QCAA Maths Methods Logarithmic Functions Mini Test 1
External Assessment Paper 2 — Technology-active
Number of marks: 9
Perusal time: 1 minute
Writing time: 15 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.
Solve \(\ln(x) + \ln(3.70) = \ln(9.25)\) for \(x\).
- (A) 0.92
- (B) 1.71
- (C) 2.50
- (D) 5.55
The solution of \(e^{2x-3} = 42\) is
- (A) 1.48
- (B) 2.31
- (C) 3.37
- (D) 4.54
Determine the equation of the asymptote of the function \(f(x) = \log_9(x-3) - 4\).
- (A) \(x = -4\)
- (B) \(x = -3\)
- (C) \(x = 3\)
- (D) \(x = 4\)
The graphs of the functions \(f(x) = 2e^x + 5\) and \(g(x) = \frac{3}{e^x}\) intersect at point A. Determine the coordinates of point A.
- (A) (1.609, 15)
- (B) (1.099, 1)
- (C) (0.4065, 2)
- (D) (-0.693, 6)
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 magnitude of an earthquake can be modelled by the logarithmic equation \(M_A = \log_{10} \left( \frac{I_A}{I_0} \right)\), where \(M_A\) is the magnitude at a location A, \(I_A\) is the intensity of the earthquake at location A and \(I_0\) is a constant.
An earthquake at location P had a magnitude of 5.2.
A different earthquake at location Q had a magnitude of 3.5.
a) Determine an equation involving logarithms that expresses the difference in magnitudes between the earthquakes at locations P and Q. [1 mark]
b) How many times more intense was the earthquake at location P than the earthquake at location Q? [4 marks]
END OF PAPER
