Name: ________________________ Exam Date: __________
ID: A
UNIT #8 PRACTICE EXAM ~ UNIT RATES AND SCALE FACTORS
~ USE A RULER TO HELP YOU ANSWER SOME OF THE QUESTIONS ~
Multiple Choice
Identify the choice that best completes the statement or answers the question.
9. The original eraser for these scale diagrams was
7.0 cm long.
Which diagram was drawn using a scale factor of
0.9?
1. It takes 7.5 h to fill a 6000 L ornamental pond.
What is the rate in litres per second?
A 800 L/s B 13.3 L/s C 0.22 L/s D 0.125 L/s
2. Maureen ran 15 km in 1.25 h. What is her running
speed?
A 12 km/h B 200 m/s C 15 km/h D 120
m/min
A
3. A 454 g block of butter costs $4.37. What is the
price per 100 g?
A $1.09/100 g B $0.10/100 g C $0.96/100 g
D $1.04/100 g
4. A dozen eggs cost $2.63. What is the unit rate?
A $0.22/egg B $0.26/egg C $0.45/egg
D $2.63/dozen
B
5. An 8 kg bag of potatoes costs $9.15. What is the
unit rate?
A $9.15/8 kg B $0.87/kg C $1.14/kg
D $0.99/kg
C
10. The graph shows how a cyclist travels over time.
Over which interval is the cyclist travelling the
slowest?
6. A 2 L carton of milk costs $3.26. What is the unit
rate?
A $0.83/500 mL B $1.63/L C $0.61/L
D $3.27/2 L
7. Olga drove 346 km and used up 28.7 L of gas.
What is her car's fuel efficiency?
A 12 km/L B 12 mL/km C 0.083 L/km D 8.29
L/100 km
8. A 4.5 kg package of wild Pacific salmon costs
$108. Which equation determines
the amount of salmon, A, in kilograms, you could
buy for $8?
ÊÁ 4.5kg ˆ˜
ÁÊ $108 ˜ˆ˜
Á
˜˜
˜˜
A A = ($8) Á
ÁÁ
˜˜ B A = ($8) ÁÁÁÁ
˜
Á $108 ˜
Ë 4.5kg ¯
Ë
¯
ÊÁ 4.5kg ˆ˜
Á
˜˜˜ D A = ($8) ÊÁ 4.5 kg ˆ˜
C A = ($108) Á
ÁÁ
Ë
¯
Á $8 ˜˜
Ë
¯
A
1
BC
B
DE
C
EF
D
FG
Name: ________________________
ID: A
11. The graph shows how a cyclist travels over time.
Over which interval is the cyclist travelling at 4.5
km/h?
14. Which situations could be described using the rates
$15.56/lb, 80 km/h, and $1.58/L?
A price of nails, average human running speed,
price of sunflower oil B price of coffee, cruising
speed of an airplane, price of milk C price of
lobster, highway speed limit, price of apple juice
D price of crude oil, average speed of a truck, price
of cola
15. It takes 4 h 26 min to fill a 3600 L water tank.
Which equation determines
the length of time, t, in minutes, it will take to fill a
1700 L water tank?
A
A
AB
B
BC
C
CD
D
FG
B
12. The graph shows how a cyclist travels over time.
What does a zero slope mean in the context of this
graph?
C
D
ÊÁ 4 ⋅ 60min+ 26min ˆ˜
˜˜
t = (1700L) ÁÁÁ
˜˜
ÁË
3600L
¯
ÊÁ
ˆ˜
3600L
˜˜
t = (1700L) ÁÁÁÁ
˜˜
4
⋅
60min+
26min
Ë
¯
ÁÊÁ 4 ⋅ 60min+ 26min ˜ˆ˜
˜˜
t = (3600L) ÁÁÁ
˜
1700L
Ë
¯
ÁÊÁ 4.26h ˜ˆ˜
˜˜
t = (1700L) ÁÁÁ
˜
Ë 3600L ¯
16. The dosage of an antibiotic medicine for a person
with a mass of 90 kg
is 12 mL. Which equation determines the amount
of medicine, A,
in millilitres, needed for a person with a mass of
65 kg?
A
The cyclist is travelling very fast. B The
cyclist is travelling parallel to the starting point.
C The cyclist is travelling on a flat surface.
D The cyclist is not moving.
C
A
ÊÁ 12mL ˆ˜
˜˜
P = ÊÁË 90kg ˆ˜¯ ÁÁÁÁ
˜˜
65kg
Ë
¯
ÁÊ 12mL ˜ˆ˜
˜˜
P = ÊÁË 65kg ˆ˜¯ ÁÁÁÁ
˜
Ë 90kg ¯
B
D
ÊÁ 90kg ˆ˜
Á
˜˜
P = (12mL) ÁÁÁ
˜
Á 65kg ˜˜
Ë
¯
ÊÁ 90kg ˆ˜
Á
˜˜˜
P = ÊÁË 65kg ˆ˜¯ ÁÁÁ
Á 12mL ˜˜
Ë
¯
17. Lamar jogs, at 11 km/h, burning 276 Cal in 15 min.
Angela jogs at 9 km/h, burning 320 Cal in 30 min.
Lamar jogs for 1 h. Which equation determines the
length of time, t, in minutes, that Angela needs to
jog to burn the same number of calories as Lamar?
13. Which factors would not affect your
decision to buy electronics in the U.S.
rather than in Canada?
distance from Canada/U.S. border, merchandise
prices, shipping method B duty, merchandise
availability, gas prices C payment method,
merchandise colour, exchange policy D budget,
time of year, exchange rate
A
2
A
t = 4 (276Cal) − 2 (320Cal)
C
t = (4) (276 Cal)(2) (320Cal)
B
2(320Cal)
4(276Cal)
4(276Cal)
t=
2(320Cal)
t=
D
Name: ________________________
ID: A
20. Lucas drove 116 km in 1 h 45 min and
used 14 L of fuel.
Which equation determines his average
fuel consumption, C,
in litres per 100 km?
18. Cashews cost $8.72 for 350 g. Peanuts
cost $19.80 for 2 kg.
Jack buys 750 g of cashews. Which
equation determines
the number of kilograms of peanuts, A,
Jack could buy for the same cost?
A
B
C
D
A=
A=
A=
A=
A
ÊÁ 750g ⋅ $8.72 ˆ˜ ÊÁ 2kg ˆ˜
ÁÁ
˜˜ ÁÁ
˜˜
ÁÁ
˜˜ ÁÁ
˜
Á
˜ Á $19.80 ˜˜
350g
Ë
¯Ë
¯
ÊÁ 750g ⋅ $8.72 ˆ˜ ÁÊ $19.80 ˜ˆ
ÁÁ
˜˜ ÁÁ
˜˜
ÁÁ
˜˜ ÁÁ
Á
˜ Ë 2kg ˜˜¯
350g
Ë
¯
Ê
ˆ˜
750 g
ÁÊÁ $19.80 ˜ˆ˜ ÁÁÁ
˜˜
ÁÁ
˜˜ ÁÁ
Á 2kg ˜ Á 350 g ⋅ $8.72 ˜˜˜
Ë
¯Ë
¯
ÊÁ 350g ⋅ $8.72 ˆ˜ ÊÁ 2kg ˆ˜
ÁÁ
˜˜ ÁÁ
˜˜
ÁÁ
˜˜ ÁÁ
˜
Á
˜
Á
750g
$19.80 ˜˜
Ë
¯Ë
¯
C
C
D
B
116 km ⋅ 14L
100km
ÊÁ 14L ˆ˜
˜˜ (100 )
C = ÁÁÁÁ
˜˜
116
km
Ë
¯
C=
D
21. Which scale factor(s) will produce an image that is
larger than the original?
I. 0.86
II. 116%
8
III.
5
19. It costs $2.25/lb, plus a loading
fee of $30, to send freight by
airplane around the Yukon and
the Northwest Territories.
Which equation determines the
amount of fresh fruit, A, you
can ship from Vancouver to
Whitehorse for $81, in
pounds?
A
ÊÁ 116 km ˆ˜
˜˜ (14L)
C = ÁÁÁÁ
˜˜
1.75h
Ë
¯
ÊÁ 14L ˆ˜
˜˜
C = (1.75h ) ÁÁÁÁ
˜˜
116km
Ë
¯
A I only
II, and III
B
I and II only
C
II and III only
D
I,
22. Which scale factor(s) will produce an image that is
smaller than the original?
I. 37%
4
II.
12
III. 9.6
$81
$81 − $30
B A=
$2.25/lb
$2.25/lb
$81
A=
+ $30
$2.25/lb
A = ($81 − $30) ($2.25/lb)
A=
A I only
II, and III
3
B
I and II only
C
II and III only
D
I,
Name: ________________________
ID: A
23. The original pushpin for these scale diagrams was 24 mm long.
Which diagram was drawn using a scale factor of 3.5?
A
B
C
D
24. A billboard is 5.0 m by 2.5 m. A scale diagram of the billboard must fit in a space that is 18 cm by 15
cm. Which scale would be the most reasonable one to use for the scale diagram??
A
1 m:3 cm
B
30 cm:1 cm
C
1 cm:3 m
D
300%
25. A picture is 46 cm by 32 cm. A scale diagram of the picture must fit in a space that is 3 m by 2 m.
Which scale would be the most reasonable one to use for the scale diagram?
A
60%
B
1 cm:60 cm
C
6 cm:1 m
D
1 cm:6 cm
26. A computer chip is 12 mm by 26 mm. A scale diagram of the computer chip must fit in a space that is
40 cm by 70 cm. Which scale would be the most reasonable one to use for the scale diagram?
A
1 mm:33.3 cm
B
1 mm:26 cm
C
1 mm:3.3 cm
D
1 mm:2.6 cm
27. 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
28. Leo has a microscope with a lens that magnifies by a factor of 80. He was able to capture the image of
a slide containing human skin cells. In the image, the cell was about 5.6 mm long. Determine the
length of the actual human skin cell, to nearest hundredth of a millimetre.
4
Name: ________________________
ID: A
29. Suppose that tap water, flowing from a faucet at a
constant rate, is used to fill a container. Draw the
container represented by the graph. Justify your
answer.
30. The gas tank of Salma's van holds
about 110 L. She can either buy gas
in her town at $1.18/L or travel
across the U.S. border to fill up at
$3.03 U.S./gal (1 U.S. gallon = 3.79
L). The current exchange rate is $1
U.S./$1.05 Cdn. Salma will use less
than 1 L of gas to drive 5 min to her
local gas station and one third of a
tank to make the 2 h round trip to
the nearest gas station across the
U.S. border. Which option makes
more sense? Justify your decision.
31. A passenger jet leaves an airport that is
2000 ft above sea level at
10.40 a.m. The jet climbs steadily to a
cruising altitude of 44 000 ft,
at a rate of 6000 ft/min. After cruising
at this altitude for 3 h 15 min,
the jet descends steadily at a rate of
4150 ft/min to an airport that is
2500 ft above sea level. What time
does the jet land? Show your work.
5
ID: A
UNIT #8 PRACTICE EXAM ~ UNIT RATES AND SCALE FACTORS
~ USE A RULER TO HELP YOU ANSWER SOME OF THE QUESTIONS ~
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
C
A
C
A
C
B
C
A
C
B
B
D
C
C
A
C
D
A
B
D
C
B
A
A
D
D
C
SHORT ANSWER
28. 0.07 mm
1
ID: A
PROBLEM
29. The container will be a flask with a wide bottom and a narrow top because the water fills the container slowly at
first then more rapidly.
30. Fill up in Canada: (110 L)($1.18 Cdn/L) = $129.80 Cdn
Fill up in U.S.:
ÊÁ 1gal ˆ˜
Á
˜˜˜ = 29.023... gal
Convert 110 L into gallons: (110 L) ÁÁÁ
Á 3.79L ˜˜
Ë
¯
Determine the cost for a full tank: (29.023... gal)($3.03 U.S./gal) = $87.94 U.S.
Determine the cost in Canadian dollars: ($87.94 U.S)($1.05 Cdn/$1 U.S.) = $92.34 Cdn
Because Salma must use one third of a tank of gas to travel to the U.S., she is paying $92.34 Cdn for two thirds of
2
a tank of gas. Since this amount is more than ($129.80 Cdn) = $86.53, filling up in Canada makes most sense
3
because it costs less, takes less time, and wastes less fuel.
31. For 2000 ft to 44 000 ft:
Altitude = 44 000 ft – 2000 ft
Altitude = 42 000 ft
altitude
Time 1 =
rate
Time 1 =
42000ft
6000ft/min
Time 1 = 7min
Time 2 = 3 h 15 min
For 44 000 ft to 2500 ft:
Altitude = 44 000 ft – 2500 ft
Altitude = 41 500 ft
altitude
Time 3 =
rate
Time 3 =
41500ft
4150ft/min
Time 3 = 10min
Time of arrival = initial time + time 1 + time 2 + time 3
Time of arrival = 10:40 a.m. + 7 min + 3 h 15 min + 10 min
Time of arrival = 1:40 p.m. + 7 min + 15 min + 10 min
Time of arrival = 1:40 p.m. + 32 min
Time of arrival = 2.12 p.m
2