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Build your understanding chapter by chapter, with worked examples and checks along the way.
Prepare for the course with the study guide and prerequisite checklist →
Assumed knowledge
Refresh the algebra and notation that later lessons build on.
0 of 1 chapters marked confident
Functions and graphs
From graph features to inverses, composition and algebraic constraints.
0 of 6 chapters marked confident
- Graphing techniques
Sketch rational curves using structural features. - Functions
What can go in, and what can come out? · When does an inverse exist? · Can one function feed another? - Graph transformations
Track translations, stretches and reflections. - Conic sections
Identify parabolas, ellipses and hyperbolas. - Solving inequalities
Solve rational inequalities with a sign diagram. - Systems of linear equations
Translate constraints into simultaneous equations.
Sequences and series
Describe patterns, sum terms and understand convergence.
0 of 1 chapters marked confident
Vectors
Use direction and geometry to describe points, lines and planes.
0 of 3 chapters marked confident
- Vectors: magnitude, direction and products
Use displacement, magnitude and unit vectors. - Vectors: lines and perpendicular feet
Write a line using a point and direction. - Vectors: planes, normals and distances
Describe planes using normals or two directions.
Calculus: differentiation
Rates, tangents, optimisation and local approximation.
0 of 3 chapters marked confident
- Techniques of differentiation
Interpret a derivative as local rate of change. - Applications of differentiation
Connect derivative signs to increasing and decreasing behaviour. - Maclaurin series and approximation
Build expansions from derivatives at zero.
Calculus: integration
Parametric curves, accumulation, areas and differential equations.
0 of 4 chapters marked confident
- Parametric equations
Trace parametric curves, retain their ranges, and solve tangent, normal and locus problems. - Techniques of integration
Recognise reverse chain-rule patterns. - Definite integrals, areas and volumes
Interpret integrals as limits of sums and signed accumulation. - Differential equations
Integrate and separate first-order equations, use substitutions, and interpret rate models with their initial conditions.
Complex numbers
Connect algebra to geometry in the Argand plane.
0 of 1 chapters marked confident
Probability and statistics
Count outcomes, choose distributions and reason from samples.
0 of 8 chapters marked confident
- Permutations and combinations
Decide whether order matters. - Probability and conditional information
Use complements, unions and intersections. - Discrete random variables
Build a probability distribution from outcomes. - The binomial distribution
Check the assumptions for a binomial model. - The normal distribution
Standardise using the standard deviation. - Sampling and the sample mean
Choose a sampling model, estimate population parameters and distinguish exact normal results from CLT approximations. - Hypothesis tests for a mean
Formulate hypotheses before examining a result. - Correlation and linear regression
Use scatterplots before fitting a line.