2021 QCE Maths Methods Paper 2 Mini Test 2
External Assessment Paper 2 — Technology-active
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.
Using the trapezoidal rule with an interval size of 1, the approximate value of the integral \(\int_0^3 0.5^x dx\) is
- (A) 1.25
- (B) 1.26
- (C) 1.31
- (D) 1.88
Solve for \(x\) given that \(\log_3(x-1) = 2\).
- (A) 7
- (B) 8
- (C) 9
- (D) 10
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 heights of students at School A are normally distributed with a mean of 165 cm and a standard deviation of 15 cm.
a) Determine the probability that a student chosen at random from School A is shorter than 180 cm. [1 mark]
b) Determine the minimum integer value of the height of a student who is in the top 2% of this distribution. [3 marks]
The heights of students at School B are also normally distributed. A student at School B has the same height as the height determined in Question 14b) but their corresponding z-score is 3.
c) Determine which student's height ranks higher in terms of percentile for their school. [3 marks]
END OF PAPER
