GCSE Maths formula sheet 2027

Area of a trapezium

$\frac{1}{2}(a+b)h$

a and b are the parallel sides. h is the perpendicular distance between them.

Volume of a prism

$\text{area of cross-section}\times \text{length}$

The cross-section is the face that stays the same along the length.

Circumference of a circle

$2\pi r=\pi d$

r is the radius and d is the diameter.

Area of a circle

$\pi r^2$

Use the radius, not the diameter.

Pythagoras

$a^2+b^2=c^2$

c is the hypotenuse, the side opposite the right angle.

Right-angled trigonometry

$\sin \theta =\frac{\text{opposite}}{\text{hypotenuse}},\cos \theta =\frac{\text{adjacent}}{\text{hypotenuse}},\tan \theta =\frac{\text{opposite}}{\text{adjacent}}$

Use the angle you are given, and name the sides from that angle.

Compound interest

$P{\left(1+\frac{r}{100}\right)}^n$

P is the starting amount, r is the percentage rate each period, and n is the number of periods. The result is the amount after interest, not the interest alone.

Probability of A or B

$P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)$

Subtract the overlap so it is not counted twice.

Quadratic formula

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

For ax^{2}+bx+c=0 with a not zero. You get two answers when the square root is not zero.

Sine rule

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Use it when you know a side and its opposite angle, plus one more side or angle.

Cosine rule

$a^2=b^2+c^2-2bc\cos A$

Use it for SAS or when all three sides are known and you need an angle.

Area of any triangle

$\frac{1}{2}ab\sin C$

C is the angle between sides a and b.

Probability of A and B

$P(A\text{ and }B)=P(A\text{ given }B)P(B)$

This is on the Higher sheet. If A and B are independent, P(A given B) is just P(A).

Volume of a sphere

$\frac{4}{3}\pi r^3$

Surface area of a sphere

$4\pi r^2$

Volume of a cone

$\frac{1}{3}\pi r^{2}h$

Curved surface of a cone

$\pi rl$

Volume of a pyramid

$\frac{1}{3}\times \text{base area}\times h$

Constant acceleration

$v=u+at,s=ut+\frac{1}{2}a{t}^2,v^2=u^2+2as$

Speed

$s=\frac{d}{t}$

Distance divided by time. Keep the units consistent.

Density

$d=\frac{m}{v}$

Mass divided by volume. For a metal cuboid use g/cm³ or kg/m³.

Pressure

$p=\frac{F}{A}$

Force divided by area.

Area of a rectangle

$l\times w$

Area of a triangle

$\frac{1}{2}bh$

h is the perpendicular height.

Area of a parallelogram

$bh$

h is the perpendicular height, not a sloping side.

Volume of a cuboid

$l\times w\times h$

Straight line

$y=mx+c$

m is the gradient. c is the y-intercept.

Gradient

$m=\frac{\text{change in }y}{\text{change in }x}$