2022 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.
Determine the equation of the asymptote of the function \(f(x) = \log_9(x-3) - 4\).
- (A) \(x = -4\)
- (B) \(x = -3\)
- (C) \(x = 3\)
- (D) \(x = 4\)
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.
The time spent waiting in a queue at a certain supermarket is given by (\(X + 11\)) minutes, where \(X\) is a random variable with the probability density function \[ f(x) = \begin{cases} \frac{a(4-x^2)}{32}, & -2 \le x \le 2 \\ 0, & \text{otherwise} \end{cases} \]
Determine the probability of waiting between 10 and 12 minutes in a queue at this supermarket.
Flying foxes enter and leave a fruit-growing region every evening. The rate at which the flying foxes enter the region is modelled by the function \[ A(t) = 42 \sin\left(0.03t - \frac{\pi}{3}\right) + 71, \quad 0 \le t \le 240 \]
The rate at which the flying foxes leave the region is modelled by the function \[ L(t) = 42 \sin\left(0.04t - \frac{\pi}{3}\right) + 42, \quad 0 \le t \le 240 \]
Both \(A(t)\) and \(L(t)\) are measured in animals per minute and \(t\) is measured in minutes after 7 pm.
There are 100 flying foxes in the region at 7 pm.
Determine the maximum number of flying foxes in the region and the time that this occurs.
END OF PAPER
