Edexcel IALMathematicsGeneral Applications9 Marks
A curve C has equation y = x²-10x+26. The line L has equation y = -3x+c, where c is a constant.
- (a)Find, using the discriminant, the range of values of c for which L intersects C at two distinct points.[5]
- (b)Given that L is a tangent to C, find the coordinates of the point where L touches C.[4]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- Part (a) M1: Sets x²-10x+26 = -3x+c.
- Part (a) A1: Collects terms on one side to form a correct 3 term quadratic x²-7x+26-c = 0. Can be implied.
- Part (a) M1: Uses b²-4ac > 0 for their quadratic equation (dependent on previous M1).
- Part (a) A1: Correct quadratic inequality in terms of c. E.g. 49 - 4(1)(26-c) > 0.
- Part (a) A1: c > 55/4 (oe).
- Part (b) M1: For using b²-4ac=0 or (d y)/(~d x) = -3 to find x. E.g. 2x-10 = -3 or using c=55/4 in x²-7x+26-c=0.
- Part (b) A1: Correct x value x=7/2.
- Part (b) M1: Substitutes their x value into y = x²-10x+26 or y = -3x+c (using their c value from b²-4ac=0). E.g. y = (7/2)² - 10(7/2) + 26.
- Part (b) A1: Point (7/2, 13/4) (oe). (Must be a coordinate).
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