gcse maths equations

area of a circle

πr²

circumference of a circle

πd

volume of a prism

area of face x length

area of a triangle

½ bh

area of a triangle

½ base a sinC

quadratic equation

-b ± √ b² - 4ac / 2a

cosine rule

a² = b² + c² - 2bc cosA

sum of interior angles

180 x (n - 2)

an exterior angle

360 ÷ n

cosine rule for the angle

A = cos⁻¹ ( b² + c² - a² / 2bc )

sine rule

a / sinA = b / sin B = c / sin C

area of a trapezium

½ ( a + b ) x h

length of an arch

πd x θ / 360

area of a sector

πr² x θ / 360

area of a parallelogram

base x height

pythagorean theorem

a² + b² = c²

density

mass / volume

speed

distance / time

pressure

force / area

1cm

10mm

1km

1000m

1m

100cm

1m

1000mm

1kg

1000g

1 tonne

1000 kg

sin 0

0

1 litre

1000 ml

1 litre

100cl

sin 30

½

sin 45

√2 / 2

sin 90

1

sin 60

√3 / 2

cos 0

1

cos 30

√3 / 3

cos 45

√2 / 2

cos 90

0

cos 60

½

tan 0

0

tan 30

√3 / 3

tan 90

undefined

tan 45

1

tan 60

√3

P ( A or B )

P ( A ) + P ( B ) - P ( A and B )

aⁿ x aⁿ

a²ⁿ

( a³ )⁴

a¹²

a⁶ⁿ - aⁿ

a⁵ⁿ

a¹

a

a⁻ⁿ

1 / aⁿ

a⁰

1

x^¾

( ⁴√x )³

√a ÷ √b

√a ÷ b

√a x √b

√ab

√a + √a

2√a

equation of a line

y = mx + c

equation of a circle

( x - a )² + ( y - b )² where ( a, b ) is the center

equation of a cubic graph

y = x³ + c

equation of an exponential graph

y = m x n^x

v

u + at

v²

u² + 2as

s

ut + ½at²

volume of a cylinder

πxr²

volume of a sphere

⁴/₃πr³

surface area of a sphere

4πr²

volume of a cone

¹/₃πr²h

surface area of a cone

πr² + πr x slantheight

volume of a square-based pyramid

¹/₃bh