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AQA GCSE Maths formula sheet (8300): every formula and how to use it

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Formula sheet

Open the card to sit today's Maths paper with the sheet beside you. Below is what AQA prints, regrouped by topic. The inserts are marked "for exams in 2027 only" and come as two files, Foundation and Higher, so read the one for your tier.

Formula sheet

GCSE Maths Foundation

Open formula sheet

Perimeter, area and volume

\text{Area}=\frac{1}{2}(a+b)harea of a trapezium with parallel sides a and b and perpendicular height h
\text{Volume}=\text{area of cross section}\times\text{length}volume of a prism = area of cross section × length
C=2\pi r=\pi dcircumference of a circle, where r is the radius and d is the diameter
A=\pi r^2area of a circle

Quadratic formula

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}the solutions of ax² + bx + c = 0, where a is not 0 (Higher Tier only)

Pythagoras' theorem and trigonometry

a^2+b^2=c^2right-angled triangle with hypotenuse c
\sin A=\frac{a}{c}sine in a right-angled triangle ABC, with c the hypotenuse
\cos A=\frac{b}{c}cosine in a right-angled triangle ABC
\tan A=\frac{a}{b}tangent in a right-angled triangle ABC
\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}sine rule, for any triangle ABC (Higher Tier only)
a^2=b^2+c^2-2bc\cos Acosine rule, for any triangle ABC (Higher Tier only)
\text{Area}=\frac{1}{2}ab\sin Carea of a triangle (Higher Tier only)

Compound interest

\text{Total accrued}=P\left(1+\frac{r}{100}\right)^nP is the principal, r is the interest rate for each period in percent and n is the number of times the interest is compounded

Probability

P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)P(A) and P(B) are the probabilities of outcomes A and B
P(A\text{ and }B)=P(A\text{ given }B)\times P(B)conditional probability (Higher Tier only)

Foundation and Higher

FormulaFoundationHigher
Trapezium, prism, circleYesYes
Pythagoras and right-angled trigonometryYesYes
Compound interestYesYes
P(A or B)YesYes
Quadratic formulaNoYes
Sine rule, cosine rule, area ½ab sin CNoYes
P(A and B) = P(A given B) × P(B)NoYes
acbAABChypotenuse
AQA's sheet labels sides a, b and c this way: a faces angle A.

Two inserts, one tier each

AQA prints a separate insert for each tier, so a Foundation candidate never sees the quadratic formula or the sine rule on the page. The sheets are two pages: a cover and one page of formulae. AQA also issues sheets for the Level 2 Certificate in Further Mathematics (8365), which this guide does not cover.

What you must still learn

  • Area of a triangle as ½ × base × height, and areas of rectangles and parallelograms.
  • Volumes and surface areas of cylinders, cones and spheres, and arc length and sector area.
  • Speed, density and pressure triangles, and exact trigonometric values.
  • The skill of rearranging: the sheet prints sin A = a/c and leaves you to get a = c sin A.

Worked example: savings with compound interest

Priya puts £1,800 into an account paying 2.5% a year, and leaves it for 6 years. The sheet's line is total accrued = P(1 + r/100)ⁿ, with P = 1800, r = 2.5 and n = 6.

1800\times\left(1+\frac{2.5}{100}\right)^6=1800\times1.025^6=2087.45

She ends with £2,087.45, so the interest earned is £287.45. Round money to the nearest penny at the end only.

Worked example: the sine rule on Higher

In triangle ABC, angle A is 38°, angle B is 71° and side a is 9.2 cm. Find side b. The sine rule pairs each side with the angle opposite it.

\frac{b}{\sin71^\circ}=\frac{9.2}{\sin38^\circ}\quad\text{so}\quad b=\frac{9.2\times\sin71^\circ}{\sin38^\circ}=14.1\ \text{cm}

A longer side faces the bigger angle, and 71° is bigger than 38°, so 14.1 cm is believable.

Test the quadratic formula on a question from our Algebra course, then press Mark to check it there:

Use the quadratic formula to find both roots.

Press Mark to have your answer marked in the Algebra course.

Other boards

Edexcel and OCR print the same formulae, as we found comparing AQA's 2027 insert with Pearson's 2026 Exam Aid and OCR's 2027 sheet. For papers, marks and boundaries, read our GCSE Maths guide. From 2028 the sheets are published by 1 September the year before and a clean copy goes in every paper; AQA says the rule against questions answerable by copying from the sheet does not touch Maths (8300). Details are in AQA's announcement.

Practising with today's paper

Today's Foundation or Higher paper is 8 questions and 25 to 35 marks, a short timed mock rather than an AQA paper. Put the formula you chose beside each answer, and when you mark it, check which questions the sheet could have helped with.

Exam answers

Worked answers and a mark scheme appear with today's paper once it is marked, so you can see which formula each question was built on. There are no official or past paper answers here.

Common questions

Is there a formula sheet in AQA GCSE Maths?
Yes. For 2025, 2026 and 2027 AQA supplies a full formulae sheet as an insert, so you need not memorise the formulae on it.
Has the 2027 AQA sheet changed?
AQA says it is the same content as 2026.
Which formulae are Higher only on the AQA sheet?
The quadratic formula, sine rule, cosine rule, ½ab sin C, and P(A and B) from conditional probability.
Does AQA give ½ × base × height?
No. Only ½ab sin C appears, and only on Higher. Learn the simple one.
What happens from 2028?
AQA says Ofqual's rules keep the sheets for the life of the qualifications, with a clean copy in each paper.

Revision cards

Say the answer first, then flip the card to check it.

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UK · GCSEGCSE Maths Formula Sheet 2027, Dates and Grade BoundariesEvery formula on the 2027 GCSE Maths sheet, what you must still learn, exam dates, real grade boundaries and the hardest questions worked through.