QCAA Maths Methods Differential Calculus Mini Test 6
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.
The equation of the tangent to the curve \(f(t) = te^t\) at \(t = 1\) is
- (A) \(y = et\)
- (B) \(y = 2et - e\)
- (C) \(y = et - e^2 + 1\)
- (D) \(y = 2et - 2e^2 + 1\)
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 the derivative with respect to \(x\) of the following functions.
a) \(y = (e^x + 1)^3\) [2 marks]
b) \(y = \frac{\sin(x)}{x^2}\) (Give your answer in simplest form.) [3 marks]
Consider the function \(f(x) = \ln(3x+4)\), for \(x > \frac{-4}{3}\).
a) Determine \(f'(x)\). [1 mark]
b) Determine the \(x\)-intercept of the graph of \(f(x)\). [2 marks]
c) Determine the gradient of the tangent to the graph of \(f(x)\) at the \(x\)-intercept. [1 mark]
END OF PAPER
