QCAA Maths Methods Differential Calculus Mini Test 5
External Assessment Paper 2 — Technology-active
Number of marks: 5
Perusal time: 30 seconds
Writing time: 7 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.
An object travels in a straight line so that its velocity at time \(t\) seconds is given by \(v(t) = 2t + \sin(2t)\). Determine the expression for acceleration as a function of time.
- (A) \(a(t) = 2 + 2\cos(2t)\)
- (B) \(a(t) = 2 - \frac{1}{2}\cos(2t)\)
- (C) \(a(t) = t^2 + 2\cos(2t)\)
- (D) \(a(t) = t^2 - \frac{1}{2}\cos(2t)\)
The displacement (in metres) of a particle is given by \(s(t) = -3\cos(t) + 2\sin(t)\), where \(t\) is in seconds.
The instantaneous velocity of the particle at time \(t = \frac{\pi}{2}\) seconds is
- (A) -3 m s\(^{-1}\)
- (B) -2 m s\(^{-1}\)
- (C) 2 m s\(^{-1}\)
- (D) 3 m s\(^{-1}\)
A substance is being heated such that its temperature \(T\) in °C after \(t\) minutes is given by the function \(T = 2e^{0.5t}\).
The first integer value of \(t\) for which the instantaneous rate of change of temperature is greater than 100 °C per minute is
- (A) \(t=10\)
- (B) \(t=9\)
- (C) \(t=8\)
- (D) \(t=7\)
The approximate value of \(x\) where the graph of the function \(y = x^3 + 6x^2 + 7x - 2\cos(x)\) changes concavity is
- (A) -3.26
- (B) -2.85
- (C) -2.20
- (D) -1.89
The displacement of a particle (in metres) at time \(t\) (in seconds) is represented by the function
\[ s(t) = t \ln(t) - t, \quad 0 < t < 4 \]Determine the approximate acceleration of the particle at time \(t = 3\).
- (A) 0.66 m s\(^{-2}\)
- (B) 0.33 m s\(^{-2}\)
- (C) -0.33 m s\(^{-2}\)
- (D) -0.66 m s\(^{-2}\)
END OF PAPER
