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Edexcel GCE Core Mathematics C3 Advanced June 2012




 

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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C3 Advanced June 2012. The questions are given here.

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C3 Edexcel Core Mathematics June 2012 Question 6

Range of a Function

6. The functions f and g are defined by

f: x |→ ex + 2 , x ∈ ℜ

g : x |→ ln x , x > 0

(a) State the range of f.

(b) Find fg(x) , giving your answer in its simplest form.

(c) Find the exact value of x for which f(2x +3) = 6

(d) Find f−1 , the inverse function of f, stating its domain.

(e) On the same axes sketch the curves with equation y = f(x) and y = f-1(x) coordinates of all the points where the curves cross the axes.

6 (b)(c) Functions



6 (d)(e) Inverse Functions
C3 Edexcel Core Mathematics June 2012 Question 7

7. (a) Differentiate with respect to x,

(i) x1/2ln(3x)

(ii) (1 - 10x)/(2x - 1)5 giving your answer in its simplest form.

(b) Given that y = 3 tan 2y, find dy/dx, in terms of x.

7 (a)(i) Product Rule/Chain Rule


 
7 (a)(ii) Quotient Rule/Chain Rule
7 (b) dy/dx = 1/[dx/dy] rule


C3 Edexcel Core Mathematics June 2012 Question 8

8. f(x) = 7 cos 2x - 24 sin 2x

Given that f(x) = R cos(2x + α) , where R > 0 and 0 < α < 90°,

(a) find the value of R and the value of α.

(b) Hence solve the equation

f(x) = 7 cos 2x - 24 sin 2x = 12.5

for 0 ≤ x < 180° , giving your answers to 1 decimal place.

(c) Express 14 cos2x - 14 sinx cosx in the form a cos 2x + b sin 2x + c, where a, b, and c are constants to be found.

(d) Hence, using your answers to parts (a) and (c), deduce the maximum value of

14 cos2x - 14 sinx cos

8 (a) Rcos( ) method

8(b) Trig. Equation


 
8 (c)
8 (d)


C3 Edexcel Core Mathematics June 2012 Question 9

Transformations of graphs (mod types)

Figure 2 shows part of the curve with equation y = f(x)

The curve passes through the points P(−1.5, 0) and Q(0, 5P) as shown.

On separate diagrams, sketch the curve with equation

(a) y = |f(x)|

(b) y = f(|x|)

(c) y = 2f(3x)

Indicate clearly on each sketch the coordinates of the points at which the curve crosses or meets the axes.

C3 Edexcel Core Mathematics June 2012 Question 10

Trig. Identities

5. (a) Express 4cosec22θ cosec2θ − in terms of sinθ and cosθ.

(b) Hence show that

4cosec22θ cosec2θ = sec2θ

(c) Hence or otherwise solve, for 0 < θ < π,

4cosec22θ cosec2θ = 4

giving your answers in terms of π.



 
5 (c)

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