Year 7 Maths Formula Sheet (Free, Printable PDF)

Year 7 maths formula sheet

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

Number

Order of operations: Brackets $\to$ Indices $\to \times \div \ ($ left to right $) \to + - \ ($ left to right $)$
Square and square root: $5^2 = 25$ $\sqrt{25} = 5$
Index notation: $2^4 = 2 \times 2 \times 2 \times 2 = 16$
Prime factor form: $60 = 2^2 \times 3 \times 5$
Percentage of an amount: $p\%$ of $A = \dfrac{p}{100} \times A$
Fraction to percentage: $\dfrac{\text{part}}{\text{whole}} \times 100\%$
Dividing fractions: $\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c}$
Ratio: $a : b = ka : kb$ $($ multiply or divide both parts by the same number $)$

Distributive law: $a(b + c) = ab + ac$
Substitution: If $x = 3, \ 2x + 5 = 2(3) + 5 = 11$
Solving an equation: Do the same to both sides: $2x + 5 = 11 \Rightarrow 2x = 6 \Rightarrow x = 3$

Angles on a straight line: add to $180^\circ$
Angles around a point: add to $360^\circ$
Vertically opposite angles: are equal
Parallel lines: corresponding and alternate angles are equal; co-interior angles add to $180^\circ$
Angle sum: triangle $180^\circ,$ quadrilateral $360^\circ, \ n$ -sided polygon $(n - 2) \times 180^\circ$

Mean: mean $= \dfrac{\text{sum of the values}}{\text{number of values}}$
Median, mode, range: median: middle value in order; mode: most common; range $=$ highest $-$ lowest
Probability: $P($ event $) = \dfrac{\text{number of favourable outcomes}}{\text{total number of equally likely outcomes}}$
Probability scale: $0 \le P \le 1$ $(0 =$ impossible $, \ 1 =$ certain $)$

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