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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.

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^{x} e^{3x+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

7 (c) Unusual functions equation

7 (d)

C3 Edexcel Core Mathematics June 2013 Question 8

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^{–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 can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for A Level Maths

Math Worksheets

Are you looking for A-level Maths help?

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.

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. Solving an Exponential equation

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) Unusual functions equation

7 (d)

C3 Edexcel Core Mathematics June 2013 Question 8

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°.

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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