GCSE Maths Equations | Formulae to Learn | MME

GCSE Maths Equations

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GCSE Maths Predicted Papers

GCSE Maths Equations to memorise 

GCSE Maths Equations to memorise Z-Card is our full list of the maths formulae you need to learn for your GCSE 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 formula

The solutions for 

\textcolor{blue}{a}x^2+\textcolor{red}{b}x+\textcolor{Orange}{c}=0
Solutions are given 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{blue}{k}x

y \propto x^2 \rightarrow y = \textcolor{blue}{k}x^2

Indirect proportionality:
(y is inversely proportional to x, x^2)

y \propto \dfrac{1}{x} \rightarrow y = \dfrac{\textcolor{blue}{k}}{x}

y \propto \dfrac{1}{x^2} \rightarrow y = \dfrac{\textcolor{blue}{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}}

 

GCSE Maths Equations to memorise 

Click here to see our Equations To Memorise Z-Card

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{ 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{limegreen}{a}}{\sin \textcolor{limegreen}{A}}=\dfrac{\textcolor{blue}{b}}{\sin \textcolor{blue}{B}}=\dfrac{\textcolor{red}{c}}{\sin \textcolor{red}{C}}

Cosine Rule: \textcolor{limegreen}{a}^2=\textcolor{blue}{b}^2+\textcolor{red}{c}^2-2\textcolor{blue}{b}\textcolor{red}{c}\cos \textcolor{limegreen}{A}

or

\cos(\textcolor{limegreen}{A}) = \dfrac{\textcolor{blue}{b}^2+\textcolor{blue}{c}^2 - \textcolor{limegreen}{a}^2}{2\textcolor{blue}{b}\textcolor{red}{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}}{total} \times 100
Percentage change: = \dfrac{\text{new group} - \text{original}}{\text{original}} \times 100
Histograms  = \dfrac{\text{frequency}}{\text{class width}}

 

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