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Edexcel Core Mathematics C3 June 2010

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Questions and Worked Solutions for C3 Edexcel Core Mathematics June 2010.
Edexcel Core Mathematics C3 June 2010 Past Paper

C3 Mathematics Edexcel June 2010 Question 1

1. (a) Show that
sin2θ/(1 + cos2θ) = tanθ
(b) Hence find, for –180° ≤ θ < 180°, all the solutions of
2sin2θ/(1 + cos2θ) + 1 = tanθ
Give your answers to 1 decimal place.
1 (a) 1 (b) C3 Mathematics Edexcel June 2010 Question 2

2. A curve C has equation
y = 3/(5 - 3x)2, x ≠ 5/3
The point P on C has x-coordinate 2. Find an equation of the normal to C at P in the form ax + by + c = 0, where a, b and c are integers.
C3 Mathematics Edexcel June 2010 Question 3

3. f(x) = 4cosec x - 4x + 1, where x is in radians.
(a) Show that there is a root α of f(x) = 0 in the interval [1.2, 1.3].
(b) Show that the equation f(x) = 0 can be written in the form
x = 1/sin x + 1/4
(c) Use the iterative formula
xn+1 = 1/sin xn + 1/4, x0 = 1.25
to calculate the values of x1, x2 and x3 , giving your answers to 4 decimal places.
(d) By considering the change of sign of f(x) in a suitable interval, verify that α = 1.291 correct to 3 decimal places.
3 (a) 3 (b) 3 (c) 3 (d)

C3 Mathematics Edexcel June 2010 Question 4

4. The function f is defined by

f: x ↦ |2x -5|, x ∈ ℝ

(a) Sketch the graph with equation y = f(x), showing the coordinates of the points where the graph cuts or meets the axes.
(b) Solve f(x) = 15 + x
The function g is defined by
g: x ↦ x2 - 4x + 1, x ∈ ℝ, 0 ≤ x ≤ 5
(c) Find fg(2).
(d) Find the range of g.
4 (a) 4 (b) 4 (c) 4 (d)

C3 Mathematics Edexcel June 2010 Question 5

Figure 1 shows a sketch of the curve C with the equation y = (2x2 - 5x + 2)e-x
(a) Find the coordinates of the point where C crosses the y-axis.
(b) Show that C crosses the x-axis at x = 2 and find the x-coordinate of the other point where C crosses the x-axis.
(c) Find dy/dx
(d) Hence find the exact coordinates of the turning points of C.
5 (a)(b) 5 (c) 5 (d) More Questions

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