1Topic 1
Number & Algebra
Number skills, sequences, series, and financial mathematics
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Topic 1
Number & Algebra
Number skills, sequences, series, and financial mathematics
Core Number Skills
Scientific notation, index laws, logarithm basics, approximation, upper and lower bounds, percentage error, accuracy and estimation, and solving equations with a GDC.
Sequences and Series
Sequence and series notation, sigma notation, arithmetic sequences and series, geometric sequences and series, and real-world applications.
Financial Mathematics
Compound growth and depreciation, loan amortisation, and annuities.
2Topic 2
Functions
Linear, quadratic, exponential, sinusoidal, and piecewise models
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Topic 2
Functions
Linear, quadratic, exponential, sinusoidal, and piecewise models
Linear Graphs
Straight-line equations and relationships between parallel and perpendicular lines.
More Functions and Their Graphs
Function notation and mappings, inverse functions, key graph features, intersections of graphs, and quadratic, cubic, exponential, and sinusoidal functions.
Function Modelling
Linear and piecewise models, quadratic and cubic models, exponential models, direct and inverse variation, sinusoidal models, and strategies for selecting and developing suitable models.
3Topic 3
Geometry & Trigonometry
Coordinate geometry, 3D geometry, trigonometry, and Voronoi diagrams
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Topic 3
Geometry & Trigonometry
Coordinate geometry, 3D geometry, trigonometry, and Voronoi diagrams
Essential Geometry
Coordinate geometry, perpendicular bisectors, arcs, and sectors.
Three-Dimensional Geometry
Coordinates in three dimensions, volume, and surface area.
Trigonometry
Pythagoras’ theorem, right-angled trigonometry, the sine rule, the cosine rule, triangle area, elevation and depression angles, bearings, and geometric constructions.
Voronoi Diagrams
Constructing and interpreting Voronoi diagrams and applying them to optimisation problems, including the toxic-waste-site problem.
4Topic 4
Statistics & Probability
Data, regression, probability, distributions, and hypothesis testing
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Topic 4
Statistics & Probability
Data, regression, probability, distributions, and hypothesis testing
Statistical Essentials
Sampling and data collection, measures of centre and spread, frequency tables, data transformations, outliers, box plots, cumulative frequency graphs, histograms, and data interpretation.
Correlation and Regression
Scatter plots, correlation, Pearson’s correlation coefficient, Spearman’s rank correlation coefficient, comparison of correlation measures, and linear regression.
Probability Basics
Probability rules, event types, independent and mutually exclusive events, conditional probability, Venn diagrams, and tree diagrams.
Probability Distributions
Discrete probability distributions and expected values.
Binomial Distributions
The binomial distribution and the calculation of binomial probabilities.
Normal Distributions
The normal distribution and related probability calculations.
Hypothesis Testing
Principles of hypothesis testing, chi-squared tests for independence, goodness-of-fit tests, and the t-test.
5Topic 5
Calculus
Differentiation, integration, and applications
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Topic 5
Calculus
Differentiation, integration, and applications
Differentiation
The derivative concept, differentiating powers of x, gradients, tangents and normals, increasing and decreasing behaviour, local maxima and minima, and applications of differentiation in modelling.
Integration
Numerical integration using the trapezoidal rule, the basic principles of integration, and integrating powers of x.
Need theory or method first?
Read the AI SL Revision Notes before tackling exam questions.