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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C4 Advanced June 2012. Try out the Past paper for Edexcel C4 June 2012 and check out the video solutions if you need any help.

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C4 Edexcel Core Mathematics June 2012 Question 6

Figure 2 shows a sketch of the curve C with parametric equations

x = (√3) sin 2t, y = 4cos^{2}t, 0 ≤ t ≤ π

(a) Show that dy/dx = k(√3) tan 2t, where k is a constant to be determined.

(b) Find an equation of the tangent to C at the point where t = π3

Give your answer in the form y = ax + b, where a and b are constants.

(c) Find a Cartesian equation of C.

6 (a) Parametric differentiationFigure 3 shows a sketch of part of the curve with equation y = x

The finite region R, shown shaded in Figure 3, is bounded by the curve, the x-axis and the lines x = 1 and x = 4

(a) Use the trapezium rule, with 3 strips of equal width, to find an estimate for the area of R, giving your answer to 2 decimal places.

(b) Find ∫x^{1/2}ln2x dx

(c) Hence find the exact area of R, giving your answer in the form aln2 + b where a and b are exact constants.

7 (a) Trapezium Rule7 (b) Integration

C4 Edexcel Core Mathematics June 2012 Question 8

8. Relative to a fixed origin O, the point A has position vector (10i + 2j + 3k) and the point B has position vector (8i + 3j + 4k).

The line l passes through the points A and B.

(a) Find the vector AB.

(b) Find a vector equation for the line l.

The point C has position vector (3i + 12j + 3k).

The point P lies on l. Given that the vector CP is perpendicular to l,

(c) find the position vector of the point P.

8 (a)(b) Vectors

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