GCSE Maths Equations
GCSE Maths Equations
GCSE Maths Formula Sheet
The GCSE maths formula sheet Zcard 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:

\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}^24\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} 
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}^22\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 
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