2023 QCE Maths Methods Paper 2 Mini Test 5
External Assessment Paper 2 — Technology-active
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.
The number of koalas in a conservation park is modelled by \(N = 15 \ln(7t + 1)\), \(t \ge 1\), where \(t\) represents the time (years) since the park opened. There were 20 koalas in the park when it opened.
Determine the approximate rate of change in the number of koalas when \(t = 3\).
- (A) 46
- (B) 26
- (C) 25
- (D) 5
If \(f(x) = e^{3x}(x+1)^2\) and \(f'(x) = ae^{3x}(x+1)\), determine the expression for \(a\).
- (A) 3x + 5
- (B) 3x + 3
- (C) 5x + 5
- (D) 5x + 3
A student is trying to determine which subject they performed best in compared to other students. Results from recent tests in four subjects (A to D) are shown. Assume student results in each subject are normally distributed.
In which subject did the student perform best compared to other students?
| Class mean | Class standard deviation |
Student's result |
|
|---|---|---|---|
| (A) | 62 | 22 | 77 |
| (B) | 55 | 25 | 74 |
| (C) | 61 | 15 | 70 |
| (D) | 73 | 20 | 82 |
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.
Over a suitable domain, a hill has a cross-sectional area given by \(\int h(x)dx = \frac{a}{b}e^{bx} + c\), where:
- • \(a\), \(b\) and \(c\) are constants, \(b \ne 0\)
- • \(h(x)\) represents vertical distance (m), \(x\) represents horizontal distance (m).
It is known that \(h(0) = 1.22\) and \(h(40) = 25\).
Where the gradient of the hill is 0.86 there is a tree stump. A second tree stump is located further up the hill. The difference in hill gradient between the two tree stumps is 0.44.
A surveyor predicts that the vertical distance separating the two tree stumps is between 7.5 m and 8.5 m. Evaluate the reasonableness of this prediction.
END OF PAPER
