GCSE Maths Equations

GCSE Maths Equations

GCSE 1 - 3GCSE 4 - 5GCSE 6 - 7GCSE 8 - 9AQAEdexcelOCRWJECFoundationHigherAQA 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.

Click here to see our Equations To Memorise Z-Card

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AQA Edexcel OCR WJEC

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}

 

AQA Edexcel OCR WJEC

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)}}

 

AQA Edexcel OCR WJEC

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}}

 

AQA Edexcel OCR WJEC

Circles 

Circumference =c=2\pi r=\pi d

 

Area =A=\pi r^{2}

 

AQA Edexcel OCR WJEC

GCSE Maths Equations to memorise

Click here to see our Equations To Memorise Z-Card

AQA Edexcel OCR WJEC

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

 

AQA Edexcel OCR WJEC

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:
AQA Edexcel OCR WJEC

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}

 

AQA Edexcel OCR WJEC

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

 

AQA Edexcel OCR WJEC

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