Higher Mathematics

Mixed revision

Cross-topic Higher Mathematics revision across algebra, functions, coordinate geometry, trigonometry, calculus, vectors, logarithms and recurrence relations, with balanced family selection to keep one topic from dominating a set.

Mixed revision

Higher Mathematics mixed checkpoint

Choose a mode, answer the generated set, then use the feedback to target the weakest Higher topic families.

Score: 0/6

Polynomials and quadratics · support3 marksNon-calculator

1. Solve (x + 4)(x − 2)(x − 3) = 0.

Use arrow keys to move through your answer. Use ↑ and ↓ between fraction parts. Tab moves to the maths tools.

Hint

Set each factor equal to zero and reverse its sign.

Straight line and circles · challenge3 marksNon-calculator

2. The tangent to a curve at P(1, 4) has gradient −3. Find the equation of the normal at P.

Use arrow keys to move through your answer. Use ↑ and ↓ between fraction parts. Tab moves to the maths tools.

Hint

Use the negative reciprocal, then the point-gradient equation through P.

Algebra and functions · challenge5 marksNon-calculator

3. Find the intersections of y = x² − 1 and y = 2x² − 2x − 4.

Use arrow keys to move through your answer. Use ↑ and ↓ between fraction parts. Tab moves to the maths tools.

Hint

Move every term to one side before factorising.

Trigonometry · core4 marksNon-calculator

4. Write 3 cos x + 4 sin x as k cos(x − α), where α is acute

5 cos(x − α), tan α = 435 cos(x + α), tan α = 437 cos(x − α), tan α = 345 sin(x − α), tan α = 34

Hint

Compare coefficients after expanding the proposed wave form.

Differentiation · core3 marksNon-calculator

5. Given f'(x) = −(x − (-1))(x − 1), state the intervals where f is strictly decreasing

Use arrow keys to move through your answer. Use ↑ and ↓ between fraction parts. Tab moves to the maths tools.

Hint

A function decreases where its derivative is negative.

Integration · challenge2 marksCalculator optional

6. Find the area between y = 16 − x² and the x-axis from x = −4 to x = 4.

Use arrow keys to move through your answer. Use ↑ and ↓ between fraction parts. Tab moves to the maths tools.

Hint

Use symmetry or evaluate the definite integral carefully.

Revision mode

Quick practice

Try a short mixed set to warm up key Higher Mathematics skills.

5-10 minutes
Algebra, functions, calculus and trig
Short answers with method checks

Open quick check

Revision mode

Balanced revision

Work through a broader mixed set across the main course areas.

20-30 minutes
Cross-course revision
Method choice and interpretation

Open full mixed revision

Revision mode

Calculus and functions challenge

Practise linking functions, graphs, differentiation and integration.

15-20 minutes
Functions and calculus
Tangents, areas and graph features

Open calculus challenge

Revision mode

Exam-style practice

Choose methods, combine topics and explain your reasoning.

20-30 minutes
Multi-step questions
Reasoning and communication

Open exam-style practice

Mixed revision

Higher Mathematics mixed checkpoint

1. Solve (x + 4)(x − 2)(x − 3) = 0.

2. The tangent to a curve at P(1, 4) has gradient −3. Find the equation of the normal at P.

3. Find the intersections of y = x2 − 1 and y = 2x2 − 2x − 4.

4. Write 3 cos x + 4 sin x as k cos(x − α), where α is acute

5. Given f'(x) = −(x − (-1))(x − 1), state the intervals where f is strictly decreasing

6. Find the area between y = 16 − x2 and the x-axis from x = −4 to x = 4.

Quick practice

Balanced revision

Calculus and functions challenge

Exam-style practice

3. Find the intersections of y = x² − 1 and y = 2x² − 2x − 4.

6. Find the area between y = 16 − x² and the x-axis from x = −4 to x = 4.