Questions and Worked Video Solutions for C3 Edexcel Core Mathematics June 2011.

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Edexcel Core Mathematics C3 June 2011 Past Paper

C3 Mathematics Edexcel June 2011 Question 1

1. Differentiate with respect to x

(a) ln(x^{2} + 3x + 5)

(b) cos x /x^{2}

f(x) = 2sin (x

(a) Show that f (x) = 0 has a root Į between x = 0.75 and x = 0.85

The equation f (x) = 0 can be written as x =[arsin(1 - 0.5x)]^{1/2}

(b) Use the iterative formula

x_{n+1} =[arsin(1 - 0.5x_{n})]^{1/2}, x_{0} = 0.8

to find the values of x_{1} , x_{2} and x_{3} , giving your answers to 5 decimal places.

(c) Show that α = 0.80157 is correct to 5 decimal places.

Figure 1 shows part of the graph of y = f (x), x ∈ ℝ.

The graph consists of two line segments that meet at the point R (4, – 3), as shown in Figure 1.

Sketch, on separate diagrams, the graphs of

(a) y = f(x + 4)

(b) = y = |f(-x)|

On each diagram, show the coordinates of the point corresponding to R.

3 (b)

4. The function f is defined by

f: x |→ 4 - ln(x + 2), x ∈ ℝ, x ≥ -1

(a) Find f^{-1}(x)

(b) Find the domain of f^{−1}

The function g is defined by

g: x |→e^{x2}-2, x ∈ ℝ

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

(d) Find the range of fg.

5. The mass, m grams, of a leaf t days after it has been picked from a tree is given by

m = pe

where k and p are positive constants.

When the leaf is picked from the tree, its mass is 7.5 grams and 4 days later its mass is 2.5 grams.

(a) Write down the value of p.

(b) Show that k = 1/4 ln3

(c) Find the value of t when dm/dt = -0.6ln3

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