Edexcel GCE Core Mathematics C4 Advanced January 2013
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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C4 Advanced January 2013. The questions are given here.
C4 Edexcel Core Mathematics January 2013 Question 1
Binomial Expansion
- Given
f(x) = (2 + 3x)–3, |x| < 2/3 find the binomial expansion of f(x), in ascending powers of x, up to and including the term in x3.
Give each coefficient as a simplified fraction.
C4 Edexcel Core Mathematics January 2013 Question 2
Integration
2. (a) Use integration to find
∫ 1/x3 ln x dx (b) Hence calculate
C4 Edexcel Core Mathematics January 2013 Question 3
3. Express
(9x2 + 20x -10)/[(x + 2)(3x -1)]
in partial fractions.
C4 Edexcel Core Mathematics January 2013 Question 4
Trapezium Rule
Figure 1 shows a sketch of part of the curve with equation y = x/(1 + √x). The finite region R, shown shaded in Figure 1, is bounded by the curve, the x-axis, the line with equation x = 1 and the line with equation x = 4.
(a) Complete the table with the value of y corresponding to x = 3, giving your answer to 4 decimal places.
(b) Use the trapezium rule, with all the values of y in the completed table, to obtain an estimate of the area of the region R, giving your answer to 3 decimal places.
(c) Use the substitution u = 1 + √x, to find, by integrating, the exact area of R.
4 (c) Integration (substitution)
C4 Edexcel Core Mathematics January 2013 Question 5
Parametric Equations
Figure 2 shows a sketch of part of the curve C with parametric equations x = 1 - ½t, y = 2t - 1
The curve crosses the y-axis at the point A and crosses the x-axis at the point B.
(a) Show that A has coordinates (0, 3).
(b) Find the x coordinate of the point B.
(c) Find an equation of the normal to C at the point A.
The region R, as shown shaded in Figure 2, is bounded by the curve C, the line x = –1 and the x-axis.
(d) Use integration to find the exact area of R.
5 (c) Normal to Parametric Curve
5(d) Area under a Parametric Graph
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