Edexcel A Level Maths C4 · Core Mathematics 4 January 2011 question paper 6666

Use integration to find the exact value of

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

Find the particular solution of the differential equation

position vector 2i 2j k. The points A and B lie on a straight line l.

Find a vector equation of l.

Given that AC is perpendicular to l, find

the value of p,

the distance AC.

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.

f x = , x where a and b are constants.

the value of a and the value of b,

The curve C has parametric equations

Find

a cartesian equation of C.

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 through360 about the x-axis.

Use calculus to find the exact volume of the solid generated.

⁵

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.

Using the substitution x = u 4² +1, or otherwise, and integrating, find the exact value of I.