What Formulae Are You Given in GCSE Maths — and What Must You Still Know?

Every Board Now Gives You a Formulae Sheet

Whichever board you sit, AQA, Edexcel, OCR or Eduqas, you will be given a formulae sheet in your GCSE Maths exams. This is not a board perk or a one-off concession: Ofqual, the exams regulator, required all boards to provide one from 2025 and has confirmed the arrangement continues for the lifetime of the current specifications. So the sheet is a stable part of the exam, not something that might quietly vanish the year you sit.

One honest caveat before you plan any revision around this post: boards publish their own versions of the sheet, so check the current formulae sheet your own board publishes for your exam year rather than relying on any blog's summary, including this one. Your teacher can show you the exact sheet, and the boards publish them freely on their websites. The rest of this post describes what such sheets typically provide and, more importantly, what they do not, because the gap between the two is where students lose easy marks.

Key points

All four boards provide a formulae sheet, required by Ofqual from 2025
The arrangement continues for the lifetime of the current specifications
Each board publishes its own sheet: check yours for your exam year
Knowing what is NOT on the sheet matters as much as knowing what is

What the Sheet Typically Provides

The sheet exists to hand you the formulae that are long, rarely used outside their one topic, and easy to misremember under pressure. Typical residents: the curved surface area of a cone, $\pi r l$ , where $l$ is the slant height; the volume of a sphere, $\frac{4}{3}\pi r^3$ ; and, at Higher tier, the quadratic formula and the sine and cosine rules for non-right-angled triangles.

The quadratic formula, for solving $ax^2 + bx + c = 0$ , is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . The sine rule is $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ , and the cosine rule is $a^2 = b^2 + c^2 - 2bc\cos A$ . These are exactly the formulae students used to garble from memory: a lost minus sign in the quadratic formula, or $+2bc\cos A$ instead of $-2bc\cos A$ , each of which wrecks the answer while looking almost right. Having them printed removes the garbling risk, but notice what it does not remove: you still have to recognise which formula the question needs, and substitute into it correctly. The sheet gives you the words; the sentence is still yours to build.

Key points

Curved surface area of a cone: $\pi r l$, with $l$ the slant height
Volume of a sphere: $\frac{4}{3}\pi r^3$
Higher tier: the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Higher tier: the sine rule and the cosine rule $a^2 = b^2 + c^2 - 2bc\cos A$

What You Must Still Recall Fluently

Here is the part that catches students out: the everyday formulae are generally not on the sheet, because fluent recall of them is itself part of the specification. Expect to know from memory the basic areas: rectangle $lw$ , triangle $\frac{1}{2}bh$ , parallelogram $bh$ and trapezium $\frac{1}{2}(a+b)h$ . Expect to know the circle formulae, circumference $C = \pi d = 2\pi r$ and area $A = \pi r^2$ , and which is which, since mixing them up is one of the most common errors in the topic.

You must also carry Pythagoras' theorem, $a^2 + b^2 = c^2$ , and the three trigonometric ratios, $\sin\theta = \frac{\text{opp}}{\text{hyp}}$ , $\cos\theta = \frac{\text{adj}}{\text{hyp}}$ , $\tan\theta = \frac{\text{opp}}{\text{adj}}$ , in your head. The same goes for the index laws, $a^m \times a^n = a^{m+n}$ , $a^m \div a^n = a^{m-n}$ and $(a^m)^n = a^{mn}$ , covered in the indices topic, and the compound-measure relationships such as speed equals distance over time. These come up constantly, across many topics and on every paper, which is precisely why the exam expects them to live in your memory rather than on a crib sheet.

Key points

Basic areas from memory: rectangle, triangle, parallelogram, trapezium $\frac{1}{2}(a+b)h$
Circle formulae from memory: $C = 2\pi r$ and $A = \pi r^2$, and which is which
Pythagoras $a^2 + b^2 = c^2$ and the three trig ratios must be instant recall
Index laws and compound measures (speed, density) are expected knowledge

Using a Given Formula Is the Skill Being Tested

It is tempting to see a printed formula as a free mark. It is the opposite: because the boards know you have the formula in front of you, the marks sit entirely in what you do with it. Choosing the right formula for the situation, matching the letters to the numbers in the question, substituting carefully, and rearranging when the unknown is not the subject: that is the examined skill, and no sheet does it for you.

The classic failure is substitution against the letters' meaning. In the cosine rule, $A$ is the angle opposite side $a$ ; pair the angle with the wrong side and the formula punishes you while looking perfectly used. In the cone formula, $l$ is the slant height, not the vertical height, and questions deliberately give you both. Read the formula's letters as words with meanings, not as slots to fill left to right, and write the substitution line in full before touching a calculator: that line usually carries a method mark on its own.

Key points

Printed formulae move the marks onto selection, substitution and rearrangement
Match letters by meaning: in the cosine rule, angle $A$ faces side $a$
Watch for deliberate distractors, like vertical height given where slant height is needed
Write the full substitution line down: it usually earns a method mark by itself

In triangle $ABC$ , $b = 7$ cm, $c = 9$ cm and angle $A = 60°$ . Use the cosine rule to find the length of side $a$ , to 3 significant figures.

1
Take the cosine rule from the sheet: $a^2 = b^2 + c^2 - 2bc\cos A$ . Side $a$ is opposite angle $A$ , which is the side we want, so the formula is already arranged for us.
2
Substitute, writing the line in full: $a^2 = 7^2 + 9^2 - 2 \times 7 \times 9 \times \cos 60°$ .
3
Evaluate the pieces: $49 + 81 = 130$ , and $2 \times 7 \times 9 = 126$ with $\cos 60° = 0.5$ , so the subtracted term is $63$ .
4
So $a^2 = 130 - 63 = 67$ , giving $a = \sqrt{67} = 8.185...$
5
Round: $a \approx 8.19$ cm.

$a \approx 8.19$ cm (3 s.f.)

The Quadratic Formula: Given, but Substitution Is Everything

The quadratic formula is the sheet's most used resident, and also the one where substitution errors are most punishing. Two habits protect you. First, write the equation in the form $ax^2 + bx + c = 0$ before you identify $a$ , $b$ and $c$ , moving every term to one side; half of all quadratic-formula errors happen because a term was still sitting on the right-hand side. Second, substitute negative values in brackets, so $b = -5$ goes in as $(-5)$ , which stops $-b$ and $b^2$ from going wrong.

On a calculator paper, evaluate the discriminant $b^2 - 4ac$ first and write it down; it is a checkpoint the mark scheme often rewards, and its sign tells you immediately whether real solutions exist. Then compute both roots. For a full refresher on when to factorise instead, see the quadratics topic, and for the calculator habits that protect these multi-step calculations, our calculator paper guide pairs naturally with this section.

Key points

Rearrange to $ax^2 + bx + c = 0$ before reading off $a$, $b$ and $c$
Substitute negatives in brackets to protect $-b$ and $b^2$
Evaluate and write the discriminant $b^2 - 4ac$ as its own step
Give both roots unless the question's context rules one out

Solve $2x^2 + 3x - 4 = 0$ , giving your answers to 2 decimal places.

1
The equation is already in the form $ax^2 + bx + c = 0$ , with $a = 2$ , $b = 3$ , $c = -4$ .
2
Take the formula from the sheet: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
3
Work out the discriminant first: $b^2 - 4ac = 3^2 - 4 \times 2 \times (-4) = 9 + 32 = 41$ . It is positive, so there are two real solutions.
4
Substitute: $x = \frac{-3 \pm \sqrt{41}}{4}$ , and $\sqrt{41} = 6.403...$
5
So $x = \frac{-3 + 6.403...}{4} = 0.8508...$ or $x = \frac{-3 - 6.403...}{4} = -2.3508...$

$x = 0.85$ or $x = -2.35$ (2 d.p.)

Foundation and Higher See Different Sheets

The tiers do not need the same formulae, so the sheets differ. The sine rule, cosine rule and quadratic formula support Higher-tier content; at Foundation, non-right-angled trigonometry and the quadratic formula are not part of the specification, so a Foundation student's sheet is shorter and their recall burden is correspondingly lighter. If you are unsure which tier you are sitting, or whether to move, our guide to Foundation versus Higher walks through the decision properly.

This is another reason to look at your own board's actual sheet for your tier rather than a generic list. Print it, stick it inside your revision folder, and make it the first page you see each session. Within a fortnight you will know its contents without trying, which is exactly the relationship you want: familiar enough that finding a formula in the exam takes five seconds, with your deliberate memorising effort saved for the formulae the sheet does not carry.

Key points

Foundation and Higher receive different sheets matched to their content
Sine rule, cosine rule and the quadratic formula belong to Higher-tier content
Work from your own board and tier's actual sheet throughout revision
Familiarity with the sheet's layout saves exam time on its own

How to Revise Now the Sheet Exists

The sheet should change how you allocate memorising effort, not whether you make any. Split your formulae into two lists. List one, the given formulae: for these, practise recognition and use, working questions that require choosing and substituting into each, because that is where their marks live. List two, the must-know formulae: for these, use retrieval practice, writing them from memory at the start of each revision session and checking, rather than re-reading them, since testing beats re-reading for long-term recall.

Then rehearse under real conditions. Exam Ladder's practice sessions and mock exams put formula-driven questions in front of you across every GCSE Maths topic, with mocks matched to your board's paper structure and graded on real exam-board grade boundaries, so you find out before exam day whether your recall holds under time pressure. The non-calculator paper deserves specific attention here, because recalling and applying formulae with no calculator to lean on is its own skill: our non-calculator paper guide covers it, and resit students short on time should read the November resits guide for how to prioritise. On the day itself, skim your board's sheet once as part of the night-before routine, then trust it. You can start a 7-day free trial and test your two lists against a timed mock this week.

Key points

Given formulae: practise choosing and using them in real questions
Must-know formulae: daily retrieval practice, written from memory then checked
Rehearse under timed conditions so recall is tested under pressure, not just at a desk
Skim your board's actual sheet the night before, then trust it on the day

Frequently asked questions

Do all exam boards give a formulae sheet in GCSE Maths?

Yes. Ofqual required every board to provide one from 2025, and has confirmed it continues for the lifetime of the current specifications, so AQA, Edexcel, OCR and Eduqas students all receive one. Each board publishes its own version, so check the current sheet for your board and exam year.

Is the quadratic formula given in the exam?

At Higher tier, the quadratic formula is typically on the formulae sheet, alongside the sine and cosine rules. The marks are in using it: rearranging the equation to equal zero, identifying a, b and c correctly, and substituting negatives in brackets.

Do I still need to memorise the area of a circle?

Yes. The everyday formulae, including the circle's circumference and area, basic shape areas, Pythagoras' theorem and the trig ratios, are expected knowledge and are generally not what the sheet is for. Fluent recall of them is part of what the exam tests.

Is the formulae sheet the same for Foundation and Higher?

No. The sheets are matched to each tier's content. The sine rule, cosine rule and quadratic formula support Higher-tier topics, so a Foundation sheet is shorter. Always revise from the actual sheet your board publishes for your tier.

If a formula is printed on the sheet, are those questions easy marks?

No, and that is the trap. Because the formula is given, the marks sit in selecting the right one, matching each letter to the right value, substituting carefully and rearranging. A printed formula with the slant height and vertical height swapped still scores nothing.

What Formulae Are You Given in GCSE Maths — and What Must You Still Know?

Every Board Now Gives You a Formulae Sheet

What the Sheet Typically Provides

What You Must Still Recall Fluently

Using a Given Formula Is the Skill Being Tested

The Quadratic Formula: Given, but Substitution Is Everything

Foundation and Higher See Different Sheets

How to Revise Now the Sheet Exists

Frequently asked questions

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