2021 QCE Maths Methods Paper 1 Mini Test 1
External Assessment Paper 1 — Technology-free
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.
\(2\log_{10}(x) - \log_{10}(3x)\) is equal to
- (A) \(\log_{10}\left(\frac{x}{3}\right)\)
- (B) \(\log_{10}(x^2 - 3x)\)
- (C) \(\frac{2\log_{10}(x)}{\log_{10}(3x)}\)
- (D) \(-\log_{10}(x)\)
The table shows the time a technician has spent servicing photocopiers.
| Time (in minutes) | Frequency |
|---|---|
| \(0 \le t < 5\) | 10 |
| \(5 \le t < 10\) | 20 |
| \(10 \le t < 15\) | 30 |
| \(15 \le t < 20\) | 40 |
What is the probability that a given service required at least 10 minutes but less than 20 minutes?
- (A) 0.15
- (B) 0.35
- (C) 0.70
- (D) 0.85
Determine \(\int 10e^{4x} dx\)
- (A) \(\frac{10e^{4x+1}}{4x+1} + c\)
- (B) \(40e^{4x} + c\)
- (C) \(\frac{5}{2}e^{4x} + c\)
- (D) \(2e^{5x} + c\)
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 population of rabbits (\(P\)) on an island, in hundreds, is given by \(P(t) = t^2 \ln(3t) + 6\), \(t > 0\), where \(t\) is time in years.
Determine the intervals of time when the population is increasing and the intervals when it is decreasing.
END OF PAPER
