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

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Edexcel Core Mathematics C4 January 2011 Past Paper

6. The curve C has parametric equations

x = ln t, y = t^{2} - 2, t > 0

Find

(a) an equation of the normal to C at the point where t = 3 ,

(b) a cartesian equation of C.

The finite area R, shown in Figure 1, is bounded by C, the x-axis, the line x = ln 2 and the

line x = ln 4 . The area R is rotated through 360° about the x-axis.

(c) Use calculus to find the exact volume of the solid generated.

6 (a) Parametric Equations

(a) Given that y = 1/[4 + √(x - 1)], complete the table below with values of y corresponding to x = 3 and x = 5 . Give your values to 4 decimal places.

(b) Use the trapezium rule, with all of the values of y in the completed table, to obtain an estimate of I, giving your answer to 3 decimal places.

(c) Using the substitution (u - 4)^{2} + 1, or otherwise, and integrating, find the exact value of I.

7 (c) Integration by Substitution

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