Higher June 2017 Paper 2 Q20
20 The diagram shows part of the graph of \(y = x^2 - 2x + 3\)
(a) By drawing a suitable straight line, use your graph to find estimates for the solutions of \(x^2 - 3x - 1 = 0\) (2)
\(P\) is the point on the graph of \(y = x^2 - 2x + 3\) where \(x = 2\)
(b) Calculate an estimate for the gradient of the graph at the point \(P\). (3)
| Answer | Mark | Notes |
|---|---|---|
| \(-0.4\) to \(-0.2\) and 3.2 to 3.4 | M1 | for \((y =)\ x + 4\) |
| A1 | for answers in the range \(-0.4\) to \(-0.2\) and 3.2 to 3.4 |
| Answer | Mark | Notes |
|---|---|---|
| 1.6 to 2.5 | M1 | for drawing a tangent to the curve at \(x = 2\) |
| M1 | for method to find gradient of their tangent | |
| A1 | for answer in the range 1.6 to 2.5 |