Edexcel A Level Maths C4 · Core Mathematics 4 June 2010 question paper 6666

Figure 1 shows part of the curve with equation y = √(0.75 + cos² 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

Complete the table with values of y corresponding to x = and x =

Use the trapezium rule

with the values of y at x 0, x = and x = to find an estimate of the area of R. Give your answer to 3 decimal places.

further estimate of the area of R. Give your answer to 3 decimal places.

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

A curve C has equation

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

A curve C has parametric equations

Find the x-coordinate of P.

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

term in x². Give each coefficient as a simplified fraction.

₂₂ f(θ) = 4 cos θ – 3 sin θ

Given that l₁ and l₂ meet at the point C, find

the coordinates of C.

The point A is the point on l₁ where λ = 0 and the point B is the point on l₂ where μ = –1.

Find the size of the angle ACB. Give your answer in degrees to 2 decimal places.

Hence, or otherwise, find the area of the triangle ABC.

Figure 2 shows a cylindrical water tank. The diameter of a circular cross-section of the tank is 6 m. Water is flowing into the tank at a constant rate of 0.48π m³ min¹. At time t minutes, the depth of the water in the tank is h metres. There is a tap at a point T at the bottom of the tank. When the tap is open, water leaves the tank at a rate of 0.6πh m³ min¹.

Show that t minutes after the tap has been opened

When t 0, h 0.2

Find the value of t when h 0.5