Higher Maths practice questions

Original questions for every topic, with worked answers, and Section A and Section B style questions where each answer you type is checked.

Quick checks	Multiple choice, worked or timed
Paper-style questions	Section A and Section B, broken into steps
Answers	Checked in any equivalent form, then the full working
Topics	Eleven, covering all five strands

Try 4 questions

Question 1Paper 1

What is the largest possible domain of

f(x)

= \ln(2x - 6)

x \in \mathbb{R}

Question 2Paper 2

A two-way table. 5th year: 22 cycle, 58 do not cycle, 80 in total. 6th year: 35 cycle, 85 do not cycle, 120 in total. Totals: 57 cycle, 143 do not cycle, 200 students.
Year	Cycles	Does not cycle	Total
5th year	22	58	80
6th year	35	85	120
Total	57	143	200

The table shows how 200 students in a school travel to school. A student is chosen at random from those who cycle. What is the probability that this student is in 5th year?

Question 3Paper 2

A

and

B

are acute angles with

\sin A

= \frac{3}{5}

and

\cos B

= \frac{5}{13}

. Find the exact value of

\sin(A + B)

Question 4Paper 2

A solid metal sphere of radius 6 cm is melted down and recast as a solid cylinder of radius 4 cm. Find the height of the cylinder.

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Questions people ask

Are these past exam questions?

No. Every question is written for this course, in the style of Higher Level questions, with its own context and numbers.

How are typed answers checked?

By value or form: 0.375 and 3/8 both count for a probability, and (x + 4)(2x - 3) counts for (2x - 3)(x + 4), unless the question asks for one form. Complex numbers are typed as a + bi.