MAT1501 Supp 2026 exam paper — questions

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  1. Question 1.1 · Differentiation · 1 mark

    Determine the derivative with respect to x of sin⁻¹(e^x), that is d/dx[sin⁻¹(e^x)].Show the full question

  2. Question 1.2 · Limits and continuity · 1 mark

    Work out the limit as x approaches 3 of the expression (x² + 3x − 18) divided by (x − 3).Show the full question

  3. Question 1.3 · Functions, domains and graphs · 1 mark

    Simplify ln√[(x³ − 1)/(3x⁵)] using logarithm laws.Show the full question

  4. Question 1.4 · Differentiation · 1 mark

    Determine the 53rd derivative of sin x with respect to x, i.e. d⁵³/dx⁵³(sin x).Show the full question

  5. Question 1.5 · Limits and continuity · 1 mark

    Given that 2x − 1 ≤ f(x) ≤ x² for 0 < x < 3, find the limit of f(x) as x approaches 1.Show the full question

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