Cylinder
Question 1
A cylinder has radius 3 cm and height 10 cm. Find its volume in terms of π.
V = π × 3² × 10 = 90π cm³.
Every GCSE maths candidate in 2027 gets an official formulae sheet in all three papers, on every board. It holds eight formulae at Foundation and thirteen at Higher, so plenty still has to be learned. Here is exactly what is given, what questions print when needed, and what nobody hands out.
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ClassArc is live one-to-one online maths tutoring for school-age children. One teacher and one child, for 55 minutes. The same teacher every week. Classes run inside our own classroom software, not a video call: a shared worksheet you both write on, a shared whiteboard, and answers that sync live.
The short answer
Yes. Students sitting GCSE maths in 2027 are given an official formulae sheet in all three papers, whichever board they sit. Ofqual confirmed the sheets for the 2025, 2026 and 2027 exams, and has since decided they continue for the remaining lifetime of the current GCSE specifications.
The sheet is short: eight formulae at Foundation, thirteen at Higher. Ofqual requires the boards to keep the sheets consistent with each other and with previous years, so AQA, Pearson Edexcel and OCR give the same formulae in their own layouts, published by 1 September of the year before each series.
What the sheet does not do is say which formula a question needs. Questions are deliberately set so that copying from the sheet is not enough.
On the sheet
Foundation and Higher sheets, as published for the 2025 to 2027 exams.
| Formula | Given on the sheet? | Example |
|---|---|---|
| Area of a trapezium = ½(a + b)h | Yes, Foundation and Higher | a = 5, b = 9, h = 4: area = 28 |
| Volume of a prism = area of cross-section × length | Yes, Foundation and Higher | Cross-section 12 cm², length 10 cm: 120 cm³ |
| Circumference of a circle = 2πr = πd | Yes, Foundation and Higher | r = 5: 10π ≈ 31.4 |
| Area of a circle = πr² | Yes, Foundation and Higher | r = 6: 36π |
| Pythagoras' theorem: a² + b² = c², c the hypotenuse | Yes, Foundation and Higher | Legs 6 and 8: hypotenuse 10 |
| sin A = a/c, cos A = b/c, tan A = a/b (right-angled triangle) | Yes, Foundation and Higher | Opposite 5, hypotenuse 10: sin A = 0.5, so A = 30° |
| Compound interest: total accrued = P(1 + r/100)n | Yes, Foundation and Higher | £500 at 4% for 3 years: £562.43 |
| P(A or B) = P(A) + P(B) − P(A and B) | Yes, Foundation and Higher | 0.5 + 0.4 − 0.2 = 0.7 |
| Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a | Higher only | x² + 4x − 7 = 0: x = 1.32 or −5.32 |
| Sine rule: a/sin A = b/sin B = c/sin C | Higher only | Two angles and a side known |
| Cosine rule: a² = b² + c² − 2bc cos A | Higher only | Two sides and the angle between them |
| Area of a triangle = ½ab sin C | Higher only | 7, 9 and 40°: 20.2 cm² |
| P(A and B) = P(A given B) × P(B) | Higher only | 0.3 × 0.5 = 0.15 |
Contents of the formulae sheets the boards publish in line with Ofqual's conditions. Use your own board's printed sheet in practice so your child knows where each formula sits on the page.
Printed in the question
The DfE subject content says these are not to be memorised: when a question needs one, the question prints it. Substituting into them confidently is the skill.
| Formula | Given on the sheet? | Example |
|---|---|---|
| Volume of a cone = ⅓πr²h | No — printed in the question | r = 3, h = 10: 30π |
| Curved surface area of a cone = πrl, l the slant height | No — printed in the question | r = 3, l = 5: 15π |
| Volume of a sphere = ⁴⁄₃πr³ | No — printed in the question | r = 3: 36π |
| Surface area of a sphere = 4πr² | No — printed in the question | r = 3: 36π |
| Kinematics: v = u + at, s = ut + ½at², v² = u² + 2as | No — printed in the question | u = 0, a = 2, t = 5: v = 10 |
Learn these
Not on the sheet and not printed in questions. Several of these come up far more often than anything about cones or spheres, especially at Foundation.
| Formula | Given on the sheet? | Example |
|---|---|---|
| Area of a triangle = ½ × base × perpendicular height | No — learn it | Base 10, height 6: 30 |
| Area of a parallelogram = base × perpendicular height | No — learn it | Base 8, height 5: 40 |
| Volume of a cylinder = πr²h | No — learn it (a prism with a circular cross-section) | r = 3, h = 10: 90π |
| Curved surface area of a cylinder = 2πrh | No — learn it | r = 3, h = 10: 60π |
| Volume of a pyramid = ⅓ × base area × height | No — learn it | Base 36, height 5: 60 |
| Arc length = (θ/360) × 2πr; sector area = (θ/360) × πr² | No — learn it | 90°, r = 4: arc 2π, sector 4π |
| Interior angles of an n-sided polygon sum to (n − 2) × 180° | No — learn it | Hexagon: 720° |
| Exterior angle of a regular polygon = 360° ÷ n | No — learn it | Exterior 24°: 15 sides |
| Speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area | No — learn it | 150 km in 2.5 h: 60 km/h |
| Percentage change = change ÷ original × 100 | No — learn it | £40 to £50: 25% increase |
| Multiplier: 1 + r/100 up, 1 − r/100 down; reverse percentage = new ÷ multiplier | No — learn it | £92 after +15%: £92 ÷ 1.15 = £80 |
| Straight line y = mx + c; gradient = change in y ÷ change in x | No — learn it | (1, 3) to (3, 7): m = 2 |
| Perpendicular gradients multiply to −1 (Higher) | No — learn it | m = 2: perpendicular m = −½ |
| Circle centred at the origin: x² + y² = r² (Higher) | No — learn it | Radius 5: x² + y² = 25 |
| Difference of two squares: a² − b² = (a + b)(a − b) | No — learn it | x² − 49 = (x + 7)(x − 7) |
| nth term of a linear sequence = dn + (first term − d) | No — learn it | 7, 11, 15…: 4n + 3 |
| Exact trig values for 0°, 30°, 45°, 60°, 90° | No — learn it | sin 30° = ½; tan 45° = 1; cos 30° = √3/2 |
| P(not A) = 1 − P(A); independent events: P(A and B) = P(A) × P(B) | No — learn it | 0.3 and 0.5 independent: 0.15 |
| Expected frequency = trials × probability | No — learn it | 200 spins at 0.25: 50 |
| Estimated mean = Σfx ÷ Σf | No — learn it | Midpoints × frequencies, over the total |
| Frequency density = frequency ÷ class width (Higher) | No — learn it | Frequency 30, width 5: 6 |
| Similar shapes: length factor k gives area × k², volume × k³ (Higher) | No — learn it | k = 3: area × 9, volume × 27 |
The formulae for proportion — y = kx and y = k/x at both tiers, with forms like y = kx² at Higher — are also worth knowing by heart.
Using it well
Having the sheet and using it well are different things. Six habits close the gap.
Self-test
Cover the tables above and try these four.
A cylinder has radius 3 cm and height 10 cm. Find its volume in terms of π.
V = π × 3² × 10 = 90π cm³.
A regular polygon has exterior angles of 24°. How many sides does it have?
360 ÷ 24 = 15 sides.
A car travels 150 km in 2 hours 30 minutes. What is its average speed?
150 ÷ 2.5 = 60 km/h. Using 2.30 hours is the trap.
AB = 7 cm, AC = 9 cm, angle BAC = 40°. Find the area to 3 significant figures.
½ × 7 × 9 × sin 40° = 20.2 cm².
With a teacher
The commonest formula problem isn't recall. It is looking at a triangle and not knowing whether it wants Pythagoras, the sine rule or ½ab sin C. In a 55-minute one-to-one ClassArc class, the teacher sees each line your child writes on the shared worksheet and catches the wrong choice as it happens.
The free first class is a full lesson with the teacher who would go on to teach your child. Bring a past paper; no card is needed.
formulae on the Foundation and Higher sheets — everything else is learned or read from the question
Next
Every topic, so you can see where the formulae fit in the wider picture.
Open the checklistA twelve-week plan, with the formula sheet reviewed in the final week.
Plan revisionThe exam year: mocks, past papers and what the papers look like.
Year 11 guideOne-to-one classes for Foundation and Higher on your child's board.
GCSE tutoringFormula sheet questions
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Last updated · May 2026
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Last updated · May 2026
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