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 at 4.5 km/h?
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2.
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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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3.
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It costs $0.3172/lb to ship freight by barge
along the Pacific coast.
Which equation determines the cost, C, in dollars, to ship 2470
kg of building supplies from Vancouver to Prince Rupert?
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4.
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A screw has 64 turns over a distance of 40 mm of
thread.
Which equation does not determine the number of turns, t,
that a screw
with the same pattern has over 30 mm of thread?
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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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A photograph is 12 cm by 25 cm. A copy is made
using a scale factor of 75%. What are the dimensions of the copy?
a. | 9 cm by 19 cm | b. | 90 cm by 19 cm | c. | 9 mm by 19
cm | d. | 9 m by 19 m |
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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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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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9.
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Data for circle O is shown on the first line of the table. Circle
O is enlarged by a scale factor of 600%. Which circle is the enlargement of circle
O? Circle Name | Radius (cm) | Scale Factor | Area (cm2) | | O | 24 | 1 | 1809.56 |
1 | P | 122 | 600% | 65 122.00 | 36 | Q | 144 | 600% | 65 144.00 | 36 | R | 144 | 600% | 56 144.00 | 216 | S | 144 | 600% | 56 122.00 | 216 | | | | | |
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10.
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Data for rectangle ABCD is shown on the first line of the table.
Rectangle ABCD is reduced to an area of 13 cm 2. Which rectangle is the
reduction of rectangle ABCD?
Rectangle Name | Length (cm) | Width (cm) | Scale Factor | Area (cm2) | | ABCD | 9 | 13 | 1 | 117 | 1 | EFGH | 3 | 4 | | 13 | | JKLM | 4 | | | 13 | | NOPQ | 1 | | | 13 | | RSTU | 3 | | | 13 | | | | | | | |
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11.
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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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12.
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Data for trapezoid ABCD is shown on the first line of the table.
Trapezoid ABCD is reduced so the height is 2 cm. Which rectangle is the reduction 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 | | 2 | | | | | JKLM | 2 | 2 | 4 | | 8 | | NOPQ | | 2 | | | | | RSTU | | 2 | 6 | | 16 | | | | | | | | |
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13.
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Which one of the following cylinders is similar
to a cylinder that is 8 cm long and 2.5 cm in diameter? Choose the best answer.
a. | a cylinder 4 cm long and 1.5 cm in diameter | b. | a cylinder 12 cm
long and 3.5 cm in diameter | c. | a cylinder 16 cm long and 5 cm in
diameter | d. | all of the above |
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14.
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Which of the following saucepans are similar to a saucepan that is 9 cm deep, 16
cm in diameter, and has a handle 20 cm long?
a. | a saucepan 18 cm deep, 26 cm in diameter, and with a 40 cm handle | b. | a saucepan 12 cm
deep, 21.3 cm in diameter, and with a 26.7 cm handle | c. | a saucepan 5 cm deep, 8 cm in diameter, and
with an 11.5 cm handle | d. | none of the
above |
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15.
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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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Short Answer
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16.
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The base and height of a triangle with an area of 80 cm 2 will be
reduced by a scale factor of  . Determine the area of the reduced triangle to two
decimal places.
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17.
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The scale factor for two similar trapezoids is 1:3.
The sum of their areas
is 80 cm2.
Determine the area of each trapezoid.
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18.
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A carpenter creates two similar boxes with their dimensions related by a scale
factor of  . The smaller box has a surface area of 670 m 2. Determine the surface area of
the larger box.
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Problem
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19.
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Robert works 25 h every two weeks. At this rate, how many hours will he work in
one year? Explain how you could solve this problem using two different strategies.
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20.
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Lamar jogs at 11 km/h. When Lamar jogs at this
rate for 15 min, he burns 276 Cal. Angela jogs at a slower rate, 9 km/h, burning 641 Cal in 60
min. If Angela jogs for 2.5 h, how long will Lamar have to jog in order to burn the same amount of
Calories as Angela?
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21.
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Miniature villages in Europe are usually built with a scale of 1:25, while
miniature villages in England are usually built with a scale of 1:12. A European miniature post
office is 48 cm long, 32 cm wide, and 64 cm tall.
a) Estimate what the dimensions of the
post office would be using the English scale.
b) Determine the conversion ratio for
European:English.
c) Determine the dimensions of the building using the English scale, to
the nearest centimetre.
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