Polynomials and quadratics · support3 marksNon-calculator
1. Solve (x + 4)(x − 2)(x − 3) = 0.
Hint
Set each factor equal to zero and reverse its sign.
Back to Higher Mathematics
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
Straight line and circles · challenge3 marksNon-calculator
2. A tangent has gradient −3. Find the gradient of the normal.
Hint
Take the negative reciprocal of the tangent gradient.
Algebra and functions · challenge5 marksNon-calculator
3. Find the intersections of y = x² − 1 and y = 2x² − 2x − 4.
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
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
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.
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
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
Revision mode
Calculus and functions challenge
Practise linking functions, graphs, differentiation and integration.
- 15-20 minutes
- Functions and calculus
- Tangents, areas and graph features
Revision mode
Exam-style practice
Choose methods, combine topics and explain your reasoning.
- 20-30 minutes
- Multi-step questions
- Reasoning and communication