Additional Mathematics
IGCSE · 31 topics available
Chapter 1 · Functions
Functions, Domain and Range
A function gives each input one output; the domain is the allowed inputs and the range is the outputs.
OpenComposite and Inverse Functions
fg(x) means f(g(x)), applying g first; the inverse f⁻¹ reverses a one-one function.
OpenThe Modulus Function
The modulus |x| is a number's distance from zero, so it is never negative; |A| = b gives A = ±b.
OpenChapter 2 · Quadratic Functions
Chapter 3 · Factors of Polynomials
Chapter 4 · Equations, Inequalities and Graphs
Solving Equations and Inequalities
Solve quadratic and modulus equations, and quadratic and modulus inequalities, using factorising, the discriminant and sign analysis.
OpenGraphs of Modulus and Polynomial Functions
Sketch and interpret graphs of modulus functions y = |ax + b| and polynomial functions, reading off vertices, intercepts and the number of solutions.
OpenChapter 5 · Simultaneous Equations
Intersection of a Line and a Curve
Substitute the line into the curve, solve the quadratic, and use the discriminant to classify the intersection.
OpenLinear and Non-Linear Simultaneous Equations
Solve one linear and one non-linear equation by substitution, find intersection points, and use the discriminant for tangency conditions.
OpenChapter 6 · Logarithmic and Exponential Functions
Laws of Logarithms
Apply the product, quotient and power laws of logarithms, plus special values and change of base, to simplify and evaluate expressions.
OpenExponential and Logarithmic Equations and Graphs
Solve exponential and logarithmic equations using logs and indices, and recognise the shape, intercepts and asymptotes of their graphs.
OpenChapter 7 · Straight-Line Graphs
Determining Constants from a Linear Graph
Reduce y = abˣ or y = axⁿ to Y = mX + c, then read the gradient and intercept to find the constants.
OpenReducing Relationships to Linear Form
Transform relationships such as y = axⁿ and y = abˣ into straight-line form Y = mX + c, then find constants from the gradient and intercept.
OpenChapter 8 · Coordinate Geometry of the Circle
Chapter 9 · Circular Measure
Chapter 10 · Trigonometry
Chapter 11 · Permutations and Combinations
Chapter 12 · Series
Chapter 13 · Vectors in Two Dimensions
Chapter 14 · Calculus
Differentiation
Finding derivatives using the power rule and the chain, product and quotient rules, plus standard results.
OpenApplications of Differentiation
Using derivatives for tangents, normals, stationary points, increasing/decreasing behaviour and rates of change.
OpenIntegration
Integration as the reverse of differentiation: the power rule, standard integrals and definite integrals.
OpenApplications of Integration and Kinematics
Using integration to find areas under curves and to relate displacement, velocity and acceleration in kinematics.
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