National 5 Maths exam questions by topic
Four free PDF practice books, one for each area of the National 5 course: Number, Algebra, Geometry and Trigonometry, and Statistics. Each book has eight modules of 45 numbered questions, with marks shown on every question and worked answers at the back.
These are not past papers. Every question is independently written for the National 5 course, so you can work through these books alongside official past papers and marking instructions.
Free to download. No sign up, no email required. Independent resources aligned to National 5 Mathematics (C847 75), not produced, approved, endorsed by or affiliated with Qualifications Scotland or the former SQA.
Which National 5 topics can I practise?
Four books, one for each area of the course. Download each book free as a PDF and print what you need. Want the method taught first? Start with our National 5 lesson notebooks, then come back here to practise.
Number
Number skills for both papers: surds and indices, scientific notation, rounding and significant figures, fractions, percentages, appreciation and depreciation, and reverse percentages.
Download the Number bookAlgebra
Expanding brackets, factorising, solving equations and inequations, working with formulae, straight-line graphs and algebraic reasoning in context.
Download the Algebra bookGeometry and Trigonometry
Pythagoras and right-angled trigonometry, bearings, arcs and sectors, volumes of prisms, cylinders, cones and spheres, and geometric reasoning in context.
Download the Geometry bookStatistics
Averages and spread, quartiles and interquartile range, standard deviation, comparing data sets and interpreting results in context.
Download the Statistics bookHow is each book organised?
Every module follows the same four-stage sequence of 45 questions, with marks rising as the demand builds. Worked answers are collected at the back of each book, and a scorecard helps you decide which modules to retest.
The four stages in every module
- Core Skills, questions 1 to 18: secure the basic method before the demand rises
- Course Practice, questions 19 to 30: apply the method with growing confidence
- Exam Practice, questions 31 to 40: work at exam pace without notes
- Course-Standard Challenge, questions 41 to 45: finish the module and check readiness
What else is inside
- a contents and study plan page with score boxes, so weak modules get flagged for a second attempt
- a five-step routine on every book: attempt, show, mark, repair, then retest after 2 to 7 days
- marks shown on every question, so students learn how much working each answer needs
- worked answers for every question, collected at the back of each book
- a diagnostic scorecard for planning which modules to revisit
What do the four books cover?
The books follow the four main areas of the National 5 course. Each one is self-contained, so you can start with whichever area needs the most work.
| Book | Modules | Questions per module | Main skills |
|---|---|---|---|
| Number | 8 | 45 | Surds, indices, percentages, rounding |
| Algebra | 8 | 45 | Expressions, equations, formulae, lines |
| Geometry and Trigonometry | 8 | 45 | Trigonometry, bearings, arcs, volume |
| Statistics | 8 | 45 | Averages, spread, comparing data |
The questions were written against the current National 5 Mathematics course specification without reproducing any past-paper wording, diagrams, data or marking instructions. Course references identify curriculum alignment only, and the marks are an independent teaching allocation rather than official marks.
How should a student use these?
Work one module at a time, mark against the worked answers, and retest anything weak after 2 to 7 days. Paper 1 is non-calculator, so practise some questions without one. Official past papers and marking instructions are published free by Qualifications Scotland, and they work well alongside these books.
If the exam is months away
Work through each book in order, one or two modules a week. A correction only counts as secure when you can reproduce it from a blank page a few days later.
If the exam is weeks away
Go straight to the Exam Practice and Course-Standard Challenge stages of your weakest topics, then drop back to Core Skills only where marks are lost.
If you are aiming for an A
Start every module at the Course-Standard Challenge to find your ceiling fast. Show full working even when the answer feels obvious, because National 5 marking rewards the method you can see.
Exam habit: standard deviation
Use the formula on the National 5 formulae list, which divides by n minus 1. For the data 2, 4 and 6, that gives a standard deviation of 2. If a worked answer gives a different value, check it against the formulae list.
Exam habit: simplify surds fully
Take out the largest square factor, and write the square root of a perfect square as a whole number. The square root of 36 is 6, and the square root of 392 is 14 root 2.
Exam habit: factorise fully
When a question says factorise fully, take out the highest common factor of every term. 24x + 8 becomes 8(3x + 1), not 4(6x + 2).
Practice book questions
The short version: the books are free for personal use, they include worked answers, and they are written for National 5 Mathematics, grades A to D.
Are these real National 5 past paper questions?
No. Every question is independently written for the National 5 Mathematics course, without reproducing any past-paper wording, diagrams, data or marking instructions. You can use these books and official past papers together without overlap.
Do the books include answers?
Yes. Every book collects worked answers at the back, and every question shows its marks, so students can see how much working an answer needs and where marks are lost.
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 is the National 5 Maths exam set out?
There are two papers. Paper 1 is non-calculator, worth 40 marks in 1 hour. Paper 2 allows a calculator and is worth 50 marks in 1 hour 30 minutes. A formulae list is provided, and the course is graded A to D.
Which standard deviation formula should I use?
Use the formula on the National 5 formulae list, which divides by n minus 1. Your calculator may offer two versions, so make sure you pick the one that matches the formulae list.
How are these different from your National 5 lesson notebooks?
They do different jobs. The lesson notebooks teach each topic with explanations, worked examples and four practice questions per chapter. These practice books assume the method has been taught and exist to build fluency and exam pace across eight modules per book.
My child keeps scoring low on the same module. What next?
Repeating the same questions rarely fixes it, because the problem is usually the method rather than the practice. If a module scores low after two honest attempts, that is the point to get the method retaught, whether by a teacher at school or a tutor. The first 30 minutes with one of our maths tutors 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 a module keeps scoring low after two attempts, that is usually the sign to get help with the method rather than repeat the questions.