Summary IGCSE Extended Mathematics Revision Guide

MATHEMATICS REVISION WORKSHEET

Indices:
𝑚 𝑛 𝑚+𝑛
𝑎 + 𝑎 = 𝑎
𝑚 𝑛 𝑚−𝑛
𝑎 ÷ 𝑎 = 𝑎
𝑚 𝑛 𝑚×𝑛
(𝑎 ) = 𝑎

𝑚
𝑎 𝑚 𝑎
( ) 𝑏
= 𝑚
𝑎


−𝑚 1
𝑎 = 𝑚
𝑎
𝑥
𝑦 𝑥
𝑎 𝑦
= 𝑎

Area and Perimeter:

Perimeter for all: add all the sides together

Rectangle:
Area = base x height

Triangle:
1
Area = base x height x 2


Parallelogram:
Area = base x height

Trapezium:
(𝑎 + 𝑏)ℎ
Area = 2

,Area and Circumference Of a circle:

Circumference:
𝐶 = π𝑑 𝑜𝑟 2π𝑟

Area:
2
𝐴 = π𝑟

Arc Lengths and Areas of Sectors:
θ
Arc length = 360 × 2π𝑟


θ 2
Area of sector = 360 × π𝑟


Surface area and Volume:

Prism:
V = area of cross section x length

Cuboid:
S.A = sum of all the areas of all the faces
V = length x width x height

Cylinder:
2
S.A = 2π𝑟ℎ + 2π𝑟
2
V = π𝑟 × ℎ (𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 × ℎ𝑒𝑖𝑔ℎ𝑡)

Pyramid:
S.A = sum of all the areas of all the faces
1
V = 3 × 𝑏𝑎𝑠𝑒 𝑎𝑟𝑒𝑎 × ℎ𝑒𝑖𝑔ℎ𝑡

Cone:
2
S.A = π𝑟 + π𝑟𝑙

, * 𝑙 is the slant height
1 2 1
V= 3
× π𝑟 ℎ ( 3
× 𝑏𝑎𝑠𝑒 𝑎𝑟𝑒𝑎 × ℎ𝑒𝑖𝑔ℎ𝑡 )


Sphere:
2
S.A = 4π𝑟
4 3
V= 3
π𝑟


Hemisphere:
2
S.A = 2π𝑟 (𝑡ℎ𝑒 𝑐𝑢𝑟𝑣𝑒𝑑 𝑆. 𝐴) + 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑏𝑎𝑠𝑒
2 3
V= 3
π𝑟


Similar shape:

Ratio of lengths:
𝑙1
𝑙2
=𝑘

Ratio of area:
𝐴1 2
𝐴2
=𝑘


Ratio of volumes:
𝑉1 3
𝑉2
=𝑘


Quadratic formula:

2
−𝑏± 𝑏 − 4𝑎𝑐
𝑥 = 2𝑎