2022 QCE Maths Methods Paper 1 Mini Test 5
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 circle with radius \(r\) and internal angle \(\theta\) has a shaded segment as shown.
If \(\theta\) is in radians, the area of the shaded segment is
- (A) \(\frac{r^2}{2} \left( \frac{\theta\pi}{180} - \sin(\theta) \right)\)
- (B) \(\frac{r^2}{2} (\theta - \sin(\theta))\)
- (C) \(\frac{r^2}{4} \left( \frac{\theta\pi}{90} - 1 \right)\)
- (D) \(\frac{r^2}{2} (\theta - 1)\)
In a survey, 80 respondents exercised daily, while 120 did not. When calculating the approximate 95% confidence interval for the proportion of people who exercise daily, the margin of error is
- (A) \(1.96\sqrt{\frac{0.4(1-0.4)}{200}}\)
- (B) \(0.95\sqrt{\frac{0.4(1-0.4)}{200}}\)
- (C) \(1.96\sqrt{\frac{0.67(1-0.67)}{120}}\)
- (D) \(0.95\sqrt{\frac{0.67(1-0.67)}{120}}\)
The approximate area under the curve \(f(x) = \sqrt{2x+1}\) between \(x=0\) and \(x=4\) using the trapezoidal rule with four strips is
- (A) \(2+\sqrt{3}+\sqrt{5}+\sqrt{7}\)
- (B) \(2+2(\sqrt{3}+\sqrt{5}+\sqrt{7})\)
- (C) \(4+2(\sqrt{3}+\sqrt{5}+\sqrt{7})\)
- (D) \(4+\sqrt{3}+\sqrt{5}+\sqrt{7}\)
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.
The probability that a debating team wins a debate can be modelled as a Bernoulli distribution. Given that the probability of winning a debate is \(\frac{4}{5}\).
a) Determine the mean of this distribution. [1 mark]
b) Determine the variance of this distribution. [1 mark]
c) Determine the standard deviation of this distribution. [1 mark]
A section of the graphs of the first and second derivatives of a function are shown.
Sketch a possible graph of the function on the same axes over the domain \(0 \le x \le 2\pi\). Explain all reasoning used to produce the sketch.
Note: If you make a mistake in the graph, cancel it by ruling a single diagonal line through your work and use the additional response space on page 17 of this question and response book.
END OF PAPER
