QCAA Maths Methods Logarithmic Functions Mini Test 4
External Assessment Paper 1 — Technology-free
Number of marks: 6
Perusal time: 30 seconds
Writing time: 9 minutes
Section 1
Instructions
• This section has 10 questions and is worth 10 marks.
• Use a 2B pencil to fill in the A, B, C or D answer bubble completely.
• Choose the best answer for Questions 1 10.
• If you change your mind or make a mistake, use an eraser to remove your response and fill in the new answer bubble completely.
\(2\log_{10}(x) - \log_{10}(3x)\) is equal to
- (A) \(\log_{10}\left(\frac{x}{3}\right)\)
- (B) \(\log_{10}(x^2 - 3x)\)
- (C) \(\frac{2\log_{10}(x)}{\log_{10}(3x)}\)
- (D) \(-\log_{10}(x)\)
Which graph represents the function \(f(x) = -3 - \ln(x+3)\)?
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]
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