Questions and Worked Solutions for C2 Edexcel Core Mathematics January 2013.

Edexcel Core Mathematics C2 January 2013 Past Paper

Core 2 Mathematics Edexcel January 2013 Question 6

6. Given that

2log_{2}(x + 15) - log_{2}x = 6

(a) Show that

x^{2} - 34x + 225 = 0

(b) Hence, or otherwise, solve the equation

2log_{2}(x + 15) - log_{2}x = 6

The triangle XYZ in Figure 1 has XY = 6 cm, YZ = 9 cm, ZX = 4 cm and angle ZXY = α. The point W lies on the line XY.

The circular arc ZW, in Figure 1 is a major arc of the circle with centre X and radius 4 cm.

(a) Show that, to 3 significant figures, α = 2.22 radians.

(b) Find the area, in cm^{2}, of the major sector XZWX.

The region enclosed by the major arc ZW of the circle and the lines WY and YZ is shown shaded in Figure 1.

Calculate

(c) the area of this shaded region,

(d) the perimeter ZWYZ of this shaded region.

8. The curve C has equation y = 6 - 3x - 4/x

(a) Use calculus to show that the curve has a turning point P when x = √ 2

(b) Find the x-coordinate of the other turning point Q on the curve.

(c) Find d^{2}y/dx^{2}

(d) Hence or otherwise, state with justification, the nature of each of these turning points P and Q.

The finite region R, as shown in Figure 2, is bounded by the x-axis and the curve with

equation

y = 27 - 2x - 9√x - 16/x^{2} , x > 0

The curve crosses the x-axis at the points (1, 0) and (4, 0).

(a) Complete the table below, by giving your values of y to 3 decimal places.

(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.

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