Download Enriched Pre-Algebra Chapter 4 Test Review Short Answer Each

Enriched Pre-Algebra Chapter 4 Test Review
Short Answer
Each pair of polygons is similar. Write a proportion to find each missing measure. Then solve. Show your
work.
1.
18.8
9.4
k
5
14.8
16.8
7.4
8.4
Solve.
2. An architect’s blueprint for a house shows the master bedroom being 4.5 inches wide. If the scale used to
create the blueprint is 0.25 in. = 1 ft, what is the actual width of the master bedroom?
3. A scale model of the Statue of Liberty is 5 feet tall. If the Statue of Liberty is 305 feet tall, find the scale of
the model.
4. A map has a scale of 2 centimeters = 15 kilometers. If the distance between two cities on the map is 9
centimeters, what is the actual distance between the cities?
Express each ratio in simplest form.
5. 12 yards to 18 feet
6. 40 chosen out of 96 applicants
7. 36 minutes per hour
Express each rate as a unit rate.
8. 355 yards in 43 seconds
9. $894 for 36 hours
10. $32.50 for 6.5 pounds of ham
Tamara works in the gift wrapping department of a retail store. The table shows the number of gifts the
department wrapped between 3:00 and 4:55 P.M.
3:00
0
Time
Gifts Wrapped
3:25
27
4:05
51
4:55
105
11. Find the rate of change in gifts wrapped per minute between 3:00 and 4:05 P.M.
12. Find the rate of change in gifts wrapped per minute between 3:25 and 4:55 P.M.
The triangles shown are similar. Write a proportion to solve the problem. Round to the nearest tenth, if
necessary. Show your work.
13. What is the height of the tree?
Write a proportion to determine the missing measure. Round to the nearest tenth, if necessary.
14. The Eiffel Tower in Paris casts a shadow that is about 558.7 feet long. At the same time, a nearby tourist casts
a shadow that is 3.4 feet long. If the tourist is 6 feet tall, what is the height of the Eiffel Tower?
15. From the shoreline of a lake, the ground slopes down under the water at a constant decline. If the water is 4
feet deep at a horizontal distance of 10 feet from the shore, how far from the shore is the water 30 feet deep?
Solve each proportion. Show your work.
16.
17.
The points given in each table lie on a line. Find the slope of the line.
18.
x
y
–9
–9
–4
7
1
23
6
39
x
y
–2
30
–1
24
0
18
1
12
19.
Enriched Pre-Algebra Chapter 4 Test Review
Answer Section
SHORT ANSWER
1. ANS:
10
Sample:
25.8
8.6
k
5
21.6
7.2
22.8
7.6
Set up a proportion using any two pairs of sides and solve for k.
PTS: 1
DIF: Average
OBJ: 4-5.2 Find missing measures of similar polygons.
STA: GSS.1
TOP: Find missing measures of similar polygons.
KEY: Similar polygons | Proportions
MSC: 1999 Lesson 5-6 | 1999 Lesson 8-7
2. ANS:
18 ft
Set up a proportion and solve for the width.
PTS: 1
DIF: Average
OBJ: 4-6.1 Solve problems involving scale drawings.
STA: GSS.1
TOP: Solve problems involving scale drawings.
KEY: Scale drawing | Proportions
MSC: 1999 Lesson 8-9
3. ANS:
1:61
The model and the actual statue have the same units, so it is not necessary to include them in the scale. Divide
out the common factor from both terms.
(5 ÷ 5):(305 ÷ 5)
1:61
PTS: 1
DIF: Basic
OBJ: 4-6.1 Solve problems involving scale drawings.
STA: GSS.1
TOP: Solve problems involving scale drawings.
KEY: Scale drawing | Proportions
MSC: 1999 Lesson 8-9
4. ANS:
67.5 km
Set up a proportion and solve for the distance.
PTS: 1
DIF: Average
OBJ: 4-6.1 Solve problems involving scale drawings.
STA: GSS.1
TOP: Solve problems involving scale drawings.
KEY: Scale drawing | Proportions
MSC: 1999 Lesson 8-9
5. ANS:
2 to 1
Write both terms with a common unit. Then reduce the numbers by dividing out the greatest common factor.
1 yd = 3 ft
PTS: 1
DIF: Average
OBJ: 4-1.1 Express ratios as fractions in simplest form.
STA: NSO.6
TOP: Express ratios as fractions in simplest form.
KEY: Ratios | Fractions
MSC: 1999 Lesson 3-1
6. ANS:
5 to 12
Reduce the numbers by dividing out the greatest common factor.
PTS: 1
DIF: Basic
OBJ: 4-1.1 Express ratios as fractions in simplest form.
STA: NSO.6
TOP: Express ratios as fractions in simplest form.
KEY: Ratios | Fractions
MSC: 1999 Lesson 3-1
7. ANS:
3 to 5
Write both numbers using the same unit. Then reduce the numbers by dividing out the greatest common
factor.
1 hr = 60 min
36 to 60
3 to 5
PTS: 1
DIF: Average
OBJ: 4-1.1 Express ratios as fractions in simplest form.
STA: NSO.6
TOP: Express ratios as fractions in simplest form.
KEY: Ratios | Fractions
MSC: 1999 Lesson 3-1
8. ANS:
about 8.3 yards/second
The unit rate is the distance in 1 second.
PTS: 1
STA: NSO.6
DIF: Average
OBJ: 4-1.2 Determine unit rates.
TOP: Determine unit rates.
KEY: Unit rates | Ratios
MSC: 1999 Lesson 3-1
9. ANS:
$24.83/hour
The unit rate is the amount earned for 1 hour.
$894 ÷ 36 = $24.83/hour
PTS: 1
DIF: Average
OBJ: 4-1.2 Determine unit rates.
STA: NSO.6
TOP: Determine unit rates.
KEY: Unit rates | Ratios
MSC: 1999 Lesson 3-1
10. ANS:
$5.00/pound
The unit rate is the cost of 1 pound of turkey breast.
$32.50 ÷ 6.5 = $5.0/ham
PTS: 1
DIF: Average
OBJ: 4-1.2 Determine unit rates.
STA: NSO.6
TOP: Determine unit rates.
KEY: Unit rates | Ratios
MSC: 1999 Lesson 3-1
11. ANS:
0.78 gifts/minute
The rate of change is the difference in gifts wrapped divided by the difference in time.
gifts/minute
PTS: 1
DIF: Average
OBJ: 4-2.1 Find rates of change.
STA: NSO.6 | MEA.7
TOP: Find rates of change.
KEY: Rate of change | Ratios
12. ANS:
0.87 gifts/minute
The rate of change is the difference in gifts wrapped divided by the difference in time.
PTS: 1
DIF: Average
STA: NSO.6 | MEA.7
KEY: Rate of change | Ratios
13. ANS:
about 17.6 m
OBJ: 4-2.1 Find rates of change.
TOP: Find rates of change.
Set up a proportion using the sides of the similar triangles. Solve for the height of the tree, h.
PTS: 1
DIF: Average
STA: GSS.1 | GSS.3
KEY: Similar triangles | Proportions
14. ANS:
about 985.9 ft
OBJ: 4-7.1 Solve problems involving similar triangles.
TOP: Solve problems involving similar triangles.
MSC: 1999 Lesson 8-8
Set up a proportion using the sides of the similar triangles. Solve for the height, h.
PTS: 1
DIF: Average
STA: GSS.1 | GSS.3
KEY: Similar triangles | Proportions
15. ANS:
75 feet from the shore
OBJ: 4-7.1 Solve problems involving similar triangles.
TOP: Solve problems involving similar triangles.
MSC: 1999 Lesson 8-8
Set up a proportion using the sides of the similar triangles. Solve for the distance, d.
PTS: 1
DIF: Average
STA: GSS.1 | GSS.3
KEY: Similar triangles | Proportions
16. ANS:
6
Sample:
Cross multiply and solve for m.
OBJ: 4-7.1 Solve problems involving similar triangles.
TOP: Solve problems involving similar triangles.
MSC: 1999 Lesson 8-8
PTS: 1
DIF: Basic
STA: NSO.6 | MEA.7
KEY: Proportions | Problem solving
17. ANS:
16.5
Sample:
Cross multiply and solve for y.
OBJ: 4-4.1 Use proportions to solve problems.
TOP: Use proportions to solve problems.
MSC: 1999 Lesson 3-3 | 1999 Lesson 8-1
PTS: 1
DIF: Average
STA: NSO.6 | MEA.7
KEY: Proportions | Problem solving
18. ANS:
OBJ: 4-4.1 Use proportions to solve problems.
TOP: Use proportions to solve problems.
MSC: 1999 Lesson 3-3 | 1999 Lesson 8-1
16
5
Sample:
x
y
6
–3
10
–1
14
1
18
3
Select two points and use the slope formula:
(14, 1) and (18, 3)
PTS: 1
DIF: Average
STA: PFA.6 | PFA.13
KEY: Slope | Lines
19. ANS:
–6
Sample:
1
2
3
4
x
20
25
30
35
y
OBJ: 4-3.2 Find the slope of a line given a table.
TOP: Find the slope of a line given a table.
Select two points and use the slope formula:
(1, 20) and (2, 25)
PTS: 1
DIF: Basic
STA: PFA.6 | PFA.13
KEY: Slope | Lines
OBJ: 4-3.2 Find the slope of a line given a table.
TOP: Find the slope of a line given a table.