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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C4 Advanced January 2012. Try out the Past paper for Edexcel C4 January 2012 and check out the video solutions if you need any help.

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C4 Edexcel Core Mathematics January 2012 Question 1

1. The curve C has the equation 2x + 3y

The point P on the curve has coordinates (–1, 1).

(a) Find the gradient of the curve at P.

(b) Hence find the equation of the normal to C at P, giving your answer in the form ax + by + c = 0, where a, b and c are integers.

2. (a) Use integration by parts to find ∫x sin 3x dx

(b) Using your answer to part (a), find ∫x^{2} cos 3x dx

3. (a) Expand

1/(2 - 5x)^{2}, |x| < 2/5

in ascending powers of x, up to and including the term in x^{2}, giving each term as a simplified fraction.

Given that the binomial expansion of (2 + kx)/(2 - 5x)^{2}, |x| < 2/5 is

1/2 + 7/4x + Ax^{2} + ...

(b) find the value of the constant k,

(c) find the value of the constant A.

3 (a) Binomial ExpansionC4 Edexcel Core Mathematics January 2012 Question 4

Figure 1 shows the curve with equation

y = [2x/(3x^{2} + 4)], x ≥ 0

The finite region S, shown shaded in Figure 1, is bounded by the curve, the x-axis and the line x = 2

The region S is rotated 360° about the x-axis.

Use integration to find the exact value of the volume of the solid generated, giving your answer in the form k ln a, where k and a are constants.

Volume of RevolutionC4 Edexcel Core Mathematics January 2012 Question 5

Figure 2 shows a sketch of the curve C with parametric equations

x = 4 sin (t + π/6), y = cos 2t, 0 ≤ t < 2π

(a) Find an expression for dy/dx in terms of t.

(b) Find the coordinates of all the points on C where dy/dx = 0

5 (a) Parametric Curves5 (b)

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