IGCSE / O-Level

Additional Mathematics

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Functions

• Types of functions

• Domain and range

• Composite functions

• Inverse functions

• absolute-value functions (modulus)

• All topics

Full-length Papers

• Paper 1

• Paper 2

Quadratic Functions

• Maximum and minimum values

• Factorization, completing the square, and quadratics formula

• Roots of a quadratic function

• Solving quadratic inequalities

• Intersection between a line and a quadratic curve

• All topics

Factors of Polynomials

• Multiplication and division of polynomials

• Polynomial identities

• Remainder and factor theorems

• Solving cubic polynomials

• All topics

Equations, Inequalities, and Graphs

• Modulus functions and graphs

• Modulus inequalities

• Using substitution to solve a quadratic equation

• Using graphs to solve cubic inequalities

• All topics

Simultaneous Equations

• Simultaneous linear equations

• Simultaneous linear and non-linear equations

• Simultaneous non-linear equations

• All topics

Logarithmic and Exponential Functions

• Logarithms

• Graphs of logarithms

• Common and natural logarithms

• Laws of logarithms

• Logarithmic equations

• Indices (exponents) and surds

• Exponential equations

• Exponential growth and decay

• All topics

Straight Line Graph

• Equation of a line

• Length and midpoint of a line

• Parallel and perpendicular lines

• Linear law

• All topics

Coordinates Geometry of a Circle

• Equation of a circle

• Intersection of a circle and a straight line

• Tangents to a circle

• Intersection of two circles

• All topics

Circular Measure

• Radian measure

• Arc length

• Area of a sector

• All topics

Trigonometry

• Trigonometric ratios and general angles

• Reciprocal trigonometric functions

• Graphs of sine, cosine, and tangent functions

• Transformations of trigonometrical graphs

• Trigonometric identities and equations

• Cosec x, sec x, and cot x

• All topics

Permutations and Combinations

• The basic counting principles

• Permutations

• Combinations

• All topics

Series

• Binomial theorems

• Arithmetic progression

• Geometric progression

• All topics

Vectors in 2 Dimensions

• Basic concepts and operations

• Magnitude and unit vectors

• Position vectors

• Vectors expressed in terms of two non-parallel vectors

• Velocity problems

• All topics

Differentiations

• The gradient functions

• Chain rule

• Product rule

• Quotient rule

• Tangents and normals

• Stationary point problems

• Rate of change, small increments, and approximations

• Minima and maxima (second derivative)

• Derivative of trigonometric functions

• Derivative of exponential and logarithmic functions

• All topics

Integrations

• Integration techniques

• Integration of trigonometric functions

• Integration of exponential functions

• Area between a curve and an axis

• Area bounded by 2 curves

• All topics

Kinematics

• Displacement, velocity, and acceleration

• Displacement-time and velocity-time graphs

• All topics