Edexcel Core Mathematics C2 June 2013 (II)

 

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

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Edexcel Core Mathematics C2 June 2013 Past Paper

Core 2 Mathematics Edexcel June 2013 Question 6

Figure 3 shows a sketch of part of the curve C with equation

y = x(x + 4)(x – 2)

The curve C crosses the x-axis at the origin O and at the points A and B.
(a) Write down the x-coordinates of the points A and B.

The finite region, shown shaded in Figure 3, is bounded by the curve C and the x-axis.
(b) Use integration to find the total area of the finite region shown shaded in Figure 3.

Core 2 Mathematics Edexcel June 2013 Question 7

7. (i) Find the exact value of x for which log₂(2x) = log₂(5x + 4) -3

(ii) Given that log_a y + 3log_a 2 = 5

express y in terms of a.

Give your answer in its simplest form.

Core 2 Mathematics Edexcel June 2013 Question 8

8. (i) Solve, for –180° < x < 180°,

tan(x – 40°) = 1.5, giving your answers to 1 decimal place.

(ii) (a) Show that the equation
sinθtanθ = 3cosθ + 2

can be written in the form
4cos²θ + 2cosθ – 1 = 0

(b) Hence solve, for 0° < x < 360°,

sinθtanθ = 3cosθ + 2

showing each stage of your working.

Core 2 Mathematics Edexcel June 2013 Question 9

The curve with equation y = x² – 32√x + 20 has a stationary point P.

Use calculus

(a) to find the coordinates of P,

(b) to determine the nature of the stationary point P.

Core 2 Mathematics Edexcel June 2013 Question 10

The circle C has radius 5 and touches the y-axis at the point (0, 9), as shown in Figure 4.

(a) Write down an equation for the circle C, that is shown in Figure 4.

A line through the point P(8, – 7) is a tangent to the circle C at the point T.

(b) Find the length of PT.