QCAA Maths Methods Logarithmic Functions Mini Test 3
External Assessment Paper 1 — Technology-free
Number of marks: 12
Perusal time: 1 minute
Writing time: 18 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.
Solve the following equations.
a) \(4e^x = 100\) [1 mark]
b) \(2 \log_4 x - \log_4(x - 1) = 1\) [3 marks]
The function \(f(x)\) has the form given by \(f(x) = 3 \log_2 (x + a) + b\)
The function \(g(x)\) has the form given by \(g(x) = -\log_3 (x + c) + 5\)
A section of the graphs of the two functions is shown.
Determine the values of \(a\), \(b\) and \(c\).
END OF PAPER
