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OCR GCSE Maths formulae sheet (J560): every formula and how to use it

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Formula sheet

OCR names its sheets by paper number and series. The 2027 pair, Foundation and Higher, is "for use in June 2027 and November 2027 only". Press the card to put the formulae beside a practice paper, then read the contents below.

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
OCR labels the triangle with a opposite A, so keep to those letters.

Which sheet goes with which paper

J560 papers 01, 02 and 03 are Foundation and carry the Foundation sheet. Papers 04, 05 and 06 are Higher and carry the Higher sheet. Each sheet is two pages and says you may write on it, though it is never sent for marking, so annotate it freely with a triangle sketch or a note about units.

Worked example: depreciation with compound interest

A car bought for £14,000 loses 12% of its value each year. The sheet's formula takes r as a rate of interest, and a loss is a negative rate, so r = −12 and n = 3.

14000\times\left(1-\frac{12}{100}\right)^3=14000\times0.88^3=9540.61

After three years the car is worth about £9,540.61. This is a favourite way to make a sheet formula look unfamiliar.

Worked example: finding an angle with the cosine rule (Higher)

Triangle ABC has sides a = 7, b = 5 and c = 8. To find angle A, rearrange a² = b² + c² − 2bc cos A.

\cos A=\frac{b^2+c^2-a^2}{2bc}=\frac{25+64-49}{80}=0.5\quad\text{so}\quad A=60^\circ

Worked example: conditional probability (Higher)

P(B) = 0.35 and P(A given B) = 0.6. The Higher sheet says P(A and B) = P(A given B) × P(B).

P(A\text{ and }B)=0.6\times0.35=0.21

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.

Comparing with AQA and Edexcel

The three boards print the same formulae. OCR sets out its sheets by series, so check that the file you revise from matches your exam month. Our GCSE Maths guide covers the boards, papers and boundaries.

A short mock with the sheet

The daily Foundation and Higher papers are 8 questions, 25 to 35 marks, set by us and not by OCR. Sit one in 20 minutes with the sheet open.

Exam answers

Today's paper arrives with worked answers and a mark scheme once it has been marked. No official OCR answers or past paper solutions are published here.

Common questions

Does OCR give a formula sheet at GCSE?
Yes, with the J560 papers: a Foundation sheet for 01 to 03 and a Higher sheet for 04 to 06.
Can I draw on the sheet?
Yes. The sheet says you can write on it, but it is not marked.
Does one sheet cover June and November 2027?
Yes. Both 2027 sheets say "for use in June 2027 and November 2027 only".
Is the quadratic formula on the Foundation sheet?
No, only on Higher.
Do OCR, AQA and Edexcel differ?
Their formulae are the same. Layout and wording differ.

Revision cards

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

Where to go next

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UK · GCSEOCR GCSE Maths (J560): papers, calculators, gradesOCR GCSE Maths (J560) explained: three papers per tier, which are calculator papers, formulae, worked examples and June 2026 grade boundaries.