(a) The variables x and y are connected by the equation y = `3+x-x²/2`. Some corresponding values of x and y are given in the table below. x (t minutes) | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 --------------|----|----|----|---|---|---|-----|----|--- y | | -1 | 1.5| 3 | 3.5| 3 | 1.5 | -1 | (b) This is a sketch of the graph of y = `pa^x`, where a > 0. The graph passes through the points (0, 4) and (2, 36). [Figure of exponential curve with points (0,4) and (2,36)]

1. (a)(i)Complete the table.[1]
2. (a)(ii)Using a scale of 2 cm to 1 unit, draw a horizontal x-axis for −3 ≤ x ≤ 5. Using a scale of 1 cm to 1 unit, draw a vertical y-axis for -5 ≤ y ≤ 5. Draw the graph of y = `3+x-x²/2` for −3 ≤ x ≤ 5.[3]
3. (a)(iii)By drawing a tangent, estimate the gradient of the curve at (3, 1.5).[2]
4. (a)(iv)(a)The points of intersection of the graph of y = `3+x-x²/2` and the line y = k are the solutions of the equation `10 + 2x – x² = 0`. Find the value of k.[1]
5. (a)(iv)(b)By drawing the line y = k on your graph, find the solutions of the equation `10 + 2x -x² = 0`.[2]
6. (b)(i)Write down the value of p.[1]
7. (b)(ii)Find the value of a.[1]
8. (b)(iii)The graph passes through the point (4, q). Find the value of q.[1]

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