In a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.
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)
Area of a Trapezium
area = 1/2(a+b)x height (a and b are the two parrallel lengths)
Circumference of a circle
Circumference = πd or 2πr
Area of a circle
area = πr squared
Arc length, of a circle
arc length, l = θ/360 x 2πr
Sectro area, of a circle
Sector area, A = θ/ x πr squared
Volume of a prism
volume of a prism = (area of cross section) x length
e.g. volume of a cylinder = πr squared x length
Volume of a Pyramid
volume = 1/3(basexarea) x height
Volume and surface area of a Sphere
volume = 4/3 π r cubed
surface area = 4πr squared
Volume and surface area of a Cone
volume = 1/3 πr squared x height
surface area = πr x length
Using Trig to find missing length of right angled
e.g. cos24(given angle) = x/91(given lenth)
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
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...)
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
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.
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