Diagram, givens, target
Mark every given on the diagram and state the target clearly. Start from a relationship that connects exactly those quantities.
A Level Year 13 / Mathematics / Curriculum
Pure Mathematics 3: structured theory, worked examples, answered practice, and a mastery checklist for A Level Year 13.
Unit
The essential chapter ideas in a clear sequence before practice.
Mark every given on the diagram and state the target clearly. Start from a relationship that connects exactly those quantities.
Every geometric step needs a property, theorem, or definition. A result without justification is not a complete proof.
Length, area, volume, and angle use different units. Round only at the end and keep sufficient intermediate precision.
Mathematics
Follow the method step by step and check why every step is valid.
A right triangle has perpendicular sides 12 cm and 16 cm. Find its hypotenuse and area.
Mathematics
Start from the board specification and work topic by topic before full papers.
The structure follows the official textbook layout and is used to organise study.
Hypotenuse 20 cm, area 96 cm².
Before calculating, explain the key idea from “Advanced functions” and which conditions must be checked.
The answer should show not only which rule is used for “Advanced functions”, but also why it is valid here.
Pure Mathematics 3
Try independently, use the hint if needed, then open the answer guide.
1. Explain the idea and give one correct foundation example for “Advanced functions”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Advanced functions”, shows equivalent steps, and includes a final check.
2. Solve an application and show every intermediate step for “Modulus functions where applicable”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Modulus functions where applicable”, shows equivalent steps, and includes a final check.
3. Compare a correct and an incorrect approach and justify the difference for “Partial fractions”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Partial fractions”, shows equivalent steps, and includes a final check.
4. Create a short exam-style question and check your answer for “Logarithmic functions”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Logarithmic functions”, shows equivalent steps, and includes a final check.
The areas that usually create mistakes or need extra revision.
Where to start: textbook, daily material, PDFs, videos, and worked examples.
Targeted practice before full tests so coverage is clear.
How to measure progress in this chapter and when it enters a cumulative mock.
What to do after finishing the chapter and how it connects to the next unit.
Note: for the official examinable syllabus of each school year, always confirm with the school, tutor, and current Ministry/IEP announcements.