# Edexcel GCE Core Mathematics C3 Advanced June 2012

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C3 Edexcel Core Mathematics June 2012 Question 1

Simplifying algebraic fractions

1. Express

2(3x + 2)/(9x2 - 4) - 2/(3x + 1)

as a single fraction in its simplest form.

C3 Edexcel Core Mathematics June 2012 Question 2

f(x) = x3 + 3x2 + 4x -12

(a) Show that the equation f(x) = 0 can be written as

The equation x3 + 3x2 + 4x -12 = 0 has a single root which is between 1 and 2

(b) Use the iteration formula

with x0 = 1 to find, to 2 decimal places, the value of x1, x2, and x3.

The root of f(x) = 0 is α.

(c) By choosing a suitable interval, prove that α = 1 272 . to 3 decimal places.

2 (b) Iteration
2 (c) Roots

C3 Edexcel Core Mathematics June 2012 Question 3

Turning Points

Figure 1 shows a sketch of the curve C which has equation

y = ex√3sin3x , −π/3 ≤ x ≤ π/3

(a) Find the x coordinate of the turning point P on C, for which x 0

(b) Find an equation of the normal to C at the point where x = 0

3 (b) Normal to a curve

C3 Edexcel Core Mathematics June 2012 Question 4

Transformations of graphs (mod types)

Figure 2 shows part of the curve with equation y = f(x)

The curve passes through the points P(−1.5, 0) and Q(0, 5P) as shown.

On separate diagrams, sketch the curve with equation

(a) y =|f(x)|

(b) y = f(|x|)

(c) y = 2f(3x)

Indicate clearly on each sketch the coordinates of the points at which the curve crosses or meets the axes.

C3 Edexcel Core Mathematics June 2012 Question 5

Trig. Identities

5. (a) Express 4cosec22θ cosec2θ − in terms of sinθ and cosθ.

(b) Hence show that

4cosec22θ cosec2θ = sec2θ

(c) Hence or otherwise solve, for 0 < θ < π,

4cosec22θ cosec2θ = 4

5 (c)

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