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### C4 Mathematics Edexcel June 2010 Question 1

Figure 1 shows part of the curve with equation y = √(0.75 + cos^{2}x)
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.### C4 Mathematics Edexcel June 2010 Question 2

2. Using the substitution u = cos x + 1, or otherwise, show that

∫e^{cos x + 1} sin x dx = e(e - 1)

### C4 Mathematics Edexcel June 2010 Question 3

3. A curve C has equation 2^{x} + y^{2} = 2y

Find the exact value of dx/dy at the point on C with coordinates (3, 2).### C4 Mathematics Edexcel June 2010 Question 4

4. A curve C has parametric equations

x = sin^{2}t, 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.### C4 Mathematics Edexcel June 2010 Question 5

(a) (2x^{2} + 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 (2x^{2} + 5x - 10)/(x - 1)(x + 2) in ascending powers of x, as far as the term in x^{2}. Give each coefficient as a simplified fraction.

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Questions and Video Solutions for C4 Edexcel Core Mathematics June 2010

Edexcel Core Mathematics C4 June 2010 Past Paper

(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.

∫e

Find the exact value of dx/dy at the point on C with coordinates (3, 2).

x = sin

(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.

Find the values of the constants A, B and C.

(b) Hence, or otherwise, expand (2x

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