Edexcel GCE Core Mathematics C4 Advanced June 2013
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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C4 Advanced June 2013. The questions are given here.
C4 Edexcel Core Mathematics June 2013 Question 1
Integration by Parts
1. (a) Find ∫x2 ex dx
(b) Hence find the exact value of
C4 Edexcel Core Mathematics June 2013 Question 2Binomial Expansion for non-integer powers
2. (a) Use the binomial expansion to show that
(b) Substitute x = 1/26 into
to obtain an approximation of &radical;3
Give your answer in the form a/b where a and b are integers.
2(b) Root using the Binomial ExpansionTrapezium Rule Figure 1 shows the finite region R bounded by the x-axis, the y-axis, the line π/2
the curve with equation
y = sec (1/2 x), 0 ≤ x ≤ π/2
The table shows corresponding values of x and y for y = sec(1/2 x)
(a) Complete the table above giving the missing value of y to 6 decimal places.
(b) Using the trapezium rule, with all of the values of y from the completed table, find an approximation for the area of R, giving your answer to 4 decimal places.
Region R is rotated through 2π radians about the x-axis.
(c) Use calculus to find the exact volume of the solid formed.
3(c) Volumes of RevolutionC4 Edexcel Core Mathematics June 2013 Question 4
dy/dx for a parametric curve
4. A curve C has parametric equations
x = 2sin t, y = 1 – cos 2t, –π/2 ≤ t ≤ π/2
(a) Find dy/dx at the point where t = π/6
(b) Find a cartesian equation for C in the form
y = f(x), –k ≤ x ≤ k, stating the value of the constant k.
(c) Write down the range of f(x).
4 (b)(c) Parametric to Cartesian form C4 Edexcel Core Mathematics June 2013 Question 5Integration by Substitution
5. (a) Use the substitution x = u2 , u > 0, to show that
(b) Hence show that
where a and b are integers to be determined.
5 (b) More QuestionsRotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
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