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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

x_{n+1} = 1/sin x_{n} + 1/4, x_{0} = 1.25

to calculate the values of x_{1}, x_{2} and x_{3} , 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 ↦ x^{2} - 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 = (2x^{2} - 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

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More videos, activities and worksheets that are suitable for A Level Maths

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)

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

x

to calculate the values of x

(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)

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 ↦ x

(c) Find fg(2).

(d) Find the range of g.

4 (a) 4 (b) 4 (c) 4 (d)

Figure 1 shows a sketch of the curve C with the equation y = (2x

(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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