MAT1501 Oct/Nov 2025 exam paper — questions

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  1. Question 1.1 · Applications of differentiation · 1 mark

    Consider the four functions: (i) y = √x, (ii) y = e^(-x), (iii) y = x^2, (iv) y = x^3. Determine which of these functions are increasing everywhere on their domains.Show the full question

  2. Question 1.2 · Functions, domains and graphs · 1 mark

    Consider the four functions: (i) y = x^4; (ii) y = x if x < 0 and y = x^2 if x ≥ 0; (iii) y = x^2 if x < 0 and y = x if x ≥ 0; (iv) y = x^3. Determine which of these functions are one-to-one.Show the full question

  3. Question 1.3 · Differentiation · 1 mark

    Find the 99th derivative with respect to x of sin x, i.e. find d^99/dx^99 (sin x).Show the full question

  4. Question 1.4 · Differentiation · 1 mark

    Find the derivative with respect to x of cos^(-1)(e^x), i.e. determine d/dx [cos^(-1)(e^x)].Show the full question

  5. Question 1.5 · Functions, domains and graphs · 1 mark

    Simplify the expression ln √[(x^2 + 1)/(2x^3)].Show the full question

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