Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 1

K11C Taller de Repaso 05-may-2016

1a. [3 marks]

The diagram shows a circle of radius metres. The points ABCD lie on the circumference of the circle.

BC = m, CD = m, AD = m, , and .

Find AC.

1b. [5 marks] (i) Find .

(ii) Hence, find .

1c. [2 marks] Find the area of triangle ADC.

1d. [6 marks] Hence or otherwise, find the total area of the shaded regions.

1e. [4 marks] Hence or otherwise, find the total area of the shaded regions.

3a. [3 marks] The following diagram shows triangle ABC.

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 2

Find AC.

3b. [3 marks] Find .

4a. [2 marks] The following diagram shows a right-angled triangle, , where .

Show that .

4b. [3 marks] Find .

5a. [2 marks] The following diagram shows a circle with centre and radius .

The points A, B y C lie on the circumference of the circle, and radians.

Find the length of the arc .

5b. [2 marks] Find the perimeter of the shaded sector.

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 3

5c. [2 marks] Find the area of the shaded sector.

6a. [4 marks] In triangle , and . The area of the triangle is .

Find the two possible values for .

6b. [3 marks] Given that is obtuse, find .

7a. [3 marks] Consider a circle with centre and radius cm. Triangle is drawn such that its

vertices are on the circumference of the circle.

cm, cm and radians.

Find .

7b. [5 marks] Find .

7c. [6 marks] Hence or otherwise, find the length of arc .

8a. [3 marks] Let . Find an expression for in terms of m.

8b. [1 mark] Let . Find an expression for in terms of m.

8c. [2 marks] Let . Find an expression for in terms of m.

9a. [3 marks] The following diagram shows a circular play area for children.

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 4

The circle has centre O and a radius of 20 m, and the points A, B, C and D lie on the circle. Angle AOB is 1.5

radians.

Find the length of the chord [AB].

9b. [2 marks] Find the area of triangle AOB.

9c. [3 marks] Angle BOC is 2.4 radians.

Find the length of arc ADC.

9d. [3 marks] Angle BOC is 2.4 radians.

Find the area of the shaded region.

9e. [4 marks] Angle BOC is 2.4 radians.

The shaded region is to be painted red. Red paint is sold in cans which cost each. One can covers

. How much does it cost to buy the paint?

11a. [4 marks]

The following diagram shows a triangle ABC.

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 5

, radians , , , where .

(i) Show that .

(ii) Find p .

11b. [1 mark] Consider the circle with centre B that passes through the point C. The circle cuts the line

CA at D, and is obtuse. Part of the circle is shown in the following diagram.

Write down the length of BD.

11c. [4 marks]

Find .

11d. [6 marks]

(i) Show that radians, correct to 2 decimal places.

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 6

(ii) Hence, find the area of the shaded region.

12a. [3 marks]

The following diagram shows a triangle ABC.

The area of triangle ABC is cm , AB cm , AC cm and .

Find .

12b. [3 marks] Find BC.

13. [6 marks] Celeste wishes to hire a taxicab from a company which has a large number of taxicabs.

The taxicabs are randomly assigned by the company.

The probability that a taxicab is yellow is 0.4.

The probability that a taxicab is a Fiat is 0.3.

The probability that a taxicab is yellow or a Fiat is 0.6.

Find the probability that the taxicab hired by Celeste is not a yellow Fiat.

14a. [3 marks] Bill and Andrea play two games of tennis. The probability that Bill wins the first game is .

If Bill wins the first game, the probability that he wins the second game is .

If Bill loses the first game, the probability that he wins the second game is .

Copy and complete the following tree diagram. (Do not write on this page.)

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 7

14b. [2 marks] Find the probability that Bill wins the first game and Andrea wins the second game.

14c. [4 marks] Find the probability that Bill wins at least one game.

14d. [5 marks] Given that Bill wins at least one game, find the probability that he wins both games.

15a. [2 marks] The following table shows the average weights ( y kg) for given heights (x cm) in a

population of men.

Heights (x cm) 165 170 175 180 185

Weights (y kg) 67.8 70.0 72.7 75.5 77.2

The relationship between the variables is modelled by the regression equation .

Write down the value of and of .

15b. [2 marks] The relationship between the variables is modelled by the regression equation

.

Hence, estimate the weight of a man whose height is 172 cm.

15c. [1 mark] Write down the correlation coefficient.

15d. [2 marks] State which two of the following describe the correlation between the variables.

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 8

strong zero Positive

negative no

correlation

Weak

16a. [1 mark] The weights in grams of 80 rats are shown in the following cumulative frequency diagram.

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 9

16b. [3 marks] Find the percentage of rats that weigh 70 grams or less.

16c. [2 marks] The same data is presented in the following table.

Weights Grams

Frequency

Write down the value of .

16d. [2 marks] The same data is presented in the following table.

Weights Grams

Frequency

Find the value of .

16e. [3 marks] The same data is presented in the following table.

Weights Grams

Frequency

Use the values from the table to estimate the mean and standard deviation of the weights.

16f. [2 marks] Assume that the weights of these rats are normally distributed with the mean and

standard deviation estimated in part (c).

Find the percentage of rats that weigh 70 grams or less.

16g. [3 marks] Assume that the weights of these rats are normally distributed with the mean and

standard deviation estimated in part (c).

A sample of five rats is chosen at random. Find the probability that at most three rats weigh 70 grams or

less.

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 10

17a. [2 marks] The following table shows the amount of fuel ( litres) used by a car to travel certain

distances ( km).

Distance (x km)

40 75 120 150 195

Amount of fuel (y litres)

3.6 6.5 9.9 13.1 16.2

This data can be modelled by the regression line with equation .

Write down the value of and of .

17b. [1 mark] Explain what the gradient represents.

17c. [2 marks] Use the model to estimate the amount of fuel the car would use if it is driven km.

18a. [2 marks] Let and be independent events, where and . Find

.

18b. [2 marks] Find .

18c. [1 mark] On the following Venn diagram, shade the region that represents .

18d. [2 marks] Find .

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 11

19a. [3 marks] A forest has a large number of tall trees. The heights of the trees are normally distributed

with a mean of metres and a standard deviation of metres. Trees are classified as giant trees if they are

more than metres tall.

A tree is selected at random from the forest.

Find the probability that this tree is a giant.

19b. [3 marks] A tree is selected at random from the forest.

Given that this tree is a giant, find the probability that it is taller than metres.

19c. [2 marks] Two trees are selected at random. Find the probability that they are both giants.

19d. [3 marks] trees are selected at random.

Find the expected number of these trees that are giants.

19e. [3 marks] trees are selected at random.

Find the probability that at least of these trees are giants.

20a. [2 marks] The following is a cumulative frequency diagram for the time t, in minutes, taken by 80

students to complete a task.

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 12

Find the number of students who completed the task in less than 45 minutes.

20b. [3 marks] Find the number of students who took between 35 and 45 minutes to complete the task.

20c. [2 marks] Given that 50 students take less than k minutes to complete the task, find the value of .

21a. [2 marks] The time taken for a student to complete a task is normally distributed with a mean of

minutes and a standard deviation of minutes.

A student is selected at random. Find the probability that the student completes the task in less than

minutes.

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016 13

21b. [5 marks] The probability that a student takes between and minutes is . Find the value of

.

22a. [4 marks] Samantha goes to school five days a week. When it rains, the probability that she goes to

school by bus is 0.5. When it does not rain, the probability that she goes to school by bus is 0.3. The

probability that it rains on any given day is 0.2.

On a randomly selected school day, find the probability that Samantha goes to school by bus.

22b. [3 marks] Given that Samantha went to school by bus on Monday, find the probability that it was

raining.

22c. [2 marks] In a randomly chosen school week, find the probability that Samantha goes to school by

bus on exactly three days.

22d. [5 marks] After school days, the probability that Samantha goes to school by bus at least once is

greater than . Find the smallest value of .

Printed for Colegio Aleman de Barranquilla © International Baccalaureate Organization 2016

International Baccalaureate® - Baccalauréat International® - Bachillerato Internacional®