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 2
Binomial 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 Expansion
C4 Edexcel Core Mathematics June 2013 Question 3
Trapezium 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 Revolution
C4 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 5
Integration 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)
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