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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced January 2013. The questions are given here.
C3 Edexcel Core Mathematics January 2013 Question 1
Chain Rule Application
C3 Edexcel Core Mathematics January 2013 Question 2
2. g(x) = ex-1 + x - 6
(a) Show that the equation g(x) = 0 can be written as
x = ln(6 -x) + 1, x < 6
The root of g(x) = 0 is α.
The iterative formula
xn + 1 = ln(6 -xn) + 1, x0 = 2
is used to find an approximate value for α.
(b) Calculate the values of x1 , x2 and x3 to 4 decimal places.
(c) By choosing a suitable interval, show that α = 2.307 correct to 3 decimal places.
C3 Edexcel Core Mathematics January 2013 Question 3
Functions - Transformation of Graphs
Figure 1 shows part of the curve with equation y = f(x), x ∈ ℜ.
The curve passes through the points Q(0, 2) and P(−3, 0) as shown.
(a) Find the value of ff(−3) .
On separate diagrams, sketch the curve with equation
(b) y = f-1(x)
(c) y = f(|x|) - 2
(d) y = 2 f(½ x)
Indicate clearly on each sketch the coordinates of the points at which the curve crosses or meets the axes.
C3 Edexcel Core Mathematics January 2013 Question 4
4. (a) Express 6 cos θ + 8 sin θ in the form Rcos(θ - α), where R > 0 and 0 < α < π/2
Give the value of α to 3 decimal places.
(b) p(θ) = 4/(12 + 6cosθ + 8 sinθ, 0 ≤ θ ≤ 2π
(i) the maximum value of p(θ),
(ii) the value of θ at which the maximum occurs.
C3 Edexcel Core Mathematics January 2013 Question 5
Differentiation - Product and Chain Rule
5. (i) Differentiate with respect to x
(a) y = x3ln2x
(b) y = (x + sin2x)3
Given that x = cot y ,
(ii) show that dy/dx = -1/(1 + x2)
5(i)(b) Differentiation - Chain Rule
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