GCSE Maths Exam Study Guide (2027)
Everything the GCSE Maths (9-1) Exam tests, topic by topic: what each section covers, the facts that come up most, and how to study it. Pair it with the free 15-question practice test.
The exam at a glance
| Questions | AQA and Edexcel: 3 written papers, 80 marks each (240 marks in total). OCR: 3 papers of 100 marks each |
|---|---|
| Time | 4 hours 30 minutes in total (3 × 1 hour 30 minutes) |
| Grades and pass mark | Grade 4 is a standard pass and grade 5 a strong pass. Boundaries are set after every exam series, so aim for 70% in practice |
| Format | Written exam, Foundation tier (grades 1 to 5) or Higher tier (grades 4 to 9). AQA and Edexcel: paper 1 non-calculator, papers 2 and 3 calculator. OCR: the middle paper of each tier is non-calculator. A formulae sheet is provided |
| Exam boards | AQA, Pearson Edexcel and OCR |
| Test provider | At your school or college, or as a private candidate at an exam centre that accepts them |
Mind map: the whole exam on one screen
Read the complete GCSE Maths study notes for “Number”
Our first full set of comprehensive notes, about 18 minutes of reading: Order of operations and negative numbers · Primes, factors, HCF and LCM · Fractions, decimals and percentages · Powers, roots and the index laws · Standard form · Rounding, estimation and bounds · Surds (Higher), a worked exam example, the traps examiners use and a one-minute recap. Create a free account to read it and see how premium notes work before you decide.
1. Number
Place value, the four operations with integers, decimals and fractions, powers and roots, primes, standard form, surds (Higher), rounding, estimation and bounds. About a quarter of the Foundation marks and around 15% of Higher.
Key facts
- Order of operations is BIDMAS: brackets, indices, division and multiplication (left to right), addition and subtraction (left to right).
- Prime factor decomposition: divide by primes until you reach 1 and write the result in index form, e.g. 360 = 2³ × 3² × 5. Use it to find the HCF (common primes, lowest powers) and LCM (all primes, highest powers).
- Fractions: to add or subtract use a common denominator; to multiply, multiply tops and bottoms; to divide, flip the second fraction and multiply. Convert mixed numbers to improper fractions first.
- Index laws: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m-n), (a^m)^n = a^(mn), a⁰ = 1, a^(-n) = 1/a^n, a^(1/n) = ⁿ√a and a^(m/n) = (ⁿ√a)^m.
- Standard form is A × 10^n with 1 ≤ A < 10 and n an integer. To multiply, multiply the A values and add the powers, then readjust so A is between 1 and 10.
- Rounding: to significant figures count from the first non-zero digit; to estimate, round each number to 1 significant figure before calculating.
- Error intervals: a value rounded to the nearest unit lies within half a unit either side, written as lower bound ≤ x < upper bound. Truncation intervals only go upwards from the truncated value.
- Higher: simplify surds with √(ab) = √a × √b (√48 = 4√3) and rationalise denominators by multiplying by the surd, or by the conjugate for a + √b. Recurring decimals convert to fractions by subtracting multiples, e.g. 0.4545... = 45/99 = 5/11.
Flashcards
Exam tip: Most Number marks are lost on the non-calculator paper through slips, not lack of knowledge. Write every step of a written method and check with a rough estimate.
2. Algebra
Notation, expressions, equations, inequalities, sequences, graphs and, at Higher, functions, algebraic proof and iteration. Algebra is the largest Higher content area at about 30% of the marks.
Key facts
- Expand single brackets by multiplying every term inside; expand double brackets by multiplying every term in one by every term in the other (FOIL or a grid).
- Factorise by taking out the highest common factor. Quadratics x² + bx + c factorise to (x + p)(x + q) where pq = c and p + q = b; difference of two squares a² - b² = (a + b)(a - b).
- Solve linear equations by doing the same to both sides. Solve quadratics by factorising, the quadratic formula x = (-b ± √(b² - 4ac)) / 2a, or completing the square (Higher).
- Straight lines: y = mx + c, where m is the gradient (change in y ÷ change in x) and c the y-intercept. Parallel lines have equal gradients; perpendicular gradients multiply to -1.
- Sequences: the nth term of a linear sequence is dn + (first term - d), where d is the common difference. Higher: quadratic sequences have a constant second difference; the n² coefficient is half of it.
- Simultaneous equations: eliminate one variable by matching coefficients, or substitute. At Higher, one equation may be quadratic or a circle; substitute the linear one into it.
- Inequalities: solve like equations, but reverse the sign when you multiply or divide by a negative. Show solutions on a number line (open circle for < or >, filled for ≤ or ≥).
- Higher: rearrange formulae to change the subject, find composite and inverse functions, use iteration x(n+1) = f(x(n)), and recognise graphs of quadratic, cubic, reciprocal, exponential and trigonometric functions and their transformations.
Flashcards
Exam tip: Substitute your answer back into the original equation. It takes 20 seconds and catches sign errors before they cost you the accuracy mark.
3. Ratio, Proportion and Rates of Change
Ratio, percentages, direct and inverse proportion, compound measures, growth and decay, and gradients as rates of change. About a quarter of Foundation and around 20% of Higher.
Key facts
- Share in a ratio: add the parts, divide the total by the number of parts, then multiply by each share. If you know the difference between shares, divide that by the difference in parts.
- Percentage change = (change ÷ original) × 100. Multipliers: an increase of r% is × (1 + r/100), a decrease of r% is × (1 - r/100).
- Reverse percentages: divide the new amount by the multiplier, e.g. a price after a 20% rise of £96 was £96 ÷ 1.2 = £80.
- Compound interest and growth: amount = original × multiplier^n. Depreciation uses a multiplier less than 1.
- Direct proportion: y = kx (straight line through the origin). Inverse proportion: y = k/x. Higher: y = kx², y = k/√x and similar forms, find k first from the given pair of values.
- Compound measures: speed = distance ÷ time, density = mass ÷ volume, pressure = force ÷ area. Convert time in minutes to hours by dividing by 60.
- Scale factors: lengths × k, areas × k², volumes × k³. Map scales 1 : 25 000 mean 1 cm represents 25 000 cm = 250 m.
- Rates of change: the gradient of a distance-time graph is speed; of a velocity-time graph is acceleration, and the area under a velocity-time graph is distance (Higher).
Flashcards
Exam tip: With percentages, decide first whether you know the original amount or the new amount. Reverse percentage questions are the classic trap: never take the percentage of the new amount.
Test yourself on these topics
Take the free 15-question GCSE Maths test, then save your results to unlock your Readiness Score and the mistakes bank.
4. Geometry and Measures
Angles, polygons, constructions, transformations, area and volume, Pythagoras, trigonometry, circle theorems and vectors (Higher). About 15% of Foundation and 20% of Higher.
Key facts
- Angles on a straight line sum to 180°, around a point 360°, in a triangle 180°. Alternate angles are equal, corresponding angles are equal, co-interior angles sum to 180°.
- Polygons: the exterior angles of any polygon sum to 360°; interior angle sum = (n - 2) × 180°.
Flashcards
Exam tip: In angle questions give a geometric reason for every step ('alternate angles are equal'). Reasons are often worth their own mark.
5. Probability
Probability scales, relative frequency, sample spaces, Venn diagrams, tree diagrams and, at Higher, conditional probability. Probability and statistics together are about 15% of both tiers.
Key facts
- Probabilities lie between 0 (impossible) and 1 (certain). P(not A) = 1 - P(A). The probabilities of all mutually exclusive outcomes sum to 1.
- Relative frequency = number of times an outcome happens ÷ number of trials. More trials give a more reliable estimate.
Flashcards
Exam tip: Write probabilities as fractions, decimals or percentages, never as ratios or '3 in 10'. Leave fractions unsimplified if that avoids an arithmetic slip; any equivalent fraction scores.
6. Statistics
Sampling, averages and spread, charts and diagrams, scatter graphs and correlation, and at Higher, cumulative frequency, box plots and histograms.
Key facts
- Mean = total ÷ number of values; median = middle value when ordered (position (n + 1)/2); mode = most common; range = largest - smallest.
- From a frequency table, the mean is Σfx ÷ Σf. For grouped data use midpoints, which gives an estimate of the mean.
Flashcards
Exam tip: 'Compare' questions need two comparisons, one of average and one of spread, each written in context, e.g. 'Class A's median score is higher, so on average they did better'.
How to pass
- AQA and Edexcel papers have 80 marks in 90 minutes, a little over 1 minute per mark. A 4-mark question deserves about 4 to 5 minutes; if you have spent double that, move on and come back.
- Show your working on every question worth 2 marks or more. Method marks are given even when the final answer is wrong, and a correct answer with no working can score zero on 'show that' questions.
- On the non-calculator paper, practise written methods for long multiplication, division with decimals and fraction arithmetic until they are automatic. These are the marks most often lost to slips.
- Read the last line of the question again before you write the answer: check the units, the rounding asked for (decimal places or significant figures) and whether it says 'give your answer in terms of π'.
- Use the formulae sheet, but still learn the formulae it does not include, such as the area of a circle, Pythagoras' theorem and the trigonometric ratios.
Frequently asked questions
How long should I study for the GCSE Maths exam?
Most students do best starting 10 to 12 weeks before the first paper, with 30 to 45 minutes a day per subject. You're ready once your Readiness Score has stayed at 80 or higher for about a week.
Can I take the GCSE Maths exam online?
No. GCSE Maths is a written exam sat in person at your school, college or an approved exam centre. Format: written exam, Foundation tier (grades 1 to 5) or Higher tier (grades 4 to 9). AQA and Edexcel: paper 1 non-calculator, papers 2 and 3 calculator. OCR: the middle paper of each tier is non-calculator. A formulae sheet is provided. Check your exam board's timetable for dates.
What score do I need to pass the GCSE Maths exam?
Grade 4 is a standard pass and grade 5 a strong pass. Boundaries are set after every exam series, so aim for 70% in practice. The exam has aqa and edexcel: 3 written papers, 80 marks each (240 marks in total). ocr: 3 papers of 100 marks each and a time limit of 4 hours 30 minutes in total (3 × 1 hour 30 minutes).
What are the most tested topics?
The outline covers number, algebra, ratio, proportion and rates of change, geometry and measures, probability, statistics. Use the free practice test to see which ones you need most.
The premium GCSE Maths study path
Premium GCSE Maths prep is studied one topic at a time. Each step starts with that topic's key notes and flashcard deck, then its own question sets of 25, so you master one topic before you move to the next. When every topic is strong, the 6 full mock exams show you're ready.
Your step-by-step study path
- 1Number10 key notes, 135 flashcards, then 500 practice questions in 20 sets of 25Notes free with an account
- 2Algebra10 key notes, 135 flashcards, then 500 practice questions in 20 sets of 25Premium
- 3Ratio, Proportion and Rates of Change10 key notes, 135 flashcards, then 500 practice questions in 20 sets of 25Premium
- 4Geometry and Measures10 key notes, 135 flashcards, then 500 practice questions in 20 sets of 25Premium
- 5Probability10 key notes, 130 flashcards, then 500 practice questions in 20 sets of 25Premium
- 6Statistics10 key notes, 130 flashcards, then 500 practice questions in 20 sets of 25Premium
- Final step: 6 full mock exams50 questions each, timed like exam day. Hit your target on them before your first paper.Premium
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Summarised from the exam boards' published specifications and the rules cited, checked November 2026. Confirm current requirements with AQA, Pearson Edexcel and OCR.