QCE Maths Methods practice questions

Original questions for all ten topics of Units 3 and 4, in the style of both papers: multiple choice where each wrong option names its slip, and short response questions in parts, marked step by step with follow-through from earlier parts.

External assessment	One examination worth 50%, set and marked by the QCAA
Paper 1	Technology-free, 25%: short response and multiple choice
Paper 2	Technology-active, 25%: short response and multiple choice
Time	5 minutes perusal and 90 minutes working time for each paper; the formula book is provided
Internal assessment	Set by your school: a modelling task 20%, two short response examinations 15% each

Try 4 questions

Paper 1 · Multiple choice · 1 mark · Calculus of exponential and logarithmic functions
If $y = e^{x^{2} - 3 x}$ , then $\dfrac{dy}{dx}$ is
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Paper 1 · Short response · 4 marks · Calculus of exponential and logarithmic functions
Answer each part without technology.
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Paper 2 · Multiple choice · 1 mark · Calculus of exponential and logarithmic functions
The table shows values of $\dfrac{a^{h} - 1}{h}$ for $h = 0.0001$ , correct to four decimal places. $\begin{array}{c|cccc} a & 2.5 & 2.7 & 2.8 & 3.0 \\ \hline \dfrac{a^{h} - 1}{h} & 0.9163 & 0.9933 & 1.0297 & 1.0987 \end{array}$ Based on the table, which interval contains the value of $a$ for which $\displaystyle\lim_{h \to 0} \dfrac{a^{h} - 1}{h} = 1$ ?
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Paper 2 · Short response · 10 marks · Calculus of exponential and logarithmic functions
After a dose of a medicine, its concentration in a patient's blood is modelled by $C(t) = 20\left(e^{-0.1 t} - e^{-0.3 t}\right)$ milligrams per litre, where $t$ is the time in hours after the dose, $t \geq 0$ .
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Are these past examination questions?

No. Every question is original, written for the QCAA Mathematical Methods 2025 syllabus.