2024 QCE Maths Methods Paper 1 Mini Test 3
External Assessment Paper 1 — Technology-free
Number of marks: 9
Perusal time: 1 minute
Writing time: 15 minutes
Section 1
Instructions
• This section has 10 questions and is worth 10 marks.
• Use a 2B pencil to fill in the A, B, C or D answer bubble completely.
• Choose the best answer for Questions 1 10.
• If you change your mind or make a mistake, use an eraser to remove your response and fill in the new answer bubble completely.
Twenty families are selected to participate in a lifestyle study related to family size. The number of children in these families is uniformly distributed as shown.
A random sample of five families is chosen from this group, without replacement. A possible mean number of children in the sample is
- (A) 5.0
- (B) 2.0
- (C) 1.0
- (D) 0.0
The graph of \(f(x)\) is shown.
Identify the graph of the second derivative \(f''(x)\).
At a certain location, the temperature (°C) can be modelled by the function \(T = 5\sin\left(\frac{\pi}{12}x\right) + 23\), where \(x\) is the number of hours after sunrise.
Determine the rate of change of temperature (°C/hour) when \(x = 4\).
- (A) \(\frac{5\pi}{48}\)
- (B) \(\frac{5\pi}{24}\)
- (C) \(\frac{5\pi\sqrt{3}}{24}\)
- (D) \(\frac{5\pi\sqrt{3}}{6}\)
Section 2
Instructions
• Write using black or blue pen.
• Questions worth more than one mark require mathematical reasoning and/or working to be shown to support answers.
• If you need more space for a response, use the additional pages at the back of this book.
– On the additional pages, write the question number you are responding to.
– Cancel any incorrect response by ruling a single diagonal line through your work.
– Write the page number of your alternative/additional response, i.e. See page …
– If you do not do this, your original response will be marked.
• This section has nine questions and is worth 45 marks.
a) \(F(x) = \int (4e^{2x} + \sin(2x)) \, dx\). Use integration to determine \(F(x)\), if \(F(0) = 5\). [3 marks]
b) If \(\frac{dy}{dx} = \left( \frac{3x^7 - 2x}{x^4} \right)^2\), determine \(y\). [3 marks]
END OF PAPER
