June 2011 Exam
1.
Which of the following is the simplified version of this expression?
4(7x + 5)  2 (3x  6) + 22 + 62 ÷ 8
A)
22x + 25.5
C)
22x + 22.5
B)
22x + 40.5
D)
22x + 16.5
2.
What is the total surface area of the following decomposable solid?
h=4m
4m
4m
4m
A)
144 m2
C)
96 m2
B)
112 m2
D)
64 m2
3.
The following are the heights of all the students in Mr. Math’s history class.
140
155
180
164
137
175
167
143
158
179
165
176
168
149
135
154
180
146
135
170
Which of the following is false?
A)
The mean of this distribution is 161 cm.
B)
The range of this distribution is 45 cm.
C)
The minimum of this distribution is 135 cm.
D)
The maximum of this distribution is 180 cm.
4. Which of the following shows a direct proportional situation for graph, table
and rule?
Graph
A)
Rule
Table
y
10
9
8
x
y
0
4
1
6
2
8
3
10
y = 2x + 4
x
y
0
0
1
3
2
6
3
9
y = 3x + 2
x
y
0
0
1
4
2
8
3
12
y = 4x
x
y
2
10
4
5
5
4
10
2
y=
7
6
5
4
3
2
1
0
B)
0
0.5
1
1.5
2
2.5
3
x
y
10
9
8
7
6
5
4
3
2
1
0
C)
0
0.5
1
1.5
2
2.5
3
x
y
10
9
8
7
6
5
4
3
2
1
0
D)
0
0.5
1
1.5
2
2.5
3
x
y
25
20
15
10
5
0
0
5
10
15
20
25
30
x
20
x
5.
Solve the following algebraic equation (round to the nearest hundredth):
 74 x  9
86 x  2

5
3
6.
Place the following rates in order from slowest to fastest:
a) 0.018 km/s
b) 1020 m/min
c) 15 m/s
d) 57.6 km/h
7.
Construct a regular octagon with side lengths measuring 3 cm.
8.
The lunch menu at a sandwich shop consists of a combination of options. There
are 4 sandwiches (chicken, meatball, ham, and turkey) and 3 drink options
(soda, milk and juice) to choose from.
Create a tree diagram to and list all the possible lunch combinations.
9.
Catering Expenses
Student Council is hiring a catering company to provide food for the end of year
celebration.
The catering company expenses are:
 The rental of equipment is $150
 The catering company charges a rate of $120/hour
The Student Council’s budget for food is $750.
You must create a table of values, graph the situation and write the rule.
Due to budget restrictions, what is the maximum number of hours the catering
company can be hired for?
10. Triangle Projection
A triangle is projected on a game board screen. The triangle has a base of 3 cm
and a height of 2 cm.
Liane says that if a dilatation scale factor of 5 is applied to the initial triangle,
the area of the triangle projected on the screen will be 5 times greater.
Is she right or wrong? Show your work.
11. Teachers in Jeopardy
Marc is planning the very popular Teachers in Jeopardy games. Students can
select from two games: the Dunk Tank and the Pie Toss. Due to high interest in
the games, students are only allowed to choose one.
Game Descriptions
Dunk Tank:
Soak your teacher in ice cold water if the spinner lands on a prime number.
24
2
17
75
12
51
68
21
Pie Toss:
Toss a pie if a token, chosen at random, has a higher value than the average
(mean) of all ten tokens.
10
5
10
5
5
25
5
25
10
10
Marc thinks that the Dunk Tank has the highest probability of winning.
Is he correct?
11. Floating Ducks
Sandra is planning the “Floating Ducks” game booth. She found instructions to
create a 3 m2 rectangular pond which holds 75 rubber ducks. Unfortunately, she
only has enough material to build a similar 20 000 cm2 rectangular pond.
Rectangular pond from instructions
Area = 3 m2
Holds 75 ducks
Sandra’s Rectangular pond
Area = 20 000 cm2
Holds ? ducks
Diagrams are not drawn to scale
In keeping with proportionality requirements, how many ducks are
needed to fill Sandra’s rectangular pond?
12. Stage Decorations
The band, Limits to Infinity, requests two cylindrical towers as stage
decorations.
Both cylindrical towers have the same total surface area but different heights.
 Total surface of each tower is 120 m2.
 The area of the base of the cylindrical tower A is 16.6 m2.
 The radius of cylindrical tower B is 3 less than triple the radius of
cylindrical tower A.
Diagrams are not drawn to scale
Cylindrical tower A
Cylindrical tower
Tower A
Tower B
Height = ?
Height = ?
Radius = ?
Radius = ?
Area of base = 16.6 m2
Area of base = ?
Total surface area = 120 m2
Total surface area = 120 m2
What is the height of each cylindrical tower?
B
June 2012 Exam
1.
Given the following statements:
1.
2.
3.
4.
The measurement of an exterior angle is 45.
The sum of all the interior angles is 1080.
The measurement of a central angle is 60.
It consists of 8 equilateral triangles.
Which statements accurately describe a regular octagon?
A)
1 and 2
C)
2 and 4
B)
1 and 3
D)
3 and 4
2. What algebraic expression can be used to calculate the area of the shaded
region?
a
a
A)
a2  2a
C)
𝑎 2
a2 − π (2 )
_______________
2
B)
3.
a2 − πa2
2
D)
𝑎 2
2
a2 – π ( )
Which of the following equations is not equivalent to the other three?
A)
3x + 2 = 4x  1
B)
3x  3 = 6
C)
2 (2x  1) = -5 + 5x
D)
4x + 2(3x  2) = 38
4.
Paul bought a new skateboard on sale. He spent $207, taxes included, for a
skateboard that originally cost $225 before taxes.
Given that the tax is 15%, what percentage discount did Paul receive on the
original price of $225?
A)
12%
C)
25%
B)
20%
D)
80%
5.
Each of the following five situations represents a cell phone plan based on the
cost and the number of minutes used.
Plan 1
Plan 2
Number of minutes
0
10
Cost $
5
5.30
C = 0.05x + 3
100 200
8
where x : is the number of minutes
C : cost of the plan
Plan 4
11
Plan 3
Cost $
Number of
minutes
0.0
8
0.0
6
0.0
4
0.0
2
Cost $
1 2 3 4 Number of
minutes
Plant 5
Cost $
Number of
minutes
How many of these plans represent a proportional situation?
A)
2
C)
4
B)
3
D)
5
10
50
200
0.04
0.20
0.80
6.
For your birthday party, you organize 3 games of chance to entertain your guests.
Game 1:
A person flips a coin that has “Heads” on one side and “Tails” on the
other. The person wins if he/she manages to get “tails” twice in two
flips of the coin.
Game 2:
A bag contains 3 red marbles, 2 blue marbles and 1 green marble.
The person wins if he/she manages to pick 2 red marbles in 2 draws
(each draw is done with replacement.)
Game 3:
A person rolls two die, each numbered 1 to 6. The person wins if the
product of the two resulting numbers is an odd number.
Which of the three games are equiprobable (equally probable)?
A)
1 and 2
C)
1 and 3
B)
2 and 3
D)
1, 2 and 3
7.
Jack ran a 15 000 meter race in 1.8 hours. His next challenge is a 20 km race.
If he runs at the same speed, how many extra minutes will it take to complete
the 20 km race?
8.
At J-Mart, a shirt costs $32 less than a pair of pants.
For $292, you are able to purchase three pairs of pants and four shirts.
Write the equation that represents this situation.
9.
A circle whose area is 50.27 cm2 is placed inside a regular pentagon.
The area of the regular pentagon is 59.14 cm2.
What is the measure of the perimeter of the pentagon?
10. Jeremy built a skateboarding ramp. The ramp has a height of 54 cm and a length
of 2.1 m. There are three equally spaced beams that support the structure.
 54 cm


2.1 m
What is the total length of the three supporting beams?
11. The New York to Hong Kong Flight
A new high-end aircraft is about to make a flight from New York to Hong Kong.
This new aircraft can carry 480 passengers in three different classes (1st class,
business class, and economy class). For a flight to be financially profitable, the
amount generated by the sale of seats must be greater than $635 000.
Cost of the tickets
Class
Cost of ticket
Economy
$1 000
Business
$4 775
1st class
$16 400
Distribution of the seats aboard the
aircraft
Business Class 10%
1st Class
2.5%
Economy Class
87.5%
The flight attendant notices that:

3
of economy class seats are unoccupied;
20

3
of business class tickets have been sold;
4

Half of the 1st class seats are occupied
The flight attendant states before takeoff that today's flight will be profitable.
Is the statement made by the flight attendant accurate or inaccurate?
12. The Play Pen
Bernard would like to build a fenced-in enclosure for his dogs to play. This
enclosure will be a circular sector whose central angle is 45 and will have an
area of 40 m2.
The fencing is sold by the metre and he already has 5 m of fence.
How many metres of fencing does he need to buy in order to construct
this enclosure?
13. Marbles
A bag contains 5 red marbles, 3 green marbles and two yellow marbles. Two
consecutive draws are performed without replacement.
Nadia claims that the probability of drawing a green marble in the first draw is
higher than the probability of drawing at least one yellow marble during both
draws.
Marianne disagrees.
Who is right?
14. Claude’s Argument
If an arc measures twice its radius, Claude argues that the measure of the central
angle will be
360

.
Help him prove his argument with 3 examples.
15. The Parking Lot
The parking lot of a bakery is shaped like the figure below:
12x
2x
4x +
4
6x 
3
The owner of the bakery wants to redo the asphalt that covers the parking lot and is
curious to see how much it would cost.
The following information is important in assessing the total cost:

The cost of asphalt is $15 per m2;

The perimeter of the parking lot is 360 m;

The owner’s budget is $80 000.
Is the owner’s budget large enough to cover the cost of paving the parking lot?
16.
The Gift Boxes
Kish has two boxes. Box #1 is in the form of a prism with a rectangular base and a
height of 10 cm.
Box #2 is cylindrical in shape.
The radius of box #2 measures
3
of the height of Box #1.
5
Kish wants to use the same amount of paper to wrap both boxes.
Box #1
Box #2
height
30 cm
10 cm
r
20 cm
What should the height of box #2 be in order to ensure that the same amount of
paper is used for each box?
June 2013 Exam