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Mathematics — 563-504
Secondary V June 2012
MMaatthh 550044 CCSSTT CCoommppeetteennccyy TTwwoo
UUsseess MMaatthheemmaattiiccaall RReeaassoonniinngg
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
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 2
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 ________________________.
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 3
9. 0x 4 3 2 1 0
0y
____________________
____________________
____________________
____________________
10. The distance from A to J is: ________________________________. 4 0
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 4
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?
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 5
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
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 6
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
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 7
Show your work or explain your reasoning.
ANSWER
The mapping rules are:
II: _____________________________________.
III: ____________________________________.
IV: ____________________________________.
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
x
y
II
III IV
I
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 8
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
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 9
Show your work or explain your reasoning.
ANSWER
The maximum price Pierre can pay for a plane
ticket between Zurich and Rome is
$____________.
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
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 10
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
BIM Société GRICS Page 11
Show your work or explain your reasoning.
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
BIM Société GRICS Page 12
BIM Société GRICS Page 13
ANSWER
The difference between the maximum possible
daily revenues for Super Fun Time! before and
during the renovation period is
$____________________.
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
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 14
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.
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 15
Show your work or explain your reasoning.
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:
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 Cr. 5
40 32 24 16 8 0
Cr. 4 20 16 12 8 4 0
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 16
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.
Mathematics — CST-504 C2 Student Booklet
BIM Société GRICS Page 17
Show your work or explain your reasoning.
CONJECTURE
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
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 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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