2022 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 position (in cm) of a particle is given by \(x = \cos(4t)\), where \(t\) is time (in seconds). The velocity of the particle when \(t = 5\) is
- (A) 1.6323 cm s\(^{-1}\)
- (B) 0.4081 cm s\(^{-1}\)
- (C) –0.9129 cm s\(^{-1}\)
- (D) –3.6518 cm s\(^{-1}\)
Identify the correct features of the function \(f(x) = xe^x\)
- (A) \(f'(-1) = 0, f''(-1) < 0\)
- (B) \(f'(-1) = 0, f''(-1) > 0\)
- (C) \(f'(-1) < 0, f''(-1) < 0\)
- (D) \(f'(-1) < 0, f''(-1) > 0\)
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.
Ravi randomly sampled 200 different pet owners in Brisbane and found that 50 celebrate their pet's birthday.
a) Determine an approximate 95% confidence interval for the proportion of Brisbane pet owners who celebrate their pet's birthday. [2 marks]
Two of Ravi's friends also randomly sampled Brisbane pet owners. The results are shown in the table.
| Friend's name | Number sampled | Number who celebrate their pet's birthday |
| Khadija | 100 | 26 |
| Tim | 150 | 34 |
Khadija suggested a more precise estimate for the proportion of Brisbane pet owners who celebrate their pet's birthday could be obtained by combining their results.
b) Using all available data, determine an approximate 95% confidence interval for the proportion of Brisbane pet owners who celebrate their pet's birthday. [2 marks]
c) Use the results from Questions 14a) and 14b) to evaluate the reasonableness of Khadija's suggestion. [2 marks]
The proportion of all Brisbane pet owners who celebrate their pet's birthday is 0.24.
d) Using the normal approximation, determine the probability that in a randomly selected sample of size 200, more than 30% of pet owners celebrate their pet's birthday. [2 marks]
END OF PAPER
