# Edexcel GCE Core Mathematics C3 Advanced June 2012

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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced June 2012.

The questions are given here.

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

1. 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

1. 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

1. 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

1. (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,

5. (c)

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