Year 10A Maths Formula Sheet (Free, Printable PDF)

Year 10A maths formula sheet

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

Surds, indices and logarithms

Surds: $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$ $\dfrac{\sqrt{a}}{\sqrt{b}} = \sqrt{\dfrac{a}{b}}$ $\dfrac{1}{\sqrt{a}} = \dfrac{\sqrt{a}}{a}$
Fractional indices: $a^{\frac{1}{n}} = \sqrt[n]{a}$ $a^{\frac{m}{n}} = \left(\sqrt[n]{a}\right)^m$
Definition of a logarithm: $\log_a x = y \iff a^y = x$
Log laws: $\log_a (mn) = \log_a m + \log_a n$ $\log_a \dfrac{m}{n} = \log_a m - \log_a n$ $\log_a m^p = p\log_a m$
Special values: $\log_a 1 = 0$ $\log_a a = 1$

Quadratic formula: $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Remainder theorem: the remainder when $P(x)$ is divided by $(x - a)$ is $P(a)$
Factor theorem: if $P(a) = 0,$ then $(x - a)$ is a factor of $P(x)$
Function notation: $f(x) = 2x + 1 \Rightarrow f(3) = 7$

Sine rule: $\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$
Cosine rule: $c^2 = a^2 + b^2 - 2ab\cos C$
Area of a triangle: $A = \tfrac{1}{2}ab\sin C$
Exact values: $\sin 30^\circ = \tfrac{1}{2}$ $\cos 30^\circ = \tfrac{\sqrt{3}}{2}$ $\sin 45^\circ = \cos 45^\circ = \tfrac{\sqrt{2}}{2}$ $\tan 45^\circ = 1$
Circle theorems: angle at the centre $= 2 \times$ angle at the circumference; angle in a semicircle $= 90^\circ$
More circle theorems: opposite angles of a cyclic quadrilateral add to $180^\circ;$ a tangent is perpendicular to the radius

Pyramid: $V = \tfrac{1}{3}A h$
Cone: $V = \tfrac{1}{3}\pi r^2 h$ $SA = \pi r^2 + \pi r l$ $(l$ is the slant height $)$
Sphere: $V = \tfrac{4}{3}\pi r^3$ $SA = 4\pi r^2$

Standard deviation (population): $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$
Permutations: ${}^nP_r = \dfrac{n!}{(n - r)!}$
Combinations: ${}^nC_r = \dbinom{n}{r} = \dfrac{n!}{r!(n - r)!}$

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