2022 QCE Maths Methods Paper 2 Mini Test 4
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.
A marble moves in one direction in a straight line with velocity \(v = 2\ln(t+1)\) (in metres per second) where \(t\) is time (in seconds) since the marble passed through the origin. Determine the distance from the origin the marble has rolled after 4 seconds.
- (A) 0.40 m
- (B) 1.60 m
- (C) 3.22 m
- (D) 8.09 m
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.
Suppose that the distance travelled by vehicles in a year can be modelled by a normal distribution. In 2021, vehicles travelled a mean of 13 700 km with a standard deviation of 3400 km.
a) Determine the probability that a vehicle chosen at random travelled less than 12 000 km in 2021. [2 marks]
b) Determine the value of \(x\) where 60% of vehicles travelled less than \(x\) km in 2021. [2 marks]
A sandy beach has a fence on one side and ocean on the other. The width of the beach is the distance (in metres) from the fence to the water's edge. The width, \(w(t)\), at a certain point is given by \[ w(t) = a + b \sin\left(\frac{\pi}{6}t - \frac{\pi}{3}\right), \quad 0 \le t \le 24 \]
where \(t\) is time (in hours) since 6 am. The width of the beach is 8 metres at 8 am and 3 metres at 5 pm.
a) Determine \(a\) and \(b\). [2 marks]
b) Determine the rate of change of the width of the beach at 8 am and the first time after this when this rate of change is repeated. [2 marks]
END OF PAPER
