Edexcel GCE Core Mathematics C3 Advanced June 2013

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Edexcel GCE Core Mathematics C3 Advanced June 2012
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C3 Edexcel Core Mathematics June 2013 Question 1
Algebraic Long Division Example

1. Given the identity, find the values of the constants a, b, c, d and e.

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C3 Edexcel Core Mathematics June 2013 Question 2
Curve sketching involving transformations

2. Given that f(x) = ln x, x > 0
   sketch on separate axes the graphs of
   (i) y = f(x),
   (ii) y = |f(x)|,
   (iii) y = –f(x – 4).
   Show, on each diagram, the point where the graph meets or crosses the x-axis. In each case, state the equation of the asymptote.

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C3 Edexcel Core Mathematics June 2013 Question 3
Trigonometric equations

3. Given that 2cos(x + 50)° = sin(x + 40)°
   (a) Show, without using a calculator, that tan x° = 1/3 tan 40°
   (b) Hence solve, for 0 ≤ θ < 360, 2cos(2θ + 50)° = sin(2θ + 40)°
   giving your answers to 1 decimal place.

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Solving a trigonometric equation
3. (b)

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C3 Edexcel Core Mathematics June 2013 Question 4
Turning Points

4. (a) Using calculus, find the exact coordinates of the turning points on the curve with equation y= f(x).
   (b) Show that the equation f(x) = 0 can be written as x = ± 4/5 e^–x
   The equation f(x) = 0 has a root a , where a = 0.5 to 1 decimal place.
   (c) Starting with x₀ = 0.5, use the iteration formula x_n+1 = 4/5 e^-x_n
   to calculate the values of x₁, x₂ and x₃, giving your answers to 3 decimal places.
   (d) Give an accurate estimate for a to 2 decimal places, and justify your answer.

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4. (b)

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Using an Iteration Formula
4. (c)

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4. (d)

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C3 Edexcel Core Mathematics June 2013 Question 5
Trig. differentiation question

5. Given that x = sec² 3y, 0 < y < π/6
   (a) find dy/dx in terms of y.
   (b) Hence show that dy/dx = 1/[6x(x - 1)]^1/2
   (c) Find an expression for d²y/dx² in terms of x. Give your answer in its simplest form.

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2nd Differential Question
5. (c)

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