Edexcel Core Mathematics C2 January 2011

Questions and Worked Solutions for C2 Edexcel Core Mathematics January 2011.
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Core 2 Mathematics Edexcel January 2011 Question 6

y = 5/(3x² - 2)

(a) Complete the table below, giving the values of y to 2 decimal places.

(b) Use the trapezium rule, with all the values of y from your table, to find an approximate value for

Figure 2 shows a sketch of part of the curve with equation y = 5/(3x² - 2), x > 1

At the points A and B on the curve, x = 2 and x = 3 respectively.

The region S is bounded by the curve, the straight line through B and (2, 0), and the line through A parallel to the y-axis. The region S is shown shaded in Figure 2.

(c) Use your answer to part (b) to find an approximate value for the area of S. Core 2 Mathematics Edexcel January 2011 Question 7
7. (a) Show that the equation 3 sin² x + 7 sin x = cos² x - 4

can be written in the form 4 sin² x + 7 sin x + 3 = 0

(b) Hence solve, for 0 ≤ x < 360°,

3 sin² x + 7 sin x = cos² x - 4

giving your answers to 1 decimal place where appropriate. Core 2 Mathematics Edexcel January 2011 Question 8
8. (a) Sketch the graph of y = 7^x, x is real, showing the coordinates of any points at which the graph crosses the axes.
(b) Solve the equation 7^2x - 4(7^x) + 3 = 0 giving your answers to 2 decimal places where appropriate.

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Core 2 Mathematics Edexcel January 2011 Question 9
9. The points A and B have coordinates (–2, 11) and (8, 1) respectively.

Given that AB is a diameter of the circle C,

(a) show that the centre of C has coordinates (3, 6),

(b) find an equation for C.

(c) Verify that the point (10, 7) lies on C.
(d) Find an equation of the tangent to C at the point (10, 7), giving your answer in the form y = mx + c, where m and c are constants.

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Core 2 Mathematics Edexcel January 2011 Question 10

10. The volume V cm³ of a box, of height x cm, is given by

V = 4x(5 - x)²

(a) Find dV/dx

(b) Hence find the maximum volume of the box.

(c) Use calculus to justify that the volume that you found in part (b) is a maximum.

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