Edexcel GCE Core Mathematics C3 Advanced January 2010
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C3 Edexcel Core Mathematics January 2010 Question 1
Algebraic Fractions
1. Express
(x + 1)/(3x2 - 3) - 1/(3x + 1)
as a single fraction in its simplest form. C3 Edexcel Core Mathematics January 2010 Question 2
Numerical solutions and iterative methods
2. Given f(x) = x3 + 2x2 - 3x - 11
(a) Show that f(x) = 0 can be rearranged as
2. The equation f(x) = 0 has one positive root α.
The iterative formula is used to find an approximation to α.
(b) Taking x1 = 0, find, to 3 decimal places, the values of x2 , x3 and x4.
2 (c) Show that α = 2.057 correct to 3 decimal places.
C3 Edexcel Core Mathematics January 2010 Question 3
3. (a) Express 5 cos x – 3 sin x in the form R cos(x + α), where R > 0 and 0 < α < 1/2 π.
3 (b) Hence, or otherwise, solve the equation
5 cos x – 3 sin x = 4
for 0 ≤ x < 2π, giving your answers to 2 decimal places.
C3 Edexcel Core Mathematics January 2010 Question 4
4. (i) Given that y = ln(x2 + 1)/x find dy/dx.
4 (ii) Given that x = tan y, show that dy/dx = 1/(1 + x2)
C3 Edexcel Core Mathematics January 2010 Question 5
5. Sketch the graph of y = ln|x|, stating the coordinates of any points of intersection with the axes. More Questions
The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced January 2010. Download the questions (pdf).
Related Topics
More Worked Solutions and A-level Maths help
Free Math Worksheets
C3 Edexcel Core Mathematics January 2010 Question 1
Algebraic Fractions
1. Express
(x + 1)/(3x2 - 3) - 1/(3x + 1)
as a single fraction in its simplest form. C3 Edexcel Core Mathematics January 2010 Question 2
Numerical solutions and iterative methods
2. Given f(x) = x3 + 2x2 - 3x - 11
(a) Show that f(x) = 0 can be rearranged as
2. The equation f(x) = 0 has one positive root α.
The iterative formula is used to find an approximation to α.
(b) Taking x1 = 0, find, to 3 decimal places, the values of x2 , x3 and x4.
2 (c) Show that α = 2.057 correct to 3 decimal places.
3. (a) Express 5 cos x – 3 sin x in the form R cos(x + α), where R > 0 and 0 < α < 1/2 π.
3 (b) Hence, or otherwise, solve the equation
5 cos x – 3 sin x = 4
for 0 ≤ x < 2π, giving your answers to 2 decimal places.
C3 Edexcel Core Mathematics January 2010 Question 4
4. (i) Given that y = ln(x2 + 1)/x find dy/dx.
4 (ii) Given that x = tan y, show that dy/dx = 1/(1 + x2)
C3 Edexcel Core Mathematics January 2010 Question 5
5. Sketch the graph of y = ln|x|, stating the coordinates of any points of intersection with the axes. More Questions
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