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

f(x)

= 2x + 1

and

g(x)

= x^2 - 3

. Find an expression for

f(g(x))

Question 2Paper 1 style · no calculator

Solve

\log_2 (x + 3)

= 5

Question 3Paper 1 style · no calculator

\mathbf{u} = \begin{pmatrix} k \\ 3 \\ -1 \end{pmatrix}

and

\mathbf{v} = \begin{pmatrix} 2 \\ k \\ 4 \end{pmatrix}

are perpendicular. Find

k

Question 4Paper 1 style · no calculator

Find the area enclosed between the curve

y

= x^2 - 3x

and the

x

axis.

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Questions people ask

How are typed answers checked?

By a maths checker that accepts equivalent forms: (x + 4)(2x - 3) counts for (2x - 3)(x + 4), and sqrt(13) counts as an exact value, unless the question asks for one form.