National 5 Maths revision guides and grade boundaries
Four free PDF handbooks for National 5 Mathematics (C847 75), 71 pages in all. Together they cover the whole course, the formulas you are given and the ones you are 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 National 5 Mathematics C847 75, 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 National 5 books: the lesson notebooks teach each topic and the exam practice books give the questions.
Course specification reference
Covers all 40 course topics, from surds and reverse percentages to bearings, comparing data and explaining a solution, with what each one requires, what secure looks like and the evidence to keep, plus readiness checklists for Paper 1 and Paper 2.
Download the course specification referenceFormula handbook
Covers the formulae list and what it leaves out, then 24 formula cards from the quadratic formula to scale factors, each with its conditions, a worked check, whether it is supplied in the exam, a common trap and a way to verify the answer, plus a method selection guide.
Download the formula handbookCommon mistakes handbook
Covers 36 mistakes that the published National 5 course reports identify, from reverse percentages to communication, each with the typical error, a repair routine, a rapid retest and a mastery rule, plus a diagnostic log and the habits recent reports ask for.
Download the common mistakes handbookGrade boundary handbook
Covers the official grade boundaries out of 90 for 2022 to 2026, five-year ranges and medians for grades A to D, a historic grade calculator, a Paper 2 marks-needed planner, and the award profile and pass rates for each year.
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, 40 marks in 1 hour, and Paper 2 allows a calculator, 50 marks in 1 hour 30 minutes. The grade, A to D, comes from the combined total out of 90
- one course for every student: National 5 is not tiered, so there is no Foundation or Higher split to choose
- sources cited throughout, so a parent or tutor can check the facts
- worked checks written for these guides, with no exam question or marking instruction reproduced
- boundaries shown as history, not predictions: they move every year
- 71 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 8, 71 pages in all.
Course specification reference
- How the course is assessed: two papers, 90 marks, grades A to D
- 40 course topics across number, algebra, geometry, trigonometry, statistics and reasoning
- What each topic requires and what secure looks like
- A revision audit and the evidence to keep for each topic
- Paper 1 non-calculator and Paper 2 calculator readiness checklists
Formula handbook
- What the official formulae list supplies, and what it does not
- 24 formula cards, each with a worked check
- Exam status: supplied, or expected knowledge
- A method selection guide for triangles, quadratics and statistics
- Exact-value habits for the non-calculator paper
Common mistakes handbook
- Evidence method: course-report findings, no invented percentages
- 36 mistake entries, each with the report years shown
- A repair routine and rapid retest on every entry
- A mastery rule: two correct unseen questions on different days
- Diagnostic log and high-priority habits from recent reports
Grade boundary handbook
- How the 90-mark total becomes a grade
- Official A to D boundaries for 2022 to 2026
- Five-year range and median for every grade
- Historic grade calculator and Paper 2 marks-needed planner
- Award profiles and pass rates for each year
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 S4
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: it shows, for a given Paper 1 score, what Paper 2 has needed in past years for each grade. It is a planning aid, not a forecast.
National 5 lesson notebooks
Four notebooks that teach the course in 51 chapters, each with worked examples and practice questions.
Browse the lesson notebooksNational 5 exam practice books
Four books, eight modules each, with marks on every question and worked answers.
Browse the exam practice booksHigher Maths revision guides
The same four handbooks for Higher Mathematics, for students moving on after National 5.
See the Higher guidesRevision guide questions
The guides are free for personal use and written for National 5 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 National 5 Mathematics (C847 75). The boundaries and results figures are taken from the published course reports and grade boundary documents, 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. Between 2022 and 2026 the grade A boundary ranged from 62 to 65 marks and grade C from 36 to 47, which is why a prelim should be reported as a mark first and converted second.
Which formulas are given in the National 5 exam?
The formulae list gives the quadratic formula, the sine and cosine rules, the area of a triangle using sine, the volumes of a sphere, cone and pyramid, and standard deviation. Pythagoras, gradient, arc length, sector area, trigonometric identities and percentage models are not given, and the formula handbook marks each card with its exam status.
How is National 5 Maths assessed?
National 5 Mathematics (C847 75) has two papers. Paper 1 is non-calculator, 40 marks in 1 hour, and Paper 2 allows a calculator, 50 marks in 1 hour 30 minutes. The grade, A to D, comes from the combined total out of 90.
Where do the common mistakes come from?
Every entry is supported by the published National 5 Mathematics course reports, and the report years are shown on each one. The reports do not give frequencies, so the handbook does not invent percentages or rankings.
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.