Learning Guide
This guide explains how to study each module effectively, how to maintain an error log, and how to plan your revision across the eight-week course.
How to Prepare for Each Module
Before opening a module page, spend five minutes on self-preparation:
- Recall the prerequisites. Ask yourself: what did the previous module cover? Can I recall the key formula or definition without looking?
- Attempt the diagnostic questions cold. The Diagnostic Activity at the top of each module is designed to surface gaps — attempt it before reading any theory.
- Write your prediction for the Opening Problem. The Opening Problem introduces the module’s central concept through a real scenario; forming a prediction (even a wrong one) primes your attention.
Prerequisites by module
| Module | Prerequisites to review |
|---|---|
| 1 — Numerical calculations | Basic arithmetic; fractions |
| 2 — Algebra and equations | Module 1: percentages and index numbers |
| 3 — Graphs and systems | Module 2: first-degree equations |
| 4 — Sequences | Module 1: powers and percentages |
| 5 — Financial mathematics | Module 4: arithmetic and geometric sequences |
| 6 — Functions | Module 2: algebra; Module 1: powers |
| 7 — Derivatives and optimisation | Module 6: quadratic functions |
| 8 — Revision | Modules 1–7 |
Recommended Study Sequence
Each module is designed for a session of approximately 90 minutes. The six-step sequence below matches the 12-section template of the module pages:
| Step | Activity | Time | Module section |
|---|---|---|---|
| 1 | Diagnose | 15 min | §1 Diagnostic Activity |
| 2 | Understand | 20 min | §2 Opening Problem + §3 Core Concepts |
| 3 | Observe | 10 min | §4 Worked Example |
| 4 | Practise | 20 min | §5 Guided Practice (hint first, then solution) |
| 5 | Experiment | 10 min | §6 Interactive Exploration + Investigation |
| 6 | Apply | 15 min | §7 Applied Problem + §8 Common Errors |
After the session:
- Attempt §9 Check Your Understanding without notes.
- Read §10 Summary and try to recall the three takeaways aloud.
- Record any errors in your error log before closing the page.
- Complete the §11 Independent Work exercises within 48 hours.
How to use the Guided Practice
Always expand the Hint before the Solution. The hint gives you a single guiding step; attempting the exercise with only the hint develops problem-solving skill. Revealing the solution before attempting the exercise reduces retention.
How to use the Interactive Exploration
- Set the sliders to the values in the first Investigation question.
- Record what you observe.
- Try to explain the result without looking at the graph again.
- Then test your explanation by changing parameters.
Error Log
An error log is a personal record of every mistake you make during exercises, quizzes, and practice exams. Reviewing it before assessments is one of the most efficient revision strategies.
What to record
Use this template for each error:
| Field | What to write |
|---|---|
| Error | Copy the incorrect working exactly as you wrote it. |
| Root cause | Name the underlying reason: wrong formula, wrong method, arithmetic slip, sign error, incorrect reference value, domain error, etc. |
| Correct method | Write the correct step-by-step solution. |
| Prevention rule | Write one rule or check you will apply next time. |
Example:
| Field | Entry |
|---|---|
| Error | \(\Delta\% = (100 - 80)/100 \times 100 = 20\%\) |
| Root cause | Divided by the final value instead of the initial value. |
| Correct method | \(\Delta\% = (100 - 80)/80 \times 100 = 25\%\). The initial value is always the reference base. |
| Prevention rule | Before computing, circle the initial value and label it “denominator”. |
When to update the log
- Immediately after completing a Guided Practice or Check Your Understanding section.
- After each practice exam or timed exercise.
- After receiving corrected assessments.
How to use the log before exams
- One week before: read through every entry; highlight those you are still unsure about.
- Two days before: attempt a fresh exercise for each highlighted error; can you now avoid it?
- The night before: read only the prevention rules — do not rework problems.
Revision Schedule
This schedule assumes the course meets once per week over eight weeks, with the final exam in week 11 or 12.
Eight-week course schedule
| Week | Module | Focus | Study actions |
|---|---|---|---|
| 1 | Module 1 | Numerical calculations | Read + practise; start error log |
| 2 | Module 2 | Algebra and equations | Read + practise; update log |
| 3 | Module 3 | Graphs and systems | Read + practise; update log |
| 4 | Module 4 | Sequences | Read + practise; update log |
| 5 | Module 5 | Financial mathematics | Read + practise; update log |
| 6 | Module 6 | Functions | Read + practise; update log |
| 7 | Module 7 | Derivatives and optimisation | Read + practise; update log |
| 8 | Module 8 | Mixed revision | Attempt all 8 challenge problems; practice exam |
Two-week consolidation block (before the final exam)
Week 9 — Formula sheet and error-log review
- Day 1–2: Read the formula sheet from cover to cover. For each formula, can you state what it computes and give one example of its use?
- Day 3–4: Read your error log. Attempt a fresh exercise for each highlighted error category.
- Day 5–6: Work through the Check Your Understanding questions for every module without notes. Record new errors.
- Day 7: Rest.
Week 10 — Timed practice exam
- Day 1: Attempt the practice exam from Module 8 under exam conditions (no notes, no formula sheet, 90 minutes).
- Day 2: Correct and record all errors in the log.
- Day 3–4: Review only the topics where errors appeared.
- Day 5: Final read-through of prevention rules in the error log.
- Day 6: Rest and prepare materials.
- Day 7 (or exam day): Exam.
Tips for exam day
- Read each problem fully before writing anything. Identify the mathematical structure (linear? quadratic? geometric?) and the method before applying any formula.
- Show all steps, even if the calculation seems obvious. Partial credit is awarded for correct method even if arithmetic is wrong.
- Check the sign of \(a\) before declaring a maximum or minimum for a quadratic optimisation.
- Verify your answer in context: a negative quantity, an impossibly large interest rate, or a cost below zero signals a method error.
- Use the formula sheet (if provided) systematically: scan all formulas relevant to the topic before choosing one.