2023 QCE Maths Methods Paper 1 Mini Test 1
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.
\(e^{\ln(x)}\) is equivalent to
- (A) \(0\)
- (B) \(1\)
- (C) \(x\)
- (D) \(\frac{1}{x}\)
If \(f(x) = e^{6-2x}\), determine the value of \(f'(2)\).
- (A) \(e^2\)
- (B) \(2e^2\)
- (C) \(-e^2\)
- (D) \(-2e^2\)
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.
Jaxon and Shari each own a shop and have recorded the number of customers entering their shop on two consecutive days.
| Day 1 | Day 2 | |
| Jaxon's customers | 40 | 30 |
| Shari's customers | 10 | 20 |
| Total | 50 | 50 |
The number of daily customers for each shop can be modelled by the equation \(y = A \ln(Bx)\), where \(x\) is the day and \(y\) is the number of customers. The constants \(A\) and \(B\) are different for each shop.
Determine algebraically whether the total number of customers for Jaxon and Shari's shops will be the same every day in the future.
END OF PAPER
