# GCSE Maths Equations

GCSE 1 - 3GCSE 4 - 5GCSE 6 - 7GCSE 8 - 9AQAEdexcelOCRWJECAQA 2022Edexcel 2022OCR 2022WJEC 2022

### GCSE Maths Formula Sheet

The GCSE maths formula sheet Z-card includes the formulae you will need to learn for your GCSE maths exam. Whether you are doing AQA, Edexcel or OCR, the following list of maths equations are relevant to you.

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## Algebra

 Higher Only

 The quadratic equation: $\textcolor{blue}{a}x^2+\textcolor{red}{b}x+\textcolor{Orange}{c}=0$ Its solutions are found using the quadratic formula: $x=\dfrac{-\textcolor{red}{b}\pm\sqrt{\textcolor{red}{b}^2-4\textcolor{blue}{a}\textcolor{Orange}{c}}}{2\textcolor{blue}{a}}$ Direct proportionality: ($y$ is proportional to $x$, $x^2$) $y \propto x \rightarrow y = \textcolor{limegreen}{k}x$ $y \propto x^2 \rightarrow y = \textcolor{limegreen}{k}x^2$ Inverse proportionality: ($y$ is inversely proportional to $x$, $x^2$) $y \propto \dfrac{1}{x} \rightarrow y = \dfrac{\textcolor{limegreen}{k}}{x}$ $y \propto \dfrac{1}{x^2} \rightarrow y = \dfrac{\textcolor{limegreen}{k}}{x^2}$

## Compound measures

 $\text{Speed (s)} = \dfrac{\text{distance (d)}}{\text{time (t)}}$ $\text{Density (d)} = \dfrac{\text{mass (m)}}{\text{volume (V)}}$ $\text{Pressure (p)} = \dfrac{\text{force (F)}}{\text{area (A)}}$

## Geometry

 Area of a rectangle $=l \times w$ Area of a triangle $=\dfrac{1}{2} b \times h$ Area of a Parallelogram $= b \times h$ Area of a Trapezium $= \dfrac{1}{2}(a + b) \times h$ Sum of interior angles for a regular polygon $= (\text{number of sides } – \, 2) × 180$ Interior angle of a regular polygon $=\dfrac{(\text{number of sides } – \, 2) \times 180}{\text{number of sides}}$ Exterior angle of a regular polygon $=\dfrac{360}{\text{number of sides}}$

## Circles

 Circumference $=c=2\pi r=\pi d$   Area $=A=\pi r^{2}$

## Volumes

 Higher Only

 Volume of a cuboid $=\text{ length }\times\text{ width }\times\text{ height}$ Volume of a prism $=\text{ area of cross section }\times{ \text{length}}$ Volume of a cylinder $=\pi r^2 h$ Volume of a pyramid $=\dfrac{1}{3}\times\text{ area of base }\times\text{ vertical height }$ Volume of sphere $=\dfrac{4}{3}\pi r^{3}$ Surface area of sphere $=4\pi r^{2}$ Volume of cone $=\dfrac{1}{3}\pi r^{2}h$ Curved surface area of cone $=\pi rl$ where $l$ is the slant height

## Pythagoras and Trigonometry

 Higher Only

 Pythagoras’ theorem: $a^2 +b^2 = c^2$ $\sin(x) = \dfrac{\text{opp}}{\text{hyp}}\,\,\,\,$ $\cos(x) = \dfrac{\text{adj}}{\text{hyp}}\,\,\,\,$ $\tan(x) = \dfrac{\text{opp}}{\text{adj}}$ Sine Rule:  $\dfrac{\textcolor{red}{a}}{\sin \textcolor{red}{A}}=\dfrac{\textcolor{limegreen}{b}}{\sin \textcolor{limegreen}{B}}=\dfrac{\textcolor{blue}{c}}{\sin \textcolor{blue}{C}}$ Cosine Rule: $\textcolor{red}{a}^2=\textcolor{limegreen}{b}^2+\textcolor{blue}{c}^2-2\textcolor{limegreen}{b}\textcolor{blue}{c}\cos \textcolor{red}{A}$ or $\cos(\textcolor{red}{A}) = \dfrac{\textcolor{limegreen}{b}^2+\textcolor{blue}{c}^2 - \textcolor{red}{a}^2}{2\textcolor{limegreen}{b}\textcolor{blue}{c}}$ Area of a triangle: $\dfrac{1}{2}ab\sin(C)$
 Trigonometry common values:

## Probability and more

 Higher Only

 Compound interest: $\text{New value} = \text{original}\times \bigg(1 +\dfrac{\text{percentage}}{100} \bigg)^{\text{time}}$ Depreciation: $\text{New value} = \text{original}\times \bigg(1 -\dfrac{\text{percentage}}{100} \bigg)^{\text{time}}$ Percentage of amount: $\dfrac{\text{percentage}}{100} \times \text{amount}$ Percentage change: $\text{Percentage Change }= \dfrac{\text{new} - \text{original}}{\text{original}} \times 100$ Histograms: $\text{Frequency Density }= \dfrac{\text{frequency}}{\text{class width}}$ Probability: \begin{aligned}P(A\text{ or }B)&=P(A)+P(B)-P(A\text{ and }B)\\P(A\text{ and }B)&=P(A\text{ given }B)P(B)\end{aligned}

## Kinematics

 Higher Only

 \begin{aligned}v&=u+at\\s&=ut+\dfrac{1}{2}at^{2}\\v^{2}&=u^{2}+2as\end{aligned} $s=$ distance $u=$ start speed $v=$ end speed $a=$ acceleration $t=$ time

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