Edexcel A Level Maths C4 · Core Mathematics 4 June 2012 question paper 6666

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

where a and b are constants.

Figure 1 shows a metal cube which is expanding uniformly as it is heated. At time t seconds, the length of each edge of the cube is x cm, and the volume of the cube is V cm³.

Given that the volume, V cm³, increases at a constant rate of 0.048 cm³s^–1,

find the rate of increase of the total surface area of the cube, in cm²s^–1, when x = 8

Find the binomial expansion of f (x) in ascending powers of x, up to and including the term in x³. Give each coefficient in its simplest form.

Use your answer to part (a) to find the binomial expansion in ascending powers of x, up to and including the term in x³, of

Given that y = 2 at x = solve the differential equation

The curve C has equation

Find the coordinates of the points on C where = 0.

Figure 2 shows a sketch of the curve C with parametric equations

Show that = kt, where k is a constant to be determined.

Find an equation of the tangent to C at the point where t = Give your answer in the form y = ax + b, where a and b are constants.

Find a cartesian equation of C.

Figure 3 shows a sketch of part of the curve with equation y = ln 2x. The finite region R, shown shaded in Figure 3, is bounded by the curve, the x-axis and the lines x = 1 and x 4

Use the trapezium rule, with 3 strips of equal width, to find an estimate for the area of R, giving your answer to 2 decimal places.

Hence find the exact area of R, giving your answer in the form a ln 2 b, where a and b are exact constants.

Relative to a fixed origin O, the point A has position vector 10 i + 2j + 3k, and the point B has position vector 8 i + 3j + 4k. The line l passes through the points A and B.

Find a vector equation for the line l.

The point C has position vector 3 i + 12j + 3k. The point P lies on l. Given that the vector is perpendicular to l,

find the position vector of the point P.