Download Bridgeport School

Cape Breton Victoria Regional
School Board
Bridgeport
Mathematics 9 Examination
January 29, 2009
Ms. T. Jamieson
Student Name:_____________
Exam Mark:_____
GOOD LUCK!!!
Bridgeport School
Grade 9 Math Examination
Part I:
Selected Response
25%
1. What is the greatest common factor of the expression 9a2b3z4 +
15ab2z3 + 33bz2
A bz2
B abz2
C 3bz2
D 3bz
2. Which is the simplified expression for the perimeter of a
rectangle with a width of 3x and a length of 2x + 4?
A 3x + 2x + 4
B 3x + 2x+ 4 + 3x + 2x + 4
C 6x2
D 10x+ 8
3. A restaurant allows only children who are at least 60 cm tall but
no more than 120 cm in its play area. Which set notation
represents the statement?
A {x | 60 < x < 120, x  R}
B {x | 60  x  120, x  R}
C {x | x  120, x  R}
D {x | x  60, x  R}
4. Solve: 15x – 7x = –52 – 5x
Ax=4
Bx=3
C x = –4
D x = –3
5. Which graph represents {x | –2 < x  3, x

I}?
A
–4 –3 –2 –1 0 1 2 3
4 5 6
B
–4 –3 –2 –1 0 1 2 3
4 5 6
C
–4 –3 –2 –1 0 1 2 3
4 5 6
–4 –3 –2 –1 0 1 2 3
4 5 6
D
2
6. Which equation is incorrect?
A 23 + 33 = 53
B 45  43 = 48
C (54)2 = 58
D (–2)3  (–2)  (–2)5 = (–2)9
7. Which number represents 0.000 000 008 02
A 8.02  1010
B 8.02  10–8
C 8.02  10–9
D 8.02  108
8. Which number is equal to 2-3?
A –8
B –16
1
8
1
D
16
C
9. Solve for m: m(5-7) = 10
Am=5
B m = -5
C x = 20
D x = 12
10. √144 is
A a whole number
B a rational
C an integer
D all of these
11.What two terms were multiplied to give the tile model shown?
A
B
C
D
x2
x2
xy
xy
xy
x2
x2
xy
xy
xy
x( x  y )
2 x( x  y )
2 x(2 x  3 y )
2 x( x  3 y )
3
12. The expanded form of 3m(2m  2) is:
A
B
C
D
6m 2  6m
6m 2  6m
 6m 2  6m
2 x( x  3 y )
13. In the term 3y 4 , the literal coefficient is ______.
A 3
B y
C y3
D 4
14. 5k 2 + 5k is an example of a(n):
A
B
C
D
expression
monomial
binomial
literal coefficient
15. The distributive property is used to ____ an expression.
A
B
C
D
factor
expand
binomial
divide
16. Which expression is the simplified form of the tiles shown?
+
A
B
C
D
xy  y 2  x  y
 xy  y 2  x  y
 xy  2y 2  x  y
5 xy  y 2  x  y
17. Which of the following is true?
A All real numbers are rational.
B All integers are whole numbers.
C All natural numbers are integers.
D All real numbers are irrational.
4
18. On her way to school, Cora takes a diagonal short cut across a
rectangular parking lot that measures 60m  40m.
Approximately how much longer would her route be if she
walked along the sides instead?
A
B
C
D
72.1m
27.9m
100m
50m
19.Which sentence is replaced by the equation 3(n  4)  30 ?
A
B
C
D
Four more than three times a number is thirty.
Three times the sum of a number and four is thirty.
A number tripled and increased by four is thirty.
Three times a number plus four is thirty.
20.Which equation has the solution p  7 ?
A 5 p  6  26
B 7 p  1  49
C  6 p  8  34
D
2p  4
4
4
21.I am irrational. I am the ratio of the circumference of a circle
and its diameter. What am I?
A
B
C
D
the radius

diameter
none of these
22.The number of hairs in the human body is 1.5  10 5 . There are
approximately 5  10 9 people in the world. Calculate the
approximate number of human hairs in the world.
A
B
C
D
6.5  1014
7.5  10 45
7.5  1014
6.5  10 45
5
23.Which equation is incorrect?
 1
 
 4
A (–4)–3 =
B 5–3 =
5
C
 2
 
 3
 1
 
 3
2
D
 1
 
 5
=
3
3
 3
 
 2
5
= 32
24.A rule for expanding expressions:
A
B
C
D
factoring
distributive property
zero principle
algebraic modeling
25.Which number is equal to 3-2?
A –6
B –9
1
27
1
D
9
C
6
Part II:
Short Response
40%
Instructions: COMPLETE 8 QUESTIONS. Read each question carefully.
Please note that each question has a choice; do either the first or the second
of each number. SHOW YOUR WORK!
#1.
a) Draw an area model for the expression y 2  6 y  8 . Write an equation
that relates the factors to the algebraic expression for the area. (2
points)
b) Expand and simplify. (3 points)
m 2 (m  3)
(2m  n 2 )(m  n 2 )
 4( x 2  2 x  1  3( x 2  3)
7
OR
#1
a) What two binomials are multiplied in the diagram below? Show the
product by filling in the missing tiles. Write an equation that shows
the factors and the product. (1.5 points)
x
x
1 1
x
1
1
b) Write a simplified expression to show the area of the shaded region in
the diagram below. Show all your work. (3.5 points)
x-1
x
2x-2
X+4
8
#2
a) Show how you would find expressions for the perimeter and the area
of the rectangle below. (2 points)
x2
x2
x x
x2
x2
x
x x
x x
x
x x
b) Using an area model, show how you would find the perimeter of a
rectangle with an area of x 2  8 x  15 . (3 points)
OR
#2
a) The perimeter of a square is 4xy + 8x.
i. What is the length of one side? (1 point)
ii. What is the area of this square? (1 point)
b) Find the area and perimeter of this figure. (3 points)
2x
2x + 3
3y
4y
9
#3
Kathryn swims across a river that is 30 m wide. The current carries her
downriver 40 m from where she wanted to land. Show a diagram. Calculate
the distance from her starting point to where she arrived on shore.
OR
#3
The sun deck attached to Bob’s house is made up of two squares ( A and B)
and a triangle C . The area of square A is 64m2. The area of square B is 9m2.
A step has to be cut and placed along the longest side of the triangle. How
long will the step be? Give your answer rounded to one decimal place.
10
#4
Solve and verify your answers. Plot your solutions on the number line
provided.
a)
c
28
5
b)
y
y
1
≤ +
where y belongs to the set of real numbers
4
3
2
11
OR
#4
a) 2(f + 4)  7f – 27 where f belongs to the set of natural numbers
b)
3 x  6 5 x  10

4
10
12
#5
The dinner roll sales for three outlets of Bread Bakery for two weeks are
shown.
Shop 1
Shop 2
Shop 3
Week 1
104
90
75
Week 2
99
108
120
a) Write a matrix to display the data. What are the dimensions of the
matrix?
b) Write a matrix for the total number of dinner roll sales for each store.
c) Calculate the revenue for each store if each roll sells for $0.45. Which
store has the greatest revenue?
OR
#5
Find the missing terms in each of the following matrices. (5 points)
 2
a) 

 2 4



y  1 5   3 5
x=______
x
y=_______

3
 3

4
b)  0
n
7


1
2
 p  2
3
m=_____

m  3

6 


7 

n=_____


 3 3 3 


2
 0
6
3


 5

2 7 
 1

8
p=_____
13
#6
a) Janie has three children. She bought two fish and one fish bowl for
each child. Each fish cost x dollars. Each fish bowl cost y dollars.
Draw the area model and give the algebraic expression that
determines how much Janie spent.
OR
#6
Sam went on a trip and decided to leave his car parked at the airport. The
cost was $12 for the first day and $9 for each additional day. Using an
algebraic expression, find out how many days he was away if Sam paid $120
for his parking.
14
#7
The area of a dining room is 12x2 and the area of the living room and the
dining room together is 47x2 + 5x.
balcony
5x
living
room
dining
room
3x
7x + 1
a) What is the length of the balcony?
b) What is the area of the living room only?
OR
#7
The area of a skate park can be described by 12 x 2  36 x in km2. Give 3
possible models for this park based on the expression for the area. Which
model would give the park with the greatest values for both length and
width? If x=2km, what is the area of the park?
15
#8
Halifax Regional Municipality (HRM) white pages telephone book contains
585 pages of telephone numbers. Each page has 4 columns, each with 90
phone numbers. Each phone number has 7 digits.
a) How many phone numbers are in the white pages? Write the answer
in scientific notation.
b) How many digits are there in the white pages? Write the answer in
scientific notation.
c) Is this an accurate reflection of how many people live in HRM or how
many phones are in HRM?
OR
#8
Arrange the following on a number line in ascending order.
22
7

-12 -11
-10
10
3.141 592
-9
-8
-7
-6
-5
-4
9.5
-3
-2
-1
 22
7

0
1
2
3
 355
113
4
5
6
7
8
9
10
11
12
Group these numbers as rational or irrational and justify your groupings.
Rational
Irrational
16
Part III:
Extended Response
35%
Instructions: COMPLETE 7 OF 10 questions.
1.
During the basketball playoffs, Leslie Thomas Junior High won 4 times
as many games as Cavalier, and Sackville Heights won 13 more games
than Cavalier. In total, the three schools won 79 games. How many
games did each team win? Solve using an algebraic equation.
2.
A movie theatre has to sell at least $1000 of tickets per movie in order
to pay for the cost of wages and the cost of the movie. The tickets sale
for a new movie is shown. How many adult tickets need to be sold in
order for the theatre to not lose money? Write an inequality and solve.
Ticket
Type
Adult
Number
Sold
$10.75
Youth
52
$8.75
Child
21
$5.50
Golden
15
age $5.00
17
3.
Stephan bought a cell phone, a hands-free ear piece, and a carrying case
all for $105.50, including tax. The phone was 7 times more expensive
than the ear piece, and the case was $20 more than the ear piece. How
much did each item cost?
4.
The perimeter of an isosceles triangle is 23 cm. The base is 4 cm less
than one of its other sides. What are the dimensions of the triangle?
18
5.
Determine the length of each side. Both figures have the same
perimeter. Write an algebraic equation and solve.
3x + 3
5x – 2
2x + 1
6.
The Murphy family decided to build a pool of the shape you see below.
The sides of the yard which measures 12 x  6 meters by 9x meters are
trisected. Because of municipal safety regulations, a rail must be placed
around the top of the pool. How much railing, in meters, will they
need? Because of the shape of the pool, they will have to get a custom
made solar blanket; how much material will they need?
12 x  6
9x
9x
19
7.
A rectangular garden must have a perimeter of at least 66 m and no
more than 82 m. The base must be 3 times the height plus 1 m. Solve
the inequality.
8.
Air Canada offers two different airline rates from Halifax to other
locations. From Halifax to Edmonton the best rate is $675, and the lastminute booking is $1250. From Halifax to Toronto the best rate is $230
and the last-minute booking is $550. From Halifax to St. John's the best
rate is $330 and the last-minute booking is $825.
A)
Create Matrix A to represent the charges for a round-trip ticket.
B)
Due to increased fuel costs, Air Canada increases ticket costs
by 15%. Create Matrix B to reflect these changes.
20
9.
Jay wants to plant a rectangular garden in which the length is 12m more
than four times the width. Ideally, he would like a garden that is at least
40m2 but not more than 91m2. If he surrounds the garden with a fence,
what will be the total length of fencing he will need? If the fencing
costs $9.00/meter, how much will the fence cost plus tax?
10. Using tiles, explain why a rectangle cannot be formed with an area of:
i) x 2  3x  1
ii) x 2  6 x  6
Create one other trinomial so that no rectangle is possible. What can
you conclude about these trinomials?
21