Questions and Video Solutions for C4 Edexcel Core Mathematics June 2010Related Topics:
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.
2. Using the substitution u = cos x + 1, or otherwise, show that
∫ecos x + 1 sin x dx = e(e - 1)
3. A curve C has equation 2x + y2 = 2y
Find the exact value of dx/dy at the point on C with coordinates (3, 2).
4. A curve C has parametric equations
x = sin2t, y = 2tan t, 0 ≤ t < π/2
(a) Find dy/dx in terms of t.
The tangent to C at the point where t = π/3 cuts the x-axis at the point P.
(b) Find the x-coordinate of P.
(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.