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

Related Topics:

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

Edexcel Core Mathematics C3 January 2011 Past Paper

C3 Mathematics Edexcel January 2011 Question 1

1. (a) Express 7 cos x - 24 sin x in the form R cos (x + α) where R > 0 and 0 < α < π/2

Give the value of α to 3 decimal places.

(b) Hence write down the minimum value of 7 cos x – 24 sin x.

(c) Solve, for 0 ≤ x < 2π, the equation

7 cos x – 24 sin x = 10

giving your answers to 2 decimal places.

1 (a) Trigonometry

2. (a) Express

(4x -1)/[2(x -1)] - 3/[2(x - 1)(2x - 1)]

as a single fraction in its simplest form.

Given that

f(x) =
(4x -1)/[2(x -1)] - 3/[2(x - 1)(2x - 1)] - 2,
x > 1

(b) show that f(x) = 3/(2x -1)

(c) Hence differentiate f(x) and find f'(2).

2(b)

C3 Mathematics Edexcel January 2011 Question 3

3. Find all the solutions of

2 cos 2θ = 1 – 2 sin θ

in the interval 0 ≤ θ < 360°.

4. Joan brings a cup of hot tea into a room and places the cup on a table. At time t minutes after Joan places the cup on the table, the temperature, θ °C, of the tea is modelled by the equation

θ = 20 + Ae^{-kt} ,

where A and k are positive constants.

Given that the initial temperature of the tea was 90°C,

(a) find the value of A.

The tea takes 5 minutes to decrease in temperature from 90°C to 55°C.

(b) Show that k = 1/5 ln2.

(c) Find the rate at which the temperature of the tea is decreasing at the instant when t = 10. Give your answer, in °C per minute, to 3 decimal places.

4(a)4 (b)

C3 Mathematics Edexcel January 2011 Question 5

Figure 1 shows a sketch of part of the curve with equation y = f(x) , where

f(x) = (8 - x)ln x , x > 0

The curve cuts the x-axis at the points A and B and has a maximum turning point at Q, as shown in Figure 1.

(a) Write down the coordinates of A and the coordinates of B.

(b) Find f'(x)

(c) Show that the x-coordinate of Q lies between 3.5 and 3.6

(d) Show that the x-coordinate of Q is the solution of

x = 8/(1 + ln x)To find an approximation for the x-coordinate of Q, the iteration formula

x

is used.

(e) Taking x_{0} = 3.55, find the values of x_{1}, x_{2} and x_{3}.

Give your answers to 3 decimal places. 5(a)

5 (c)

5 (e)

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

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.

data-ad-region="y21">