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.



QUESTION 1 (4 marks) [2023 Paper 2 Q13]

The curved lines represent graphs of the equations \(y = x^2 - 4x + 8\) and \(y = 10\cos(x+10)\).

Graphs of two intersecting functions

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]

QUESTION 2 (5 marks) [2023 Paper 2 Q17]

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.

END OF PAPER

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