2023 QCE Maths Methods Paper 2 Mini Test 3
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
\(\int_{a}^{5a} \frac{1}{x+a} dx\), \(a \neq 0\) is
- (A) 1.7918
- (B) 1.6094
- (C) 1.3863
- (D) 1.0986
The distribution of a certain sample proportion has a mean of 0.70 and a standard deviation of 0.02.
Determine the sample size.
- (A) 525
- (B) 750
- (C) 1750
- (D) 2500
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.
A particle is moving in a straight line. The velocity (m s\(^{-1}\)) of the particle is given by \[v(t) = \frac{20\sin(2t)}{6-5\cos(2t)}, t \ge 0,\] where \(t\) is time (s) after moving from its initial position.
The initial position of the particle is +6.0 m from the origin.
a) Use calculus methods to determine an equation for the position of the particle from the origin at any time \(t\). [3 marks]
b) Determine the position of the particle relative to the origin when it first reaches maximum velocity. [3 marks]
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