2023 QCE Maths Methods Paper 1 Mini Test 2
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.
A bag contains 10 buttons of the same shape and size in different colours: 5 blue, 3 green and 2 red. If 3 buttons are randomly drawn from the bag, which probability can be calculated using the binomial distribution?
- (A) \(P(3 \text{ green})\) with replacement
- (B) \(P(3 \text{ blue})\) without replacement
- (C) \(P(2 \text{ green and } 1 \text{ red})\) with replacement
- (D) \(P(2 \text{ red and } 1 \text{ blue})\) without replacement
If the gradient of the function \(f(x)\) is given by \(\frac{20}{x^3}\), then \(f(x)\) is equal to
- (A) \(-\frac{60}{x^4} + c\)
- (B) \(-\frac{5}{x^4} + c\)
- (C) \(-\frac{10}{x^2} + c\)
- (D) \(-\frac{40}{x^2} + c\)
Determine \(\int_1^3 \frac{1}{2x} dx\).
- (A) \(\frac{1}{2} \ln 6\)
- (B) \(\frac{1}{2} \ln 5\)
- (C) \(\frac{1}{2} \ln 4\)
- (D) \(\frac{1}{2} \ln 3\)
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.
A chemical is added to the water in a swimming pool at 10:00 am to prevent algae. The amount of chemical absorbed into the water over time \(t\) (hours) is represented by
\[A = 10t^2 - 4t^3, \quad 0 < t \le 1\frac{2}{3}\]Determine the time of day when the rate of absorption of the chemical is at its maximum. Use calculus techniques to verify that your time corresponds to a maximum rate.
END OF PAPER
