O-LevelAdditional MathematicsQuadratic functions4037/22 · Oct/Nov 2023 · Q25 Marks
Find the non-zero value of k for which the line y=-2x-6k-1 is a tangent to the curve y = x(x+2k).
- Find the non-zero value of k for which the line y=-2x-6k-1 is a tangent to the curve y = x(x+2k).[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [M1] x² + 2kx = -2x - 6k - 1
- [A1] x² + (2k+2)x + 6k + 1 [= 0]
- [M1] Correctly uses b² – 4ac [*0] for their equation
- [A1] 4k² - 16k [*0] nfww
- [A1] k = 4 dep on all previous marks awarded
- [M1] Alternative method: 2x + 2k
- [A1] Alternative method: k = -x-1 or x = -k – 1 oe
- [M1] Alternative method: -2(k-1) - 6k – 1 = (–k – 1)² + 2k(-k – 1) oe or -2x-6(-1 - x) – 1 = x (x + 2(−1 – x)) oe
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