Formula sheetYears 10 and 11
GCSE Maths Formulas to Learn
The formulas and facts GCSE Maths expects you to recall quickly. Even when an exam gives a formula sheet, knowing these by heart saves minutes on every paper.
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01Area and volume
- Trapezium A = ½(a + b)h
- Circle A = πr2, C = 2πr = πd
- Triangle A = ½bh = ½ab sinC
- Prism volume = area of cross-section × length
- Cylinder V = πr2h
- Pyramid and cone V = ⅓ × base area × height
- Sphere V = (4/3)πr3, surface area 4πr2
02Pythagoras and trigonometry
- Pythagoras a2 + b2 = c2
- SOH CAH TOA sin = opp/hyp, cos = adj/hyp, tan = opp/adj
- Sine rule a/sinA = b/sinB = c/sinC
- Cosine rule a2 = b2 + c2 − 2bc cosA
- Exact values sin30° = ½, cos60° = ½, tan45° = 1, sin60° = cos30° = √3/2, sin45° = cos45° = √2/2
03Algebra
- Quadratic formula x = [−b ± √(b2 − 4ac)]/2a
- Straight line y = mx + c; gradient = change in y/change in x
- Perpendicular lines gradients multiply to −1
- nth term of a linear sequence an + b
- Difference of two squares a2 − b2 = (a + b)(a − b)
04Number and measures
- Compound interest A = P(1 + r/100)n
- Speed speed = distance/time
- Density density = mass/volume
- Pressure pressure = force/area
- Percentage change change/original × 100
- Standard form A × 10n, with 1 ≤ A < 10
05Angles and circle theorems
- Polygons interior angles sum to (n − 2) × 180°; exterior angles sum to 360°
- Centre the angle at the centre is twice the angle at the circumference
- Semicircle the angle in a semicircle is 90°
- Same segment angles in the same segment are equal
- Cyclic quadrilateral opposite angles add to 180°
- Tangent a tangent meets the radius at 90°; tangents from a point are equal
- Alternate segment theorem the angle between a tangent and a chord equals the angle in the alternate segment
06Probability and statistics
- AND (independent events) multiply the probabilities
- OR (mutually exclusive events) add the probabilities
- Not happening P(not A) = 1 − P(A)
- Averages mean, median, mode; range = largest − smallest
How to use this sheet
- Write the formula before substituting in every answer; method marks reward it.
- Learn circle theorems with a sketch each: you must quote the reason in words.
- Always check whether your calculator is in degrees.
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