GCSE Maths Guide

Foundation tier is graded 1–5. Higher tier is graded 4–9 (with a safety net grade 3). Choose Foundation if you're working at grade 4 or below in mock exams — you'll have more time per question and better chance of a strong pass.

Choose Higher if you're consistently scoring grade 5+ in mocks and aiming for sixth-form A-level Maths (most schools require grade 6 or 7). Higher includes topics that don't appear at Foundation: trigonometry beyond the basics, vectors, advanced algebra, circle theorems.

All boards use three 90-minute papers (80 marks each). Paper 1 is non-calculator; Papers 2 and 3 are calculator. Total 240 marks across the three papers.

Don't leave the calculator papers to chance — they have specific topics (statistics, probability, complex algebra) that benefit from calculator work. Practise with the exact calculator you'll use on the day (Casio fx-83 or fx-85 are the standards).

Foundation: Number 25%, Algebra 20%, Ratio & Proportion 25%, Geometry 15%, Statistics & Probability 15%. Higher: Number 15%, Algebra 30%, Ratio & Proportion 20%, Geometry 20%, Statistics & Probability 15%.

At Higher, algebra is the single biggest area and the topic that separates grade 6 from grade 8. Master quadratics, simultaneous equations, functions and graph transformations.

Six-month plan: Months 1–2 work through a topic-by-topic revision guide (CGP, Collins) doing every example. Months 3–4 drill past papers by topic. Months 5–6 full timed past papers — at least one a week, marked against the official mark scheme.

Past papers are the single most important resource. Each board publishes 5+ years of past papers free on their website. Aim to complete 12+ full papers before the real exam.

Showing no working on calculator papers — even right answers can lose method marks. Misreading the question (especially negatives, units and rounding instructions). Spending too long on one question instead of moving on.

Calculator slips: forgetting BIDMAS / order of operations, mis-typing fractions, leaving the calculator in degrees mode for radian questions (or vice versa).

Surds and indices: simplifying √48, rationalising 1/√2, fractional and negative powers. These appear on every Higher paper and are worth easy marks if you've drilled the rules.

Compound and reverse percentages: '£2,400 after a 20% increase — what was the original?' Most candidates divide by 1.2; many forget. Practise until the method is automatic.

Vectors and circle theorems: typically the hardest Higher questions, worth 4–6 marks each. Learn the eight named circle theorems (angle at centre, angle in semicircle, alternate segment, etc.) and the column-vector arithmetic for parallel and collinear questions.

On Foundation, the killer topics are area/perimeter of compound shapes, ratio sharing, and time-table reading. None are conceptually hard — they need slow, careful reading.

Each board provides a small formula sheet at the front of the exam (since 2022). It includes the quadratic formula, sine and cosine rules, area of a trapezium, volume of cone/sphere, and the kinematics SUVAT equations.

You still must memorise: area and circumference of a circle, area of a triangle (½ × base × height), Pythagoras, the standard trigonometric ratios (SOH-CAH-TOA), exact trig values (sin/cos/tan of 0°, 30°, 45°, 60°, 90°), and the equation y = mx + c. Make a one-page formula card and review it daily for the last two weeks.

If you don't get a grade 4 in summer, you can resit in November (Edexcel and AQA both offer a November series for English Language and Maths only). Otherwise the next sitting is the following June.

Functional Skills Level 2 in Maths is accepted by most apprenticeship providers, employers and many colleges as an equivalent to GCSE grade 4. It's a different style of exam — entirely applied, no algebra — and many resit students find it a faster route to a pass than a GCSE retake.

Universities and competitive sixth forms usually still want GCSE Maths grade 4 (sometimes 5 or 6 for STEM A-levels). If university is in the picture, prioritise the GCSE retake over Functional Skills.