Year 10 Math Methods Formula Sheet

Year 10 Mathematical Methods
FORMULA SHEET


Mensuration
circumference of a 𝐶 = 2𝜋𝑟 or 𝐶 = 𝜋𝐷 area of a circle 𝐴 = 𝜋𝑟 2
circle

area of a parallelogram 𝐴 = 𝑏ℎ area of a trapezium 1
𝐴= (𝑎 + 𝑏)ℎ
2

area of a triangle 1 total surface area of a 𝑆 = 𝜋𝑟𝑠 + 𝜋𝑟 2
𝐴= 𝑏ℎ
2 cone

total surface area of a 𝑆 = 2𝜋𝑟ℎ + 2𝜋𝑟 2 surface area of a sphere 𝑆 = 4𝜋𝑟 2
cylinder
volume of a cone 1 2 volume of a cylinder 𝑉 = 𝜋𝑟 2 ℎ
𝑉= 𝜋𝑟 ℎ
3
volume of a prism 𝑉 = 𝐴ℎ volume of a pyramid 1
𝑉= 𝐴ℎ
3
volume of a sphere 4 3
𝑉= 𝜋𝑟
3


Trigonometry
trigonometric ratios 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑠𝑖𝑛 𝜃 = 𝑐𝑜𝑠 𝜃 = 𝑡𝑎𝑛 𝜃 =
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Pythagoras’ theorem 𝑐 2 = 𝑎2 + 𝑏2

sine rule 𝑎 𝑏 𝑐
= =
𝑠𝑖𝑛 𝐴 𝑠𝑖𝑛 𝐵 𝑠𝑖𝑛 𝐶

cosine rule 𝑐 2 = 𝑎2 + 𝑏2 − 2𝑎𝑏 𝑐𝑜𝑠 𝐶

area of a triangle 1
𝐴= 𝑎𝑏𝑠𝑖𝑛𝐶
2