Higher November 2019 Unit 2 Q3
3. The table below shows some of the values of \(y = x^2 - 2x - 4\) for values of \(x\) from –3 to 4.
| \(x\) | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|---|
| \(y = x^2 - 2x - 4\) | 11 | 4 | −1 | −4 | −4 | –1 | 4 |
(a) Complete the table by finding the value of \(y\) when \(x\) = 1. [1]
(b) On the graph paper below, draw the graph of \(y = x^2 - 2x - 4\) for values of \(x\) from –3 to 4. [2]
(c)
(i) Draw the line \(y + x = 4\) on the graph paper. [2]
(ii) Write down the values of \(x\) where the line \(y + x = 4\) cuts the curve \(y = x^2 - 2x - 4\). [1]
Values of \(x\) are …………………… and ……………………
| Scheme | Marks | Comments |
|---|---|---|
| –5 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| At least 7 correct plots and no incorrect plot. | P1 | F.T. ‘their (1,−5)’ Allow ± ‘½ a small square’. |
| A smooth curve drawn through their plots. | C1 | F.T. ‘their 8 plots’. OR a curve through the 7 given points and (1,−5) Allow intention to pass through their plots. (± 1 small square horizontal or vertical.) |
| Scheme | Marks | Comments |
|---|---|---|
| (i) Line \(y + x = 4\) drawn. | B2 | B1 for a straight line going through(0,4) or (4,0) BUT NOT line \(y = 4\) nor line \(x = 4\) |
| (ii) −2·4 AND 3·4 | B1 | F.T. intersection of ‘their curve’ with ‘their \(y + x = 4\)’ (even for line \(y = 4\)) only if exactly two points of intersection. Must be seen to intersect their curve at two points. Allow ± ‘1 small square’. |