QCAA Maths Methods Differential Calculus Mini Test 7

 External Assessment Paper 1 — Technology-free 

Number of marks: 11

Perusal time: 1 minute

Writing time: 16 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.



QUESTION 1 (4 marks) [2021 Paper 1 Q16]

A tangent is drawn at the point \((1, e)\) on the graph of the function \(y = e^{2-x}\) as shown.

Graph of y = e^(2-x) with a tangent at (1, e)

Determine the area of the shaded triangle.

QUESTION 2 (7 marks) [2020 Paper 1 Q13]

A function is defined as \(f(x) = x(\ln(x))^2, x > 0\).
The graph of the function is shown and has a local maximum at point \(A\) and a global minimum at point \(B\).
The derivative of the function is given by \(f'(x) = 2 \ln(x) + (\ln(x))^2, x > 0\).

Graph of f(x) with points A and B

a) Verify that there is a stationary point at \(x = 1\). [2 marks]

b) Determine the coordinates of \(A\). [3 marks]

c) The graph of the function has a point of inflection at \(x = e^p\).
Determine \(p\). [2 marks]

END OF PAPER

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