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2 marksNumber Sequences and Rules

CSEC Mathematics · January 2006 · Paper 2 · Question 8(a)

The path of a ball thrown in the air is given by the equation h = 20t - 5t^2 where h is the vertical distance above the ground (in metres) and t is the time (in seconds) after the ball was thrown. The table shows some values of t and the corresponding values of h, correct to 1 decimal place.

Copy and complete the table of values: t (0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4) and h (0.0, 8.8, 15, 18.8, __, 18.8, __, 8.8, 0.0).

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  1. 8(b)(i)Draw the graph of h = 20t - 5t^2 for 0 ≤ t ≤ 4. You may proceed as follows: Using a scale of 2 cm to represent 0.5 seconds, draw the horizontal t-axis for 0 ≤…[1 mark]
  2. 8(b)(ii)Using a scale of 1 cm to represent 1 metre, draw the vertical h-axis for 0.0 ≤ h ≤ 21.0.[1 mark]
  3. 8(b)(iii)Plot the points from your table of values on the axes drawn.[2 marks]
  4. 8(b)(iv)Join the points with a smooth curve.[1 mark]
  5. 8(c)(i)Using your graph, calculate estimates of the GREATEST height above the ground reached by the ball.[1 mark]
  6. 8(c)(ii)Using your graph, calculate estimates of the number of seconds for which the ball was MORE than 12 metres above the ground.[2 marks]
  7. 8(c)(iii)Using your graph, calculate estimates of the interval of time during which the ball was moving upwards.[1 mark]

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