1MA0 Higher June 2016 Paper 1 Q19
19 The diagram shows the graph of \(y = x^2 - 4x - 2\)
(a) Use the graph to find estimates for the solutions of
(i) \(x^2 - 4x - 2 = 0\)
(ii) \(x^2 - 4x - 6 = 0\) (3)
(b) Use the graph to find estimates for the values of \(x\) that satisfy the simultaneous equations \[\begin{aligned} y &= x^2 - 4x - 2 \\ x + y &= 6 \end{aligned}\] (3)
| Answer | Mark | Notes |
|---|---|---|
| (i) \(-0.4\) to \(-0.5\) 4.4 to 4.5 | B1 for value in range \(-0.4\) to \(-0.5\) and value in range 4.4 to 4.5 NB: condone values given as part of coordinates. | |
| (ii) \(-1.0\) to \(-1.2\) 5.0 to 5.2 | 3 | M1 for \(x^2 - 4x - 2 = 4\) or line \(y = 4\) drawn on graph or points marked with a \(y\) coord. of 4 or a value in range \(-1.0\) to \(-1.2\) or a value in range 5.0 to 5.2 A1 for value in range \(-1.0\) to \(-1.2\) and value in range 5.0 to 5.2; do not accept coordinates. |
| Answer | Mark | Notes |
|---|---|---|
| \(-1.6\) to \(-1.8\) 4.6 to 4.8 | 3 | M1 for \(x + y = 6\) drawn on graph A2 for value in range \(-1.6\) to \(-1.8\) and value in range 4.6 to 4.8 (A1 for one correct value or both values given as coordinates) |