Edexcel C4 january 2011 exam answers review

Use integration to find the exact value of

(6)

The current, I amps, in an electric circuit at time t seconds is given by

Use differentiation to find the value of dI/dt when t=3

Give your answer in the form ln a , where a is a constant.

(5)

1. Express 5/(x-1)(3x+2) in partial fractions. (3)
2. Hence \(\int\)5/(x-1)(3x+2)dx, where x>1 (3)
3. Find the particular solution of the differential equation
   (x-1)(3x+2)dy/dx = 5y, x>,

   for which y = 8 at x = 2 . Give your answer in the form y = f (x).(6)

Relative to a fixed origin O, the point A has position vector i − 3j + 2k and the point B has position vector −2i + 2j − k . The points A and B lie on a straight line l.

1. Find AB. (2)
2. Find a vector equation of l. (2)

The point C has position vector 2i + pj− 4k with respect to O, where p is a constant. Given that AC is perpendicular to l, find

3. the value of p,(4)
4. the distance AC.(2)

Use the binomial theorem to expand

in ascending powers of x, up to and including the term in x3 . Give each coefficient as a
simplified fraction. (5)

…where a and b are constants.

In the binomial expansion of f (x), in ascending powers of x, the coefficient of x is 0 and the coefficient of x² is 9/16. Find

1. the value of a and the value of b,(5)
2. the coefficient of x³, giving your answer as a simplified fraction.(3)

The curve C has parametric equations

Find

1. an equation of the normal to C at the point where t = 3, (6)
2. a cartesian equation of C.(3)

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The finite area R, shown in Figure 1, is bounded by C, the x-axis, the line x = ln 2 and the line x = ln 4 . The area R is rotated through 360° about the x-axis.

3. Use calculus to find the exact volume of the solid generated.(6)

1. Given that y = 1/4+√(x-1) complete the table below with values of y corresponding to x = 3 and x = 5 . Give your values to 4 decimal places.
   

   x	2	3	4	5
   y	0.2		0.1745

   (2)

2. Use the trapezium rule, with all of the values of y in the completed table, to obtain an estimate of I, giving your answer to 3 decimal places.(4)
3. Using the substitution x = (u − 4)² + 1, or otherwise, and integrating, find the exact value of I.(8)