secondary v june 2012 mmaatthh 550044 ccsstt · mathematics — cst-504 c2 student booklet bim...

Mathematics — 563-504

Secondary V June 2012

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Cultural, Social and Technical Option

Student Booklet

(Parts A, B and C)

Name:

Group:

Time: 3 hours

TEACHER USE ONLY

Part A _______ /24

Part B _______ /16

Part C _______ /60

Total ______ /100

Mathematics — CST-504 C2 Student Booklet

BIM Société GRICS Page 1

1. Write all the required information in this Student Booklet. Answers written in the

Question Booklet will not be evaluated; only the Student Booklet will be evaluated.

2. In Part C you must show all your work to justify your answers. The steps in your procedure must be organized and clearly presented. Always write down your procedure and reasoning along with aspects of the situation that you think are relevant. Do this even if you are unsure of how to complete your solution.

3. Permitted materials

Geometry set (ruler, compass, set square, protractor)

Calculator (with or without graphic display)

Handwritten memory aid prepared by the student prior to the evaluation situation. The memory aid consists of one letter-sized sheet of paper (8½ x 11). Both sides of the sheet may be used. Any mechanical reproduction of this memory aid cannot be used.

Note: Figures have not necessarily been drawn to scale.

The following are the evaluation criteria required to complete the tasks in this booklet.

Evaluation Criteria Competency Two: Uses Mathematical Reasoning

Cr. 1 - Formulation of a conjecture suited to the situation

Cr. 2 – Correct use of appropriate mathematical concepts and processes

Cr. 3 – Proper implementation of mathematical reasoning suited to the situation

Cr. 4 – Proper organization of the steps in an appropriate procedure

Cr. 5 – Correct justification of the steps in an appropriate procedure



Part A

Questions 1 to 6 Darken the letter that corresponds to your answer.

Each question is worth 4 marks.

1. [A] [B] [C] [D]

2. [A] [B] [C] [D]

3. [A] [B] [C] [D]

4. [A] [B] [C] [D]

5. [A] [B] [C] [D]

6. [A] [B] [C] [D]

Part B

Questions 7 to 10 Write your answer in the space provided.

Each question is worth 4 marks.

7. A' (_____, _____) B' (_____, _____) 4 3 2 1 0

8. In order to create an Euler path, we would need to remove 4 0

edge ________________________.



9. 0x 4 3 2 1 0

0y

____________________

____________________

____________________

____________________

10. The distance from A to J is: ________________________________. 4 0



Part C

This part of the examination consists of Questions 11 to 16. For each question, you must show all your work to justify your answer. The work you show on all the pages of Part C will be considered. Your work must be organized and clearly presented and cannot simply involve listing the calculator applications or programs used to obtain results or information. Each question in Part C is worth 10 marks.

11. Honest Rahim’s Cars and Trucks Rahim sells new and used cars and trucks.

There are 80 vehicles in total

There are 55 trucks

If a vehicle is randomly selected, the probability of it being new is 0.625

If a new vehicle is randomly selected, the probability of it being a car is 20%

How many used trucks does Rahim have?



Show your work or explain your reasoning.

ANSWER

Rahim has ________________ used trucks.

Uses mathematical reasoning

Observable indicators correspond to level

Evalu

ati

on

Cri

teri

a

LEVEL A B C D E

Cr. 3 40 32 24 16 8 0

Cr. 2 40 32 24 16 8 0

Cr. 4 Cr. 5

20 16 12 8 4 0



12. The Mighty Kites You have been hired as a graphic designer for your summer job after graduating from

Secondary 5. One of your first tasks is to design a logo based on the polygon located in

the Cartesian plane below:

You must create a design that adheres to the following criteria:

There must be one similar polygon constructed in each quadrant of the plane.

The initial figure must be used as the starting point for each transformation.

There must be two polygons that are the same size as the initial figure, and

one other whose dimensions are twice the original.

Construct the other 3 polygons in the logo and give the mapping rules that allow you

to construct them.

x

y




ANSWER

The mapping rules are:

II: _____________________________________.

III: ____________________________________.

IV: ____________________________________.



Evalu

ati

on

Cri

teri

a

LEVEL A B C D E

Cr. 3 40 32 24 16 8 0

Cr. 2 40 32 24 16 8 0

Cr. 4 Cr. 5

20 16 12 8 4 0

x

y

II

III IV

I



13. Eurotrip 2012 Pierre is planning a summer vacation in Europe and would like to visit seven European

cities once and only once, starting with Paris. Pierre has a budget of $400 to spend on

travel between the cities. Pierre can travel by train or by plane between each city. The

graphs below indicate the one-way cost of traveling by train and by plane between the

cities:

Cost of traveling by Train Cost of traveling by Plane

What is the maximum price Pierre can pay for a plane ticket between Zurich and

Rome?

Zurich

Rome

Antwerp

Paris

Frankfurt

Luxembourg

Brussels

140

90

80

90

200

175 240

40

25

55

150

Rome

Paris

Brussels

Luxembourg

Antwerp

Frankfurt

Zurich

80

80

?

90

240 400

110

110

100

115




ANSWER

The maximum price Pierre can pay for a plane

ticket between Zurich and Rome is

$____________.



Evalu

ati

on

Cri

teri

a

LEVEL A B C D E

Cr. 3 40 32 24 16 8 0

Cr. 2 40 32 24 16 8 0

Cr. 4 Cr. 5

20 16 12 8 4 0



14. Super Fun Time! “Super Fun Time!” is a large amusement park. A ticket to get into the amusement park

costs $60 per adult and $37 per youth. Super Fun Time! can accommodate 24 000

customers per day. The number of adults in the park is no more than the number of

youths. There are at least 6000 adults and at most 16 000 youths visiting the park per

day.

On August 1st a section of the amusement park will be closed for renovations, and as a

result, Super Fun Time! will only be able to accommodate 18 000 customers per day.

What is the difference between the maximum possible daily revenues for Super Fun Time! before and during the renovation period? Let x: the number of adults per day Let y: the number of youths per day



0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

(×1000)

y

x


ANSWER

The difference between the maximum possible

daily revenues for Super Fun Time! before and

during the renovation period is

$____________________.



Evalu

ati

on

Cri

teri

a

LEVEL A B C D E

Cr. 3 40 32 24 16 8 0

Cr. 2 40 32 24 16 8 0

Cr. 4 Cr. 5

20 16 12 8 4 0



15. Valid Voting The student government at a local high school is planning an end of the year carnival for

the student body. Along with various other activities there will be sports competitions.

The sports facilities at the school allows for the possibly of soccer, rugby, baseball and

lacrosse. However, the budget only allows for two of the sporting competitions to take

place.

The executive could not decide on which sports to include so they asked all the students

in the school to vote. Students were given a ballot listing the four sports and asked to

indicate his or her first, second, third and fourth choice with no ties allowed.

Preference Schedule for the sports voting

Number of students (who ranked the sport in the

order shown) 180 220 150 160

First choice soccer rugby baseball lacrosse

Second choice baseball soccer lacrosse soccer

Third choice rugby lacrosse rugby baseball

Fourth choice lacrosse baseball soccer rugby

The student government, looking at the results, said that rugby and soccer were the top

choices.

Using at least 2 voting procedures, prove whether or not rugby and soccer are the top

two preferences of the student population.




ANSWER

Rugby and soccer ARE the top two preferences of the student population.

Rugby and soccer ARE NOT the top two preferences of the student population. Justification:



Evalu

ati

on

Cri

teri

a

LEVEL A B C D E

Cr. 3 40 32 24 16 8 0

Cr. 2 Cr. 5

40 32 24 16 8 0

Cr. 4 20 16 12 8 4 0



16. Prism Conjecture A square based right prism without a top surface has a fixed volume of 256 cm3.

The length of the base is an integer between 5 and 10 cm.

Formulate a conjecture describing the mathematical relationship between the length

of the base and the height of this prism in order that the surface area of this prism is

minimized.

N.B. Do not include the top surface of the cube.




CONJECTURE

______________________________________

______________________________________

______________________________________

______________________________________

______________________________________



Evalu

ati

on

Cri

teri

a

LEVEL A B C D E

Cr. 3 40 32 24 16 8 0

Cr. 2 20 16 12 8 4 0

Cr. 4 Cr. 5

20 16 12 8 4 0

Cr. 1 20 16 12 8 4 0

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