GCSE Maths Formulas You Must Know: Foundation & Higher (2025)

One of the most common revision mistakes is assuming you will be given all the formulas you need in the exam. You will not. Each board provides a small formula sheet with a handful of higher-level formulas, but the vast majority of what you need must come from memory. This guide tells you exactly what to learn.

What the formula sheet gives you (Higher tier)

AQA, Edexcel and OCR all provide a formula sheet for the Higher tier exam. The formulas typically included are:

• Quadratic formula: x = (-b ± √(b²-4ac)) / 2a
• Volume of a sphere: V = (4/3)πr³
• Surface area of a sphere: A = 4πr²
• Volume of a cone: V = (1/3)πr²h
• Sine rule: a/sinA = b/sinB = c/sinC
• Cosine rule: a² = b² + c² - 2bc cosA
• Area of a triangle: A = (1/2)ab sinC

Formulas you MUST memorise (Foundation & Higher)

Area & Perimeter

• Area of a rectangle: A = l × w
• Area of a triangle: A = ½ × b × h
• Area of a parallelogram: A = b × h
• Area of a trapezium: A = ½(a + b)h
• Area of a circle: A = πr²
• Circumference of a circle: C = 2πr = πd

Volume & Surface Area

• Volume of a cuboid: V = l × w × h
• Volume of a prism: V = cross-sectional area × length
• Volume of a cylinder: V = πr²h
• Surface area of a cylinder: A = 2πrh + 2πr²
• Volume of a pyramid: V = ⅓ × base area × height

Algebra & Number

• Difference of two squares: a² - b² = (a+b)(a-b)
• Compound interest: A = P(1 + r/100)ⁿ
• Percentage change: (new - old) / old × 100
• Reverse percentage: original = amount ÷ (1 ± r/100)
• Speed = Distance ÷ Time
• Density = Mass ÷ Volume
• Pressure = Force ÷ Area

Pythagoras & Trigonometry (Foundation & Higher)

• Pythagoras: a² + b² = c² (c is the hypotenuse)
• sin θ = opposite/hypotenuse
• cos θ = adjacent/hypotenuse
• tan θ = opposite/adjacent

Higher-only formulas (not on formula sheet)

• Arc length: l = (θ/360) × 2πr
• Area of a sector: A = (θ/360) × πr²
• nth term of a geometric sequence: arⁿ⁻¹
• Sum of interior angles of a polygon: (n-2) × 180°
• Frequency density (histograms): FD = frequency ÷ class width

How to memorise formulas effectively

The best method is retrieval practice — not re-reading. Write out the formula from memory, check it, correct it, and repeat. Do this daily for formulas you struggle with. Making formula cards (one formula per card, written by hand) and testing yourself until you can write every one without looking takes about two weeks of daily practice.