Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Determine the cube root of 512w3.
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2.
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Evaluate  . a. | 3 | c. |  | b. |  | d. | 9 |
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3.
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Which of the following is equivalent to  ?
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4.
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Write  as a power with a single positive exponent.
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5.
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Determine the product (x + 2)(x – 6).
a. | x2 – 12x – 12 | c. | x2 –
4x – 12 | b. | x2 + 2x –
12 | d. | x2
– 12x – 4 |
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6.
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The surface of Aaron’s computer desk has a width equal to 2x
– 4 and a length equal to 2x – 2. What equation represents the area of the surface
of the computer desk?
a. | A = 4x2 + 4x + 8 | c. | A = 4x2 +
12x + 8 | b. | A = 4x2 – 4x + 8 | d. | A = 4x2 –
12x + 8 |
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7.
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What is the greatest common factor (GCF) for the following set of terms? 12,
4x, 8x2, 16x2
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8.
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The area of a rectangular school gym floor is represented by the equation
A = 120x2 + 1800x. When the expression is factored fully, the factors
are the dimensions of the floor. The dimensions of the floor are
a. | 12x by x + 15 | c. | 60x by 2x +
30 | b. | 12x by 10x + 15 | d. | 120x by x +
15 |
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9.
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Which pair of integers has a product of –60 and a sum of 4?
a. | 6 and –10 | c. | 6 and 10 | b. | –6 and 10 | d. | –6 and
–10 |
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10.
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Identify the factored form of 2x2 + 13x + 20.
a. | (2x + 10)(x + 2) | c. | (2x + 2)(x +
10) | b. | (2x + 5)(x + 4) | d. | (2x + 1)(x +
20) |
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11.
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Which expression is equal to (a – b)2?
a. | a2 – ab + b2 | c. | a2 + ab + b2 | b. | a2
– 2ab + b2 | d. | a2 + 2ab +
b2 |
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12.
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Suppose the area of a rectangle is represented by the expression
100x2 – 49. When the expression is fully factored, the factors represent the
dimensions of the rectangle. What expressions represent the dimensions of the rectangle?
a. | 10x + 7 and 10x – 7 | c. | 10x – 7 and 10x
– 7 | b. | 10x + 7 and 10x + 7 | d. | 10 and 10x2 –
49 |
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13.
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State the domain of this function in set notation. 
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14.
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Which of the following represents the domain of the function  ?
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15.
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Use the table of values to determine the slope of the relation.  a. | –4 | c. |  | b. |  | d. | 4 |
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16.
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Which line segment(s) in the graph has (have) a positive slope?  a. | line segment AB | c. | line segments EF, IJ, and KL | b. | line segments AB,
EF, and CD | d. | line segments
IJ, KL, and GH |
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17.
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Which equation represents the line containing points M and N?  a. | y = –4x – 3 | c. | y =  x
– 3 | b. | y =  x – 3 | d. | y = 4x –
3 |
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18.
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The equation 3x – 6y – 2 = 0 in slope-intercept form
is
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19.
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What is the value of p in the equation of the line px + 2y
+ 8 = 0, such that the x-intercept is 4?
a. | 2 | c. |  | b. |  | d. | –2 |
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20.
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Points G(–3, 8) and H(0, 5) are on a line. Which equation represents a
line that is parallel to this line?
a. | y = 2x – 8 | c. | y = –x +
5 | b. | y = x – 5 | d. | y = –2x +
8 |
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21.
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Translate the statement “eight less than five times a number is two less
than three times the number” into an equation.
a. | 5x – 8 = 3x – 2 | c. | 5x + 8 = 3x –
2 | b. | 5x – 8 = 2 – 3x | d. | 5x + 8 = 2 +
3x |
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Answer the following question(s) using the information from the scenario
below.
FunNGames Video rents game machines for $10 and video games for $3 each. Big Vid
rents game machines for $7 and video games for $4 each. Let y represent the total rental cost,
in dollars, and let x represent the number of games rented.
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22.
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Determine which system of linear equations represents this situation.
a. | FunNGames: y = –3x + 10
Big Vid: y = –4x +
7 | c. | FunNGames: y = 4x + 7
Big Vid: y = 3x +
10 | b. | FunNGames: y = 3x + 10
Big Vid: y = 4x +
7 | d. | FunNGames: y =
10x + 3
Big Vid: y = 7x + 4 |
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Answer the following question(s) using the information from the scenario
below.
Katrin is looking at banquet halls for her parents’ anniversary party.
Moonlight Hall charges a fixed cost of $1000 plus $75 per guest. Riverside Hall charges $1500 plus
$50 per guest. Let C represent the total cost, in dollars, and let n represent the
number of guests.
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23.
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What are the coordinates of the solution?
a. | (20, 2500) | c. | (–20, 2500) | b. | (20, 0) | d. | (–20, 0) |
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24.
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What value of m gives a linear system with no
solution?
x(m – 1) – y = –6
2x + y =
3
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25.
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Determine the solution to the linear system y = 4x – 22 and
y = –6x + 18 by using the substitution method.
a. | (4, 6) | c. | (–6, 4) | b. | (–4, –6) | d. | (4, –6) |
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26.
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Which of the following ordered pairs represents the solution to the linear
system 6x + 4y = –12 and –x – 4y = 12?
a. | (–3, 0) | c. | (3, 0) | b. | (0, –3) | d. | (0, 3) |
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27.
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Ruby is 10 years older than Sam. The sum of their ages is 52. How old is
Sam?
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28.
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Larry’s rate of pay per hour is  of the amount that Poonam makes per hour.
Their combined salary after a 40-h workweek is $1960. What is Larry’s hourly rate of
pay?
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29.
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A surveyor, S, is measuring the width of a street, using a marker, M. The
surveyor cannot measure the width directly, because there is too much traffic. She stands on the east
side of the intersection. The marker is on the west side of the intersection, and is 18 m north of
the intersection. Determine the width of the street, to the nearest tenth of a
metre.  a. | 36.9 m | c. | 13.1 m | b. | 24.8 m | d. | 8.8 m |
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Use the diagram to answer the following question(s).
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30.
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Determine the length of y, to the nearest tenth of a metre.
a. | 5.7 m | c. | 7.0 m | b. | 6.3 m | d. | 8.2 m |
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31.
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Evaluate sin 67°, to four decimal places.
a. | 2.3558 | c. | 0.8554 | b. | 0.9205 | d. | 0.3907 |
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32.
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A window cleaner places a ladder that is 8 m long against a wall. The top of the
ladder is 6 m above the ground. Determine the angle between the base of the ladder and the ground, to
the nearest tenth of a degree.  a. | 36.9° | c. | 48.5° | b. | 41.4° | d. | 51.2° |
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33.
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The basic unit of length in the SI system is the
a. | centimetre | c. | metre | b. | kilometre | d. | millimetre |
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34.
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Jim wants to build a trundle wheel. He wants the wheel to go around once for
every 0.5 m the trundle wheel is pushed. What will be the diameter of his trundle wheel, to the
nearest hundredth?
a. | 1.57 m | c. | 0.08 m | b. | 3.14 m | d. | 0.16 m |
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35.
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Brenda states that her bedroom is 4.5 _____ wide. What unit is most appropriate
for this measurement?
a. | centimetre | c. | metre | b. | kilometre | d. | millimetre |
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36.
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The school gymnasium floor needs to be resurfaced. Hardwood flooring costs $5.75
per square foot plus $2.25 per square foot for installation. The gym measures 67 m by 66 m. At this
rate, how much will it cost to buy and install the hardwood flooring, to the nearest dollar?
a. | $380 784 | c. | $318 384 | b. | $273 689 | d. | $107 096 |
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37.
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Which formula can be used to calculate the volume of a right cylinder?
a. | V = pr2h | c. |  | b. | V = pr3h | d. |  |
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38.
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Which formula can be used to calculate the volume of a sphere?
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39.
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To the nearest tenth of a centimetre, what is the radius of a right cone with
volume 4353 cm3 and height 18 cm?
a. | 15.2 cm | c. | 6.1 cm | b. | 8.8 cm | d. | 5.1 cm |
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40.
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A can of soup has a radius of 3 cm and a height of 10 cm. The label on the can
covers the entire curved surface of the can. What is the area of the label, to the nearest
centimetre?
a. | 57 cm2 | c. | 245 cm2 | b. | 188 cm2 | d. | 283
cm2 |
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Short Answer
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1.
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Factor 15x2 + 9x + 5x + 3.
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2.
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a) What is the equation of the vertical line that passes through the
point (3, 4)?
b) What is the equation of the horizontal line that passes through the point
(3, 4)?
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3.
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Supplementary angles are angles that have a sum of 180°. If  and  are
supplementary, and  is 32° greater than  , what are the values of
 and  ?
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4.
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A ski jumper begins at the top of a ski jump hill that is 90 m high. The hill
makes an angle of 30° with the horizontal. Determine the length of the hill, to the nearest
metre.
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Problem
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1.
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Matthew’s pay increases by 10% every month. If his first pay is $400,
determine the amount of his pay in month 6.
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2.
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Jim likes to rock climb in his spare time. He recently climbed from the top to
the bottom of a 2500-ft cliff at a rate of 20 ft/min.
a) Write an equation, in function
notation, to represent Jim’s height, h, in feet, above the ground after t
minutes.
b) Make a table of values for Jim’s height above the ground for values of
t from 0 to 4 min.
c) What was Jim’s height above the ground
after 40 min?
d) How many minutes did it take Jim to reach the ground?
e) What
are the domain and range for this relation?
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3.
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The school chess club is selling T-shirts for a profit of $4 each and baseball
caps for a profit of $5 each. The club wants to sell 50 items and make a profit of $230.
a) Use a graph to determine how many of each item the chess club needs to
sell.
b) The chess club needs $400 to fund a tournament. The club would like to sell all 40
of the remaining caps to fund the tournament. How many T-shirts must the club sell?
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4.
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Gordon is buying some cheese. The cheese wedges are sold in three
sizes. 
a) What is the volume of each wedge of cheese?
Assume that the holes are part of the cheese wedge. b) Cheese wedge A costs $1.99, wedge B
costs $2.89, and wedge C costs $1.79. Which is the best buy? Explain your answer.
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5.
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Janet needs a rectangular piece of cardboard
measuring 21 ft by 24 ft for a school project.
a) What
is the area of the cardboard in square feet?
b) What is the area of the cardboard in square
yards? Show your calculations in two different ways.
c) The store charges
$0.35/m2 for cardboard. How much will the cardboard Janet needs cost?
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