2023 QCE Maths Methods Paper 1 Mini Test 5
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.
The region bounded by the x-axis and the curve of \(f(x) = x(4-x)\) represents the plan of a garden bed. All measurements are in metres.
a) Estimate the area of the garden bed using sums of the form \(\sum_{i} f(x_i)\delta x_i\) where \(x_1 = 1\), \(x_2 = 2\), \(x_3 = 3\) and \(x_4 = 4\). [1 mark]
b) Use a definite integral to determine the area of the garden bed. [3 marks]
Solve for \(x\) in the equation \(4 + 7e^{-2x} = 3e^{2x}\).
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