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Edexcel GCE Core Mathematics C3 Advanced January 2010




 

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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 = e2x sec 3x,
(b) find dy/dx

The curve with equation y = e2x 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
cosec2 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) 3x e7x + 2 = 15

(ii) The functions f and g are defined by
f (x) = e2x + 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)


 

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