2020 QCAA Maths Methods Paper 1 Mini Test 4

 External Assessment Paper 1 — Technology-free

Number of marks: 10

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) [2020 Paper 1 Q15]

Solve the following equations.

a) \(4e^x = 100\) [1 mark]

b) \(2 \log_4 x - \log_4(x - 1) = 1\) [3 marks]

QUESTION 2 (6 marks) [2020 Paper 1 Q19]

A horizontal point of inflection is a point of inflection that is also a stationary point.

Determine the value/s of \(k\) for which the graph of \( f(x) = \frac{\ln(x)}{k} - \frac{kx}{x+1} \) has only one horizontal point of inflection.

END OF PAPER

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