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Higher November 2022 Paper 2 Q8

EduqasHigherCurrent spec8 marksDrawing & Using Graphs

8. The table shows some of the values of \(h = -3(t + 1)(t - 4)\) for \(0 \leqslant t \leqslant 5\).

\(t\)012345
\(h = -3(t + 1)(t - 4)\)18180
(a) Complete the table above. [2]
(b) On the graph paper below, draw the graph of \(h = -3(t + 1)(t - 4)\) for \(0 \leqslant t \leqslant 5\). [2]
Graph paper with t-axis from 0 to 5 (extending to 6) and h-axis from −20 to 20
(c)
Derek standing on a raised step throwing a ball upwards; the ball’s dashed path rises then falls to the ground below

Diagram not drawn to scale

Derek throws a ball upwards from a point above horizontal ground.
The height, \(h\) metres, of the ball above the ground \(t\) seconds after Derek throws it is \(h = -3(t + 1)(t - 4)\).
(i) What is the height of the ball above the ground at the start of Derek’s throw? [1]
(ii) How many seconds after Derek throws the ball does it first hit the ground? [1]
(iii) How many seconds after Derek throws the ball is it at its maximum height? [1]
(iv) What is the maximum height of the ball above the ground? [1]
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