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Edexcel GCE Core Mathematics C2 January 2012




 

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C2 Edexcel Core Mathematics January 2012 Question 6

Figure 1 shows the graph of the curve with equation

y = 16/x2 - 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.

6 (c) Integration - Area under a graph.



C2 Edexcel Core Mathematics January 2012 Question 7

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.
7 (c)


 
7 (d)(e)
C2 Edexcel Core Mathematics January 2012 Question 8

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 m2

(a) show that

y = (16 - πx2)/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.
8 (d)


 
C2 Edexcel Core Mathematics January 2012 Question 9

(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)
9 (ii) Transformation Trig. Graph.


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