Homeschool → the UK → Year 13 → Mathematics

Year 13 mathematics

These Year 13 topics extend foundational senior mathematics. Learners apply differentiation rules to find stationary points and solve optimisation problems, meet integration as the reverse of differentiation and as a way to find areas, and use the normal distribution and discrete random variables to reason about data and chance. A financial topic connects recurrence relations to loans and annuities. Families should check the specific requirements of their state or territory's senior courses.

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Number

Loans, annuities and recurrence relationsTopic outlineModel reducing-balance loans and annuities with recurrence relations, and explore how interest rates, repayments and time affect the total amount paid.

Algebra

Statistics

The normal distribution and z-scoresFull lesson · 55 minRecognise normally distributed data, use the 68–95–99.7 rule to estimate proportions, and use z-scores to compare values from different distributions.

Probability

Discrete random variablesTopic outlineDescribe discrete probability distributions with tables, calculate the expected value and variance, and introduce the binomial distribution for repeated independent trials.

Plan with these topics

Curriculum notes

Australian Curriculum v9.0. Senior secondary mathematics study and certification are set by each state and territory's own authority (for example, through the HSC, VCE, QCE, WACE, SACE, TCE, ACT Senior Secondary Certificate or NTCET). The topics here are foundational preparation only, building on the Australian Curriculum v9.0 F–10 Mathematics strands. This is an independent learning resource; it is not endorsed by ACARA or any state or territory authority and does not follow any particular senior syllabus.

These lessons were written around Australian Curriculum strands and matched to UK year groups by age (Year 1 is the year a child turns 6 in England). They are not mapped to the National Curriculum in England or the curricula of Scotland, Wales or Northern Ireland, so check them against your own plans.

For parents

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