1Topic 1
Number & Algebra
Numerical skills, sequences, finance, complex numbers, matrices
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Topic 1
Number & Algebra
Numerical skills, sequences, finance, complex numbers, matrices
Numerical Skills
Scientific notation, rounding, upper and lower limits, percentage uncertainty, accuracy and estimation.
Exponents and Logarithms
Index rules, foundations of logarithms, logarithmic laws and simplification.
Sequences and Series
Sigma notation, arithmetic and geometric progressions, sums, and real-world applications.
Mathematics of Finance
Compound growth and depreciation, loan repayment, amortisation and annuity calculations.
Foundations of Complex Numbers
Arithmetic with complex numbers, quadratic equations with complex roots, modulus, argument, and the Argand plane.
Advanced Complex Numbers
Polar and Euler forms, converting between representations, geometrical interpretations, frequency and phase in trigonometric models.
Matrix Methods
Matrix calculations, determinants, inverse matrices, and solving simultaneous equations through matrices.
2Topic 2
Functions & Mathematical Models
Linear, quadratic, exponential, logistic, transformations, modelling
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Topic 2
Functions & Mathematical Models
Linear, quadratic, exponential, logistic, transformations, modelling
Straight Lines and Linear Graphs
Forming equations of straight lines, gradients, intercepts, parallel and perpendicular relationships.
Exploring Functions and Graphs
Function notation, key graphical features, intersections, quadratic, cubic, exponential, and sinusoidal graphs.
Building Mathematical Models
Linear, quadratic, cubic, exponential and sinusoidal modelling, direct and inverse variation, selecting and evaluating models.
Function Operations
Combining functions, composite functions, determining and interpreting inverse functions.
Graphical Transformations
Horizontal and vertical translations, reflections, stretches and compressions, and combinations of transformations.
3Topic 3
Geometry & Trigonometry
Triangles, trig equations, vectors, Voronoi diagrams, graph theory
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Topic 3
Geometry & Trigonometry
Triangles, trig equations, vectors, Voronoi diagrams, graph theory
Essential Geometry
Coordinate methods, perpendicular bisectors, arc length and sector area in degrees and radians.
Three-Dimensional Geometry
Coordinates in 3D, distances in space, volumes and surface areas of three-dimensional solids.
Trigonometry
Pythagoras, right-triangle trig, sine rule, cosine rule, triangle area, elevation and depression, bearings.
Trigonometric Relationships and Equations
Unit circle, fundamental identities, trigonometric graphs, graphical solutions of trigonometric equations.
Voronoi Diagrams
Constructing and interpreting Voronoi diagrams, applying Voronoi methods to location problems including the toxic-waste-site model.
Geometric Transformations with Matrices
Applying matrices to transformations, standard geometric transformations, combining matrices, interpreting determinants.
Vectors
Vector notation, addition, position and displacement, magnitude, dot product, cross product, angles, and geometric proofs.
Vector Equations of Lines
Vector and parametric equations, angles between lines, minimum distance from a point to a line, shortest distance between two lines.
Vector-Based Modelling
Describing motion with vectors, constant velocity and variable-velocity models.
4Topic 4
Statistics & Probability
Data, regression, distributions, hypothesis testing, Markov chains
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Topic 4
Statistics & Probability
Data, regression, distributions, hypothesis testing, Markov chains
Data and Statistical Analysis
Sampling, averages, spread, frequency distributions, outliers, box plots, cumulative-frequency diagrams, and histograms.
Association and Linear Regression
Pearson’s and Spearman’s correlation coefficients, constructing and interpreting linear-regression models.
Nonlinear Regression Models
Least-squares regression curves, coefficient of determination, logarithmic scales, and linearising nonlinear relationships.
Foundations of Probability
Probability rules, independence, mutual exclusivity, conditional probability, Venn diagrams, and probability trees.
Discrete Probability Models
Constructing discrete probability distributions and calculating expected values.
Random Variables and Estimation
Linear combinations of random variables, means and variances of combinations, unbiased estimators.
Binomial Models
Conditions for a binomial model, calculating exact and cumulative binomial probabilities.
Normal Distributions
Properties of the normal distribution, standardisation, and calculator-based normal probability calculations.
Combined Normal Variables and Sampling Distributions
Distributions of sample means, the central limit theorem, and confidence intervals for a population mean.
Poisson Models
Conditions for Poisson modelling, calculating and interpreting Poisson probabilities.
Chi-Squared Hypothesis Tests
Chi-squared tests for independence and goodness-of-fit, principles of hypothesis testing.
Tests for Population Parameters
One- and two-sample tests for means, binomial, Poisson, and correlation tests, Type I and Type II errors.
5Topic 5
Calculus
Differentiation, integration, motion, differential equations
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Topic 5
Calculus
Differentiation, integration, motion, differential equations
Foundations of Differentiation
Derivatives, powers of x, gradient functions, tangents, normals, increasing/decreasing intervals, optimisation.
Advanced Differentiation
Chain, product and quotient rules, related rates, second derivatives, stationary points, concavity and points of inflection.
Foundations of Integration
Trapezoidal rule, antiderivatives, integrating powers of x, constants of integration, areas using technology.
Advanced Integration and Applications
Reverse chain rule, substitution, definite integrals, signed areas, regions between curves, volumes of revolution.
Motion and Calculus
Displacement, velocity and acceleration, interpreting motion graphs, applying calculus to kinematic models.
First-Order Differential Equations
Separation of variables, constructing differential-equation models, slope fields, Euler’s method.
Need theory or method first?
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