June 2010 Exam
1. THE BEST BUY
Some students from Percé High School are shopping for a hiking trip. They each want to
buy a tent, a sleeping bag, a gas stove and a rain jacket. They want to buy all their
equipment at the same store. They have the flyers from two different stores (below)
Brown’s Camping and Clara’s Outdoor Shop.
At which retail shop should the students buy their equipment?
2. TRAIL MIX
The recipe below is a trail mix recipe for a group of campers.
TRAIL MIX RECIPE:
2½ cups
1¾ cups
1½ cups
1¼ cups
1½ cups
1¾ cup
1¾ cups
of dry roasted peanuts
of dry roasted sunflower seeds
of cashews
of walnuts
of Sultana raisins
of golden raisins
of currants
Thirty campers are going on a four-day camping trip. Each camper will eat a ½ cup of trail mix
per day.
How many trail mix recipes must be made so that everyone has a serving of trail
mix for every day of the trip?
3. SETTING UP THE TENT
Yianni has just set up his tent whose front is an equilateral triangle. In order to keep
his tent dry, Yianni will install a tarp over the tent. He was told by an expert that the
tarp must form an isosceles triangle with the ground and that the angle between the
tarp and the tent must be 15°.
B
15°
15°
A
E
C
D
What are the measures of angles AEB, EBD and ABC?
4. THE TIMBER TRAIL
In the Deer River Conservation Park there are many hiking trails. Amy and Ben want to hike
from Oak Grove to Birch Valley. They would like to hike along the shortest route. Amy thinks
they should hike to Maple Lake and then take Trail B. Ben thinks Amy is wrong and that the
shortest path is to hike to Maple Lake and then Trail C. The map they have shows the distances
of each of the paths between Oak Grove and Birch Valley.
Oak Grove
5
Trail B
0.75 km
4
km
Trail A
175 dam
Maple
Lake
1 2
3
Birch Valley
9
4
km
km
1 1 km
3
2250 m
10
3
km
Trail C
Which of the 2 hikers is correct? Explain your answer.
5. HIKING TRIP
Mrs. Oliver is planning an outdoor adventure field trip with his grade 7 students. He
wants to bring two full buses of 40 students.
For the activities, the students will be split up into 5 large groups because there are
only 5 animators available. Each of those large groups will be split up into smaller
groups where the students will do either orienteering or zip-lining.

For orienteering the smaller groups must have between 2 and 7 students

For zip-lining the groups must all be the same size (same number of students)
What is the largest number of students Mrs. Oliver can put in a group if she
wants the small groups to remain the same at each activity?
6. OBSTACLE RACE
Four teams are competing in an obstacle race. The team with the lowest total time for all four
team members will win the race. Nora is on team Fox and believes that her team are the clear
winners because they have two times which are less than 1 minute.
Time to complete the
course
Team
Name
Lynx
Wolf
Fox
Coyote
1 min 6 sec
1 min 18 sec
58 sec
1 min 7 sec
1 min 11 sec
1 min 14 sec
1min10 sec
1 min 16 sec
1 min 14 sec
1 min 29 sec
1min 42 sec
1 min 36 sec
1 min 8 sec
1 min 4 sec
56 sec
54 sec
Is Nora right? Explain your reasoning.
7. GREENHOUSE GASES
Greenhouse gases (GHGs) are one of the causes of global warming. Over the last 20 years,
many countries have tried to reduce their greenhouse gas emissions.
Table 1.1 (below) and Graph 1.1 (below) show the amount of greenhouse gases in metric
tonnes (1000 kg) emitted by each country in 2000 and 2005 respectively.
Table 1.1: Greenhouse gas emissions for the year 2000
Greenhouse Gas Emissions
Country
(metric tonnes)
Australia
20.60 t
Canada
17.40 t
Germany
21.45 t
United Kingdom
21.00 t
United States
18.10 t
Graph 1.1 Greenhouse gas emissions in metric tonne for the year 2005
Greenhouse gas Emissions for 2005
30
Greenhouse
25
Gas
Emissions 20
(t)
15
10
5
0
Australia
Canada
Germany
United
Kingdom
Country
United States
Compare the 2005 Greenhouse gas emissions of each country to the average
Greenhouse gas emissions for the year 2000.
8. BEAVER DAM
Each square on the map of the conservation park (below) is 40 m in length and 40 m in width.
The entrance to the park is at point (2, A). At the entrance of the park the ranger gives you a map
but the dam that you want to see is not indicated. You as the ranger for directions and he
responds:


“You will want to go 160 m North, 120 m East, 40 m South, 80 m West, 100 m South, 160 m
East, 140 m North, 20 m West, 80 m North and 100 m East.”
“I’m thinking you may have to cross one of the rope bridges to get there.”
Map 1: Deer River Conservation Park
0
1
2
3
4
5
6
7
8
9
10
G
F
E
D
C
B
A
N
LEGEND:
BRIDGE:
40 m X 40 m
W
E
WATER:
S
PARK LIMITS:
What are the Cartesian coordinates of the location of the beaver dam?
June 2011 Exam
1. Jason got $100 for his birthday. He went to the mall and bought the following:
 2 CDs at $15.99 each
 3 T-shirts at $7.99 each
 4 bus tickets at $1.25 each
Which order of operations expression represents the change he would get from his $100?
A)
100  (2  15.99 + 3  7.99 + 4  1.25)
B)
100  (2  15.99  3  7.99  4  1.25)
C)
100  (2  15.99) + (3  7.99) + (4  1.25)
D)
100  (2  15.99  3  7.99  4  1.25)
2. Which of the following is the answer to the expression below?
53  149 


1 1
   71  3  7  200
3 9
A)
– 50
C) 40
B)
–8
D) 50
The Fishbowl store must keep the mean temperature in tropical fish tanks between 25°C and 28°C.
On December 1st, the temperature in the tank was 26°C. The following chart shows the change in
temperature from the previous day. For example, on December 3rd, +2 means the temperature is
2oC higher than on December 2nd.
Daily change in temperature
December
1
December
2
December
3
December
4
December
5
December 6
Decem
ber 7
Starting
temperature
-3
+2
+2
-3
+4
-1
26°C
Which of the following statements below describes the mean temperature of the tank?
A) The mean temperature was within an acceptable range.
B) The mean temperature was higher than the acceptable range.
C) The mean temperature was below the acceptable range.
D) The mean temperature cannot be determined.
3. The large parallelogram below has been divided into pieces.
All triangles are right, isosceles triangles.
The pieces with matching patterns are congruent, and the pieces are drawn to scale.
A
.
4.
What fraction of the diagram does parallelogram A represent?
A)
1
7
B)
1
5
C)
1
8
D)
1
16
The following questions refer to the diagram below.
Segment BD bisects angle EBC.
The angles are not drawn to scale.
a) Which line segment is the altitude of triangle ABC? _______________________
b) What is the measure of angle EBD?
_______________________
c) What is the measure of angle ABE?
_______________________
d) What type of triangle is triangle ABC?
_______________________
e) What type of triangle is triangle AEB?
_______________________
5. Consider the figure below. Perform the translation indicated by the arrow, and then reflect
your translated figure across the dotted line.
A
C
D
B
E
F
t
s
6. The energy required for physical activity varies. The number of calories burned in 15 minutes by
someone doing four different physical activities is shown in the graph below.
CALORIES BURNED AFTER 15 MINUTES
OF PHYSICAL ACTIVITY
Calories
burned
45
40
35
30
25
20
15
10
5
0
Volleyball
Swimming Badminton
Table
Tennis
Baseball
Activities
a) In which activity would your body burn the greatest number of calories in 15 minutes?
b) For how many minutes must you play volley-ball to burn off 120 calories?
c) How many calories would you burn playing baseball for 90 minutes?
8. Jonathan is playing a game on his computer. Whenever he enters a number, the game uses a set rule
and displays a result.
The following table shows the numbers that Jonathan entered, and the answers displayed.
Number entered
1
2
3
4
5
…
11
…
?
n
Computer's output
5
9
13
17
21
…
?
…
65
?
a) When Jonathan entered the number 11, what answer did the computer display?
b) Which number generates the computer’s output 65?
c) What rule is the computer game using?
9. THE FISHBOWL SALES
In 2010, The Fish Bowl store sold five different types a fish: goldfish, clown fish, sharks, guppies and
beta fish. The store sold a total of 8 000 fish.
The manager asks you to present the sales in a bar graph.
Unfortunately, some of the sales data is missing.
The following table presents the data available.
Sales of the different types of fish sold at The Fish Bowl pet store in 2010
Type of Fish
Number
of Fish
Beta Fish
2 000
Decimal
Shark
Percent
(%)
5
Clown Fish
800
Gold Fish
Guppy
0.2
Total
8 000
Complete the table and construct the bar graph requested by your manager.
10. CITY PLANNING
The owners of The Fish Bowl want to open a second shop in a new development outside of town.
The piece of property for the store is in the shape of a trapezoid. Their architect needs to know the
measures of the four angles of the property.
The map below shows the plans for the new development. The parking lot boundary and Princess
Avenue are parallel. Main Street and Front Street are also parallel.
With the aid of the given information and without the use of measuring instruments, find the
measure of each of the four angles of the non-isosceles trapezoid. Justify each answer with a
mathematical argument.
N
J
110°
P
H
B
A
L
C
50°
120°
D
E
Parking
K
M
G
F
11. THE BEST DEAL
Tammy is shopping for a new fish tank. Tammy wants to buy all her equipment at the
same store. The prices from two different websites, Perfect Pet Shop and Classy Pet
Shop were given below. She wants to buy:
 a fish tank
 a filter,
 5 Molly fish,
 some aquarium gravel,
 and one aquarium rock.
At which store should Tammy buy all her equipment and how much will she save?
Filter
1/3 off
entire
stock !!!
Filter
All filters 40% off.
$21
$28
Fish Tank
12.
$7.50
50% off
Molly Fish
$57
Rock
Rock
Gravel
Molly Fish
$4.50
$6.99
Fish Tank
$9.59
Gravel
$5.25
Mollys: Buy 4,
5th one free.
Free delivery!
$54
$5.00
Add 5% to total for delivery.
12. A PERSONAL CHALLENGE
Stephanie is a cross-country cyclist and will represent her region at the Provincial Games. She
hopes to finish the race as one of the top three competitors and win a medal. Because she is an
excellent athlete, her coach thinks that she will reach her goal if the following conditions are met:

It rains on the day of the competition.

Stephanie sleeps at least 8 hours the night before her competition.

Her warm-up period lasts at least 15 minutes.
The competition will take place tomorrow.

The weather report predicts a 60% chance of rain tomorrow.

There are 3 chances out of 4 that Stephanie is going to sleep at least 8 hours.

The probability that she does not warm up for at least 15 minutes is 0.35.
What is the probability that Stephanie will finish the race in the top three and win a medal?
13. THE RECTANGLE CONJECTURE
If the measures of each side of a rectangle are doubled, what happens to the perimeter and the
area of that rectangle?
Recall, the area of a rectangle = length x width
Use 3 examples to illustrate this situation.
Formulate a conjecture. (What pattern do you notice?)
A conjecture is a statement based on a general pattern that you have observed.
Show your work or explain your reasoning.
3
5
Perimeter =
Area = 3 x 5 = 15
June 2012 Exam
1.
William is playing a board game with three of his friends. At the start of the game, William had
$3200. During the course of the game, William lands on the bank six times. Each time he lands on
the bank he gets $175. Also, he plans to buy five houses at $140 each and has to give $50 to each of
his friends.
Which of the following expressions corresponds to the amount of money William will have
left at the end of the game?
A)
$3200 + ($175 × 6)  ($140 × 5)  ($50 × 3)
B)
$3200 + ($175 × 6)  ($140 × 5)  ($50 × 4)
C)
($175 × 6) + ($140 × 5)  ($50 × 3)  $3200
D)
($175 × 6) + ($140 × 5) + ($50 × 3)  $3200
2.
Which of the following expressions is true?
A)
(5)2 = 52
B)
7 × (3 + 6 × 2)  3  7 × 3 + 6 × 2  3
C)
50 × 8 = 80 × 5
D)
17 + 3 × 2  17 × 21 + 32
3. Which of the following figures is not a parallelogram?
1
2
3
4
A)
1
C)
3
B)
2
D)
4
4. Match each of the four figures below with the corresponding term.
Y
Y
1
2
Z
X
Z
X
Y
Y
3
4
Z
X
X
Z
A. Median
B. Bisector
C. Perpendicular Bisector
D. Altitude (Height)
A)
A-3, B-1, C-2, D-4
B)
A-3, B-2, C-4, D-1
C)
A-4, B-1, C-3, D-2
D)
A-4, B-2, C-3, D-1
5. What is the perimeter, in dm, of the figure below?
30
dm
1200 cm
24
m
A)
84 dm
C)
960 dm
B)
840 dm
D)
1284 dm
6. Which of the following images (numbered 1 – 4) was constructed from a reflection of the
original figure?
1
Original Figure
2
3
4
A)
1
B)
2
C)
3
D)
4
7.
Marie-Anne, Patricia and Olivia are having a bicycle race. After 40 minutes, Marie-Anne was threequarters of the way to the finish line. Patricia had finished 76% of the race. Olivia had
3
of the
8
race left to finish.
Which of the three friends is leading the race after 40 minutes and what percentage of the
race does she have left to do?
8. Place the following four fractions on the number line found in your Student Booklet.
2
3 7
1
;
;
;
3
4
6 2
9. A submarine is cruising at a depth of -25 m with respect to sea level. The sonar system detects that
the submarine is on a collision course with a blue whale. To avoid the whale, the submarine must
perform the following manoeuvers:
First it dives 50 m and then rises 12 m. Then it must dive again, this time by 18 m. When the whale
has passed, the submarine rises 30 m and finally rests after diving 5 m one last time.
At what depth (with respect to sea level) is the submarine after performing these
manoeuvers?
10. Consider the figure below:
45
?
15
What is the value of the missing angle?
11. The “Cabane à Sucre” (Sugar Shack)
Over the long weekend, Sandra helped her father collect sap from their maple trees. She was
responsible for collecting the sap using wooden barrels. Each barrel contains 240 litres of sap.
The table below shows the number of barrels of sap Sandra collected each day:
Day
Friday
Number of
Barrels
21
Saturday
Sunday
Monday
5
6
2.75
37
8
5
In order to make maple syrup, the sap must be boiled so that most of the water evaporates, leaving
behind a concentrated syrup. During this process
29
of the sap collected is lost due to evaporation.
30
How many 1-litre bottles of maple syrup can be produced with the sap Sandra collected?
12.The End-of-Year Trip
A Math teacher is organising an end-of-year trip for her class. The trip cost $375 per
student.
In order to bring down the cost, the 32 students did a fundraising activity and sold:

246 muffins at $2.25 each

98 granola bars at $1.75 each

557 bottles of water at $1.50 each

389 juice boxes at $0.75 each.
The money raised must be divided equally among all students in the class.
The principal of the school was so impressed with their fundraising that she agreed to
pay 30% of the remaining cost.
What is the final cost of the trip for each student?
13. Stormy Weather
The following two graphs show the amount of precipitation (snow and rain) for the city of
St-Armand-des-Monts in 2010:
Precipitation (snow) in St-Armand-des-Monts,
2010
35
Precipitation (rain) in St-Armand-des-Monts,
2010
16
14
30
12
20
10
Precipitation of rain
(mm)
Precipitation of snow
(cm)
25
15
10
5
0
J F M A M J J A S O N D
Month of the
Year
8
6
4
2
0
J F M A M J J A S O N D
Month of the
Year
Given that snow occupies more space on the ground than rain, experts agree that 1
mm of rainfall is equivalent to 1 cm of snow accumulated on the ground.
By analyzing the two graphs above, two of your friends make the following
observations:
Paul: Every month, on average, two times as much snow fell rather than rain in 2010.
Armando:On the contrary, I think more rain fell rather than snow on average in 2010.
Which one of your friends is correct?
14. Carnival Conundrum
A person has the option of playing two different games at a carnival in order to win a
teddy bear:
Game #1: In order to win, the player must draw two balls of the same colour out of a bag
containing two red balls, three green balls and four blue balls. After being picked, the
first ball is put back into the bag before the second ball can be drawn.
Game #2: In order to win, the player must spin the wheel below two times and obtain the
same colour both times.
R
B = Blue
Y
G
B
Y = Yellow
R
Y
R = Red
B
Y
G = Green
Your friend Meena says that you will have a greater chance of winning the teddy bear if
you choose to play game #2.
Is she correct?
15. The Security Zone
A construction zone requires a fence to be installed for security reasons.
The diagram below indicates the dimensions of the zone that needs to be fenced in.
̅̅̅̅ = 18 m
m 𝐴𝐵
̅̅̅̅ = 35 m
m 𝐵𝐶
m ̅̅̅̅
𝐶𝐷 =
?
̅̅̅̅ = 22 m
m 𝐷𝐸
m ̅̅̅̅
𝐸𝐹 = 15 m
̅̅̅̅ = 31 m
m 𝐹𝐺
m ̅̅̅̅
𝐺𝐻 = 41 m
̅̅̅̅ = 52 m
m 𝐴𝐻
Your supervisor asks you to study the following proposals submitted by two companies.
Marvel Fencing
Peter Fencing Inc.

One meter of fencing costs $26.

If you purchase more than 300 m,
you get a 10% rebate.

The installation cost is $1500.

Fencing is sold in section of 6
meters.

Each section costs $190.

If you purchase more than 200 m,
you get a 6% rebate.

installation cost is $1000.
Which company offers the best deal and what will be the cost of the fencing?
16. The Mystery Angle
Consider the following figure below:
ABCD is a rhombus.
CBEF is a parallelogram.
EHG is a right triangle.
Angle BAD measures 40o.
H
I
?
A
40
B
D
C
E
G
F
Note: IH , DG and CF are parallel.
What is the measure of angle IHE?
Justify each of your steps by a geometric property that you know.
Page 6
2013 June Exam
1. Solve the following problem using the correct order of operations.
−10 − 3 × (6 − 7)3
A)
−13
C)
7
B)
−7
D)
13
2. Five kites are entered into a competition. Yannick wants each kite to be decorated with
only one decoration. There are five different decorations.
The same decoration can be used more than once.
How many different ways can the kites be decorated?
A)
5+4+3+2+1=
14 different ways
C)
5+5+5+5+5=
25 different ways
B)
5×4×3×2×1=
120 different ways
D)
5×5×5×5×5=
3125 different ways
3. During a picnic on Mont-Royal, John brings two bags of snacks to share with his
friends.
In the first bag there is one chocolate muffin, four apples and three oranges.
In the second bag there are three chocolate bars, three bags of chips and six brownies.
What is the probability that John will pick the chocolate muffin from the first bag and
then a chocolate bar from the second bag?
A)
1
96
C)
1
32
B)
4
20
D)
9
24
Page 7
4. Patrick is preparing a fruit juice cocktail. He mixes 4 different fruit juices (apple,
orange, mango and peach) together in a large container.
Patrick mixes together the following amounts of each juice:
Apple juice
Orange juice
Mango juice
Peach juice
1
2 L
2
2
4 L
3
3
5 L
4
1
2 L
2
What is the total volume of fruit juice cocktail that Patrick makes?
A)
B)
6.
7
L
11
C)
5
14 L
7
D)
13
14
5
L
12
15
5
L
12
Which one of the following figures has exactly two axes of symmetry?
A)
C)
B)
D)
Page 8
5. Which of the following images (numbered 1 to 4) is the result of a 90o
counterclockwise rotation of the initial figure around the centre of rotation?
Initial
figure
A)
1
C)
3
B)
2
D)
4
7. Matthew has $550 in his bank account.
This week, he made the following bank transactions:
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Bank
transaction
Withdraw
$120
Deposit
$160
Purchase of
$25
?
Two deposits
of $65
What transaction did Matthew make on Thursday if the balance of his account is $120 at
the end of the week?
Page 9
8. A survey of 60 students from Saint-Snowdon-de-Paquetteville School was conducted to
find out what their favourite meals are.
The results of the survey are shown in the bar graph below.
However, one piece of data is missing from the graph.
Students’ favourite meals
Number
of students
30
25
20
15
10
5
0
Pasta
Beef
Chicken
Meal
What percentage of the students prefers chicken?
(Round the percentage to the nearest whole number)
9. In the following diagram, angle NKJ measures 140o and angle MLJ measures 120o.
What is the measurement of angle KJL?
Page 10
10. Beside are illustrations of four
quadrilaterals: M, N, O and P.
M
N
O
P
a) Which of these quadrilaterals has only one pair of parallel line segments?
b) Which of these quadrilaterals has two congruent diagonal lines?
c) Which of these quadrilaterals has two perpendicular diagonal lines (there could be
one or more)?
11. PICKING BLUEBERRIES
For summer vacation, Jonathan and his brother Alex went to Lac Saint-Jean to work as
blueberry pickers.
In one week, Jonathan picked 92 baskets of berries and worked 32 hours.
Alex picked 31 baskets of berries and worked 12 hours.
Their boss proposed two different methods of payment.
Each brother must choose one of the two.
Method of payment #1: receive $4.25 for each basket of berries and a base salary of $50
per week.
Method of payment #2: receive $12.55 per hour and a base salary of $35 per week.
Which method of payment is the most profitable for each of the two brothers
12. OPENING NIGHT!
The organizers of the Lac Saint-Jean International Open Water Swimming Competition
sold 150 tickets for the opening night concert at $21 each.
2
The organizers must pay of the proceeds from the ticket sales to the artists
5
performing in the concert.
The organizers also predict that 8% of the original proceeds from the ticket sales will
be necessary to pay for other expenses.
How much profit did the organizers make from this concert?
Note: the profit is the amount made from the ticket sales minus the total costs of the
concert.
Page 11
Mathematics 106 — Competency 2  Student Booklet
13. DEEP SEA DIVING
Samuel is taking a deep-sea diving course to prepare himself for a competition in
Barcelona.
He must dive from a boat, swim down and retrieve seven objects that have been placed
at different depths.
The table below shows the depth of each object.
Object
Depth
1
12 m
2
56 dm
3
18 000 mm
4
0.64 dam
5
0.095 hm
6
670 cm
7
?
In the Barcelona competition, the average depth of the objects is 10.5 metres.
At what depth must object #7 be placed in order to meet the requirements of the
Barcelona competition?
16. CROSS-TRAINING PROGRAM
Jonathan is a track and field athlete. To improve his athletic performance, his
trainer sets up a one-year cross-training program divided into three activities.



Every 2 days, he must practice track and field.
Every 5 days, he must work out at the gym.
Every 7 days, he must go running.
His trainer offers to take him out to a restaurant for dinner when he
accomplishes all three activities on the same day.
Dinner for two costs $29.75 and the trainer will leave a 15% tip after each meal.
How much money will the trainer pay for the dinners for one full year (365
days)?
Page 12
Mathematics 106 — Competency 2  Student Booklet
14. THE GREEN HEXAGON PARK
The kite competition is being held in the Green Hexagon Park. This park is in the
shape of a regular hexagon as shown in the diagram below.
In the diagram below:

ABCDEF is a regular hexagon.

Lines AB and DE are parallel.

Lines AF, CD and GH are parallel.
Using the diagram, but not using your geometry instruments, determine the
measurements of each of the five angles 1, 2, 3, 4 and 5.
Justify how you found each angle using a geometric property that you have learned.
Page 13
Mathematics 106 — Competency 2  Student Booklet
15. THE GARDEN AT CITY HALL
A tulip garden is being planned for the entrance to Sainte-Marguerite’s City Hall.
The City Director wants to have a maximum number of rows of tulips.
It is suggested to him to either have a 24th row of tulips or a final row of 168
tulips.
The table below shows the number of tulips for each row.
Row
Number of tulips
1
3
2
8
3
13
…
…
24
?
?
168
Rule
His budget for the last row of tulips is $210.
The tulips cost $1.25 each.
What is the maximum number of rows that the garden can have respecting
the budget for the final row?
Page 14
Mathematics 106 — Competency 2  Student Booklet
June 2014 Exam
1. Which of the following series of operations is true?
A)
8 + 12 ÷ ( 6 + 2) = 5
B)
(5 + 3
2)
3 = 33
C)
6 + 4
D)
( 10 + 3
(8
9)3 = 2
50)2 = 100
2. Chemical elements are classified into groups based on similar properties. Paul is
studying the temperature at which an element changes from a solid to a liquid
state for certain groups of chemical elements.
Here is the data available to him:
Temperature at which an element changes from a solid to a liquid state (oC)
Group
Element 1
Element 2
Element 3
Element 4
A
181
64
39
27
B
1287
842
727
700
C
220
7
114
302
D
249
157
112
71
Which group of chemical elements has the largest range of temperatures at
which an element in the group changes from a solid to a liquid state?
A)
Group A
C)
Group C
B)
Group B
D)
Group D
Page 15
Mathematics 106 — Competency 2  Student Booklet
3. Dennis has four pieces of wood of different lengths: 12 m; 800 cm; 130 dm
and 0.11 hm respectively.
Which of the following choices represents these lengths listed in increasing
order?
4.
A)
800 cm; 0.11 hm; 12 m; 130 dm
C)
130 dm; 0.11 hm; 12 m; 800 cm
B)
130 dm; 12 m; 0.11 hm; 800 cm
D)
800 cm; 130 dm; 12m; 0.11 hm
Here are four incomplete statements:
i. The smallest prime number is _____.
ii. The number 345676 is divisible by 4 if _____ is divisible by 4.
iii. The number 2343 is divisible by 3 if the sum of the digits forming the
number is divisible by ____.
iv. The number 5124 is divisible by 6 if it is divisible by 3 and if it is ____.
Which of the following choices accurately completes all the above statements?
A)
i:
ii:
iii:
iv:
1
76
3
even
C)
i:
ii:
iii:
iv:
2
76
3
even
B)
i:
ii:
iii:
iv:
1
76
6
even
D)
i:
ii:
iii:
iv:
2
6
6
odd
5. Cassandra uses a lock that has a combination consisting of three numbers
between 0 and 39 that can repeat. For example, her lock combination is: 22 - 0
- 35.
How many different combinations of numbers could open this type of lock with
three numbers?
A)
54834
C)
59319
B)
59280
D)
64000
Page 16
Mathematics 106 — Competency 2  Student Booklet
6. Which of the following figures is a translation of the initial figure?
A
Initial
figure
D
C
B
A)
Figure A
C)
Figure C
B)
Figure B
D)
Figure D
Page 17
Mathematics 106 — Competency 2  Student Booklet
7. Place the following numbers on the number line provided in the Student
Booklet:
3
3
; 1.4 ; 30% ;
5
2
8. What is the result of the following sequence of operations? Simplify your
answer.
2 2 1 
  
9  5 10 
9. Points ABC and the line segments AB and BC have been plotted on the following
Cartesian plane. You are to add an additional point D in order to create the
parallelogram ABCD.
What are the coordinates of point D that creates the parallelogram ABCD?
Page 18
Mathematics 106 — Competency 2  Student Booklet
10. Using the information from the diagrams below answer the following questions:
?
a) What is the measure of angle PQR?
9.8 cm
?
Perimeter
41.2 cm
9.5 cm
12.4 cm
b) What is the length of segment AB?
c) What type of trapezoid (right, isosceles or scalene) is trapezoid ABCD?
Page 19
Mathematics 106 — Competency 2  Student Booklet
11. CHOCOLATE BARS
Sonia and Julian want to raise money to pay for a camping trip by selling two
different types of chocolate bars.
Sonia is selling chocolate bars with almonds and Julian is selling chocolate bars
with caramel.
Sonia has to sell 1200 chocolate bars. Each one sells for $2.50.
She has already collected $325.
She sells 31 chocolate bars per day.
Julian has to sell 1450 chocolate bars. Each one sells for $1.75.
He has already collected $367.50.
He sells 32 chocolate bars per day.
Who will be the first to finish selling all of their chocolate bars?
13. THE INHERITANCE
In his last Will and Testament, Mr Renard is leaving an inheritance to his family:
his wife Yvonne and his three children, Myriam, Eric and Nathan.
In his Will, Mr Renard has separated the sum of $34 300 according to the
following specifications:
1- Myriam will receive
2
of the sum of money.
7
2- Eric will receive 17.3% of the sum of money.
3- Yvonne will receive $1000 less than twice the amount of money Eric
receives.
4- Nathan will receive the remainder of the money.
How much money will Nathan receive?
Page 20
Mathematics 106 — Competency 2  Student Booklet
12. THE SECURITY FENCE
A technology company wants to increase the security of its offices by
installing a security fence around their site.
Here is the map of their site:
10 m
25 m
16 m
6m
?
30 m
20 m
40 m
One metre of fence costs $121.50.
Five workers are required to carry out this job that will take 2 full days
to complete, working 8 hours per day. The salary of one worker is
$52.50 per hour.
What is the total cost of this project?
Page 21
Mathematics 106 — Competency 2  Student Booklet
14. THE FLOWER GARDEN
A gardener is planning a flower garden for the city.
Here is his plan:
-
He will plant 15 carnations.
-
The number of tulips will be 20 less than triple the number of carnations.
-
The number of roses will be seven times the greatest common divisor of
the number of tulips and the number of carnations.
-
The number of daisies will be the least common multiple of the number
of roses and the number of carnations.
-
The number of lilies will be equal to the average of the numbers of the
four types of flowers previously mentioned.
How many flowers will the gardener plant in total?
15. INTERNATIONAL FOOD WEEK
During International Food Week, David’s school organizes a dinner and 152
students sign up to come.
The meal that will be served is Spanish paella.
The recipe of Spanish paella for four people and the costs of the available sizes of
the ingredients are given in the table below.
Original recipe
for 4 people
1 onion
500 mL rice
1 litre of chicken broth
20 shrimp
20 mussels
3 mL of parsley
Cost of available sizes
$3 for a sac of 15 onions
$8 for a 1000 mL box of rice
$3.50 for 1 litre of chicken broth
$25 for a bag of 80 shrimp
$15 for a bag of 50 mussels
$4.25 for a 100 mL container of parsley
Note: All other necessary ingredients will be provided by the school cafeteria.
How much will it cost to purchase the ingredients necessary to prepare paella for all
of the students that signed up?
Page 22
Mathematics 106 — Competency 2  Student Booklet
16. THE MURAL
Annette painted a mural. It is made up of a quadrilateral CDIG and two triangles,
LCG and GIE respectively.
To draw the mural, Annette guided herself by the parallel lines NO and MK.
Lines DL and EG are also parallel.
What are the measurements of the angles numbered 1 to 5 on Annette’s mural?
Justify each of your answers with a geometric property that you have
learned.
Page 23