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

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C4 Edexcel Core Mathematics June 2012 Question 1

1. Given

(a) Find the values of the constants A, B and C.

(b) (i) Hence find ∫f(x) dx

(ii) Find

leaving your answer in the form a + ln b, where a and b are constants.

1(a) Identities (Partial Fractions)Rates of Change

Figure 1 shows a metal cube which is expanding uniformly as it is heated.

At time t seconds, the length of each edge of the cube is x cm, and the volume of the cube is V cm

(a) Show that dV/dx = 3x^{2}

Given that the volume, V cm^{3}, increases at a constant rate of 0.048 cm^{3}s^{-1}

(b) find dx/dt when x = 8

(c) find the rate of increase of the total surface area of the cube, in cm^{2}

Binomial Expansion

f(x) = 6/√(9 - 4x), |x| < 9/4

(a) Find the binomial expansion of f(x) in ascending powers of x, up to and including the term in x

Use your answer to part (a) to find the binomial expansion in ascending powers of x, up to and including the term in x^{3}, of

(b) g(x) = 6/√(9 + 4x), |x| < 9/4

(c) h(x) = 6/√(9 - 8x), |x| < 9/8

C4 Edexcel Core Mathematics June 2012 Question 4

Differential Equations 4. Given that y = 2 at x = π/4, solve the differential equation

dy/dx = 3/(y cos^{2} x)

Implicit Differentiation

5. The curve C has equation 16y

(a) Find dy/dx in terms of x and y.

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

5 (b)

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