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

Advanced Higher Maths practice questions by section

Original questions for every section, Paper 1 and Paper 2 style, with worked answers, and paper-style questions where each answer you type is checked.

Quick checks	Multiple choice, worked or timed
Paper-style questions	Paper 1 (no calculator) and Paper 2 (calculator)
Answers	Checked in any equivalent form, then the full working

Try 4 questions

Question 1Paper 1 style · no calculator

Find

\int xe^{2x}\, dx

Question 2Paper 1 style · no calculator

A proof by induction shows that

\sum_{r=1}^{n} r^3

= \frac{n^2(n + 1)^2}{4}

for all positive integers

n

. Assuming the result for

n

= k

, what must the inductive step show?

Question 3Paper 1 style · no calculator

Which is the augmented matrix for the system of equations

x + 2y - z

= 4

3x - y + 2z

= 1

2x + 5z

= -3

Question 4Paper 1 style · no calculator

Find a vector equation of the line through

A(2, -1, 3)

and

B(5, 1, -1)

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Questions people ask

Are these past exam questions?

No. Every question is written for this course, with its own context and data.