Edexcel Core Mathematics C4 June 2011

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

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Edexcel Core Mathematics C4 June 2011 Past Paper

C4 Mathematics Edexcel June 2011 Question 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

(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.

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

(a)(b) Trapezium Rule

(d) Integration by parts

C4 Mathematics Edexcel June 2011 Question 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.