes • 80 marks • Both

Paper Structure

Questions 1-1025 marks

Foundation skills: fractions, percentages, basic algebra, angles

  • •Do not use a calculator—examiners design these to test mental maths and written methods
  • •Show all working for column addition/multiplication
  • •Simplify fractions fully
Questions 11-2035 marks

Mid-tier: ratio, sequences, equations, area/perimeter

  • •Write down formulas before substituting
  • •Label diagrams with known values first
  • •Use estimation to check if your answer is realistic
Questions 21-2520 marks

High-demand: algebraic proof, problem-solving, multi-step reasoning

  • •Read the question twice—every word matters
  • •Break complex problems into smaller steps
  • •Explain your reasoning when asked to "show" or "prove"

Tackling Order

  1. 1Skim all questions first to identify easy wins
  2. 2Do Q1-10 in order to build confidence
  3. 3Cherry-pick questions you recognize from Q11 onwards
  4. 4Return to harder questions with remaining time

Time Allocation

Questions 1-10
Quick wins that build momentum. Aim for 2.5 minutes per question.
25m
Questions 11-20
These are 3-5 mark questions. Allocate 3-4 minutes each.
40m
Questions 21-25
High-mark questions. Spend up to 5 minutes if needed.
20m
Final check
Check units, signs, and that you answered what was asked.
5m

Paper 2 (Calculator)

90 minutes • 80 marks • Both

Paper Structure

Questions 1-1230 marks

Standard form, compound interest, trigonometry, data handling

  • •Use your calculator efficiently—store intermediate values
  • •Write down the calculation you're entering before pressing =
  • •Round only at the final answer, not during working
Questions 13-2235 marks

Graphs, transformations, probability, volume, Pythagoras

  • •Sketch graphs roughly first to visualize the problem
  • •Use exact values (π, √) unless told to round
  • •Check probability answers are between 0 and 1
Questions 23-2615 marks

Extended questions: multiple topics combined, wordy contexts

  • •Underline key numbers and what you need to find
  • •Use diagrams or tables to organize information
  • •Show clear method even if you make a calculation error

Tackling Order

  1. 1Scan for questions involving your strong topics (e.g., if you love trig, find those first)
  2. 2Do questions with diagrams or graphs early—they often unlock marks quickly
  3. 3Save wordy multi-step questions for when you're warmed up

Time Allocation

Questions 1-12
Allow ~2.5 minutes per question for calculator work and checking.
32m
Questions 13-22
Mid-range questions worth 3-5 marks each.
40m
Questions 23-26
High-value questions. Spend what's needed but watch the clock.
13m
Final check
Re-read questions with "show that" or "give your answer to..."
5m

Paper 3 (Calculator)

90 minutes • 80 marks • Both

Paper Structure

Questions 1-1128 marks

Algebraic manipulation, inequalities, bounds, histograms

  • •Write algebraic steps line-by-line
  • •Use inequality symbols correctly—practice < vs ≤
  • •For histograms, remember frequency density = frequency ÷ class width
Questions 12-2037 marks

Quadratics, circle theorems, vectors, cumulative frequency

  • •Factorize quadratics by inspection or formula—show both steps
  • •State circle theorems before applying them
  • •Draw vector diagrams to visualize addition/subtraction
Questions 21-2415 marks

Problem-solving: real-world contexts, multi-step reasoning

  • •Translate words into maths: "three more than twice x" = 2x + 3
  • •Check your answer makes sense in context (e.g., can't have negative people)
  • •If stuck, write down what you know and look for connections

Tackling Order

  1. 1Start with algebraic questions if you're confident—they're methodical
  2. 2Tackle geometry (circle theorems, vectors) when you're fresh
  3. 3Leave problem-solving questions until you've banked easier marks

Time Allocation

Questions 1-11
Foundation and mid-tier questions. Keep moving.
30m
Questions 12-20
Core marks. Allocate time generously here.
42m
Questions 21-24
Harder questions. Attempt all parts—even partial credit counts.
13m
Final check
Check you've answered the question (e.g., asked for perimeter, not area).
5m

Command Words Decoded

Calculate

2-4 marks: 1 for method, rest for correct answer

Work out a numerical answer

→Show every step of your working
→Write down the formula or method you're using
→Include units in your final answer
→Round only if instructed (e.g., "to 2 d.p.")
Example: "Calculate the area of the triangle." → Write A = ½bh, substitute, solve, add units.

Show that

2-3 marks: full working required for all marks

Prove the given answer is correct

→Start with what you're given
→Show full algebraic or numerical working
→Conclude by stating the result matches the given answer
→Never just write the answer—you must demonstrate the path
Example: "Show that x = 5" → Solve the equation step-by-step, ending with "therefore x = 5".

Explain

1-2 marks: clarity and mathematical reasoning

Describe why something is true using reasoning

→Use full sentences
→Reference mathematical concepts or properties
→Link your reasoning to the question context
→Avoid just stating the answer without justification
Example: "Explain why the shape is a parallelogram." → "Opposite sides are parallel (state angles/vectors), so it's a parallelogram."

Estimate

2 marks: 1 for rounding, 1 for calculation

Find an approximate answer by rounding

→Round numbers to 1 significant figure first
→Write down your rounded values
→Perform the calculation with rounded numbers
→State your estimate clearly
Example: "Estimate 19.8 × 3.2" → Round to 20 × 3, estimate = 60. Do not calculate exactly.

Solve

2-4 marks: method marks for correct steps, accuracy mark for answer

Find the value(s) of the unknown

→Show each step of rearranging/simplifying
→Balance both sides of equations
→Give exact answers unless told to round
→For quadratics, give both solutions if they exist
Example: "Solve 3x + 7 = 25" → 3x = 18, x = 6. Show the subtraction and division steps.

Sketch

2-3 marks: shape, labels, key features

Draw a rough diagram showing key features

→Label axes and key points (e.g., intercepts, turning points)
→Show the general shape accurately
→You don't need graph paper or precise plotting
→Mark any asymptotes or critical values
Example: "Sketch y = x²" → U-shape crossing (0,0), opening upwards, label the vertex.

Write down

1 mark: correct answer only

State an answer without detailed working

→You can often read this directly from a graph or given information
→Minimal working needed, but write something if it helps you
→Be precise—examiners expect the exact value
Example: "Write down the y-intercept of y = 2x + 5" → 5 (just state it).

Prove

3-4 marks: logical flow and conclusion

Show something is always true using logical steps

→Start with a general case (e.g., "let n be any integer")
→Use algebraic manipulation to reach the conclusion
→State your conclusion clearly
→This is like "show that" but more formal
Example: "Prove the sum of two odd numbers is even" → Let 2n+1 and 2m+1 be odd. Sum = 2n + 2m + 2 = 2(n+m+1), which is even.

Hence

1-2 marks: using previous result correctly

Use your previous answer to do this part

→Look at what you just worked out
→Apply it directly to the new question
→You should not need to start from scratch
→Refer to your previous result explicitly
Example: If you found x = 3 in part (a), "hence find 2x + 1" → Use x = 3, so 2(3) + 1 = 7.

Timing Strategy

~1 minute per mark, plus 5 minutes for final checks

Key Strategies

  • ✓Skim the entire paper first (2 minutes) to spot familiar questions
  • ✓Do the easiest questions first to bank marks quickly
  • ✓If stuck for >2 minutes, move on and return later
  • ✓For 5-6 mark questions, spend proportionally more time but cap at 7 minutes
  • ✓Write something for every question—even partial method earns marks
Buffer Time

Aim to finish with 5-10 minutes spare for checking

When You're Stuck

  • →Write down what you know (given values, relevant formula)
  • →Sketch a diagram or table to organize information
  • →Check if "hence" means you can use a previous answer
  • →Attempt the first step even if you can't finish—method marks count
  • →Move on and return if time allows

Mark Scheme Insights

Method marks (M)

You earn M marks for using the correct method, even if your final answer is wrong.

Examples

  • •Writing down the correct formula (e.g., area = πr²)
  • •Setting up an equation correctly (e.g., 3x + 5 = 20)
  • •Showing the first step of a calculation

Mark Boosters

  • ✓Always write the formula before substituting numbers
  • ✓Show your working line-by-line
  • ✓Even if you make an arithmetic error, you can still get method marks

Accuracy marks (A)

A marks are for the correct final answer. You usually need the method mark first.

Examples

  • •The correct numerical answer
  • •The answer in the required form (e.g., simplified fraction)
  • •The answer with correct units

Mark Boosters

  • ✓Double-check your arithmetic
  • ✓Read the question for rounding instructions (e.g., 2 d.p., 3 s.f.)
  • ✓Include units if the question involves measurements

Communication marks (C)

C marks reward clear explanations, correct notation, and logical reasoning.

Examples

  • •Using "therefore" or "so" to link steps
  • •Stating circle theorems or angle facts
  • •Explaining why an answer makes sense in context

Mark Boosters

  • ✓Write in sentences for "explain" or "prove" questions
  • ✓Quote theorems or rules (e.g., "opposite angles in a parallelogram are equal")
  • ✓Conclude with a summary statement

Follow-through marks (FT)

If you make an early error, you can still earn marks for correct working using your wrong answer.

Examples

  • •You calculate x = 7 instead of x = 5 in part (a)
  • •In part (b), you correctly use x = 7 to find y
  • •You get the FT mark for correct method in (b)

Mark Boosters

  • ✓Never give up after an error—keep going with your value
  • ✓Show all working so examiners can award FT marks
  • ✓Check if your working is consistent even if the initial answer is wrong

Quality of written communication (QWC)

Some questions assess QWC—your spelling, grammar, and organization matter.

Examples

  • •Extended response questions (usually 4+ marks)
  • •Explanations or proofs
  • •Questions asking you to "describe" or "explain"

Mark Boosters

  • ✓Use correct mathematical vocabulary
  • ✓Write neatly and organize your answer logically
  • ✓Use bullet points or numbered steps for clarity

Common Mistakes to Avoid

Not reading the question carefully

Why: Exam pressure makes you rush and assume what's being asked
Fix: Underline key words like "perimeter," "area," "positive values only." Read twice.
⚠️ Lost marks: 1-3 marks per question—adds up fast

Rounding too early

Why: Calculator display shows rounded values, you write them down mid-working
Fix: Use your calculator's memory/ANS button. Only round at the final answer.
⚠️ Lost marks: 1 accuracy mark per question

Forgetting units

Why: Focus on the number, forget the question asks for cm², km/h, etc.
Fix: Circle or highlight the unit required in the question. Write it next to your answer.
⚠️ Lost marks: 1 mark per question (and it's an easy mark to lose)

Not showing working

Why: Work out the answer in your head or on the calculator, just write the answer
Fix: Even if it's simple, write one line of working. Method marks are free points.
⚠️ Lost marks: Up to 2-3 method marks per question

Misreading negative signs

Why: Negative signs are small and easy to miss, especially in algebra
Fix: Circle or highlight negatives. Double-check when substituting into formulas.
⚠️ Lost marks: 1-2 marks per question

Using the wrong formula

Why: Confusing area/perimeter, volume/surface area, or trig ratios
Fix: Write the formula first, then check it matches what you need. Use the formula sheet.
⚠️ Lost marks: 2-4 marks (method and accuracy)

Giving rounded answers when exact is required

Why: Question asks for exact (e.g., in terms of π or √) but you use decimals
Fix: Look for "exact" or "in terms of." Leave π, √, fractions as they are.
⚠️ Lost marks: 1 accuracy mark

Not attempting all parts of a question

Why: Stuck on part (a), assume you can't do part (b)
Fix: Every part is independent unless it says "hence." Always try (b), (c), etc.
⚠️ Lost marks: Could lose 3-6 marks by skipping parts

Running out of time

Why: Spending too long on hard questions early on
Fix: Strict timing: ~1 min/mark. If stuck after 2 minutes, move on. Come back later.
⚠️ Lost marks: Variable—could be 10+ marks if you don't finish

Not checking answers make sense

Why: Write down calculator answer without thinking if it's realistic
Fix: Ask: "Is this answer too big/small? Does it fit the context?" E.g., speed can't be negative.
⚠️ Lost marks: 1-2 marks per question

Last-Minute Tips

  • ★Memorize exact trig values: sin 30° = ½, cos 60° = ½, tan 45° = 1, sin 45° = cos 45° = √2/2
  • ★Quadratic formula: x = [-b ± √(b² - 4ac)] / 2a. Write it down if you forget.
  • ★Circle theorems: angle in semicircle = 90°, angles in same segment equal, opposite angles in cyclic quad sum to 180°
  • ★Probability: always check your answer is between 0 and 1
  • ★Bounds: lower bound = value - 0.5 × unit, upper bound = value + 0.5 × unit
  • ★Frequency density = frequency ÷ class width (for histograms)
  • ★Sine rule: a/sin A = b/sin B. Cosine rule: a² = b² + c² - 2bc cos A
  • ★Area of trapezium: ½(a + b)h. Area of triangle: ½ab sin C or ½ base × height
  • ★Interior angle sum: (n - 2) × 180°. Each interior angle of regular polygon: [(n - 2) × 180°] / n
  • ★Speed = distance / time. Density = mass / volume. Pressure = force / area.

Calculator Tips

  • •Store intermediate answers using "ANS" or memory buttons—don't round and re-type
  • •For fractions: use the fraction button (a b/c) to keep answers exact
  • •For powers/roots: use the ^ key (e.g., 5^3 = 125, 2^0.5 = √2)
  • •For standard form: use "×10^" or EXP button (e.g., 6 ×10^-3)
  • •Check your calculator is in degree mode for trig (not radians)
  • •Use brackets generously: (5 + 3) / (2 × 4) to avoid order-of-operations errors
  • •For negative numbers: use (-) button, not minus key
  • •Practice entering complex calculations before the exam

Formula Sheet Tips

  • •You don't get a formula sheet in GCSE Maths—memorize all formulas
  • •Core formulas to know cold: area/perimeter of shapes, volume of prisms/cylinders/spheres, Pythagoras, trig ratios, quadratic formula, sine/cosine rules
  • •If you forget a formula in the exam, try to derive it from first principles or use logic
  • •Write formulas at the top of your answer space if it helps you remember