Higher Maths revision guides and grade boundaries
Four free PDF handbooks for Higher Mathematics (C847 76), 46 pages in all. Together they cover the whole course, what the formulae list gives you and what it does not, the mistakes the course reports keep finding, and five years of official grade boundaries.
These are not past papers or practice books. They are the reference set that sits beside them: use them to decide what to revise, check a method before practising it, and turn a mock score into a realistic grade target.
Free to download. No sign up, no email required. Independent resources aligned to Higher Mathematics C847 76, not produced, approved or endorsed by Qualifications Scotland or the former SQA.
Which revision guides can I download?
Four handbooks for the whole course. Use them alongside our other Higher books: the lesson notebooks teach each topic and the exam practice books give the questions.
Course specification reference
Covers 47 course topics, from factorising cubics and the wave function to recurrence limits and mathematical communication, each with what the course requires, what secure looks like, audit questions and the evidence to keep, plus a whole-course red, amber and green audit.
Download the course specification referenceFormula handbook
Covers what the Higher formulae list supplies and what must still be understood, then 24 formula cards from the circle equations to the wave function, each with its condition, a selection cue, a common trap and a check, plus exact values and a method selection map.
Download the formula handbookCommon mistakes handbook
Covers 25 mistakes found in the published Higher course reports from 2022 to 2026, from omitting the constant of integration to missing solutions in an interval, each with what goes wrong, a repair routine and a rapid retest, plus a diagnostic log.
Download the common mistakes handbookGrade boundary handbook
Covers the official grade boundaries out of 120 for 2022 to 2026, five-year ranges and medians for grades A to D, entries and pass rates for each year, a historic grade calculator, a Paper 2 marks-needed planner and a mock tracker.
Download the grade boundary handbookHow do the four guides work together?
Each guide answers one revision question: what is on the course, which formula or equation to use, why marks are being lost, and what grade a score is worth. Used in that order, they turn a vague plan into a list of named topics to fix.
A revision loop using all four guides
- Audit: go through the specification reference and mark each topic red, amber or green
- Prepare: before practising a red topic, read its formula card and common trap
- Practise and mark: answer exam-style questions on the topic, then mark them honestly
- Repair: match every lost mark to an entry in the common mistakes handbook and follow its repair routine
- Measure: add up a mock score and compare it with the grade boundaries for the same year
What else is inside
- the assessment structure: two papers: Paper 1 is non-calculator, 55 marks in 1 hour 15 minutes, and Paper 2 allows a calculator, 65 marks in 1 hour 30 minutes. The grade, A to D, comes from the combined total out of 120
- one course for every student: Higher is a separate qualification taken after National 5, not a GCSE tier
- sources cited throughout, so a parent or tutor can check the facts
- independently written, with no exam question or marking instruction reproduced
- boundaries shown as history, not predictions: they move every year
- 46 printable A4 pages across the four guides
What is inside each guide?
The sections below follow each handbook’s own contents. The longest is 24 pages and the shortest 4, 46 pages in all.
Course specification reference
- How the course is assessed: two papers, 120 marks, grades A to D
- 47 course topics across algebra, functions, trigonometry, vectors, calculus, geometry and sequences
- What secure performance looks like for each topic
- Audit questions and the evidence to keep
- Whole-course red, amber and green audit grid
Formula handbook
- What the formulae list supplies, and what it does not
- 24 formula cards from circles to the wave function
- A selection cue, common trap and check on every card
- Exact values and non-calculator readiness
- A method selection map for common question types
Common mistakes handbook
- Evidence method: course-report findings, no invented percentages
- 25 mistake entries, each tied to the report years
- What goes wrong and why it costs marks
- A repair routine and rapid retest on every entry
- Diagnostic log for tracking repairs
Grade boundary handbook
- How the 120-mark total becomes a grade
- Official A to D boundaries for 2022 to 2026
- Five-year range and median for every grade
- Entries and pass rates for each year
- Historic calculator, Paper 2 planner and mock tracker
How should a student use these?
Start with the specification reference, because it shows what is left to learn. Keep the formula and mistakes handbooks open during practice, and use the grade boundary handbook after each mock, not before it.
Planning revision in S5
Work through the course reference a topic at a time. Anything red goes on the revision plan, and the formula handbook is the first stop for each one.
After a prelim
Add the two paper marks, compare the total with the grade boundaries, and list the lost marks. Then match each one to the common mistakes handbook and do its retest.
Deciding where the marks will come from
Use the marks-needed planner: for a given Paper 1 score it shows what Paper 2 would have needed on the 2026 boundaries for each grade. It is a planning aid, not a forecast.
Higher lesson notebooks
Four notebooks that teach the course in 64 chapters, each with worked examples and practice questions.
Browse the lesson notebooksHigher exam practice books
Five books, from algebraic skills to integral calculus, eight modules each, with worked answers.
Browse the exam practice booksNational 5 revision guides
The same four handbooks for National 5, useful for the number and algebra skills Higher assumes.
See the National 5 guidesRevision guide questions
The guides are free for personal use and written for Higher Maths. These answers cover boundaries, formulas, sources, licensing and choosing the right course.
Are these official Qualifications Scotland or SQA documents?
No. They are independently written guides aligned to Higher Mathematics (C847 76). The boundaries and results figures are taken from the published course reports, with the source given for each, but no exam question, marking instruction or official diagram is reproduced.
Can the grade boundaries predict my grade this year?
No. Boundaries are set after each exam to reflect how the papers performed, so they move every year. The five years of figures show the range a grade has needed, which makes them useful for setting a prelim target, but they are not a forecast.
Which formulas are given in the Higher exam?
The Higher formulae list gives the circle equations, the scalar product, the addition and double-angle formulae, and standard derivatives and integrals of sin(ax) and cos(ax). Exact values, the core trigonometric identities and the National 5 methods are not given, and the formula handbook explains when each supplied formula applies.
How is Higher Maths assessed?
Higher Mathematics (C847 76) has two papers. Paper 1 is non-calculator, 55 marks in 1 hour 15 minutes, and Paper 2 allows a calculator, 65 marks in 1 hour 30 minutes. The grade, A to D, comes from the combined total out of 120.
Where do the common mistakes come from?
Every entry is tied to the published Higher Mathematics course reports from 2022 to 2026, and the report years are shown on each one. The reports describe how common a problem is in words, not numbers, so the handbook does not invent percentages.
Are they free? What is the licence?
The guides are free to download for personal and household educational use. Tutors and schools need permission before copying them for learners, and resale, paid redistribution and third-party uploading are not permitted.
The same topic stays red on the checklist. What next?
If a topic is still red after the formula card and two honest retests, the method itself needs reteaching, by a teacher at school or a tutor. Our maths tutors teach one to one on Zoom, and the first 30 minutes are free.
Practice finds the gaps. A tutor closes them
Our maths tutors teach one to one on Zoom, £30 a lesson, and the first 30 minutes are free with no card details. If the same mistake keeps coming back after the repair routine, that is the moment to have the method retaught.