 # Edexcel GCE Core Maths C4 Advanced January 2013

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C4 Edexcel Core Mathematics January 2013 Question 6

Trig. Equation

Figure 3 shows a sketch of part of the curve with equation y = 1 – 2cos x, where x is measured in radians. The curve crosses the x-axis at the point A and at the point B.

(a) Find, in terms of , the x coordinate of the point A and the x coordinate of the point B.

The finite region S enclosed by the curve and the x-axis is shown shaded in Figure 3. The region S is rotated through 2π radians about the x-axis.

(b) Find, by integration, the exact value of the volume of the solid generated.

6(b)Volume of Revolution

C4 Edexcel Core Mathematics January 2013 Question 7

Vectors - Intersection of 2 Lines

7. With respect to a fixed origin O, the lines l1 and l2 are given by the equations
l1 : r = (9i + 13j – 3k) + λ(i + 4j – 2k)
l2 : r = (2i – j + k) + μ(2i + j + k)

where λ and μ are scalar parameters.

(a) Given that l1 and l2 meet, find the position vector of their point of intersection.

(b) Find the acute angle between l1 and l2 giving your answer in degrees to 1 decimal place.

Given that the point A has position vector 4i + 16j – 3k and that the point P lies on lthat AP is perpendicular to 11

(c) find the exact coordinates of P.

7(b) 7(c)

C4 Edexcel Core Mathematics January 2013 Question 8

Solving a Differential Equation Solving a Differential Equation 8. A bottle of water is put into a refrigerator. The temperature inside the refrigerator remains constant at 3 °C and t minutes after the bottle is placed in the refrigerator the temperature of the water in the bottle is θ°C.

The rate of change of the temperature of the water in the bottle is modelled by the differential equation,

dθ/dt = (3 - θ)/125

(a) By solving the differential equation, show that,

θ = Ae–0.008t + 3

where A is a constant.

Given that the temperature of the water in the bottle when it was put in the refrigerator was 16 °C,

(b) find the time taken for the temperature of the water in the bottle to fall to 10 °C, giving your answer to the nearest minute.

8(b) Exponential Decay

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