2024 QCE Maths Methods Paper 1 Mini Test 1
External Assessment Paper 1 — Technology-free
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.
Determine \(\int x^4 dx\)
- (A) \(4x^3 + c\)
- (B) \(5x^5 + c\)
- (C) \(\frac{1}{3}x^3 + c\)
- (D) \(\frac{1}{5}x^5 + c\)
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.
Determine \(\frac{dy}{dx}\) for the function \(y = e^{\sin(x)}\)
- (A) \(\cos(x) e^{\sin(x)}\)
- (B) \(\sin(x) e^{\cos(x)}\)
- (C) \(e^{\sin(x)}\)
- (D) \(e^{\cos(x)}\)
A sample of size \(n\) can be used to obtain a sample proportion \(\hat{p}\). An approximate margin of error for the population proportion can be obtained using the formula
\[E = z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\]If the level of confidence is increased from 95% to 99%, then
- (A) the associated \(z\)-value would decrease, so \(E\) would increase.
- (B) the associated \(z\)-value would increase, so \(E\) would increase.
- (C) the associated \(z\)-value would decrease, so \(E\) would decrease.
- (D) the associated \(z\)-value would increase, so \(E\) would decrease.
a) Determine the second derivative of \(y = x^3 - 3x^2\). [2 marks]
b) Use your result from QUESTION 11a) to calculate the value of the second derivative when \(x = -1\). [1 mark]
c) Determine the x- and y-coordinates of the point on the graph of \(y = x^3 - 3x^2\) for which the rate of change of the first derivative is zero. [3 marks]
END OF PAPER
