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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C4 Advanced January 2013. The questions are given here.

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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.

Vectors - Intersection of 2 Lines

7. With respect to a fixed origin O, the lines l

l

l

where λ and μ are scalar parameters.

(a) Given that l_{1} and l_{2} 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 1_{1}

(c) find the exact coordinates of P.

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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