GCSE Maths Equations | Formulae to Learn | MME

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.

Click here to see our Equations To Memorise Z-Card


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   Higher Only


The quadratic equation:


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)}}



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}}


GCSE Maths Equations to memorise 

Click here to see our Equations To Memorise Z-Card


   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}


\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: \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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