GCSE FORMULAE
You need to know this for your exam
(Higher tier only formulae are indicated)
www.mathssandpit.co.uk/blog
Rectangle = l × w
w
l
www.mathssandpit.co.uk/blog
AREA
Parallelogram = b × h
a
h
b
www.mathssandpit.co.uk/blog
AREA
1
2
Triangle = b × h
h
b
www.mathssandpit.co.uk/blog
AREA
1
2
Trapezium = (a+b) × h
a
h
b
www.mathssandpit.co.uk/blog
AREA
Circumference = π × diameter
C = πd
www.mathssandpit.co.uk/blog
Circles
Circumference = 2 × π × radius
C = 2πr
Centre
www.mathssandpit.co.uk/blog
Circles
Area = π × radius × radius
2
A = πr
Centre
www.mathssandpit.co.uk/blog
Circles
Cuboid = 𝑙 × w × h
h
𝑙
www.mathssandpit.co.uk/blog
w
VOLUME
Prism = 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 × length
Area
of
cross section
www.mathssandpit.co.uk/blog
𝑙
VOLUME
Cylinder = area of circle × height
2
Cylinder = πr h
r
ℎ
www.mathssandpit.co.uk/blog
VOLUME
Pyramid =
1
3
area of base × height
ℎ
Higher tier only
www.mathssandpit.co.uk/blog
VOLUME
Speed = Distance ÷ Time
The clue is in the units
eg speed in m/s, indicates metres ÷ seconds
COMPOUND MEASURES
www.mathssandpit.co.uk/blog
Density = Mass ÷ Volume
The clue is in the units
eg density in g/cm3,
indicates weight in grams ÷ volume in cm3
COMPOUND MEASURES
www.mathssandpit.co.uk/blog
Pressure = Force ÷ Area
The clue is in the units
eg speed in N/m2,
indicates force in Newtons ÷ area in m2
COMPOUND MEASURES
www.mathssandpit.co.uk/blog
Pythagoras
a2 + b2 = h2
h
b
a
(h is always the hypotenuse)
RIGHT-ANGLED TRIANGLES
www.mathssandpit.co.uk/blog
Trigonometry
𝑜𝑝𝑝
sin 𝑥° =
ℎ𝑦𝑝
opp
hyp
x⁰
𝑎𝑑𝑗
cos 𝑥° =
ℎ𝑦𝑝
adj
𝑜𝑝𝑝
tan 𝑥° =
𝑎𝑑𝑗
Check your
calculator is in
degrees
RIGHT-ANGLED TRIANGLES
www.mathssandpit.co.uk/blog
C
Sine Rule
b
A
a
𝑏
𝑐
=
=
sin(𝐴) sin(𝐵) sin(𝐶)
Higher tier only
a
c
B
Check your
calculator is in
degrees
NON-RIGHT-ANGLED TRIANGLES
www.mathssandpit.co.uk/blog
Cosine Rule
C
b
A
2
2
2
Higher tier only
a
c
𝑎 = 𝑏 + 𝑐 − 2𝑏𝑐 × 𝑐𝑜𝑠(𝐴)
B
Check your
calculator is in
degrees
NON-RIGHT-ANGLED TRIANGLES
www.mathssandpit.co.uk/blog
Area of a triangle
C
b
A
Area =
1
𝑎
2
× 𝑏 × 𝑠𝑖𝑛(𝐶)
Higher tier only
a
c
B
Check your
calculator is in
degrees
NON-RIGHT-ANGLED TRIANGLES
www.mathssandpit.co.uk/blog
Higher tier only
Quadratic Equations
The solutions of
ax2+bx+c=0,
where a≠0, are given by:
−𝑏 ± √(𝑏 2 − 4𝑎𝑐)
𝑥=
2𝑎
www.mathssandpit.co.uk/blog
Algebra