Additional Mathematics
Form 4 · 29 topics available
Chapter 1 · Functions
Functions
A function maps each input to exactly one output. Learn notation, domain, range, images and objects.
OpenComposite Functions
Combine two functions by feeding the output of one into the other: fg(x) = f(g(x)).
OpenInverse Functions
The inverse function reverses a function, sending each image back to its object: f⁻¹(f(x)) = x.
OpenChapter 2 · Quadratic Functions
Quadratic Equations and Inequalities
Solve ax² + bx + c = 0 by factorisation or formula, and solve quadratic inequalities using the roots.
OpenTypes of Roots of Quadratic Equations
The discriminant b² − 4ac tells whether a quadratic equation has two, one or no real roots.
OpenSimultaneous Equations involving One Linear and One Non-Linear Equation
Solve a linear and a non-linear equation together by substitution, giving up to two solution pairs.
OpenQuadratic Functions
A quadratic function f(x) = ax² + bx + c graphs as a parabola with a vertex, axis of symmetry and max or min.
OpenChapter 3 · Systems of Linear Equations in Three Variables
Chapter 4 · Indices, Surds and Logarithms
Laws of Indices
Master the laws of indices to multiply, divide and raise powers, and to handle zero, negative and fractional exponents with confidence.
OpenLaws of Surds
Simplify, multiply and add surds, and rationalise denominators, using the surd laws to keep answers in exact form.
OpenLaws of Logarithms
Use the laws of logarithms to expand and combine log expressions, evaluate logs and solve simple logarithmic equations.
OpenChapter 5 · Progressions
Arithmetic Progressions
Work with arithmetic progressions: find the common difference, the nth term and the sum of terms using the standard formulas.
OpenGeometric Progressions
Explore geometric progressions: find the common ratio, the nth term, the sum of terms and the sum to infinity when |r| < 1.
OpenChapter 6 · Linear Law
Linear and Non-Linear Relations
How to tell a linear relation from a non-linear one, and why converting to a straight line Y = mX + c makes analysis easy.
OpenLinear Law and Non-Linear Relations
Reduce equations like y = ax^n and y = ab^x to Y = mX + c, then find the constants from the straight-line graph.
OpenApplication of Linear Law
Use experimental data and a line of best fit to find constants in a non-linear law, then predict values.
OpenChapter 7 · Coordinate Geometry
Divisor of a Line Segment
Find the midpoint and the point dividing a segment in a given ratio using the section formula.
OpenParallel and Perpendicular Lines
Parallel lines share the same gradient; perpendicular lines have gradients whose product is −1.
OpenAreas of Polygons
Find the area of a triangle or polygon from its vertices using the shoelace (determinant) formula.
OpenEquations of Loci
A locus is the path of a point that moves under a given rule; find its equation using the distance formula.
OpenChapter 8 · Vectors
Vectors
A vector has both magnitude and direction, unlike a scalar. Learn notation, equal and negative vectors, and scalar multiplication.
OpenAddition and Subtraction of Vectors
Combine vectors using the triangle and parallelogram laws. Learn to find a resultant and to subtract by adding the negative.
OpenVectors in a Cartesian Plane
Write vectors in component form using i and j, compute magnitude with √(x²+y²), and find unit vectors.
OpenChapter 9 · Solution of Triangles
Sine Rule
The sine rule relates each side of a triangle to the sine of its opposite angle. Use it to find sides or angles in non-right triangles.
OpenCosine Rule
The cosine rule finds a side from two sides and the included angle, or an angle from all three sides.
OpenArea of Triangles
Find the area of any triangle using ½ab sin C when two sides and the included angle are known, or Heron's formula from three sides.
OpenApplication of Sine Rule, Cosine Rule and Area of a Triangle
Choose the right rule for real problems — bearings, heights and three-dimensional shapes — and combine them to solve triangles fully.
OpenChapter 10 · Index Number
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