2021 QCE Maths Methods Paper 2 Mini Test 1
External Assessment Paper 2 — Technology-active
Number of marks: 10
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 scores obtained on a test can be assumed to be normally distributed with a mean of 102 and a standard deviation of 19.
What proportion of scores are over 113?
- (A) 0.2813
- (B) 0.5789
- (C) 0.7187
- (D) 0.8216
A substance is being heated such that its temperature \(T\) in °C after \(t\) minutes is given by the function \(T = 2e^{0.5t}\).
The first integer value of \(t\) for which the instantaneous rate of change of temperature is greater than 100 °C per minute is
- (A) \(t=10\)
- (B) \(t=9\)
- (C) \(t=8\)
- (D) \(t=7\)
A random sample of people were surveyed about the most important factor when deciding where to shop. The results appear in the table.
| Factor | Percentage (%) |
|---|---|
| Price | 40 |
| Quality of merchandise | 30 |
| Service | 15 |
| Shopping environment | 15 |
If the sample size was 1200, the approximate 95% confidence interval for the proportion of people who identified price as the most important factor is
- (A) (0.395, 0.405)
- (B) (0.386, 0.414)
- (C) (0.377, 0.423)
- (D) (0.372, 0.428)
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 amount of gravel (in tonnes) sold by a construction company in a given week is a continuous random variable \(X\) and has a probability density function defined by: \[ f(x) = \begin{cases} c(1-x^2), & 0 \le x \le 1 \\ 0, & \text{otherwise} \end{cases} \]
a) Show that \( c = \frac{3}{2} \). [1 mark]
b) Determine \( P(X < 0.25) \). [2 marks]
c) Determine the variance of \(X\). [4 marks]
END OF PAPER
