# GCSE Maths Equations

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### 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.

or    ## 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 $=A=\pi r^{2}$      ### GCSE Maths Equations to memorise            ## 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    ## You May Also Like... ### GCSE Maths Revision Cards

Revise for your GCSE maths exam using the most comprehensive maths revision cards available. These GCSE Maths revision cards are relevant for all major exam boards including AQA, OCR, Edexcel and WJEC.

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The MME GCSE maths revision guide covers the entire GCSE maths course with easy to understand examples, explanations and plenty of exam style questions. We also provide a separate answer book to make checking your answers easier!

From: £14.99 ### Transition Maths Cards

The transition maths cards are a perfect way to cover the higher level topics from GCSE whilst being introduced to new A level maths topics to help you prepare for year 12. Your ideal guide to getting started with A level maths!

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