GCSE Maths 2027: formula sheet, exam dates and grade boundaries

GCSE Maths formula sheet 2027: what you get

The exam boards call it a formulae sheet, Edexcel also calls it an exam aid, and you will hear it called the GCSE Maths equation sheet. It is all the same thing: a printed list that comes with each paper, in a Foundation or a Higher version. This table shows every formula on it.

AQA, Edexcel and OCR formula sheets

AQA and OCR list exactly these formulae for 2027. Download the official PDFs: AQA Foundation, AQA Higher, OCR Foundation and OCR Higher.

The newest Edexcel GCSE Maths formula sheets we could find on Pearson's public site are labelled 2026 (Foundation and Higher, checked on 7 November 2026). They list the same formulae, and AQA says its own 2027 sheets are unchanged from 2026.

The sheets are staying. Ofqual has confirmed they will continue from 2028 for the lifetime of the current GCSEs, so Year 10 students will get them too. Each year's sheets must be published by 1 September of the year before.

What you still need to memorise for GCSE Maths

The sheet does not hold everything you will use. Anything missing from it falls into one of two groups.

Given in the question: sphere, cone and constant acceleration

Ofqual lists these as formulae you should be able to use but need not memorise. They are not on the sheet. The exam supplies them when a question needs one.

• Volume of a sphere = 4/3 πr³, and surface area of a sphere = 4πr²
• Volume of a cone = 1/3 πr²h, and curved surface area of a cone = πrl
• Constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as

Not given: learn these

These are on the course but on no sheet, so they need to be in your head.

• Area of a rectangle, a parallelogram and a triangle (½ × base × height)
• Volume of a cuboid
• Straight lines: gradient and y = mx + c
• Compound units: speed = distance ÷ time, density = mass ÷ volume, pressure = force ÷ area
• Exact values of sin and cos for 0°, 30°, 45°, 60° and 90°, and of tan for 0°, 30°, 45° and 60°
• The laws of indices
• On Higher: the circle theorems and the equation of a circle, x² + y² = r²

How to use the formula sheet: two worked examples

Before you reach for the sheet, write down what the question gives you. The facts you have tell you which formula you need.

Foundation: compound interest

Question: £1,500 is saved at 4% compound interest per year for 5 years. How much is in the account at the end?

Use the compound interest formula with P = 1500, r = 4 and n = 5.

The answer is £1,824.98. The common slip is to work out 4% of £1,500 and multiply by 5. That gives simple interest of £300, so a wrong total of £1,800.

Higher: the cosine rule

Question: Two walkers set off from the same point along straight paths with an angle of 48° between them. One walks 9 km and the other walks 13 km. How far apart are they?

Draw the triangle. You know two sides and the angle between them, which means the cosine rule. Let a be the distance you want.

So a = √93.42 = 9.67 km to 3 significant figures. Keep the full value on your calculator until the last step, because rounding early can cost you the final mark.

Now try one yourself. The quadratic formula is on the Higher sheet, and this question comes from our Algebra course. Answer it here and press Mark to see how you did.

GCSE Maths exam dates 2027

The summer 2026 exams have finished, so these are the next dates. All three boards have published final timetables (AQA, Edexcel and OCR), and each paper is a morning exam.

• Results day: Thursday 19 August 2027.
• Contingency day: Wednesday 23 June 2027. If exams are seriously disrupted this is the back-up date, so you must stay available until then.
• All GCSEs: the JCQ common timetable runs from 10 May to 18 June 2027.

Your school will give you a personal timetable, and that is the one to follow.

GCSE Maths papers: marks, time and which is non-calculator

The three papers count equally and your grade comes from your total, so no single paper gets its own grade. Content from any part of the course can appear on any paper. You must sit all three papers at the same tier and in the same exam series.

Ask your teacher which board you are on, because the marks and the order of the papers differ. The full rules are in each specification: AQA GCSE Maths, Edexcel GCSE Maths specification and OCR GCSE Maths.

GCSE Maths grade boundaries

A grade boundary is the lowest total mark that earns a grade, added up across your three papers. Boundaries are set each year to reflect how hard the papers were, so nobody can tell you the marks in advance. The latest figures below are from June 2026, taken from the boards' own documents (AQA, Edexcel and OCR).

How many marks is a 4 in GCSE Maths Foundation?

In June 2026, a grade 4 on Foundation took 154 out of 240 with AQA (64%), 151 out of 240 with Edexcel (63%) and 133 out of 300 with OCR (44%). Aim well above these, because the boundary moves. In June 2025 the same grade took 160 with AQA, 144 with Edexcel and 134 with OCR.

Higher tier grade boundaries

A 4 on Higher takes far fewer marks than a 4 on Foundation because the papers are harder. Half the marks on Higher are aimed at grades 7 to 9, and Ofqual explains that only about a sixth are designed for students working at grade 4.

Edexcel GCSE Maths grade boundaries show how far things can shift in a year. Between June 2025 and June 2026, a grade 7 on Higher fell from 156 to 146, while a grade 4 on Foundation rose from 144 to 151. Treat any boundary as a guide, not a target.

AQA Further Maths is not a GCSE. It is the Level 2 Certificate in Further Mathematics (8365), marked out of 160. In June 2026 a grade 9 took 133 marks, a grade 7 took 98 and a grade 4 took 55.

GCSE Maths topics and weightings

Ofqual sets how much of the exam each topic area is worth, and boards may move each figure by up to 3 percentage points.

On Foundation, half the marks come from number and ratio. On Higher, half come from algebra and geometry, and algebra alone is worth 30%. Start with the areas worth the most on your tier:

• Number: the Prime Factorisation Calculator, LCM Calculator, GCF Calculator (for HCF), Exponent Calculator, Scientific Notation Calculator (for standard form) and Significant Figures Calculator.
• Algebra: the Algebra course runs from expressions to quadratics and simultaneous equations. Check your working with the Factoring Calculator, Simultaneous Equations Solver and Sequences and Series Calculator.
• Graphs: the Graphing Functions course, with the Linear Graph and Quadratic Graph tools.
• Ratio and proportion: practise these in the Foundation daily paper, which covers ratio and proportion.
• Geometry: the Trigonometry course, the Midpoint and Distance Calculator and the Vectors Calculator.
• Probability and statistics: the Probability course, Probability Calculator, Mean, Median and Mode Calculator, Histogram Maker and Box Plot Maker.

GCSE Maths Foundation or Higher: how to choose

Grades 4 and 5 are the overlap. At least 20% of the marks on each tier come from questions shared by both tiers, aimed at those two grades. The Department for Education recognises a grade 4 as a standard pass in all subjects, and a grade 5 in English or maths as a strong pass in its headline school performance measure.

• You need a 6 or above: choose Higher, because Foundation stops at 5. Check what your sixth form or college asks for first.
• A 4 or 5 is the goal and Higher papers feel out of reach: Foundation is often the safer route. A 4 on Higher takes fewer marks, but half of each paper is aimed at grades 7 to 9, and falling too far short leaves you unclassified.
• You are not sure: use your mock. Compare your total with the boundary tables above, then talk to your maths teacher. Your school makes the entry, and the exam boards' deadline for summer entries is 21 February 2027, so raise it early.

Hardest GCSE Maths questions, with worked answers

The hardest GCSE Maths questions usually come late in Higher papers, and the formula sheet alone won't solve them. Edexcel's Summer 2025 examiners' reports picked out proof (Paper 1H), quadratic inequalities and 3D geometry (Paper 2H), and vectors and tangents to a circle (Paper 3H). We wrote the questions below for this guide. Try each one before you read the answer.

Algebraic proof

Question: Prove that (n + 5)² − (n + 3)² is a multiple of 4 for every whole number n.

Expand both brackets, then collect like terms. Take care with the minus sign in front of the second bracket.

Finish in words: 4(n + 4) is 4 times a whole number, so it is always a multiple of 4. Testing a few numbers proves nothing. Edexcel's examiners gave no marks to answers that only used numerical values.

Quadratic inequalities

Question: List all the integers that satisfy x² − 3x − 10 < 0.

Factorise to find where the curve crosses the x-axis.

The curve crosses at x = 5 and x = −2. The question asks where it is below zero, and the graph shows that happens between those points, so −2 < x < 5. The integers are −1, 0, 1, 2, 3 and 4. Leave out −2 and 5, because the expression equals 0 there and the inequality is strict.

Check more of these with the Inequality Solver.

3D Pythagoras and trigonometry

Question: A hot air balloon hovers 200 m directly above a point P on flat ground. An observer stands 300 m east and 400 m north of P. Find the angle of elevation of the balloon from the observer.

1. Find the distance along the ground from the observer to P: √(300² + 400²) = √250000 = 500 m.
2. Picture a vertical right-angled triangle standing on that line. Its base is 500 m and its height is 200 m.
3. Use tan: tan θ = 200 ÷ 500 = 0.4, so θ = 21.8° to 1 decimal place.

Both formulae are on the sheet. The hard part is finding the flat triangle inside the 3D picture, so sketch it first. In Edexcel's report on a 3D question, students sometimes made 5 or more calculations when 3 would do, and every extra step is another chance to slip.

Vectors

Vector questions reward one habit: write every step as a route from one point to another. Say vector OA = a and vector OB = b. You can't go straight from A to B in terms of what you know, so go through O: back along a, then forward along b.

That gives vector AB = −a + b = b − a. Direction is the main trap: Edexcel's examiners often saw a − b and b − a swapped, or brackets left out. To show three points lie on a straight line, find two vectors that are multiples of each other and share a point, then say so in words. See this on the Vectors Calculator, and practise it in the Higher daily paper.

Tangent to a circle

Question: The point (5, 2) lies on the circle x² + y² = 29. The tangent at that point meets the x-axis at A and the y-axis at B. O is the origin. Find the area of triangle OAB.

1. The radius runs from (0, 0) to (5, 2), so its gradient is 2/5.
2. A tangent meets the radius at 90°, so its gradient is the negative reciprocal, −5/2.
3. Use y − 2 = −5/2 (x − 5), which tidies to 5x + 2y = 29.
4. Put y = 0 to get A at x = 5.8, and put x = 0 to get B at y = 14.5.
5. The triangle has a right angle at O, so its area = ½ × 5.8 × 14.5 = 42.05 square units.

Check the line: at (5, 2), 5 × 5 + 2 × 2 = 29. Nothing here is on the formula sheet, so it is all recall and reasoning. Edexcel's examiners named tangents to a circle among the later questions that presented more challenge.

Common GCSE Maths mistakes

• Reverse percentages: a train fare rises by 25% to £60. £60 is 125% of the old fare, so the old fare was £60 ÷ 1.25 = £48. Taking 25% off £60 gives £45, which is wrong.
• Squaring a bracket: (n + 1)² is not n² + 1. Write it as (n + 1)(n + 1) and expand both brackets.
• Rounding too early: Edexcel's examiners saw this affect final answers in Summer 2025. Keep all the digits on your calculator until the last line.
• Assuming a right angle: if the question doesn't say a line is perpendicular, you can't treat it as if it is.
• Leaving out reasons: in a geometry proof, equal angles with no reason earn nothing. Write "corresponding angles", not just "parallel lines".
• Misreading replacement: check whether items go back before the second pick. Using the wrong assumption limits your marks.
• Expanding too soon: if a quadratic inequality is already factorised, use the brackets to find the critical values.

Use a daily paper as a short timed mock

Many schools are running Year 11 mocks now, and a full paper takes 90 minutes that you won't always have. Our daily papers fill the gap, with a new one each day at Foundation and Higher. Our GCSE maths mock papers page shows how to sit them as mocks.

1. Put the 2027 formula sheet for your tier next to you and nothing else.
2. Work to the suggested time. It follows the pace of the real exam, about 1.1 minutes a mark, which comes to 30 to 40 minutes.
3. Finish and read the mark scheme under each part, especially where you lost marks.
4. Note the topic area for every lost mark. If algebra keeps costing you on Higher, that is 30% of the exam, so go to the Algebra course before tomorrow's paper.

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