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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced January 2010. The questions are given here.

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C3 Edexcel Core Mathematics January 2010 Question 1

Algebraic Fractions

1. Express

(x + 1)/(3x^{2} - 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.

f(x) = x^{3} + 2x^{2} - 3x -11

(a) Show that f(x) = 0 can be rearranged as

The equation f(x) = 0 has one positive root α.

The iterative formula is used to find an approximation to α.

(b) Taking x_{1} = 0, find, to 3 decimal places, the values of x_{2} , x_{3} and x_{4}.

(c) Show that α = 2.057 correct to 3 decimal places.

2(b)
2(c)

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 .

(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.
3(b)

C3 Edexcel Core Mathematics January 2010 Question 4

4. (i) Given that y = ln(x^{2} + 1)/x find dy/dx.

(ii) Given that x = tan y, show that dy/dx = 1/(1 + x^{2})
4 (ii)

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.
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You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced January 2010. The questions are given here.

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)/(3x

as a single fraction in its simplest form.

Numerical solutions and iterative methods

2.

f(x) = x

(a) Show that f(x) = 0 can be rearranged as

The equation f(x) = 0 has one positive root α.

The iterative formula is used to find an approximation to α.

(b) Taking x

(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 .

(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(x

(ii) Given that x = tan y, show that dy/dx = 1/(1 + x

5. Sketch the graph of y = ln|x|, stating the coordinates of any points of intersection with the axes.

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