 # Edexcel GCE Core Mathematics C4 Advanced June 2012

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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) 1 (b)(i) Indefinite Integration 1 (b)(ii) Definite Integration

C4 Edexcel Core Mathematics June 2012 Question 2

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 cm3

(a) Show that dV/dx = 3x2

Given that the volume, V cm3, increases at a constant rate of 0.048 cm3s-1

(b) find dx/dt when x = 8

(c) find the rate of increase of the total surface area of the cube, in cm2

C4 Edexcel Core Mathematics June 2012 Question 3

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 x3. Give each coefficient in its simplest form.

Use your answer to part (a) to find the binomial expansion in ascending powers of x, up to and including the term in x3, of

(b) g(x) = 6/√(9 + 4x), |x| < 9/4
(c) h(x) = 6/√(9 - 8x), |x| < 9/8

3 (b)(c)

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 cos2 x)

C4 Edexcel Core Mathematics June 2012 Question 5

Implicit Differentiation

5. The curve C has equation 16y3 + 9x2y - 54x = 0

(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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