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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
Polynomials and quadratics · challenge3 marksNon-calculator

1. For y = (x + 2)(x − 5), state the x-intercepts.

The roots are where the curve crosses the x-axis.
Maths tools
Hint

Each bracket gives one root.

Straight line and circles · core2 marksCalculator optional

2. A circle has centre (3, −1) and point P(8, 2). Find the tangent gradient at P.

The tangent at P is perpendicular to the radius CP.
Maths tools
Hint

Find the radius gradient first, then use the negative reciprocal.

Algebra and functions · challenge4 marksNon-calculator

3. f(x) = 2x − 1 and g(x) = x² − 2. Determine f(g(x)) and hence solve f(g(x)) = 5. Show your working.

Maths tools
Hint

Find the composite first, then use the word hence to solve the resulting quadratic equation.

Trigonometry · support1 markCalculator optional

4. Convert 180° to radians.

Choose an answer
Hint

Use 180° = πradians.

Differentiation · challenge3 marksNon-calculator

5. For a stationary point at x = −2, dy/dx changes from negative to positive. State the nature of the stationary point.

The sign of dy/dx shows how the curve moves through the stationary point.
Maths tools
Hint

Positive derivative means increasing; negative derivative means decreasing.

Integration · core2 marksCalculator optional

6. Find the area under y = 4x + 3 from x = 0 to x = 3.

The shaded trapezium is the area represented by the definite integral.
Maths tools
Hint

The line is above the axis, so the integral gives the area.

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