# Edexcel Core Mathematics C4 June 2011

These video lessons with Questions and Worked Solutions are for C4 Edexcel Core Mathematics June 2011.

Edexcel Core Mathematics C4 June 2011 Past Paper

C4 Mathematics Edexcel June 2011 Question 1

1. 9x2/[(x -1)2(2x + 1)] = A/(x -1) + B/(x - 1) 2 + C/(2x +1) Find the values of the constants A, B and C.

C4 Mathematics Edexcel June 2011 Question 2

f(x) = 1/√(9 + 4x2), |x| < 3/2

Find the first three non-zero terms of the binomial expansion of f( ) x in ascending powers of x. Give each coefficient as a simplified fraction.

C4 Mathematics Edexcel June 2011 Question 3

A hollow hemispherical bowl is shown in Figure 1. Water is flowing into the bowl. When the depth of the water is h m, the volume V m3 is given by

V = 1/12 π h2(3 - 4h), 0 ≤ h ≤ 0.25

(a) Find, in terms of π, dV/dh when h = 0.1

Water flows into the bowl at a rate of π/800 m3s-1.

(b) Find the rate of change of h, in m s-1, when h = 0.1

1. (b) Connected Rates of Change

C4 Mathematics Edexcel June 2011 Question 4

Figure 2 shows a sketch of the curve with equation y = x3ln(x2 + 2)

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

The table below shows corresponding values of x and y for y = x3ln(x2 + 2)

(a) Complete the table above giving the missing values of y to 4 decimal places.

(b) Use the trapezium rule, with all the values of y in the completed table, to obtain an estimate for the area of R, giving your answer to 2 decimal places.

(c) Use the substitution u = x2 + 2 to show that the area of R is

(d) Hence, or otherwise, find the exact area of R.

1. (a)(b) Trapezium Rule
1. (c)

1. (d) Integration by parts

C4 Mathematics Edexcel June 2011 Question 5

1. Find the gradient of the curve with equation

ln y = 2x ln x, x > 0, y > 0

at the point on the curve where x = 2. Give your answer as an exact value.

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