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

Edexcel Core Mathematics C2 January 2011 Past Paper

y = 5/(3x

(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/(3x^{2} - 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.

7. (a) Show that the equation 3 sin

can be written in the form 4 sin^{2} x + 7 sin x + 3 = 0

(b) Hence solve, for 0 ≤ x < 360°,

3 sin^{2} x + 7 sin x = cos^{2} x - 4

giving your answers to 1 decimal place where appropriate.

8. (a) Sketch the graph of y = 7

(b) Solve the equation 7

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.

10. The volume V cm

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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.