Year 9 Maths Formula Sheet (Free, Printable PDF)

Year 9 maths formula sheet

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

Number and algebra

Index laws: $a^m \times a^n = a^{m+n}$ $\dfrac{a^m}{a^n} = a^{m-n}$ $(a^m)^n = a^{mn}$ $(ab)^n = a^n b^n$
Zero and negative indices: $a^0 = 1$ $a^{-n} = \dfrac{1}{a^n}$
Scientific notation: $a \times 10^n,$ $1 \le a < 10$
Expanding binomials: $(a + b)(c + d) = ac + ad + bc + bd$
Special products: $(a + b)^2 = a^2 + 2ab + b^2$ $(a - b)^2 = a^2 - 2ab + b^2$ $(a + b)(a - b) = a^2 - b^2$
Null factor law: If $ab = 0,$ then $a = 0$ or $b = 0$
Simple interest: $I = PRT$ $(R$ as a decimal per year $, \ T$ in years $)$
Direct proportion: $y = kx$

Gradient: $m = \dfrac{\text{rise}}{\text{run}} = \dfrac{y_2 - y_1}{x_2 - x_1}$
Equation of a line: $y = mx + c$ $(c$ is the $y$ -intercept $)$
Midpoint: $M = \left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)$
Distance between two points: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Pythagoras' theorem: $c^2 = a^2 + b^2$
Trigonometric ratios (SOH CAH TOA): $\sin\theta = \dfrac{O}{H}$ $\cos\theta = \dfrac{A}{H}$ $\tan\theta = \dfrac{O}{A}$
Surface area of a rectangular prism: $SA = 2(lw + lh + wh)$
Cylinder: $V = \pi r^2 h$ $SA = 2\pi r^2 + 2\pi r h$
Scale factor: $k = \dfrac{\text{image length}}{\text{original length}}$
Absolute error: $\pm \tfrac{1}{2} \times$ the smallest unit on the scale

Two-step probability: multiply along the branches; add the outcomes you want
Venn diagrams: $P(A$ or $B) = P(A) + P(B) - P(A$ and $B)$
Comparing data: compare centre (mean, median) and spread (range)

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