A-LevelMathematicsQuadratics9709/12 · Feb/Mar 2025 · Q14 Marks
A curve has equation y = 5+3x-2x² and a straight line has equation y = kx+13, where k is a constant. Find the set of values of k for which the curve and the line do not meet.
- A curve has equation y = 5+3x-2x² and a straight line has equation y = kx+13, where k is a constant. Find the set of values of k for which the curve and the line do not meet.[4]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.
- [B1] [kx+13=5+3x-2x²] 2x²+(k-3)x+8 [=0] OE Eliminate y to obtain a three-term quadratic.
- [M1] Use of b²-4ac<0 or b² – 4ac = 0 with their coefficients of their new quadratic equation. Condone ± errors only. OE Use of '>0' scores M0, unless recovered.
- [A1] -5 and 11 Identification of correct critical values, may only be seen in their final answer.
- [A1] -5<k<11 CWO Do not allow 'or'. A0 if sign or signs used.
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