Part A / Questions 1to6
In the Student Booklet, darken the letter that corresponds to your answer.
Each question is worth 4 marks.
1. Given the following graph:
Which rules for the geometric transformations transform figure 1 to figure 2?
A) / r(0,-90º):(x, y) ® (y, -x) then h(0,2):(x, y) ® (2x, 2y)B) / r(0,90º):(x, y) ® (-y, x) then h(0,½):(x, y) ® (½x, ½y)
C) / sx:(x, y) ® (x,-y) then h(0,½):(x, y) ® (½x, ½y)
D) / sx:(x, y) ® (x, -y) then h(0,2):(x, y) ® (2x, 2y)
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2. The two figures below are equivalent. The circle has a circumference of 37.7 m.
What is the height of the triangle?
A) / 3.14 m / C) / 9.42 mB) / 6.28 m / D) / 18.85 m
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3. Sandeep manages a car detailing shop where the interior and exterior of vehicles are cleaned. The graph below shows the different steps involved in cleaning a car. The value on each edge indicates the numbers of minutes required to complete the corresponding step. The direction of the arrows indicates the order in which the steps must be completed. Several steps can be carried out at the same time.
What is the minimum time that it takes for a car to be completely cleaned at Sandeep's shop?
A) / 17 minutes / C) / 22 minutesB) / 20 minutes / D) / 38 minutes
4. Seven marbles are placed in a vase, four of which are red and the rest yellow.
A student consecutively draws two marbles from the vase without replacement and records their colours.
What is the probability that the student drew one marble of each colour from the vase?
A) / / C) /B) / / D) /
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5. The constraints related to a situation are represented by the following system of inequalities:
Which polygon of constraints represents this situation?
A) / /
C) /
B) / / D) /
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6. The following polygon of constraints represents the solution for an optimizing situation that involves minimizing the cost to download digital music and television episodes.
Let x: the number of song downloads
Let y: the number of television episode downloads
Each song costs $2 to download, while each television episode costs $6 to download.
What solution will minimize the cost that satisfies the polygon of constraints?
A) / (5, 5) / C) / (3, 10)B) / (2, 6) / D) / (6, 6)
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Part B / Questions 7to10
In the Student Booklet, write your answer in the space provided.
Each question is worth 4 marks.
7. The Polygon below undergoes a horizontal scale change of -0.5 and a vertical scale change of3.
What are the coordinates of A' and B' of the image?
BIM § Société GRICS / Page 14 // Mathematics — CST-500.A01 § Student Booklet
8. Given the following diagram:
Name one edge that would need to be removed in order to create an Euler path.
9. Sebastien is working as a tree planter this summer. He plants a combination of both coniferous and deciduous trees. Each day he must plant at least 300 trees. He plants at least twice as many coniferous trees as deciduous trees each day. He has a maximum of 400 coniferous trees and a maximum of 150 deciduous trees to plant each day.
In this situation, x represents the number of coniferous trees and y represents the number of deciduous trees.
Translate this situation into a system of inequalities.
10. Given the following weighted and directed graph:
What is the distance from A to J?
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?
BIM § Société GRICS / Page 14 // Mathematics — CST-500.A01 § Student Booklet
Show your work or explain your reasoning.
ANSWERRahim has ______used trucks. /
Uses mathematical reasoning
Observable indicators correspondto levelEvaluation
Criteria / 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
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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.
BIM § Société GRICS / Page 14 // Mathematics — CST-500.A01 § Student Booklet
Show your work or explain your reasoning.
ANSWERThe mapping rules are:
II: ______.
III: ______.
IV: ______. /
Uses mathematical reasoning
Observable indicators correspondto levelEvaluation
Criteria / 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
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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?
BIM § Société GRICS / Page 14 // Mathematics — CST-500.A01 § Student Booklet
Show your work or explain your reasoning.
ANSWERThe maximum price Pierre can pay for a plane ticket between Zurich and Rome is $______. /
Uses mathematical reasoning
Observable indicators correspondto levelEvaluation
Criteria / 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
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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 14 /Show your work or explain your reasoning.
ANSWERThe difference between the maximum possible daily revenues for Super Fun Time! before and during the renovation period is $______. /
Uses mathematical reasoning
Observable indicators correspondto levelEvaluation
Criteria / 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
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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 / 160First 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.
BIM § Société GRICS / Page 18 // Mathematics — CST-500.A01 § Student Booklet
Show your work or explain your reasoning.
ANSWER
o Rugby and soccer ARE the top two preferences of the student population.
o Rugby and soccer ARE NOT the top two preferences of the student population.
Justification:
/Uses mathematical reasoning
Observable indicators correspondto levelEvaluation
Criteria / 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
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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.
BIM § Société GRICS / Page 18 // Mathematics — CST-500.A01 § Student Booklet
Show your work or explain your reasoning.
CONJECTURE______
______
______
______
______/
Uses mathematical reasoning
Observable indicators correspondto levelEvaluation
Criteria / 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
Part A / Questions 1to6
4 marks or 0 marks
1. C / 4 / 0
2. D / 4 / 0
3. C / 4 / 0
4. C / 4 / 0
5. B / 4 / 0
6. A / 4 / 0
Part B / Questions 7to10
4 marks or 0 marks
7. x coordinate of A’: 2 / 4 / 3 / 2 / 1 / 0
y coordinate of A’: 9
x coordinate of B’: 1
y coordinate of B’: -9
9. In order to create an Euler path we would need to remove edge CD* / 4 / 0*(or DG, BD or BG)
8. x + y ≥ 300 / 4 / 3 / 2 / 1 / 0x ≥ 2y
x ≤ 400
y ≤ 150
10. The distance from A to J is 3 / 4 / 0BIM § Société GRICS / Page 20 /
/ Mathematics — CST-500.A01 § Administration and Marking Guide
n 11. Honest Rahim’s Cars and Trucks