Independent preparation for the SQA Advanced Higher Mathematics exam. Not affiliated with or endorsed by Qualifications Scotland (SQA).

What is in Advanced Higher Maths: the course content

Advanced Higher Maths is examined by two papers, both compulsory: Paper 1 without a calculator (1 hour, 35 marks) and Paper 2 with one (2 hours 30 minutes, 80 marks). There is no coursework.

Weeks before your first paper

Hours a week for maths

Topic 1: Partial fractions, binomial expansions and graphs

Topic 2: Differentiation

Topic 3: Integration

Topic 4: Differential equations

Topic 5: Sequences and series

Topic 6: Proof and number theory

Topic 7: Matrices and systems of equations

Topic 8: Vectors, lines and planes

Topic 9: Complex numbers

26 weeks, 104 hours in all

Start with Topic 1

Partial fractions, binomial expansions and graphs: 10.7 of your hours. It is 2 of the 40 questions on our timed checks, 11%.

Hours per topic
Topic	Your hours	Share of the checks
Topic 1: Partial fractions, binomial expansions and graphs	10.7	11%
Topic 2: Differentiation	10.7	11%
Topic 3: Integration	10.7	11%
Topic 4: Differential equations	10.7	11%
Topic 5: Sequences and series	10.7	11%
Topic 6: Proof and number theory	10.7	11%
Topic 7: Matrices and systems of equations	10.7	11%
Topic 8: Vectors, lines and planes	10.7	11%
Topic 9: Complex numbers	10.7	11%

Week by week

Week 1Section 1: Partial fractions, binomial expansions and graphs
Week 2Section 1: Partial fractions, binomial expansions and graphs
Week 3Section 1: Partial fractions, binomial expansions and graphs, Section 2: Differentiation
Week 4Section 2: Differentiation
Week 5Section 2: Differentiation
Week 6Section 2: Differentiation, Section 3: Integration
Week 7Section 3: Integration
Week 8Section 3: Integration
Week 9Section 3: Integration, Section 4: Differential equations
Week 10Section 4: Differential equations
Week 11Section 4: Differential equations, Section 5: Sequences and series
Week 12Section 5: Sequences and series
Week 13Section 5: Sequences and series
Week 14Section 5: Sequences and series, Section 6: Proof and number theory
Week 15Section 6: Proof and number theory
Week 16Section 6: Proof and number theory
Week 17Section 6: Proof and number theory, Section 7: Matrices and systems of equations
Week 18Section 7: Matrices and systems of equations
Week 19Section 7: Matrices and systems of equations, Section 8: Vectors, lines and planes
Week 20Section 8: Vectors, lines and planes
Week 21Section 8: Vectors, lines and planes
Week 22Section 8: Vectors, lines and planes, Section 9: Complex numbers
Week 23Section 9: Complex numbers
Week 24Section 9: Complex numbers
Week 25A timed check and two paper-style questions, then review every lost mark
Week 26A timed check and two paper-style questions, then review every lost mark

Check your topics with the free test

Paper 1	Non-calculator, 1 hour, 35 marks
Paper 2	Calculator, 2 hours 30 minutes, 80 marks
Total	115 marks, graded A to D
Exam day 2027	Monday 17 May

The nine sections of this course

1 Partial fractions, binomial expansions and graphs: partial fractions, the binomial theorem, asymptotes, features of graphs and related graphs.
2 Differentiation: exponential, logarithmic, trigonometric and inverse trigonometric functions, implicit, logarithmic and parametric differentiation, related rates and optimisation.
3 Integration: standard integrals, partial fractions, substitution, integration by parts, areas and volumes of revolution.

Proof runs through the course

Besides calculating, you are asked to prove results: by induction, by contradiction, by contrapositive and directly, and to disprove a claim with a counterexample.

Try 2 questions

Question 1Paper 1 style · no calculator

Given that

\frac{5x + 1}{(x - 1)(x + 2)}

= \frac{A}{x - 1}

{}+ \frac{B}{x + 2}

, find the values of

A

and

B

Question 2Paper 1 style · no calculator

The third term of an arithmetic sequence is

11

and the seventh term is

27

. Find the sum of the first

20

terms.

Next step

Take the free test Take the course tour

Questions people ask

Is there coursework in Advanced Higher Maths?

No. The grade comes from the two question papers: 35 marks without a calculator and 80 marks with one, 115 marks in all.

Which grades are awarded?

The course is graded A to D on the total mark of both papers.

Is this the same as Mathematics of Mechanics?

No. Mathematics of Mechanics and Statistics are separate Advanced Higher courses. This course is Advanced Higher Mathematics.