2022 QCE Maths Methods Paper 1 Mini Test 4
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.
The weekly amount of money a company spends on repairs is normally distributed, with a mean of $1200 and a standard deviation of $100.
Given that \(\Pr(Z \le -2.5) = 0.0062\) and \(\Pr(Z > 1) = 0.1587\), where \(Z\) is a standard normal random variable, determine the probability that the weekly repair costs will be between $950 and $1300.
- (A) 0.6525
- (B) 0.6587
- (C) 0.8351
- (D) 0.8413
Which normal distribution curve best represents a normal distribution with a mean of 1 and a standard deviation of 0.5?
Which graph represents the function \(f(x) = -3 - \ln(x+3)\)?
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 rate that water fills an empty vessel is given by \(\frac{dV}{dt} = 0.25e^{0.25t}\) (in litres per hour), \(0 \le t \le 8\ln(6)\), where \(t\) is time (in hours).
a) Determine the function that represents the volume of water in the vessel (in litres). [2 marks]
The vessel is full when \(t = 8\ln(6)\).
b) Determine the volume of water, to the nearest litre, the vessel can hold when full. [2 marks]
The table shows the approximate rate the water flows into the vessel at certain times.
| \(t\) | \(\frac{dV}{dt}\) |
| 0 | 0.25 |
| 1 | 0.32 |
| 2 | 0.41 |
| 3 | 0.53 |
c) Use information from the table and the trapezoidal rule to determine the approximate volume of water in the vessel after three hours. [2 marks]
END OF PAPER
