Mathematics 504 CST - · PDF fileMathematics 504 CST Mid-Year Examination January/February 2012 Question/Answer Booklet Student's Name Group Date 563-414 FOR TEACHER USE ONLY Part

Mathematics 504 CST

Mid-Year Examination

January/February 2012

Question/Answer Booklet

Student's Name

Group Date

563-414

FOR TEACHER USE ONLY

Part A ____________ /24

Part B ___________ /16

Part C ___________ /60

Total __________ /100

563-504

Question/Answer Booklet Page 1

Instructions

1. Provide all the required information in the spaces in this booklet. 2. There are 16 questions in this booklet divided into three parts:

A, B and C.

3. Part A contains 6 multiple choice questions worth 4 marks each. Part B contains 4 short answer questions worth 4 marks each. Part C contains 6 application questions worth 10 marks each.

4. Answer the questions in Part A by darkening the letter that corresponds to the answer chosen. Answer the questions in Part B and C in the space provided.

5. For Part C, you must show all your work to justify your answer. The steps in your procedure must be organized and clearly presented.

6. You are permitted to use graph paper, a ruler, a compass, a set square,

a protractor and a calculator.

7. You may use a calculator with or without graphic display (you must indicate the sequence of operations involved, but you do not have to rewrite all the detailed calculations performed with the calculator).

8. You may refer to the memory aid you prepared on your own before the examination. The memory aid consists of one letter-sized sheet of

paper (8½ 11). Both sides of the sheet may be used. Any mechanical reproduction of this memory aid is forbidden. All other reference materials are forbidden.

9. The length of this examination is 3 hours.

Note: Figures are not necessarily drawn to scale.


The following are the evaluation criteria for the different competencies required to

complete the tasks in this booklet.

Evaluation Criteria

Competency 2: Uses Mathematical Reasoning

Cr 1 - Formulation of a conjecture appropriate to the situation

Cr 2 - Correct application of the concepts and processes appropriate to the Situation

Cr 3 - Proper implementation of mathematical reasoning suited to the situation

Cr 4 - Proper organization of the steps in a proof suited to the situation

Cr 5 - Correct justification of the steps in a proof suited to the situation


SECTION A Questions 1 to 6 On page 20, darken the letter of the answer chosen.

1. The following inequalities represent a situation where x is the number of pine trees to be

planted and y is the number of maple trees to be planted.

x + y ≥ 80 x < 2y

Which of the following is an accurate description of the constraints above?

A) There must be at most 80 trees planted, and there cannot be more than twice the

number of pine trees as maple trees. B) There must be no less than 80 trees planted, and there must be at least twice the

number of pine trees as maple trees. C) There must be a maximum of 80 trees planted, and there must be at most twice the

number of pine trees as maple trees D) There must be a minimum of 80 trees planted in total, and there must be less than

twice the number of pine trees as maple trees.

2. Given the following system of linear inequalities :

y < x/3 and 3x + 2y < 12

where x and y are both positive.

The solution set of this system of inequalities is located in one of the regions shown in the graph.

In which region is the solution set located?

A)

Region P

C)

Region R

B)

Region Q

D)

Region S

P

Q R

S

x

y 6

5

4

3

2

1

1 2 3 4 5 6 0

3x +2 y = 12

y = x/3


3. A company is analyzing the costs associated with the number of computers (x) and

televisions (y) produced. Which of the following polygon of constraints does not yield a maximum cost?

A)

C)

B)

D)

4. A transformation in the Cartesian plane is defined by the following transformation rule:

Which of the rule defines the inverse of this transformation?

A)

C)

B)

D)


5. Josie just bought a new puppy. She wants to build an enclosure in her back yard so that

her puppy can safely play outside.

Josie has 12 meters of fence left over from a previous project, and would like to maximize the area of the puppy’s enclosure.

What shape should the enclosure be?

A)

Square

C)

Hexagon

B)

Circle

D)

Equilateral triangle

6. The two right prisms shown below are similar.

The area of the base of the smaller prism is 7 cm2 and its height measures 6 cm. The area of the base of the larger prism is 112 cm2.

6 cm

Area of the base:7 cm2

Area of the base:112 cm2

Volume: ?

What is the volume of the larger prism?

A)

672 cm3

C)

2 688 cm3

B)

1 792cm3

D)

10 752 cm3


SECTION B

Questions 7 to 10 Write the answers in the appropriate space on page 20.

7. In order to raise money for their prom, senior students at a high-school are selling boxes of

fruit. Boxes of oranges are sold for $18 each and boxes of grapefruit are sold for $23.

The fundraising committee expects to sell at most three times as many boxes of oranges as boxes of grapefruit. They also hope to sell $4100 worth of fruits.

where x : the number of boxes of oranges y : the number of boxes of grapefruit

What are the inequalities that represent these two constraints? 8. The development of a new residential housing is being built.

Both single family homes (x) and condominiums (y) are being considered. Below are the constraints associated with this situation:

x + y ≤ 12 x + y ≥ 10 x ≥ 5 y ≥ 3

How many possible solutions respect the constraints above for the development of the new residential housing?


9. The graph below displays 2 quadratic functions associated by a transformation.

What is the rule of the transformation that associates the two curves?

10. The following figures, a square and a rectangle, are equivalent.

The side length of the square measures 15 cm. The width measures 9 cm and the length of the rectangle is unknown.

15 cm x cm

9 cm

What is the numerical perimeter of the rectangle?


SECTION C

Questions 11 to 16 Show all your work as well as your answer. The work shown is taken

into consideration when marks are awarded. Your written information must be legible, complete, and clearly

stated in correct language so the marker understands exactly what you have done.

11. A FUND RAISER FOR A FOOD BANK

A group of high school students are planning a bake sale to raise money for a food bank around the holiday season. They have asked a culinary school in their area if they could buy cakes and pies from them at a discounted price and sell them to teachers and parents.

To meet demands, there must be at least 10 cakes and at least 45 pies. The culinary school can only provide a total of 80 desserts. In addition, they will make at least 3 times as many pies as cakes.

The students sell the cakes for $12 and the pies for $9. They bought them from the culinary school for $300. What is the maximum amount that the students can raise for the local food bank?

Let x : the number of cakes sold and y : the number of pies sold


100

90

80

70

60

50

40

30

20

10

100 10 20 30 40 50 60 70 80 90

Number of cakes sold

Number of pies sold

The maximum amount that the students can raise for the local food bank is ____________.

Uses mathematical reasoning

Observable indicators correspond to

level

Evalu

ati

on

Cri

teri

a

LEVEL 5 4 3 2 1 0

Cr3 40 32 24 16 8 0

Cr2 40 32 24 16 8

Cr4 Cr5

20 16 12 8 4

POSSIBLE COMBINATIONS OF SALES


12. A FUND RAISER FOR THE PROM

Benjamin, Melina and Moritz are three friends participating in a fundraiser to lower the cost of their prom. Since the fundraiser will be taking place in the winter, their school is selling gloves and scarves. The following polygon of constraints shows the possible solutions based on a system of inequalities. Where x : number of pairs of gloves sold y : number of scarves sold

Students made a profit of $3 for each pair of gloves sold and $5 for each scarf sold. Benjamin made the maximum possible profit. Moritz sold 10 fewer pairs of gloves and half as many scarves as Benjamin. Melina sold 25 less than double the number of pairs of gloves as Benjamin, but 15 fewer scarves. What is the total amount of money the three friends raised for their prom?

POSSIBLE SALES FOR THE FUNDRAISER

Number of pairs of gloves

Num

ber

of

scarv

es


The total amount of money the three friends raised for their prom is ___________________.



level

Evalu

ati

on

Cri

teri

a

LEVEL 5 4 3 2 1 0

Cr3 40 32 24 16 8 0

Cr2 40 32 24 16 8

Cr4 Cr5

20 16 12 8 4


13. A SUMMER JOB

Prasanth is a college student who is planning a trip to Prince Edward Island in August. In order to save up money for the trip, he starts working in the month of May. He works at two different part-time jobs on weekends. Prasanth must work a minimum of 10 hours per month as a cashier. However, he can only work a maximum of 40 hours per month at the salesperson. He must work at least 30 hours per month but no more than 50 hours per month. In addition, he must work at least as many hours at the second job as he does at the first. He makes $7.50 an hour as a cashier and $9 an hour as a salesperson. Let x: number of hours per month as a cashier

y: number of hours per month as a salesperson

POSSIBLE HOURS OF WORK IN MAY

In June and July, Prasanth is free to work more hours. He is able to work a maximum of 70 hours per month. Prasanth made the maximum possible revenue in all three months.

How much money did he earn in total for his trip to Prince Edward Island?

Num

ber

of

hours

as

a s

ale

spers

on

1. x ≥ 10 2. y ≤ 40 3. x + y ≥ 30 4. x + y ≤ 50 5. x ≤ y

1

2

3

4

5

Number of hours as a cashier

COORDINATES OF THE POLYGON OF CONSTRAINTS

A (10, 20)

B (10, 40)

C (25, 25)

D (15, 15)


POSSIBLE HOURS OF WORK IN JUNE AND JULY

Prasanth will have earned ________________ in the three months prior to his trip.



level

Evalu

ati

on

Cri

teri

a

LEVEL 5 4 3 2 1 0

Cr3 40 32 24 16 8 0

Cr2 40 32 24 16 8

Cr4 Cr5

20 16 12 8 4

Number of hours as a cashier

Num

ber

of

hours

as

a s

ale

spers

on


14. A DESIGN FOR A TILE A new tile store has a computer program that lets people design their own tiles. The program uses a basic design and applies a series of geometric transformations to create different patterns. A client creates a tile with the basic shape below (initial figure).

He first transforms the initial figure by using the following transformation rule:

to obtain image 1.

Because he does not want the image to overlap the initial figure, he wants to transform image 1 by using a translation so that the image of B (B’) is located at the initial location of vertex A to obtain image 2. He also wants to have a repeat of image 2 by translating it so that the image of B’’ is located at the initial location of vertex D to obtain image 3. The final design is composed of the initial figure and images 2 and 3.

A

B

C

D

x

y

1

1

What are the two rules of translations that will produce images 2 and 3?


The transformation rule to move image 1 to produce image 2 is _______________________________________. The transformation rule to move image 2 to produce image 3 is _______________________________________.



level

Evalu

ati

on

Cri

teri

a

LEVEL 5 4 3 2 1 0

Cr3 40 32 24 16 8 0

Cr2 40 32 24 16 8

Cr4 Cr5

20 16 12 8 4


15. THE FARMER’S PLOTS OF LAND

Below are the plans of 2 plots of land owned by a farmer; it is scaled in metres.

The plots of land are equivalent. The farmer has to build new fences around each plot of land. The cost of the fencing is $40/m. What is the total cost of fencing required?

4x

4x

6x

2x

48 m

36 m

32 m

26 m

2.6 x


It will cost ________________ to fence both plots of land.



level

Evalu

ati

on

Cri

teri

a

LEVEL 5 4 3 2 1 0

Cr3 40 32 24 16 8 0

Cr2 40 32 24 16 8

Cr4 Cr5

20 16 12 8 4


16. THE CANDY COATING

A confectioner makes little chocolates covered in a candy shell. He has decided to use the following molds for creating the different chocolate solids. Sphere Cylinder A Cylinder B 6cm Surface area: 201.06 cm2 The sphere and cylinder A are equivalent; whereas cylinder A and cylinder B are similar. The surface area of the sphere is 201.06 cm2, and the height of cylinder A is 6 cm. The ratio of the volumes of the cylinder A to B is 343/27. The confectioner wants to coat the chocolates made from cylinder B with a candy coating. How much would coating cost the confectioner for making 500 pieces of cylinder B chocolates, if coating costs $2.50 per 1000 cm2 of candy coating?


It will cost the confectioner _________________ to cover 500 pieces of cylinder B chocolates with candy coating.



level

Evalu

ati

on

Cri

teri

a

LEVEL 5 4 3 2 1 0

Cr3 40 32 24 16 8 0

Cr2 40 32 24 16 8

Cr4 Cr5

20 16 12 8 4


/4

/4

/4

/4

Mathematics 563-504 CST Result

Competency 2- Essential Knowledge /24

Part A - Multiple-Choice Answer Sheet Darken the letter that corresponds to the answer you have chosen. (4 marks each)

Part B – Answer Sheet

Result

/16

7. Inequalities ____________________________________ and ____________________________________ represent the two constraints. 8. There are ____________ possible solutions respect the constraints above for the

development of the new residential housing. 9. The rule of the transformation that associates the two curves is __________________________________________________________________

10. The numerical value of the perimeter of the rectangle is ________________.

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]

Documents

Mathematics 504 CST - · PDF fileMathematics 504 CST Mid-Year Examination January/February 2012 Question/Answer Booklet Student's Name Group Date 563-414 FOR TEACHER USE ONLY Part