GCSE Maths Formula Sheet Explained
Many GCSE Maths students worry about remembering formulas. Understanding what the formulas actually mean is usually more important than memorising them mechanically.
This guide explains the most important GCSE Maths formulas and how they are used in exams.
Area of a rectangle
Area = length × width
Area measures the space inside a shape.
Example 1: Rectangle area
A rectangle has length 8 cm and width 3 cm.
Area = 8 × 3 = 24 cm²
Area of a triangle
Use the perpendicular height, not the sloping side.
Example 2: Triangle area
Base = 10 cm, height = 6 cm.
Area = 1/2 × 10 × 6 = 30 cm²
Area of a circle
The radius is the distance from the centre to the edge.
Example 3: Circle area
Radius = 5 cm.
Area = π × 5² = 25π cm²
Circumference of a circle
Circumference means the distance around the outside of a circle.
Pythagoras' theorem
This formula works only in right-angled triangles.
Helpful topic:
Example 4: Pythagoras
A right-angled triangle has shorter sides 3 cm and 4 cm.
3² + 4² = 9 + 16 = 25
c = 5 cm
Trigonometry formulas
SOH → sin = opposite / hypotenuse
CAH → cos = adjacent / hypotenuse
TOA → tan = opposite / adjacent
Helpful topic:
Speed formula
Speed = distance ÷ time
Example 5: Speed
A car travels 120 km in 2 hours.
Speed = 120 ÷ 2 = 60 km/h
Density formula
Density = mass ÷ volume
Pressure formula
Pressure = force ÷ area
Probability formula
Probability = favourable outcomes ÷ total outcomes
Helpful topic:
Gradient formula
Gradient = change in y ÷ change in x
Helpful topic:
Volume formulas
Volume of a prism
Volume = cross-sectional area × length
Volume of a cylinder
Why understanding formulas matters
Strong GCSE Maths students do not just memorise formulas — they know:
- what each letter means
- when to use the formula
- which units are needed
- which measurements to substitute
Always check whether the question is asking for area, perimeter, surface area or volume. Students often confuse these in exams.
Most important GCSE formulas to practise
Video explanation
A short Worthing Maths Tutor video explanation for GCSE Maths formula sheet explained can be embedded here later to improve student engagement and time on page.
Useful GCSE Revision Guides
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