Higher November 2019 Paper 3 Q17
17 Here is the graph of \(y = x^2 - 3\)
Use the graph to find estimates for the solutions to the equation \(x^2 - 2x - 2 = 0\)
You must show how you get your solutions. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 2.7 and \(-0.7\) | M1 | for \(x^2 - 3 = 2x - 1\) oe or \(x^2 - 3 - 2x + 1\ (= 0)\) or completing the square eg \((y =)\ (x - 1)^2 - 1 - 2\) |
| M1 | (dep M1) draws graph of \(y = 2x - 1\) or drawing the translated graph or describing the translation in words or \(-1.7 + 1\ (= -0.7)\) or \(1.7 + 1\ (= 2.7)\) | |
| M1 | shows the points of intersection clearly for the given quadratic graph and linear graph or for one correct solution from appropriate supportive working | |
| A1 | for \(x\) in the range 2.6 to 2.8 and \(-0.6\) to \(-0.8\) | |
| SC B2 for plotting \(y = 2x + 1\) and values for \(x\) in the range \(-1.1\) to \(-1.3\) and 3.1 to 3.3 |
Additional guidance
Line segments required
For 1.7 allow from 1.6 to 1.8
For \(-1.7\) allow from \(-1.8\) to \(-1.6\)
Points indicated or attempt to read off \(x\)-axis at the appropriate points – maybe indicated by dashes
No marks will be awarded for correct answers only