Formulas for GCSE Maths

Formulas for Trig, Quadratic Equations, Pythagoras etc...

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Straight Line


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Pythagoras' theorem


In a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.

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Area of a triangle

area = 1/2 x base x height


area = 1/2absinC (a and b are lengths, C is the angle of the connected lengths)

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Area of a Trapezium

area = 1/2(a+b)x height (a and b are the two parrallel lengths)

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Circumference of a circle

Circumference = πd or 2πr

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Area of a circle

area = πr squared

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Arc length, of a circle

arc length, l = θ/360 x 2πr

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Sectro area, of a circle

Sector area, A = θ/ x πr squared

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Volume of a prism

volume of a prism = (area of cross section) x length

e.g. volume of a cylinder = πr squared x length

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Volume of a Pyramid

volume = 1/3(basexarea) x height

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Volume and surface area of a Sphere

volume = 4/3 π r cubed

surface area = 4πr squared

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Volume and surface area of a Cone

volume = 1/3 πr squared x height

surface area = πr x length

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Using Trig to find missing length of right angled

e.g. cos24(given angle) = x/91(given lenth)


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Using Trig to find missing angle of a right angled

e.g. 3.2/4 =sin x

0.8 = sin x

-sin (0.8) = x

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Sine Rule (2angles 2 lengths, non right angled tri

e.g. sin x(missing anlge)/19(opposite length) = sin 60(given angle)/17(opposite length)

sin x = 19 sin 60/17

sin x =0.96....

x = - sin of ANS(0.96...)

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Cosine Rule (3lengths 1angle, non right angled tri

x[wanted length] squared = a[first length] squared + b[second length] squared - (2 x a x b x cos c[only given angle])

e.g. x squared = 22 squared x 23 squared - ( 2 x 22 x 23 x cos 48)

x squared = 335.8

x = sqaure root of 335.8

x = 18.33

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Circle Theorems

The angle at the centre of the circle is twice that of the angle at the circumference.

Opposite angle of a cyclic quadrilateral add up to 180 degrees.

The angle between a tangent and the radius drawn to the point of contact is 90 degrees.

From any point outside a circle just two tangents to the circle may be drawn and they are the same length.

The angle between a tangent and a chord through the point of contact is equal to the angle subtended by the chord in the alterate segment.

Angles subtended by an arc in the same segment of a circle are equal.

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Solutions of Quadratic Equations using a Formula

x = [-b +or- the square root (b squared - 4ac)] divided by 2a

e.g. 2x squared +23 x - 17

a = 2

b = 23

c = -17

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