Higher Maths Revision Guide — Every SQA Topic, Worked Examples, Practice
A complete topic-by-topic revision guide for SQA Higher Mathematics. Each page has key formulas, a worked example, practice questions and common mistakes — written by Glasgow specialists.
How to use this guide
Pick the topic you are weakest on and work through it in this order: read the formulas → study the worked example → attempt the practice questions → review the common mistakes.
- Aligned to current SQA spec (post-2018 reform) — Expressions and Functions, Relationships and Calculus, Applications
- Original worked examples — written by Glasgow tutors with 20+ years SQA experience
- British English & SQA conventions — radians, exact values, marking-scheme style
- One-to-one support available — book a 1-hour Glasgow Higher Maths specialist if you get stuck
Expressions and Functions
The Straight Line
The Straight Line is the foundation topic in Higher Maths. It builds on National 5 work and underpins almost every other topic — from differ…
Functions and Graphs
Functions and Graphs covers the language and behaviour of functions you will use throughout Higher Maths. Composite functions, completing th…
Trigonometric Functions
Trigonometric functions in Higher Maths require fluency with radians, exact values for special angles and the basic identities. Trig appears…
Vectors
Vectors in Higher Maths extend National 5 work into 3D and introduce the scalar (dot) product. Expect a 6–8 mark vector question on Pa…
Relationships and Calculus
Differentiation
Differentiation is one of the highest-mark topics on Higher Maths. Almost every Paper 2 has an extended differentiation question worth 8&nda…
Polynomials
Polynomials questions test your ability to factorise cubic and quartic expressions using synthetic division (also called nested form), and t…
Quadratic Theory
Quadratic Theory in Higher Maths goes beyond solving equations: you need to use the <em>discriminant</em> to classify roots, link the graph …
Integration
Integration is the reverse of differentiation. In Higher Maths you will use it to find areas, evaluate definite integrals and solve simple d…
Compound Angle Formulae
Compound and double angle formulae let you expand expressions like sin(A + B) and cos 2x into expressions you can simplify or solve. They ar…
Logarithms and Exponentials
Logarithms and exponentials connect a lot of real-world modelling questions in Higher Maths — population growth, radioactive decay, compound…
The Wave Function
The Wave Function lets you rewrite expressions of the form k sin x + a cos x in the simpler R cos(x − α) form. This makes it eas…
Further Differentiation
Further Differentiation extends basic calculus to include the chain rule and differentiating trigonometric, exponential and logarithmic func…
Applications
Recurrence Relations
Recurrence Relations are a small but reliable mark-grab on Higher Maths. Most exams include a 5–7 mark question asking you to find a l…
The Circle
The Circle is one of the most reliable mark-grabbers in Higher Maths. Tangents to circles and intersections with straight lines are tested a…
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