Edexcel Core Mathematics C3 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(x² + 3x + 5)

(b) cos x /x²

1. (b)

C3 Mathematics Edexcel June 2011 Question 2

f(x) = 2sin (x²) + x - 2, 0 ≤ x < 2π

(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, x₀ = 0.8

to find the values of x₁ , x₂ and x₃ , giving your answers to 5 decimal places.

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

2.(b)

2. (c)

C3 Mathematics Edexcel June 2011 Question 3

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)

C3 Mathematics Edexcel June 2011 Question 4

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.

4. (b)

4. (c)

4. (d)

C3 Mathematics Edexcel June 2011 Question 5

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

m = pe^kt

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

5. (c)

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