Higher November 2021 Paper 3 Q16
16 The curve C has equation \(y = x^2 + 3x - 3\)
The line L has equation \(y - 5x + 4 = 0\)
Show, algebraically, that C and L have exactly one point in common. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| Shown (supported) | M1 | for eliminating \(y\) or \(x\), eg \(x^2 + 3x - 3 = 5x - 4\) |
| M1 | for rearranging, collecting terms and setting to 0 eg \(x^2 - 2x + 1\ (= 0)\) | |
| M1 | for factorising or solving eg \((x - 1)^2\ (= 0)\) | |
| C1 | for statement confirming only 1 point in common eg only 1 root or only 1 value of \(x\) so only 1 set of coordinates |
Additional guidance
There must be a statement in words for the award of this mark