Are you looking for A-level Maths help?

The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics
C3 Advanced June 2012.

**Related Pages**

Edexcel GCE Core Mathematics C3 Advanced June 2011

More Lessons for A Level Maths

The questions are given here.

C3 Edexcel Core Mathematics June 2012 Question 1

Simplifying algebraic fractions

- Express 2(3x + 2)/(9x
^{2}- 4) - 2/(3x + 1) as a single fraction in its simplest form.

C3 Edexcel Core Mathematics June 2012 Question 2

- f(x) = x
^{3}+ 3x^{2}+ 4x -12

(a) Show that the equation f(x) = 0 can be written as

The equation x^{3}+ 3x^{2}+ 4x -12 = 0 has a single root which is between 1 and 2

(b) Use the iteration formula with x_{0}= 1 to find, to 2 decimal places, the value of x_{1}, x_{2}, and x_{3}. The root of f(x) = 0 is α.

(c) By choosing a suitable interval, prove that α = 1 272 . to 3 decimal places.

2. (b) Iteration

2. (c) Roots

C3 Edexcel Core Mathematics June 2012 Question 3

- Turning Points

Figure 1 shows a sketch of the curve C which has equation y = e^{x√3}sin3x , −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

3. (b) Normal to a curve

C3 Edexcel Core Mathematics June 2012 Question 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.

C3 Edexcel Core Mathematics June 2012 Question 5

Trig. Identities

- (a) Express 4cosec
^{2}2θ cosec^{2}θ − in terms of sinθ and cosθ.

(b) Hence show that

4cosec^{2}2θ cosec^{2}θ = sec^{2}θ

(c) Hence or otherwise solve, for 0 < θ < π,

4cosec^{2}2θ cosec^{2}θ = 4, giving your answers in terms of π.

5. (c)

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.