O level Maths Formula Sheet
Rules of Indices
Rule 1: When you multiply indices of the same number you add the powers.
For example: 5 to the power 4x 5 to the power of 3= 5 to the power of 4+3 = 5to the power of 7
Rule 2: When you divide indices of the same number you subtract the powers.
For example: ( rule 2)
Rule 3: Indices outside a bracket multiply.
For example: (3 to the power of 2) 4 = 3 to the power of 2 x 4 = 3 to the power of 8
Rule 4: Negative indices mean reciprocal, i.e. ‘one over . . .’ or ‘put on the bottom of a fraction’.
For example: rule 4)
Rule 5: When the power is a fraction the top of the fraction (numerator) is a power and the bottom of the fraction is a root.
Rule 6: Anything to a power of 1 is just itself and we normally don’t bother putting the 1 there.
For example: 5 to the power 1 is just 5.
Anything to a power of 0 is equal to 1, it doesn’t matter what number it is!
For example: 10 to the power 0 = 1, 2 to the power 0 = 1, x to the power 0 = 1, etc.
The nth Term
nth term = dn + (a – d)
For example: 6, 11, 16, 21, . . . for this sequence d = 5, a = 6
Rule 1: Angles around a single point add up to 360°.
Rule 2: Angles on a straight line add up to 180°.
Rule 3: Vertically opposite angles are equal. (This is when two straight lines cross!).
Rule 4: Angles in a triangle add up to 180°.
Rule 5: Angles in a quadrilateral add up to 360°.
When a straight line crosses two parallel lines there are more angle facts we can look for and use!
Rule 1: Corresponding angles are equal — these are angles in a letter ‘F’.
Rule 2: Alternate angles are equal — these are angles in a letter ‘Z’.
Rule 3: Supplementary angles add up to 180° — these are angles in a letter ‘U’ or ‘C’ (when the ‘U’ and the ‘C’ are made of three straight sides, of course).
Sin, Cos, Tan
Rule 1: Sine is Opposite over Hypotenuse
Rule 2: Cos is Adjacent over Hypotenuse
Rule 3: Tan is Opposite over Adjacent
Rule: The square on the hypotenuse is equal to the sum of the squares on the other two sides or, a2 + b2 = c2
Square: Area = Length2
Rectangle: Area = Length x Width
Right-angled Triangle: Area = ½ x Base x Height
Other Triangle: Area = ½ x Base x Perpendicular Height
Circle: Area = p r2
Trapezium: Area = Average of Parallel sides x Distance between them
Curved Surface of a Cylinder: Area = 2p rh
Surface of a Sphere: Area = 4p r2
Curved Surface of a Cone: Area = p rl
Cube: Volume = Length3
Cuboid: Volume = Length x Width x Height
Prism: Volume = Area of Cross-section x Length
Cylinder: Volume = p r2h
Sphere: Volume = 4/3p r3
Prism: Volume = 1/3p r2h
Polygons and their angles
For a regular polygon with ‘n’ sides, External angle:
For a regular polygon with ‘n’ sides, Internal angle:
Circumference = 2p r or, Circumference = pd
Area = p r2
The equation of a straight line is y = mx + c
The gradient, m:
Quadratic functions are written in the form y = ax2 + bx + c
Cubics are in the form y = ax3 + bx2 + cx + d
In a pie chart, to find out the frequency that each section represents measure the angle for the section then:
If we call a particular event ‘A’ then the probability of A happening is:
The ‘and’ rule:
p (A and B) = p (A) x p (B)
The ‘or’ rule:
p (A or B) = p (A) + p (B)