A-LevelMathematicsCoordinate geometry9709/12 · Feb/Mar 2021 · Q45 Marks
A line has equation y = 3x + k and a curve has equation y = x² + kx + 6, where k is a constant. Find the set of values of k for which the line and curve have two distinct points of intersection.
- A line has equation y = 3x + k and a curve has equation y = x² + kx + 6, where k is a constant. Find the set of values of k for which the line and curve have two distinct points of intersection.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.
- [1] x² + kx + 6 = 3x + k leading to x² + x(k-3) + (6-k) [= 0] (Eliminate y and form 3-term quadratic.)
- [1] (k-3)² - 4(6-k) [>0] (OE. Apply b² – 4ac.)
- [1] k² - 2k - 15 [>0] (Form 3-term quadratic.)
- [1] (k+3)(k-5) [>0] (Or k = -3, 5 from use of formula or completing square.)
- [1] k < -3, k > 5 (Or any correct alternative notation, do not allow <,>. FT for their outside regions.)
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