2023 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 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 curved lines represent graphs of the equations \(y = x^2 - 4x + 8\) and \(y = 10\cos(x+10)\).
a) Determine the coordinates of the points of intersection A and B. [1 mark]
b) State an integral expression representing the area enclosed by the two graphs. [2 marks]
c) Determine the area enclosed by the two graphs. [1 mark]
Model bridges were constructed for a competition. The models that could support the heaviest loads before collapsing were given awards.
The load results of the competition were normally distributed, with a mean of 1.36 kg and a standard deviation of 0.12 kg.
Three award categories were used: honours for the top 15% of load results; distinction for the next 15%; and commendation for the next 15%.
The model bridge constructed by Finley only just missed out on a commendation. Kirby's model bridge only just qualified for honours. Determine the difference, to the nearest gram, between the loads supported by Finley and Kirby's models.
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