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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced June 2013. The questions are given here.

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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)

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

The equation f(x) = 0 has a root a , where a = 0.5 to 1 decimal place.

(c) Starting with x

(d) Give an accurate estimate for a to 2 decimal places, and justify your answer.

Using an Iteration Formula

4 (c)

Trig. differentiation question

5. Given that x = sec

(a) find dy/dx in terms of y.

(b) Hence show that dy/dx = 1/[6x(x - 1)]

5 (c)

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