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. The questions are given here.

Related Topics

More Worked Solutions and A-level Maths help

Free Math Worksheets

C3 Edexcel Core Mathematics June 2012 Question 1

Simplifying algebraic fractions

1. Express

2(3x + 2)/(9x^{2} - 4) - 2/(3x + 1)

as a single fraction in its simplest form.

f(x) = x

(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.

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

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.

Trig. Identities

5. (a) Express 4cosec

(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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

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