QCAA Maths Methods Paper 1 Integral Calculus Mini Test 4
External Assessment Paper 1 — Technology-free
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 area between the curve \(y = 9 - x^2\) and the x-axis is
- (A) 12 units\(^2\)
- (B) 18 units\(^2\)
- (C) 36 units\(^2\)
- (D) 54 units\(^2\)
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 graph of \(y = f(x)\), where \(f(x)\) is the quadratic function \(f(x) = ax^2 + bx + 4\), is shown. Two regions of the area between the graph of \(y = f(x)\) and the \(x\)-axis are shaded.
Region \(P\) has an area of \(\frac{13}{6}\) units\(^2\) and Region \(Q\) has an area of \(\frac{43}{6}\) units\(^2\).
Determine the values of \(a\) and \(b\).
An object is moving in a straight line from a fixed point. The object is at the origin initially.
The acceleration \(a\) (in m s\(^{-2}\)) of the object is given by
\[ a(t) = \pi \cos(\pi t) \quad t \ge 0, \text{where } t \text{ is time in seconds.} \]
The velocity at \(t = 1\) is 0.5 m s\(^{-1}\).
a) Determine the initial acceleration. [1 mark]
b) Determine the initial velocity. [2 marks]
c) Determine the displacement after one second. [2 marks]
END OF PAPER
