smc-976-10-Table provided

Calculus, 2ADV C4 2024 HSC 22

The graph of the function is shown.

Prove that is concave up for . (3 marks)
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A table of function values, correct to 4 decimal places, for some values is provided.

Using the function values provided and the trapezoidal rule, estimate the shaded area in the diagram. (2 marks)
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Is the answer to part (b) an overestimate or underestimate? Give a reason for your answer. (1 mark)
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♦ Mean mark (a) 47%.

♦ Mean mark (b) 50%.

♦ Mean mark (c) 49%.

Calculus, 2ADV C4 2020 HSC 20

Kenzo is driving his car along a road while his friend records the velocity of the car, , in km/h every minute over a 5-minute period. The table gives the velocity at time hours.

The distance covered by the car over the 5-minute period is given by

Use the trapezoidal rule and the velocity at each of the six time values to find the approximate distance in kilometres the car has travelled in the 5-minute period. Give your answer correct to one decimal place. (2 marks)

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Calculus, 2ADV C4 2011* HSC 5c

The table gives the speed of a jogger at time in minutes over a 20-minute period. The speed is measured in metres per minute, in intervals of 5 minutes.

The distance covered by the jogger over the 20-minute period is given by .

Use the Trapezoidal rule and the speed at each of the five time values to find the approximate distance the jogger covers in the 20-minute period. (3 marks)

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