A-LevelMathematicsQuadratics9709/12 · Oct/Nov 2009 · Q1013 Marks
the x-coordinates of A and B,
- (i)(a)the x-coordinates of A and B,[3]
- (i)(b)the equation of the tangent to the curve at B,[3]
- (i)(c)the acute angle, in degrees correct to 1 decimal place, between this tangent and the line 2y = x + 5.[3]
- (ii)Determine the set of values of k for which the line 2y = x + k does not intersect the curve y = x² - 4x + 7.[4]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2009). The mark or mark type is shown in brackets.
- [1] Complete elimination of x or y (2x² – 9x + 9 = 0) (M1)
- [2] Correct method for quadratic. co (x=3 or x=1.5) (DM1A1)
- [1] dy/dx = 2x-4 (B1)
- [2] Correct form of eqn with m numeric. co (y-4=2(x-3) or y=2x-2) (M1A1)
- [1] Finds angle with x-axis once. (M1)
- [2] Subtracts two angles. co (37.0°) (M1A1)
- [1] Eliminates y or x completely. Co (= 0) (2x² – 9x + 14 – k = 0) (M1A1)
- [1] Uses b² – 4ac = 0, or < 0 or > 0 (M1)
- [2] k < 31/8 or k < 3.875 (Co condone ≤) (A1)
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