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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced June 2013. The questions are given here.

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Questions 6 - 8

C3 Edexcel Core Mathematics June 2013 Question 6

Solving a natural log equation

6. Find algebraically the exact solutions to the equations

(a) ln(4 – 2x) + ln(9 – 3x) = 2ln(x + 1), –1 < x < 2

(b) 2

Give your answer to (b) in the form (a + ln b)/(c + ln d) where a, b, c and d are integers.

6 (b)

7. The function f has domain –2 ≤ x ≤ 6 and is linear from (–2, 10) to (2, 0) and from (2, 0) to (6, 4). A sketch of the graph of y = f(x) is shown in Figure 1.

(a) Write down the range of f.

(b) Find ff(0).

The function g is defined

(c) Find g^{–1}(x)

(d) Solve the equation gf(x) = 16

7 (c)

7 (d)

8. Kate crosses a road, of constant width 7 m, in order to take a photograph of a marathon runner, John, approaching at 3 m s

Kate is 24 m ahead of John when she starts to cross the road from the fixed point A. John passes her as she reaches the other side of the road at a variable point B, as shown in Figure 2.

Kate’s speed is Vm s

You may assume that V is given by the formula

(a) Express 24sin θ + 7cos θ in the form Rcos(θ – α ), where R and α are constants and where R > 0 and 0 < θ < 90°, giving the value of to 2 decimal places.

Given that θ varies,

(b) find the minimum value of V.

Given that Kate’s speed has the value found in part (b),

(c) find the distance AB.

Given instead that Kate’s speed is 1.68 m s^{–1},

(d) find the two possible values of the angle �, given that 0 < θ < 150°.

8(b)

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