2021 QCE Maths Methods Paper 1 Mini Test 4
External Assessment Paper 1 — Technology-free
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.
Consider the functions \(f(x) = x^2\) and \(g(x) = 4x\).
a) Determine the \(x\)-coordinates of the points of intersection of the graphs of the two functions. [2 marks]
b) Use the results from Question 13a) to calculate the area enclosed by the graphs of \(f(x)\) and \(g(x)\). [3 marks]
A tangent is drawn at the point \((1, e)\) on the graph of the function \(y = e^{2-x}\) as shown.
Determine the area of the shaded triangle.
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