Maths Formulas

The following tables give the formulas that useful for GCSE/IGCSE Maths: Number, Algebra, Geometry, Circle Theorems, Trigonometry, Coordinate Geometry, Sketching Graphs, and Statistics. Scroll down the page for more examples and videos to help you remember the formulas.

IGCSE Maths Formulas (pdf)

 

 

 

 

 

 

 

 

Videos

Formulas for IGCSE Maths

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Formulas for IGCSE Maths

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I. Number

• Percentage Change: \(\frac{\text{Change}}{\text{Original Value}}\times 100\text{%}\)
  
• Simple Interest: \(I=\frac{PRT}{100}\)(where P = Principal, R = Rate, T = Time in years)
  
• Compound Interest / Growth & Decay: \(A=P\left( 1\pm \frac{R}{100} \right)^{n}\) (where A = Amount, P = Principal, R = Rate, n = Number of periods)
  
• Distance = Speed × Time
  
• Standard Form: A × 10ⁿ (where 1 ≤ A < 10 and n is an integer)
  
• Rules of Indices

II. Algebra

• Quadratic Formula: For ax²+bx+c=0, the solutions are \(x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)
  
• nth term of an Arithmetic Sequence: T_n=a+(n−1)d (where a is the first term, d is the common difference)
  
• Direct Proportion: y=kx (where k is a constant)
  
• Inverse Proportion: \(y=\frac{k}{x}\) (where k is a constant)
  

III. Coordinate Geometry

• Gradient (m) of a Line: \(m=\frac{y_2-y_1}{x_2-x_1}\)
  
• Equation of a Straight Line: y=mx+c
  
• Distance between two points (x₁, y₁) and (x₂, y₂): \(\sqrt{\left( x_2-x_1 \right)^{2}+\left( y_2-y_1 \right)^{2}}\)
  
• Midpoint of a Line Segment between (x₁, y₁) and (x₂, y₂): \(\left( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \right)\)
  
• Perpendicular Lines: m₁ × m₂ = -1

IV. Mensuration (Area and Volume)
Circles:
Circumference: C=πd or C=2πr
Area: A=πr²
Arc Length: \(L=\frac{\theta}{360^\circ }\times 2\pi r\)
Area of Sector: \(A=\frac{\theta}{360^\circ }\times \pi r^2\)
Rectangle:
Area: A=length×width
Perimeter: P=2(length+width)
Area of Triangle: A= ½×base×height
Area of Parallelogram: A=base×height
Area of Trapezium: A= ½(a+b)h (where a and b are parallel sides, h is perpendicular height)
Volume of Prism: V=Area of cross-section×length
Cylinder:
Volume: V=πr²
Curved Surface Area: CSA=2πrh
Total Surface Area: TSA=2πr²+2πrh
Volume of Pyramid: V= ⅓×base area×height
Cone:
Volume: V= ⅓ πr²h
Curved Surface Area: CSA=πrl (where l is slant height)
Total Surface Area: TSA=πr²+πrl
Sphere:
Volume: \(V=\frac{4}{3}\pi^3\)
Surface Area: SA=4πr²

V. Probability and Statistics

• Probability of an Event: \(P\left( Event \right)=\frac{\text{Number of favourable outcomes}}{\text{Total Number of possible outcomes}}\)
  
• Mutually Exclusive Events: P(A or B)=P(A)+P(B)
  
• Independent Events: P(A and B)=P(A)×P(B)
  
• Mean from a Frequency Table: Mean= \(\frac{\sum{fx}}{\sum{f}}\) (where f is frequency, x is value/midpoint)
  
• Frequency Density (for Histograms): Frequency ÷ Class Width

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