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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.
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Algebra
| Higher Only |
|
The quadratic equation:
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\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 |
| Indirect 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}} | |
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 } |  |
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}} |
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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: | \text{Percentage} = \dfrac{\text{amount}}{\text{total}} \times 100 |
| Percentage change: | \text{Percentage Change }= \dfrac{\text{new group} - \text{original}}{\text{original}} \times 100 |
| Histograms: | \text{Frequency Density }= \dfrac{\text{frequency}}{\text{class width}} |
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