2020 QCAA Maths Methods Paper 1 Mini Test 2

 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.


QUESTION 1 [2020 Paper 1 Q4]

Pulse rates of adult men are approximately normally distributed with a mean of 70 and a standard deviation of 8. Which of the following choices correctly describes how to determine the proportion of men that have a pulse rate greater than 78?

  • (A) Determine the area to the left of \(z = 1\) under the standard normal curve.
  • (B) Determine the area to the right of \(z = 1\) under the standard normal curve.
  • (C) Determine the area to the right of \(z = -1\) under the standard normal curve.
  • (D) Determine the area between \(z = -1\) and \(z = 1\) under the standard normal curve.
Correct Answer: B
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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.



QUESTION 2 (3 marks) [2020 Paper 1 Q11]

Determine the derivative of each of the following with respect to \(x\).

a) \( y = \frac{1}{\sin(x)} \) [1 mark]

b) \( y = x^2 \times e^{-x} \)
Express your answer in factorised form. [2 marks]

QUESTION 3 (6 marks) [2020 Paper 1 Q17]

The volume of water in a tank is represented by a function of the form \[ V(t) = Ae^{kt} \text{, where } V \text{ is in litres and } t \text{ is in minutes.} \] Initially, the volume is 100 litres and it is decreasing by 50 litres per minute.
Determine the time at which the volume is decreasing at the rate of \( \frac{50}{7} \) litres per minute.
Express your answer in the form \(\ln(a)\).

END OF PAPER

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