Edexcel GCE Core Mathematics C3 Advanced June 2013
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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.
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.
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.
3 (b)
C3 Edexcel Core Mathematics June 2013 Question 4
Turning Points
(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 xn+1 = 4/5 e-xn
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.
Using an Iteration Formula
4 (c)
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.
5 (c)
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