Edexcel IALGeneralGeneral Applications10 Marks
The curve C has equation y = x^2 - 4x + 5.
- (a)Find dy/dx.[2]
- (b)The point P has x-coordinate 3. Find the equation of the tangent to C at P.[4]
- (c)The tangent to C at the point Q is parallel to the line y = 2x + 1. Find the coordinates of Q.[4]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- Part (a): M1 for attempting to differentiate x^n to nx^(n-1) for at least one term (not just x^2 to x).
- Part (a): A1 for dy/dx = 2x - 4
- Part (b): B1 for finding the y-coordinate of P: y = 3^2 - 4(3) + 5 = 2. So P(3, 2).
- Part (b): M1 for substituting x=3 into their dy/dx to find the gradient at P. (Must be from part a)
- Part (b): M1 for using y - y1 = m(x - x1) with their gradient and their coordinates.
- Part (b): A1 for y = 2x - 4 (o.e.)
- Part (c): B1 for identifying that a tangent parallel to y = 2x + 1 means the gradient is 2.
- Part (c): M1 for setting their dy/dx from part (a) equal to 2 and solving for x. (e.g. 2x - 4 = 2)
- Part (c): A1 for finding the correct x-coordinate for Q: x = 3.
- Part (c): A1 for finding the correct y-coordinate for Q: y = 3^2 - 4(3) + 5 = 2. So Q(3, 2).
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