Year 10 Maths Formula Sheet (Free, Printable PDF)

Year 10 maths formula sheet

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

Algebra

Factorising quadratics: $x^2 + bx + c = (x + p)(x + q),$ where $pq = c$ and $p + q = b$
Difference of two squares: $a^2 - b^2 = (a - b)(a + b)$
Quadratic formula: $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Discriminant: $\Delta = b^2 - 4ac$ $(> 0:$ two solutions $, \ = 0:$ one $, \ < 0:$ none $)$
Simultaneous equations: substitute one equation into the other, or add/subtract to eliminate a pronumeral
Inverse proportion: $y = \dfrac{k}{x}$

Straight line: $y = mx + c$ $m = \dfrac{y_2 - y_1}{x_2 - x_1}$
Parallel and perpendicular lines: parallel: $m_1 = m_2$ perpendicular: $m_1 \times m_2 = -1$
Parabola, turning point form: $y = a(x - h)^2 + k$ $($ turning point $(h, k))$
Axis of symmetry: $x = -\dfrac{b}{2a}$ for $y = ax^2 + bx + c$
Circle: $(x - h)^2 + (y - k)^2 = r^2$ $($ centre $(h, k),$ radius $r)$
Exponential: $y = a \times b^x$

Compound interest: $A = P(1 + r)^n$ $I = A - P$ $(r$ per period as a decimal $, \ n$ periods $)$
Trigonometry: $\sin\theta = \dfrac{O}{H}$ $\cos\theta = \dfrac{A}{H}$ $\tan\theta = \dfrac{O}{A}$
Cylinder: $V = \pi r^2 h$ $SA = 2\pi r^2 + 2\pi r h$
Prism: $V = A h$ $(A$ is the area of the cross-section $)$

Interquartile range: IQR $= Q_3 - Q_1$
Outliers: below $Q_1 - 1.5 \times$ IQR or above $Q_3 + 1.5 \times$ IQR
Independent events: $P(A$ and $B) = P(A) \times P(B)$
Conditional probability (two-way table): $P(A \mid B) = \dfrac{\text{number in } A \text{ and } B}{\text{number in } B}$

Free from Tuterly · worked examples and practice for every topic at tuterly.com.au