Edexcel GCE Core Mathematics C3 Advanced June 2013
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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced June 2013. The questions are given here.
C3 Edexcel Core Mathematics June 2013 Question 1
Algebraic Long Division Example
1. Given the identity, find the values of the constants a, b, c, d and e. C3 Edexcel Core Mathematics June 2013 Question 2
Curve sketching involving transformations
2. Given that f(x) = ln x, x > 0
sketch on separate axes the graphs of
(i) y = f(x),
(ii) y = |f(x)|,
(iii) y = –f(x – 4).
Show, on each diagram, the point where the graph meets or crosses the x-axis. In each case, state the equation of the asymptote.
C3 Edexcel Core Mathematics June 2013 Question 3
Trigonometric equations
3. Given that 2cos(x + 50)° = sin(x + 40)°
(a) Show, without using a calculator, that tan x° = 1/3 tan 40°
(b) Hence solve, for 0 ≤ θ < 360, 2cos(2θ + 50)° = sin(2θ + 40)°
giving your answers to 1 decimal place. Solving a trigonometric equation
3 (b) C3 Edexcel Core Mathematics June 2013 Question 4
Turning Points
(a) Using calculus, find the exact coordinates of the turning points on the curve with equation y= f(x).
(b) Show that the equation f(x) = 0 can be written as x = ± 4/5 e–x
The equation f(x) = 0 has a root a , where a = 0.5 to 1 decimal place.
(c) Starting with x0 = 0.5, use the iteration formula xn+1 = 4/5 e-xn
to calculate the values of x1, x2 and x3, giving your answers to 3 decimal places.
(d) Give an accurate estimate for a to 2 decimal places, and justify your answer. 4 (b) Using an Iteration Formula
4 (c) 4 (d)
C3 Edexcel Core Mathematics June 2013 Question 5
Trig. differentiation question
5. Given that x = sec2 3y, 0 < y < π/6
(a) find dy/dx in terms of y.
(b) Hence show that dy/dx = 1/[6x(x - 1)]1/2
(c) Find an expression for d2y/dx2 in terms of x. Give your answer in its simplest form. 2nd Differential Question
5 (c) More Questions
You can use the free Mathway calculator and problem solver 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.
More Lessons for A Level Maths
Math Worksheets
Are you looking for A-level Maths help?
The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced June 2013. The questions are given here.
C3 Edexcel Core Mathematics June 2013 Question 1
Algebraic Long Division Example
1. Given the identity, find the values of the constants a, b, c, d and e. C3 Edexcel Core Mathematics June 2013 Question 2
Curve sketching involving transformations
2. Given that f(x) = ln x, x > 0
sketch on separate axes the graphs of
(i) y = f(x),
(ii) y = |f(x)|,
(iii) y = –f(x – 4).
Show, on each diagram, the point where the graph meets or crosses the x-axis. In each case, state the equation of the asymptote.
Trigonometric equations
3. Given that 2cos(x + 50)° = sin(x + 40)°
(a) Show, without using a calculator, that tan x° = 1/3 tan 40°
(b) Hence solve, for 0 ≤ θ < 360, 2cos(2θ + 50)° = sin(2θ + 40)°
giving your answers to 1 decimal place. Solving a trigonometric equation
3 (b) C3 Edexcel Core Mathematics June 2013 Question 4
Turning Points
(a) Using calculus, find the exact coordinates of the turning points on the curve with equation y= f(x).
(b) Show that the equation f(x) = 0 can be written as x = ± 4/5 e–x
The equation f(x) = 0 has a root a , where a = 0.5 to 1 decimal place.
(c) Starting with x0 = 0.5, use the iteration formula xn+1 = 4/5 e-xn
to calculate the values of x1, x2 and x3, giving your answers to 3 decimal places.
(d) Give an accurate estimate for a to 2 decimal places, and justify your answer. 4 (b) Using an Iteration Formula
4 (c) 4 (d)
C3 Edexcel Core Mathematics June 2013 Question 5
Trig. differentiation question
5. Given that x = sec2 3y, 0 < y < π/6
(a) find dy/dx in terms of y.
(b) Hence show that dy/dx = 1/[6x(x - 1)]1/2
(c) Find an expression for d2y/dx2 in terms of x. Give your answer in its simplest form. 2nd Differential Question
5 (c) More Questions
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