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Questions and Video Solutions for C4 Edexcel Core Mathematics June 2010
Figure 1 shows part of the curve with equation y = √(0.75 + cos2x) The finite region R, shown shaded in Figure 1, is bounded by the curve, the y-axis, the x-axis and the line with equation x = π/3
(a) Complete the table with values of y corresponding to x = π/6 and x = π/4
(b) Use the trapezium rule
(i) with the values of y at x = 0, x = π/6 and x = π/3 to find an estimate of the area of R. Give your answer to 3 decimal places.
(ii) with the values of y at x = 0, x = π/12, x = π/6, x = π/4 and x = π/3 to find a further estimate of the area of R. Give your answer to 3 decimal places.
(a) (2x2 + 5x - 10)/(x - 1)(x + 2) ≡ A + B/(x - 1) + C/(x + 2)
Find the values of the constants A, B and C.
(b) Hence, or otherwise, expand (2x2 + 5x - 10)/(x - 1)(x + 2) in ascending powers of x, as far as the term in x2. Give each coefficient as a simplified fraction.
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