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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C2 Advanced January 2012. Try out the Past paper for Edexcel C2 January 2012 and check out the video solutions if you need any help.

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C2 Edexcel Core Mathematics January 2012 Question 6

Figure 1 shows the graph of the curve with equation

y = 16/x^{2} - x/2 + 1

The finite region R, bounded by the lines x = 1, the x-axis and the curve, is shown shaded in Figure 1. The curve crosses the x-axis at the point4, 0).

(a) Complete the table with the values of y corresponding to x = 2 and 2.5

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

(c) Use integration to find the exact value for the area of R.

6 (a)(b) Trapezium rule.

Figure 2 shows ABC, a sector of a circle of radius 6 cm with centre A. Given that the size of angle BAC is 0.95 radians, find

(a) the length of the arc BC,

(b) the area of the sector ABC.

The point D lies on the line AC and is such that AD BD = . The region R, shown shaded in Figure 2, is bounded by the lines CD, DB and the arc BC.

(c) Show that the length of AD is 5.16 cm to 3 significant figures.

Find

(d) the perimeter of R,

(e) the area of R, giving your answer to 2 significant figures.7 (a)(b) Arc length, Sector Area.

Figure 3 shows a flowerbed. Its shape is a quarter of a circle of radius x metres with two equal rectangles attached to it along its radii. Each rectangle has length equal to x metres and width equal to y metres.

Given that the area of the flowerbed is 4 m^{2}

(a) show that

y = (16 - πx^{2})/8x

(b) Hence show that the perimeter P metres of the flowerbed is given by the equation

P = 8/x + 2x

(c) Use calculus to find the minimum value of P.

8 (a)(b)

8 (c) Stationary Points.

(i) Find the solutions of the equation sin(3x - 15°) = 1/2, for which 0° ≤ x ≤ 180°

Figure 4 shows part of the curve with equation

y = sin(ax - b), where a > 0, 0 < b < π

The curve cuts the x-axis at the points P, Q and R as shown.

Given that the coordinates of P, Q and R are (π/10, 0), (3π/5, 0), 11π/10, 0) respectively, find the values of a and b.

9 (i)
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