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AS & A Level · AS/A Level

Mathematics

Calculus, logarithms and probability

Name: ____________________Date: October 10, 2026
  1. 1.

    Find and classify both stationary points of f(x) = x^3 - 3x^2 - 9x + 5.

    [4 marks] · no calculator
  2. 2.

    Solve ln(x - 1) + ln(x + 1) = ln(8), stating the domain restriction.

    [3 marks] · no calculator
  3. 3.

    X follows a binomial distribution with n = 5 and p = 0.4. Calculate P(X = 2) and state two assumptions of this model.

    [4 marks]

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Marking points are indicative, not an official mark scheme. Accept equivalent valid methods and supported interpretations that address the task; award each mark once without requiring the model wording.