 # Edexcel GCE Core Maths C4 Advanced June 2013

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

Differential Equation

6. Water is being heated in a kettle. At time t seconds, the temperature of the water is θ°C.

The rate of increase of the temperature of the water at any time t is modelled by the differential equationdθ/dt = λ(120 - θ), θ ≤ 100 where λ is a positive constant.

Given that θ = 20 when t = 0,
(a) solve this differential equation to show that θ = 120 – 100e–λt

When the temperature of the water reaches 100 °C, the kettle switches off.
(b) Given that λ = 0.01, find the time, to the nearest second, when the kettle switches off.

6(b)

C4 Edexcel Core Mathematics June 2013 Question 7

Implicit Differentiation

7. A curve is described by the equation x2 + 4xy + y2 + 27 = 0

(a) Find dy/dx in terms of x and y.

A point Q lies on the curve.

The tangent to the curve at Q is parallel to the y-axis.

Given that the x coordinate of Q is negative,

(b) use your answer to part (a) to find the coordinates of Q.

7(b)Tangent parallel to the y-axis.

C4 Edexcel Core Mathematics June 2013 Question 8

Vector Equation of a Line

8. With respect to a fixed origin O, the line l has equation

r , where λ is a scalar parameter.

The point A lies on l and has coordinates (3, – 2, 6).

The point P has position vector (–p i + 2p k) relative to O, where p is a constant.

Given that vector PA is perpendicular to l,

(a) find the value of p.

Given also that B is a point on l such that ∠BPA = 45°,

(b) find the coordinates of the two possible positions of B.

8(b) Working with vector equation of a line

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