# Edexcel Core Mathematics C4 June 2011

Questions and Worked Video Solutions for C4 Edexcel Core Mathematics June 2011.

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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

3 (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.

4 (a)(b) Trapezium Rule
4 (c)

4 (d) Integration by parts
C4 Mathematics Edexcel June 2011 Question 5

5. 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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