2024 QCE Maths Methods Paper 2 Mini Test 1
External Assessment Paper 2 — Technology-active
Number of marks: 10
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.
The probability of hitting a target in a particular binomial experiment is \(0.72\). Determine the mean of the number of hits if this experiment is repeated eight times.
- (A) 1.61
- (B) 2.24
- (C) 5.76
- (D) 7.28
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.
State the trapezoidal rule and use it with six strips to determine an approximate value of the definite integral for the curve of \(f(x) = 4(x-3)^2\) from \(x = 0\) to \(x = 3\). Show all substitutions made into the rule.
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
