Edexcel GCE Core Mathematics C3 Advanced June 2012

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Edexcel GCE Core Mathematics C3 Advanced June 2011
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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.

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C3 Edexcel Core Mathematics June 2012 Question 2

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.

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2. (b) Iteration

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2. (c) Roots

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C3 Edexcel Core Mathematics June 2012 Question 3

3. Turning Points
   Figure 1 shows a sketch of the curve C which has equation y = e^x√3sin3x , −π/3 ≤ x ≤ π/3
   (a) Find the x coordinate of the turning point P on C, for which x 0
   Give your answer as a multiple of π.
   (b) Find an equation of the normal to C at the point where x = 0

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3. (b) Normal to a curve

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C3 Edexcel Core Mathematics June 2012 Question 4

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.

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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, giving your answers in terms of π.

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5. (c)

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