Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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The graph shows how a cyclist travels over time. Over which interval is the
cyclist travelling the fastest?
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2.
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15 kg of Yukon gold potatoes costs $32.70. Which equation determines the price,
P,
in dollars, of 4 lb of potatoes?
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3.
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Cashews cost $8.72 for 350 g. Peanuts cost $19.80 for 2 kg.
Jack buys $17.45
worth of cashews. Which equation determines the number of
kilograms of peanuts, A, Jack
could buy for the same amount of money?
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4.
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Which scale factor(s) will produce an image that is smaller than the
original? I. 37% II.  III. 9.6 a. | I only | b. | I and II only | c. | II and III
only | d. | I, II, and III |
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5.
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The original stapler for these scale diagrams was 18 cm long.
Which diagram
was drawn using a scale factor of 30%?
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6.
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One way signs have a standard width of 90 cm. Measure the scale diagram of
the one way sign to determine which scale factor was used to draw it.
 a. | 20 | b. | 10% | c. |  | d. | 5% |
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7.
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A room in a floor plan is 8.4 cm by 9.12 cm. The
floor plan was made using a scale factor of 0.024. What are the dimensions of the actual
room?
a. | 2 m by 2.19 m | b. | 20.16 m by 21.9 m | c. | 3.5 m by 3.8
m | d. | 202 cm by 219 cm |
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8.
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The distance between two towns on a map is 16.5
cm. The map was made using a scale of 5 cm to 100 km. What is the actual distance between the two
towns?
a. | 135 km | b. | 825 km | c. | 330
km | d. | 165 km |
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9.
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Data for circle O is shown on the first line of the table. Circle
O is enlarged so the radius is 30 cm. Which circle is the enlargement of circle
O? Circle Name | Radius (cm) | Scale Factor | Area (cm2) | | O | 24 | 1.00 | 1809.56 | 1
| P | 30 | 1.50 | 2728.43 | 1.675 | Q | 30 | 1.25 | 2728.43 |
1.5675 | R | 30 | 1.50 | 2827.43 | 2.25 | S | 30 | 1.25 | 2827.43 |
1.5625 | | | | | |
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10.
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Data for trapezoid ABCD is shown on the first line of the table.
Trapezoid ABCD is enlarged so the length of base a is 16 cm. Which rectangle is
the enlargement of trapezoid ABCD? Trape-
zoid
Name | Length of Base a (cm) | Length of Base b
(cm) | Height of
Trape-
zoid (cm) | Scale Factor | Area (cm2) | | ABCD | 8 | 6 | 16 | 1 | 112 | 1 | EFGH | 16 | 6 | 16 | 0.5 | 176 |
0.25 | JKLM | 16 | 12 | 32 | 2 | 448 | 4 | NOPQ | 16 | 16 | 28 | 2 | 448 | 4 | RSTU | 16 | 3 | 8 | 0.5 | 76 |
0.25 | | | | | | | |
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11.
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A 1:6 scale model of canoe is 30 in. long, with a
beam (width) of 5.3 in. and a depth of 2.2 in. What are the dimensions of the actual
canoe?
a. | 15 ft long, 31.8 in. beam, 13.2 in. deep | b. | 18 ft long, 38 in.
beam, 12 in. deep | c. | 13 ft long, 32 in. beam, 15 in.
deep | d. | 12 ft long, 18.5 in. beam, 3.2 in. deep |
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12.
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A sideboard cabinet is 90 cm tall, 176 cm wide,
and 65 cm deep. What are the dimensions of a scale model built using a scale of
1 : 4?
a. | 18 cm tall, 35.2 cm wide, 13 cm deep | b. | 22.5 cm tall, 44 cm wide, 16.25 cm
deep | c. | 24 cm tall, 45 cm wide, 17.5 cm deep | d. | 20.25 cm tall, 42 cm wide, 12.5 cm
deep |
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13.
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A stage director needs a large chess pawn for a
scene. The pawn in her chess set is 35 mm tall and she estimates that the height of the enlarged
pawn must be 700 mm.
What scale factor must she apply to create the enlarged pawn?
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14.
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A stage director needs a large chess pawn for a
scene. The pawn in her chess set is 35 mm tall and she estimates that the height of the enlarged
pawn must be 700 mm.
How many times greater will the volume of the larger pawn
be?
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15.
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A cylindrical oil tank is filled with 500
m 3 of oil. A similar oil tank has dimensions that are reduced by a scale factor of
 . What volume of oil will fill the smaller tank? a. | 1687.5 m3 | b. | 148 m3 | c. | 333 m3
| d. | 222 m3 |
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Short Answer
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16.
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Orange juice is sold in 2 L cartons and 350 mL boxes.
A 2 L carton sells for
$3.99 and six 350 mL boxes sell for $4.99.
Which size has the lower cost per millilitre? Show your
calculations.
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17.
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Yogurt is sold in 750 mL tubs and 125 mL cups.
A 750 mL tub sells for $2.69
and twelve 125 mL cups sell for $4.19.
Which size has the lower unit cost? Show your
calculations.
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18.
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A 1:8 scale model of a cast iron wood stove is 3.6 cm tall, 3.0 cm wide, and 3.2
cm deep. Determine the actual dimensions of the stove.
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Problem
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19.
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The floor plan for a small industrial company is drawn as shown, using a scale
factor of 0.002. a) What are the actual dimensions of the company? Show your work. b)
What is the actual area of the kitchen? Show your work. 
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20.
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Choose a piece of furniture at home and measure its dimensions. Draw a scale
diagram of the object that shows the top, side, and front views.
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21.
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A movie theatre sells popcorn in a box shaped like a rectangular prism that is
18.0 cm high and has a square base sides with 10.0 cm long. The movie theatre wants a
similar container that can hold one-third more popcorn.
a) Determine the ratio that
compares the capacity of the new container to the volume of the original container.
b)
Determine the dimensions of the new container to the nearest tenth. Explain what you did.
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