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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.

Questions for the Edexcel GCE Core Mathematics C3 Advanced January 2010 {PDF}.

C3 Edexcel Core Mathematics January 2010 Question 6

Figure 1 shows a sketch of the graph of y = f (x).

The graph intersects the y-axis at the point (0, 1) and the point A(2, 3) is the maximum

turning point.

Sketch, on separate axes, the graphs of

(i) y = f(–x) + 1,

(ii) y = f(x + 2) + 3,

(iii) y = 2f(2x).

On each sketch, show the coordinates of the point at which your graph intersects the y-axis and the coordinates of the point to which A is transformed. C3 Edexcel Core Mathematics January 2010 Question 7

7. (a) By writing sec x as 1/cos x, show that d(sec x)/dx =sec x tan x

Given that y = e^{2x} sec 3x,

(b) find dy/dx

The curve with equation y = e^{2x} sec 3x, -π/6 < x < π/6, has a minimum turning point at (a, b).

(c) Find the values of the constants a and b, giving your answers to 3 significant figures.

7 (b) 7 (c)

C3 Edexcel Core Mathematics January 2010 Question 8

8. Solve

cosec^{2} 2x – cot 2x = 1

for 0° ≤ x ≤ 180°. C3 Edexcel Core Mathematics January 2010 Question 9

9. (i) Find the exact solutions to the equations

(a) ln (3x – 7) = 5

(b) 3^{x} e^{7x + 2} = 15

(ii) The functions f and g are defined by

f (x) = e^{2x }+ 3, x ∈ ℜ

g(x) = ln (x – 1), x ∈ ℜ, x > 1

(a) Find f^{ –1} and state its domain.

(b) Find fg and state its range. 9 (i)(b) 9 (ii)(a) 9 (ii)(b)

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 Worked Solutions and A-level Maths help

Free Math Worksheets

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

Questions for the Edexcel GCE Core Mathematics C3 Advanced January 2010 {PDF}.

C3 Edexcel Core Mathematics January 2010 Question 6

Figure 1 shows a sketch of the graph of y = f (x).

The graph intersects the y-axis at the point (0, 1) and the point A(2, 3) is the maximum

turning point.

Sketch, on separate axes, the graphs of

(i) y = f(–x) + 1,

(ii) y = f(x + 2) + 3,

(iii) y = 2f(2x).

On each sketch, show the coordinates of the point at which your graph intersects the y-axis and the coordinates of the point to which A is transformed. C3 Edexcel Core Mathematics January 2010 Question 7

7. (a) By writing sec x as 1/cos x, show that d(sec x)/dx =sec x tan x

Given that y = e

(b) find dy/dx

The curve with equation y = e

(c) Find the values of the constants a and b, giving your answers to 3 significant figures.

7 (b) 7 (c)

8. Solve

cosec

for 0° ≤ x ≤ 180°. C3 Edexcel Core Mathematics January 2010 Question 9

9. (i) Find the exact solutions to the equations

(a) ln (3x – 7) = 5

(b) 3

(ii) The functions f and g are defined by

f (x) = e

g(x) = ln (x – 1), x ∈ ℜ, x > 1

(a) Find f

(b) Find fg and state its range. 9 (i)(b) 9 (ii)(a) 9 (ii)(b)

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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.

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