National 5, then Higher, taught in order.
Higher builds directly on National 5, so our course teaches them as one path: the National 5 skills made secure, then the Higher topics, ending in timed papers in the Scottish format.
Start hereNational 5 and Higher Maths (Scotland)
National 5 Mathematics (C847 75) and Higher Mathematics (C847 76) taught live, from algebra and trigonometry to calculus, ending in timed papers.
$100/mo group · $150/mo one-to-one
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Algebra Foundations
For a learner whose algebra is shaky before National 5: expressions, equations and graphs rebuilt from the base.
$100/mo group · $150/mo one-to-one
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Middle School Maths: Pre-Algebra and Geometry
For S1 to S3 learners in the broad general education who want a firm footing before National 5.
$100/mo group · $150/mo one-to-one
View course and enrolWhere is the learner now? Follow that row.
| The learner | What we would suggest | Start with |
|---|---|---|
| S3 or S4, sitting National 5 this year | The National 5 skills strand by strand, then full papers with Paper 1 practised without a calculator | National 5 and Higher Maths |
| Passed National 5, starting Higher in S5 | Algebra and functions secured early, because calculus and logarithms lean on them | National 5 and Higher Maths |
| Algebra holding back National 5 marks | Algebra rebuilt first, then National 5 papers | Algebra Foundations |
| S1 to S3, wants a head start | Number, algebra and geometry made secure before the National 5 course begins | Middle School Maths |
National 5 and Higher Maths compared, line by line.
Every row is taken from the course specifications for National 5 Mathematics and Higher Mathematics, version 3.0, valid from session 2023 to 24.
| What | National 5 Mathematics | Higher Mathematics |
|---|---|---|
| Course code | C847 75 | C847 76 |
| SCQF level | Level 5, 24 credit points | Level 6, 24 credit points |
| Notional learning time | 160 hours | 160 hours |
| Paper 1 (non-calculator) | 40 marks, 1 hour | 55 marks, 1 hour 15 minutes |
| Paper 2 | 50 marks, 1 hour 30 minutes | 65 marks, 1 hour 30 minutes |
| Total | 90 marks, 2 hours 30 minutes | 120 marks, 2 hours 45 minutes |
| Grades | A to D, from the total mark | A to D, from the total mark |
| Recommended entry | Fourth curriculum level or National 4 Mathematics, or equivalent | National 5 Mathematics, or equivalent |
| Core Skill certified | Numeracy at SCQF level 5 | Numeracy at SCQF level 6 |
| Leads on to | Higher Mathematics, among other routes | Advanced Higher Mathematics, Mathematics of Mechanics or Statistics, among other routes |
On 1 February 2026, Qualifications Scotland replaced SQA as Scotland's national awarding body. Its course pages say the SQA-era documents remain current. Entry to both courses is at the discretion of the school or college.
Higher keeps the National 5 skills and adds a new layer.
Examples from National 5
- Surds and the laws of indices, including negative and fractional indices
- Reverse percentages
- The equation of a straight line, gradient and intercept
- Simultaneous equations
- Quadratics: sketching, the quadratic formula and the discriminant
- Volumes, and the sine and cosine rules
- Adding and subtracting two-dimensional vectors
Examples new at Higher
- Factorising and solving cubic and quartic polynomials
- Logarithms and exponentials, and their laws
- The addition and double angle formulae, and the wave function
- Differentiation, including stationary points and their nature
- Integration, including areas
- The equation of a circle
- Vectors in three dimensions, the scalar product and unit vectors i, j, k
Qualifications Scotland also offers Applications of Mathematics as a separate subject. This page is about the Mathematics courses.
Why Higher feels bigger than one level up.
More marks, little more time
Higher has 120 marks against National 5's 90, in 2 hours 45 minutes against 2 hours 30. Each mark has less time behind it.
Algebra everywhere
Calculus, logarithms and the wave function all run on algebra. A learner who scraped through the National 5 algebra will feel it in every Higher topic.
The same 160 hours
Both specifications give a notional 160 hours of learning, yet Higher holds a heavier load of new ideas. Steady weekly work matters more than a late push.
Find the equation of the line through (1, 3) and (4, 9).
y − 3 = 2(x − 1)
y = 2x + 1
Gradient first, then substitute a point.
Find the stationary points of y = x³ − 3x.
x² = 1, so x = 1 or x = −1
(1, −2) and (−1, 2)
The same line-by-line algebra as National 5, now carrying calculus.
National 5 made secure, then Higher built on it.
In the first lesson the tutor works through National 5 and early Higher questions with the learner and sorts every lost mark into a gap, a method slip or timing. You see whether the National 5 base is ready to carry Higher.
Lessons then follow the course order: algebra and functions first, then the Higher topics, with Paper 1 practised without a calculator every week. Every lesson is live with the same tutor, after school or at weekends in UK time.
We never promise a grade or a score. Results depend on the starting point, the time available and the practice done between lessons, and we say so at the start.
"My son struggled with math for years. Integrating it into coding projects has transformed his understanding and confidence. Highly recommended!"
Shewta Singh, mother of Ishan · verified Google review
National 5 and Higher Maths: what learners and parents ask.
What is the difference between National 5 and Higher Maths?
National 5 is at SCQF level 5 and Higher at SCQF level 6. Higher has more marks (120 against 90) and adds topics such as calculus, logarithms, the wave function, the circle and three-dimensional vectors.
How many papers are there in National 5 Maths?
Two: Paper 1 without a calculator (40 marks, 1 hour) and Paper 2 (50 marks, 1 hour 30 minutes).
How many papers are there in Higher Maths?
Two: Paper 1 without a calculator (55 marks, 1 hour 15 minutes) and Paper 2 (65 marks, 1 hour 30 minutes).
Is there coursework in National 5 or Higher Maths?
No. The grade is based on the total mark across the two question papers.
What grades can you get in National 5 and Higher Maths?
Both courses are graded A to D on the total mark for the course assessment.
Do you need National 5 Maths to do Higher?
The Higher specification recommends that candidates have achieved National 5 Mathematics or equivalent qualifications or experience. Entry is at the discretion of the school or college.
Is Higher Maths much harder than National 5?
It is a level higher, with more marks in only 15 more minutes and new topics that all depend on secure algebra. That is why a secure National 5 base matters so much.
Is it SQA or Qualifications Scotland now?
Qualifications Scotland replaced SQA on 1 February 2026. Its course pages say the SQA-era course documents remain current.
What comes after Higher Maths?
The Higher specification lists Advanced Higher Mathematics, Advanced Higher Mathematics of Mechanics and Advanced Higher Statistics among the progression routes.
Can you help with National 5 or Higher Maths?
Yes. Book a Priority Demo: a full live class of about 45 to 60 minutes with a mentor reserved for the learner. Afterwards the mentor sends a written skill report and a personal learning roadmap on WhatsApp.
Ready for Higher? Let a tutor see the work.
Bring a recent National 5 or Higher paper. In one live class we show where the marks go and what the next term should look like. If you enrol, the demo fee is adjusted against your first month's fee.
Sources, read in October 2026.
- SQA (now Qualifications Scotland), National 5 Mathematics course specification, version 3.0, valid from session 2023 to 24.
- SQA (now Qualifications Scotland), Higher Mathematics course specification, version 3.0, valid from session 2023 to 24.
- Qualifications Scotland, National 5 Mathematics and Higher Mathematics course pages, including the February 2026 notice that SQA documents remain current.