Higher November 2016 Unit 1 Q2
2.
(a) The table below shows some of the values of \(y = 2x^2 - 5x - 1\) for values of \(x\) from –2 to 4.
Complete the table by finding the value of \(y\) for \(x = -1\) and for \(x = 2\). [2]
Complete the table by finding the value of \(y\) for \(x = -1\) and for \(x = 2\). [2]
| \(x\) | −2 | −1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|
| \(y = 2x^2 - 5x - 1\) | 17 | −1 | −4 | 2 | 11 |
(b) On the graph paper below, draw the graph of \(y = 2x^2 - 5x - 1\) for values of \(x\) from –2 to 4. [2]
(c) Draw the line \(y = 5\) on the graph paper.
Write down the values of \(x\) where the line \(y = 5\) cuts the curve \(y = 2x^2 - 5x - 1\).
Give your answers correct to 1 decimal place. [2]
Write down the values of \(x\) where the line \(y = 5\) cuts the curve \(y = 2x^2 - 5x - 1\).
Give your answers correct to 1 decimal place. [2]
Values of \(x\) are …………………… and ……………………
(d) Circle the equation below whose solutions are the values you have given in (c). [1]
\(2x^2 - 5x - 1 = 0\) \(2x^2 - 5x - 6 = 0\) \(2x^2 - 5x - 5 = 0\)
\(2x^2 - x - 1 = 0\) \(2x^2 - 5x + 4 = 0\)
| Scheme | Marks | Comments |
|---|---|---|
| 6 −3 | B2 | B1 for each. |
| Scheme | Marks | Comments |
|---|---|---|
| 7 correct plots. | P1 | Use overlay. F.T. ‘their (−1,6)’ and ‘their (2,−3)’. Allow ± ‘½ a small square’. |
| Curve drawn. | C1 | F.T. ‘their plots’. At least 6 plots required. Clear intention to draw a curve through ‘their plotted points’. |
| Scheme | Marks | Comments |
|---|---|---|
| −0·9 and 3·4 | B2 | B1 for each. Allow (−0·9, 5) and (3·4, 5). F.T. intersection of ‘their curve’ with \(y\) = 5 provided exactly 2 intersections seen on graph. Allow ± ‘½ a small square’. If no marks gained then SC1 for either of the following. \(y\) = 5 drawn correctly, OR Two correct F.T. values given for ‘their straight line’ and ‘their curve’ provided exactly 2 intersections seen on graph. |
| Scheme | Marks | Comments |
|---|---|---|
| \(2x^2 - 5x - 6 = 0\) | B1 |