Maths Study Guide
A plain-language walkthrough of the whole syllabus. Every idea is explained simply, drawn out with a diagram, and paired with a memory trick so it sticks.
Work through one unit per sitting. Read the idea, look at the picture, copy the trick into your notebook, then try the worked example with the page covered. Each unit ends with a 3-question self-check.
The 7 units at a glance
The syllabus is really just four big chapters. Notice how they build on each other:
| Unit | Topic | CLO | Lecture hrs | Weight | Core idea in one line |
|---|---|---|---|---|---|
| 1 | Functions & Relation | 1 | 6 | ~11% | Sets and the rules that connect them |
| 2 | Counting, P & C | 1 | 4 | ~9% | Counting without actually counting |
| 3 | Probability | 2 | 6 | ~14% | How likely is something? |
| 4 | Distributions | 3 | 6 | ~14% | Probability given as a formula |
| 5 | Significance Testing | 3 | 10 | ~23% | Deciding if a result is real or noise |
| 6 | Graph Theory | 4 | 6 | ~14% | Networks of points and links |
| 7 | Trees | 4 | 6 | ~14% | Hierarchies and cheapest networks |
Unit 5 (Significance Testing) has the most lecture hours — 10 of 44. It is the single most exam-heavy topic. Give it the most revision time.
A 7-day revision plan
Days 1–2 · The maths core
Unit 1 (relations, function types, recursion) and Unit 2 (counting, P & C). Unit 2 is short but appears inside other units' questions.
Days 3–4 · The probability block
Unit 3, then Unit 4, then Unit 5 in that order. Do not jump to Unit 5 — every hypothesis test is built on the distributions from Unit 4.
Day 5 · Graphs
Unit 6: terminology, degree, adjacency/incidence matrices, Dijkstra, colouring.
Days 6–7 · Trees & mixed practice
Unit 7 (traversal, spanning trees, Kruskal/Prim), then mixed past-paper questions to catch weak spots.
Five ideas that unlock the whole syllabus
Almost every question you meet is one of these five ideas wearing a different hat.
"Without order" vs "with order". Almost the entire syllabus reduces to this one question.
- Order matters → nP r = n!/(n−r)! → Dijkstra, trees, functions
- Order does not matter → nC r = n!/[r!(n−r)!] → combinations, binomial coefficients
When an exam question looks hard, ask: "is this about order, or not?"
How to attack an exam question
- Name the unit. Counting objects? P&C. Chance? Probability. "Is it significant?" Unit 5. Network? Graph/tree.
- Find the trigger word. at least one, no two, all, exactly, round, first, cheapest, at most — each one flips the formula. The tricks page lists them all.
- Check the domain. In Unit 1 most errors come from using the wrong set. Draw the Venn diagram first.
- Write one line of justification. Almost every mark in this syllabus is for a reason, not just a number.
- Sanity-check. Probability must land between 0 and 1. Counts must be whole numbers. Degrees of an undirected graph must sum to an even number.
- Using nC r when order matters (or the reverse).
- Adding probabilities for independent events instead of multiplying.
- Forgetting to apply the continuity correction in the normal approximation.
- Confusing "accept" with "fail to reject" the null hypothesis.
- Not converting a one-tailed test to two-tail by doubling the critical area.
- In graphs: forgetting a graph with n vertices needs at least n−1 edges to be connected.
Jump straight to a unit
01 · Relations & Functions
Cartesian products, the four relation types, floor/ceiling, boolean, recursion.
02 · Counting, P & C
Basic principle, pigeonhole, nPr, nCr, Pascal's triangle.
03 · Probability & Bayes
A+B, A·B, exclusive vs independent, conditional, Bayes.
04 · Distributions
Normal curve, binomial, normal approximation to binomial.
05 · Significance Testing
H0 vs H1, critical values, one/two-tailed, z & t tests.
06 · Graph Theory
Degree, handshaking, adjacency/incidence matrix, Dijkstra, colouring.