Edexcel GCE Core Mathematics C3 Advanced June 2012
More Lessons for A Level Maths
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Questions 6 - 8 Previous Questions 1-5
C3 Edexcel Core Mathematics June 2013 Question 6
Solving a natural log equation
- 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
C3 Edexcel Core Mathematics June 2013 Question 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
Range and Composite Functions.
Inverse of a Function
Unusual functions equation
C3 Edexcel Core Mathematics June 2013 Question 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 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°.
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