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Edexcel GCE Core Mathematics C3 Advanced June 2013. (Part 2)

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Edexcel GCE Core Mathematics C3 Advanced June 2012

More Lessons for A Level Maths

C3 Edexcel Core Mathematics June 2013 Question 1

Algebraic Long Division Example

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

C3 Edexcel Core Mathematics June 2013 Question 2

Curve sketching involving transformations

- 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.

C3 Edexcel Core Mathematics June 2013 Question 3

Trigonometric equations

- 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.

Solving a trigonometric equation

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 x_{0}= 0.5, use the iteration formula x_{n+1}= 4/5 e^{-x}_{n }to calculate the values of x_{1}, x_{2}and x_{3}, giving your answers to 3 decimal places.

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

- (b)

Using an Iteration Formula

4. (c)

- (d)

C3 Edexcel Core Mathematics June 2013 Question 5

Trig. differentiation question

- Given that x = sec
^{2}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 d^{2}y/dx^{2}in terms of x. Give your answer in its simplest form.

2nd Differential Question

5. (c)

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