Polynomials and quadratics · challenge
1. Divide 3x³ − 9x² + 2x + 8 by x − 2
Hint
Use synthetic division or match coefficients.
Back to Higher Mathematics
Higher Mathematics
Mixed revision
Cross-topic Higher Mathematics revision routes for algebraic fluency, functions, calculus, trig, vectors and exam-style reasoning.
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 · core
2. Find the distance between (-4, 2) and (4, 17).
Hint
Make a right-angled triangle from the coordinate changes.
Algebra and functions · core
3. State the excluded value for f(x) = 1x + 3.
Hint
Set the denominator not equal to zero.
Trigonometry · core
4. State the amplitude of y = 6sin θ.
Hint
Amplitude is distance from the midline to a maximum.
Differentiation · challenge
5. A model has A(x) = −x² + 6x + 11. Find the maximum value of A.
Hint
For a downward-opening quadratic, the stationary point is a maximum.
Integration · core
6. Find ∫7x⁻² dx.
Hint
The power rule works for n ≠ −1.
Revision mode
Quick skills check
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
Full mixed 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 problem solving
Choose methods, combine topics and explain your reasoning.
- 20-30 minutes
- Multi-step questions
- Reasoning and communication