# Edexcel GCE Core Maths C3 Advanced June 2013

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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. (Part 2)

Questions 6 - 8 Previous Questions 1-5

C3 Edexcel Core Mathematics June 2013 Question 6
Solving a natural log equation

1. Find algebraically the exact solutions to the equations
(a) ln(4 – 2x) + ln(9 – 3x) = 2ln(x + 1), –1 < x < 2
(b) 2x e3x+1 = 10
Give your answer to (b) in the form (a + ln b)/(c + ln d) where a, b, c and d are integers.

Solving an Exponential equation
6. (b)

C3 Edexcel Core Mathematics June 2013 Question 7

1. 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

Range and Composite Functions.

Inverse of a Function
7. (c)

Unusual functions equation
7. (d)

C3 Edexcel Core Mathematics June 2013 Question 8

1. 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–1.
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–1 and she moves in a straight line, which makes an angle θ, 0 < θ < 150°, with the edge of the road, as shown in Figure 2.

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 θ, given that 0 < θ < 150°.
1. (b)
1. (c)
1. (d)

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