2022 QCE Maths Methods Paper 1 Mini Test 6
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 survey plans to draw conclusions based on a random sample of 1% of Queensland's adult population. To be regarded as a random sample, every
- (A) adult in the population will be placed in an alphabetical list and every 100th person will be selected for the sample.
- (B) adult in the population can choose to participate until the sample size has been reached.
- (C) subgroup within the population will be represented in a similar proportion in the sample.
- (D) adult in the population will have an equal chance of being selected for the sample.
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.
Determine the value of \(b\) given \(\int_a^b 3x^2 \,dx = 117\) and \(\int_a^{b-1} 3x^2 \,dx = 56\) for \(b > 1\).
A percentile is a measure in statistics showing the value below which a given percentage of observations occur.
The continuous random variable \(X\) has the probability density function
\[ f(x) = \begin{cases} 2x-2, & 1 \le x \le 2 \\ 0, & \text{otherwise} \end{cases} \]Determine the 36th percentile of \(X\).
END OF PAPER
