A-LevelMathematicsQuadratics9709/12 · Oct/Nov 2020 · Q35 Marks
The equation of a curve is y = 2x² + m(2x + 1), where m is a constant, and the equation of a line is y = 6x + 4. Show that, for all values of m, the line intersects the curve at two distinct points.
- (a)The equation of a curve is y = 2x² + m(2x + 1), where m is a constant, and the equation of a line is y = 6x + 4. Show that, for all values of m, the line intersects the curve at two distinct points.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [*M1] y eliminated and all terms on one side with correct algebraic steps. Condone ± errors
- [DM1] Any use of discriminant with their a, b and c identified correctly.
- [A1] 4m²-32m+68 or 2m² -16m+34 or m² -8m+17
- [DM1] OE. Any valid method attempted on their 3-term quadratic
- [A1] Clear and correct reasoning and conclusion without wrong working.
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