Mathematics Examination — 563-306 Secondary Cycle Two … · Secondary Cycle Two Year One – 563-306 Page 1 The following criteria will be used to evaluate your level of competency

Mathematics Examination — 563-306

Secondary Cycle Two Year One June 2008

Competency 2 and Competency 3 Situations

Student Booklet

Name :

Group :

June 2008

Time: 3 hours

Secondary Cycle Two Year One – 563-306 Page 1

The following criteria will be used to evaluate your level of competency

development in the different situations presented in this booklet.

Evaluation Criteria Competency 2: Uses Mathematical Reasoning

Cr1 - Formulation of a conjecture appropriate to the situation

Cr2 - Correct application of the concepts and processes appropriate to the situation

Cr3 - Proper implementation of mathematical reasoning suited to the situation

Cr4 - Proper organization of the steps in a proof suited to the situation

Cr5 - Correct justification of the steps in a proof suited to the situation

Evaluation Criteria Competency 3: Communicates By Using Mathematical Language

Cr1 - Correct translation of a mathematical concept or process into another register of semiotic representation

Cr2 – Correct interpretation of a mathematical message involving at least two registers of semiotic representation

Cr3 – Production of a message appropriate to the communication context

Cr4 – Production of a message in keeping with the terminology, rules and conventions of mathematics


Instructions

1. Provide all the required information in the spaces in this booklet. 2. There are 12 questions in this booklet. For each question, you must

demonstrate your reasoning to justify your answer. The steps in your procedure must be organized and clearly presented.

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

square, a protractor and a calculator. 4. 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 (8.5 × 11). Both sides of the sheet may be used. Any mechanical reproduction of this memory aid is forbidden. All other reference materials are forbidden.

Note: Figures are not necessarily drawn to scale.


1. ICE CREAM DILEMMA At one of the stops during the Amazing Race,

organizers plan to serve ice cream to both staff

and contestants. There are 15 staff members and

28 contestants. The organizers have purchased

five 1-L containers of ice cream and two boxes of

ice cream cones. Each box has 24 cones. Every

cone will have one scoop of ice cream. Each

scoop is in the shape of a sphere with a diameter

that is the same measure as the diameter of the

top of the cone.

Each cone has the following dimensions:

! height 7.8 cm

! apothem 8.4 cm

7.8

cm8.4 cm

Do they have enough ice cream?


Show or explain how you found your answer. Do they have enough ice cream?

YES " NO "

C2: Uses mathematical reasoning

Observable indicators corresponding to level… 1-5 Overall

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2. A FISHY STORY

Jeff’s aquarium, in the shape of a

rectangular prism, is filled to 80% of

its height. He wants to add three

solid food cones to the tank. He

claims that the tank will not overflow

as a result.

The interior dimensions of the tank are:

! length 40 cm

! width 30 cm

! height 25 cm

The food cone has a radius of 9 cm and a height of 24 cm.

24 cm

9 cm

40 cm

30 cm

25 cm

Is Jeff right?


Show or explain how you found your answer. Is Jeff right?

YES " NO "



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3. THE INVESTMENT BANKER Frank, John, and Jessica compare their respective savings.

# Frank has $1000 and saves $5.00 per week.

# John has $850 and saves $10.00 per week.

# Jessica has $600 and saves $12.00 per week. After a certain period, Frank and John have the same amount in savings.

Ten weeks after that period of time , how much does Jessica have ?


Show or explain how you found your answer. Ten weeks after, Jessica has $______________



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4. THE INTERIOR DECORATORS

Helen has been hired to paint a room in a building.

The room has two rectangular walls and a curved

wall. The ceiling is in the shape of a quarter of a circle.

The top view of the room is given below. She has

been asked to paint the ceiling, the curved wall and

one of the rectangular walls.

8.5 m 8.5 m

Each rectangular wall is 8.5 m long and 4 m high.

A 3.8-litre can of paint will cover 40 m2 with one coat. Two coats of

paint are needed.

How many cans of paint should Helen buy ?


Show or explain how you found your answer. Helen should buy ______________ cans of paint.



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5. TO THE POINT

During the Amazing Race contest, participants

were required to perform the following task.

They had to throw darts at one of two targets.

(A dart had to hit either the target or the

backboard to count as a throw.) The targets are

illustrated below. Most of the contestants

believed that the circular target gave the highest

probability of success. It turns out that they were correct.

The two dartboards are illustrated below.

40 cm

50 cm 50 cm

One board has a small square inside a larger square while the

other has a circle inscribed in a square.

Prove that the contestants are correct.


Show or explain how you found your answer.



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6. GEOMETRIC GARDENS

One of the stops for the participants of the Amazing Race is in

Washington, D.C. They visit two beautiful flower gardens, one in the

shape of a triangle and the other in the shape of a rectangle. The

dimensions can be represented by algebraic expressions, as shown in

the diagram below.

6x − 14 6x − 18

4x − 8 2x − 2

The brochure that John is reading about the gardens says that

these gardens are equivalent in area. (In the U.S., the unit of

measure that is used is the foot.)

What are the dimensions of each garden ?


Show or explain how you found your answer. The triangular garden has a height of ______ ft and a base of ______ ft.

The rectangular garden has a length of ______ ft and a width of ______ ft.



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7. JOSE’S NUMBER

Jose is thinking of a number.

# When he doubles the number, then subtracts 1, he has the width

of a rectangle.

# When he multiplies the original number by 4, then subtracts 3, he

has its length.

He asks his friend Chelsea what the length of the diagonal of that

rectangle would be. Chelsea claims she does not have enough

information so he gives her a hint: the perimeter of the rectangle

is 46 units.

What is the length of the diagonal of the rectangle ?


Show or explain how you found your answer. The length of the diagonal is_______________ units.



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8. JACOB’S REPORT

Jacob and his parents are upset because they

think that the average on his report card is too

low. When they calculate the average of Jacob’s

marks, they get 81.3%.

Jacob’s Report Card Subject Mark Credits Mathematics 84 6 French 76 6

English 78 6 Geography 80 4 History 75 4 Science 86 6

Phys. Ed. 90 2 Average 80.7 34

Write a memo to Jacob’s parents explaining how the

computer arrived at 80.7% and why the school reports

a weighted average rather than an arithmetic average.


Your memo:

C3: Communicates by using mathematical language


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9. BUS VS MINIVAN

A high school class is arranging a field trip. The organizers have

narrowed their transportation options to the following two:

! Option 1 Bus rental at $900/day

! Option 2 Minivan rental at $150/day # There can be a maximum of 50 students on the trip.

# They need at least 25 students to sign up

# The bus could hold all the students and their chaperones

# Each minivan can transport up to 8 students

# The amount the students are charged must cover all the transportation

costs (of students and chaperones)

$150/day $900/day

The organizers would like to analyze the cost of this trip per student, based on the transportation they choose and the number of students that sign up and pay.

Create a table or tables of value detailing the relevant

information and then write sentences that highlight at

least 2 observations you can make from your table(s).


Your table(s) of values and sentences:



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10. Glitter Girl

Sandra's little sister is making a poster.

Her idea is to cut out a rectangle, cover it

with glitter, and then attach other

decorations to it. She wants the poster to

be similar to a rectangle with a width of

4 cm and a length of 5 cm. The tube of

glitter she is using can cover 720 cm2.

She plans to use all of the glitter.

What will be the dimensions of the poster she makes?


Show or explain how you found your answer. The dimensions of the poster will be _______cm by ________cm.



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11. RICKSHAW RATES While in Japan, the Amazing Race contestants

have to take a 15-km rickshaw ride.

A rickshaw is a carriage pulled by a person.

This means of transportation originated in

Japan and is still used by tourists, much like the

caleches in Montreal. Each group of contestants is given an envelope

with information on four rickshaw companies. In Japan, the monetary

units are Japanese Yen (¥). One Canadian dollar is approximately

100 Japanese Yen.

300

0 100

200

400

500

600

700

Distance (km) 0 2 4 6 8 10 12

Cos

t (¥)

km ¥ 0 350 4 410 8 470 ... ...

Imperial Rickshaw Citizen Rickshaw

Rickshaw ToGo Samuraï Rickshaw

Which is the least expensive rickshaw company

for the 15 km-ride?

Charges ¥1500 flat rate for any ride over 10 km but less than 20 km.

C = 300 + 18d Where

d = distance in km C = total cost (¥)


Show or explain how you found your answer.

______________________is the least expensive rickshaw company for the 15 km ride.



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12. WHO’S THE BEST? The Ironman Triathlon features a 3.9-km swim, a 180-km

bike ride, and a complete marathon (42.2 km) all in

succession. Athletes have 17 hours to complete the event.

Below is a summary of the results of the 2446 competitors

who finished the race in Penticton BC in 2007. These

competitors came from all over the world to compete and

203 of them came from Quebec and Ontario.

Use your understanding of statistics to comment on the performance of the

competitors from Quebec and Ontario compared to the group as a whole. Use

measures of central tendency as well as a graph, comparing completion times

to the percentage of finishers from each population, to support your

comments.

Grouped Data Table: Completion times for Ironman competitors Hours to complete (Class)

Number of finishers

Percent of finishers

QC & ON finishers

Percent of QC & ON finishers

[8,9[ 10 2

[9,10[ 54 8

[10,11[ 307 34

[11,12[ 470 37

[12,13[ 509 41

[13,14[ 406 35

[14,15[ 339 24

[15,16[ 227 14

[16,17[ 124 8

Total finishers 2446 203

Mean 12.9

Median Class [12,13[

Modal Class [12,13[


Draw a graph and support your conclusions.

Based on my understanding of statistics, the QC and Ontario finishers …



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Mathematics Examination — 563-306 Secondary Cycle Two … · Secondary Cycle Two Year One – 563-306 Page 1 The following criteria will be used to evaluate your level of competency