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Advanced Higher Maths

The hardest maths course in the Scottish system. Two papers, 115 marks, and a genuine change in what is being asked of a student – not just harder questions.

Advanced Higher Maths is the final maths course in the Scottish system, normally taken in S6 and awarded by Qualifications Scotland. It is examined by two papers – Paper 1, 35 marks in 1 hour with no calculator, and Paper 2, 80 marks in 2 hours 30 minutes with one – giving 115 marks in total, graded A to D with no coursework. Math Wizard teaches it in person in Glasgow, Edinburgh, Aberdeen and Dundee, or online anywhere in the UK, at £60–£80 per hour.

How Advanced Higher Maths Is Assessed

Component Marks Time Calculator
Question paper 1 35 1 hour Not permitted
Question paper 2 80 2 hours 30 minutes Permitted
Total 115 3 hours 30 minutes —

Advanced Higher did not change in 2023. The May 2023 revision that altered paper marks and durations applied to National 5 and Higher. Advanced Higher still runs on its 2019 course specification, so unlike the other two, older figures for this course are still correct.

What Actually Changes at Advanced Higher

It is not simply harder questions on the same maths. The nature of the subject changes.

Proof becomes the point

Induction, contradiction, direct proof. For the first time a student is asked to demonstrate that something is true in general, not to compute an answer. Most of the early struggle is here.

Entirely new objects

Complex numbers and matrices are not extensions of anything at Higher. They are new mathematical objects with their own rules, met from a standing start.

Calculus goes much deeper

Implicit and parametric differentiation, integration by parts and substitution, differential equations. Higher’s calculus turns out to have been the introduction.

Fewer people can help

Schools often run small Advanced Higher classes, sometimes shared between schools, and many tutors who happily take Higher will not take this. It is the course where being on your own is most likely.

Stuck on something in particular?

Everything on this page is free and always will be. If a topic isn’t going in, we also teach Advanced Higher Maths one-to-one and in small groups – the first lesson is half price, with no contract.

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Free Advanced Higher Worksheets

Practice questions with full worked solutions. Free, with no account and no email address.

Browse Advanced Higher worksheets Higher Maths

Advanced Higher Maths – Common Questions

Two question papers totalling 115 marks. Paper 1 is non-calculator, 35 marks and one hour. Paper 2 allows a calculator and is 80 marks over two hours 30 minutes. There is no project or assignment - the assessment is the two papers only.
It is the most demanding maths course in the Scottish system, and the jump from Higher is comparable to the jump from National 5 to Higher. It introduces proof, complex numbers, matrices, differential equations and much deeper calculus, and it asks students to construct arguments rather than apply methods.
They are different qualifications with different content, though universities generally treat Advanced Higher as broadly comparable to A Level for entry purposes. Advanced Higher covers some material - proof, complex numbers, matrices - that goes beyond standard A Level Maths and overlaps with Further Maths.
No, and this catches people out. The May 2023 revision that changed the paper marks and durations applied to National 5 and Higher. Advanced Higher still runs on its 2019 course specification, so its figures are unchanged.
It is not usually a formal requirement, but for competitive maths, physics, engineering and economics courses it is often what separates applicants - and it makes first year substantially easier. Some courses do ask for it specifically, so check the entry requirements for the course rather than assuming.

Course structure verified against the Advanced Higher Mathematics course specification (C847 77, version 2.0, May 2019), published by SQA, now Qualifications Scotland.

Where these facts come from

Every paper structure, mark total, timing and grade scale on this page was checked against the awarding body’s own published specification. Those documents are free, and they are the only source that is definitive – if anything here ever disagrees with one of them, the specification is right and this page is wrong.

Specifications are revised from time to time. Where a course has changed – the 2023 revision to National 5 and Higher, for example – this site follows the current version, which a good deal of older revision material still does not.