Questions and Worked Solutions for C1 Edexcel Core Mathematics June 2013.

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Core 1 Mathematics Edexcel June 2013 Question 8

Transformations of Graphs

Figure 1 shows a sketch of the curve with equation y = f(x) where

f(x) = (x + 3)2(x - 1), x ∈ R

The curve crosses the x-axis at (1, 0), touches it at (–3, 0) and crosses the y-axis at (0, –9)

(a) In the space below, sketch the curve C with equation y = f(x + 2) and state the coordinates of the points where the curve C meets the x-axis.

(b) Write down an equation of the curve C.

(c) Use your answer to part (b) to find the coordinates of the point where the curve C meets the y-axis.

f'(x) = (3-x

(a) Show that f'(x) = 9x

(b) Find f"(x).

(c) find f(x).

Roots of Quadratic Equation

10. Given the simultaneous equations

2x + y = 1

x^{2} – 4ky + 5k = 0

where k is a non zero constant,

(a) show that

x^{2} + 8kx + k = 0

Given that x^{2} + 8kx + k = 0 has equal roots,

(b) find the value of k.

(c) For this value of k, find the solution of the simultaneous equations.

Normal to the curve

Length of a line segment

Figure 2 shows a sketch of the curve H with equation y = 3/x + 4, x≠ 0

(a) Give the coordinates of the point where H crosses the x-axis.

(b) Give the equations of the asymptotes to H.

This normal crosses the x-axis at A and the y-axis at B.

(d) Find the length of the line segment AB. Give your answer as a surd.

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