Year 8 Maths Formula Sheet (Free, Printable PDF)

Year 8 maths formula sheet

Australian Curriculum · tuterly.com.au/formula-sheets

Number

Index laws: $a^m \times a^n = a^{m+n}$ $a^m \div a^n = a^{m-n}$ $(a^m)^n = a^{mn}$ $a^0 = 1$
Percentage increase or decrease: new amount $=$ original $\times \left(1 \pm \dfrac{r}{100}\right)$
Profit and loss: profit $=$ selling price $-$ cost price $\%$ profit $= \dfrac{\text{profit}}{\text{cost price}} \times 100\%$
Recurring decimals: $\tfrac{1}{3} = 0.\dot{3}$ $\tfrac{1}{11} = 0.\dot{0}\dot{9}$

Pythagoras' theorem: $c^2 = a^2 + b^2$ $(c$ is the hypotenuse $)$
Circumference of a circle: $C = 2\pi r = \pi d$
Area of a circle: $A = \pi r^2$
Area of a trapezium: $A = \tfrac{1}{2}(a + b)h$
Area of a rhombus or kite: $A = \tfrac{1}{2}xy$ $(x, y$ are the diagonals $)$
Volume of a prism: $V = A \times h$ $(A$ is the area of the cross-section $)$
Capacity: $1$ L $= 1000$ mL $, \ 1$ kL $= 1000$ L $, \ 1$ m $^3 = 1000$ L
Speed, distance, time: $s = \dfrac{d}{t}$ $d = st$ $t = \dfrac{d}{s}$
Area units: $1$ m $^2 = 10\,000$ cm $^2$ $1$ ha $= 10\,000$ m $^2$

Complementary events: $P($ not $A) = 1 - P(A)$
Mean, median, mode, range: mean $= \dfrac{\text{sum}}{\text{count}}$ range $=$ highest $-$ lowest

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