Higher Maths lesson notebooks by topic
64 chapters across four free PDF notebooks: Number, Algebra, Geometry and Trigonometry, and Calculus, 16 chapters each. Every chapter explains the idea, works through two examples, sets a guided reasoning task and ends with four practice questions and worked answers.
The notebooks are for learning a Higher topic properly before practising it under exam conditions. When a chapter feels secure, move on to our Higher exam practice books.
Free to download. No sign up, no email required. Independent resources aligned to Higher Mathematics (C847 76), not produced, approved, endorsed by or affiliated with Qualifications Scotland or the former SQA.
Which Higher topics do the notebooks teach?
Four notebooks covering the whole Higher course. Download each notebook free as a PDF and print what you need. Ready to practise at exam pace? Use our Higher exam practice books.
Number
Surds and rationalising denominators, indices, exponential and logarithmic functions, the laws of logarithms, exponential and logarithmic equations, and fitting exponential and power models to data.
Download the Number notebookAlgebra
Polynomials and the factor theorem, cubic and quartic equations, completing the square, graph transformations, composite and inverse functions, the discriminant and recurrence relations.
Download the Algebra notebookGeometry and Trigonometry
Parallel and perpendicular lines, medians and altitudes, circles, tangents and intersections, vectors in three dimensions, the scalar product, trigonometric equations in degrees and radians, addition formulae and the wave function.
Download the Geometry notebookCalculus
Differentiation and the chain rule, tangents, stationary points, optimisation, rates of change, integration, areas between curves and differential equations.
Download the Calculus notebookHow is each chapter organised?
Every chapter follows the same five-step pattern: meaning first, method second, reasoning throughout. The worked answers include a check for each question, so a wrong answer becomes something to repair.
The five steps in every chapter
- Understand: the key idea, the vocabulary, a prior-knowledge check and a checkpoint question
- Build the method: two worked examples, to cover line by line and predict before reading
- Connect and reason: a common misconception and a guided task planned before calculating
- Practise independently: four questions to complete without notes
- Diagnose and revisit: worked answers with a check, and a reflection on the error type
What else is inside
- a how-to-learn page explaining the five-step routine before the first chapter
- a unit map listing all 16 chapters with their reference labels
- a communication standard in every chapter: one statement per line, exact values until rounding is asked for
- a mastery review at the end of every notebook to check each chapter can be explained, reproduced and applied
What do the 64 chapters cover?
Each notebook labels its chapters with its own reference codes, so you can track progress chapter by chapter. The chapter order is our own teaching sequence, not an official unit structure.
| Notebook | Chapters | Practice questions | Matching practice books |
|---|---|---|---|
| Number | 16 | 64 | Algebraic Skills; Functions and Graphs |
| Algebra | 16 | 64 | Algebraic Skills; Functions and Graphs |
| Geometry and Trigonometry | 16 | 64 | Trigonometry, Vectors and Geometry |
| Calculus | 16 | 64 | Differential Calculus; Integral Calculus |
The notebooks were written against the current Higher Mathematics course specification. No official question, marking instruction or diagram is reproduced, and the marks on practice questions are an independent teaching allocation rather than official marks.
How should a student use these?
Work one chapter at a time. Cover each next line of a worked example, predict it, then reveal it and explain why the step is allowed. Do the four practice questions without notes and mark them from the worked answers.
Learning a topic for the first time
Read the chapter in order and answer the checkpoint without looking back. Plan the guided reasoning task before you calculate: what is known, what is required, which relationship controls it, and how you will check it.
Filling a gap
Use the unit map to find the chapter, try the four practice questions first, and only read the teaching pages if you lose marks. That keeps revision time on what you do not know yet.
Moving to exam practice
Once a chapter feels secure, practise the same topic in the matching Higher exam practice book, where the questions build from core skills to course-standard challenge.
Exam habit: keep answers exact
On Paper 1, leave surds, fractions and π in your answer and simplify fully. Round only when the question asks you to.
Exam habit: check the angle mode
Degree and radian modes give different answers to the same input. Match your calculator to the units and interval in the question before you start.
Exam habit: check by reversing
Substitute a solution back into the original equation, and differentiate an integral to check it. Both take seconds and catch slips before they cost marks.
Lesson notebook questions
The short version: the notebooks are free for personal use, every chapter has worked answers, and they are written for Scottish Higher Mathematics, grades A to D.
Are these official Higher materials?
No. The notebooks are independently written for the Higher Mathematics course. They are not produced, approved, endorsed by or affiliated with Qualifications Scotland or the former SQA, and no official question or marking instruction is reproduced.
Do the notebooks include answers?
Yes. Every chapter ends with worked answers showing the method, the answer and a check, so students can mark their own work and see exactly where a mistake happened.
Are they free? What is the licence?
The Free Website Edition is free for personal and household educational use. Tutors and schools must obtain the appropriate licence before copying for learners, and resale, paid redistribution and third-party uploading are prohibited.
How much practice is in each chapter?
Each chapter has four practice questions, which is enough to check understanding but not enough to build exam speed. For volume and exam pace, use the Higher exam practice books.
Do the chapter numbers match the exam practice books?
No. The notebooks and the practice books are organised differently: four notebooks of 16 chapters, and five practice books of eight modules. Match them by topic, using the chapter map on this page.
Is this the same as GCSE Higher tier?
No. Scottish Higher Mathematics is a separate qualification, usually taken after National 5. It includes calculus, logarithms, vectors and the wave function, which go well beyond GCSE Higher tier.
My child keeps getting the same chapter wrong. What next?
If a chapter is still insecure after working through it twice, the method usually needs to be retaught rather than practised more. A teacher at school or a tutor can usually spot the problem quickly. The first 30 minutes with one of our maths tutors are free.
Notebooks teach the method. A tutor makes it stick
Our maths tutors teach one to one on Zoom, £30 a lesson, and the first 30 minutes are free with no card details. If a chapter still does not make sense after two attempts, that is usually the sign to get the method retaught.