Pre-Algebra Unit 8 Practice Test: Ratios, Rates, & Proportions ... - Weebly

ID: A

Pre-Algebra Unit 8 Practice Test: Ratios, Rates, & Proportions Answer Section

MULTIPLE CHOICE

1. ANS: B

PTS: 1

DIF: L2

REF: 6-1 Ratios and Unit Rates

OBJ: 6-1.1 Finding Rates and Unit Rates

STA: CA 7.MG.1.1 | CA 7.MG.1.3 | CA 7.AF.4.2

TOP: 6-1 Example 1

KEY: rate | unit rate | problem solving | ratio | word problem

2. ANS: C

PTS: 1

DIF: L2

REF: 6-1 Ratios and Unit Rates

OBJ: 6-1.1 Finding Rates and Unit Rates

STA: CA 7.MG.1.1 | CA 7.MG.1.3 | CA 7.AF.4.2

TOP: 6-1 Example 2

KEY: rate | ratio | unit rate

3. ANS: A

PTS: 1

DIF: L2

REF: 6-1 Ratios and Unit Rates

OBJ: 6-1.1 Finding Rates and Unit Rates

STA: CA 7.MG.1.1 | CA 7.MG.1.3 | CA 7.AF.4.2

TOP: 6-1 Example 2

KEY: rate | ratio | unit rate

4. ANS: B

PTS: 1

DIF: L3

REF: 6-1 Ratios and Unit Rates

OBJ: 6-1.1 Finding Rates and Unit Rates

STA: CA 7.MG.1.1 | CA 7.MG.1.3 | CA 7.AF.4.2

TOP: 6-1 Example 1

KEY: problem solving | rate | ratio | unit rate | word problem

5. ANS: D

PTS: 1

DIF: L2

REF: 6-2 Proportions

OBJ: 6-2.1 Solving Proportions

TOP: 6-2 Example 1

KEY: proportion | solving a proportion | cross products

6. ANS: D

PTS: 1

DIF: L2

REF: 6-2 Proportions

OBJ: 6-2.1 Solving Proportions

TOP: 6-2 Example 1

KEY: proportion | solving a proportion | cross products

7. ANS: C

PTS: 1

DIF: L3

REF: 6-2 Proportions

OBJ: 6-2.1 Solving Proportions

TOP: 6-2 Example 1

KEY: proportion | solving a proportion | cross products

8. ANS: A

PTS: 1

DIF: L2

REF: 6-2 Proportions

OBJ: 6-2.2 Using Proportions to Solve Problems

TOP: 6-2 Example 3

KEY: cross products | problem solving | proportion | solving a proportion | word problem

9. ANS: D

PTS: 1

DIF: L2

REF: 6-2 Proportions

OBJ: 6-2.2 Using Proportions to Solve Problems

TOP: 6-2 Example 3

KEY: problem solving | proportion | ratio | word problem

10. ANS: A

PTS: 1

DIF: L3

REF: 6-2 Proportions

OBJ: 6-2.2 Using Proportions to Solve Problems

TOP: 6-2 Example 3

KEY: cross products | problem solving | proportion | ratio | solving a proportion | word problem

11. ANS: B

PTS: 1

DIF: L3

REF: 6-2 Proportions

OBJ: 6-2.2 Using Proportions to Solve Problems

TOP: 6-2 Example 3

KEY: cross products | problem solving | proportion | rate | solving a proportion | word problem

12. ANS: B

PTS: 1

DIF: L2

REF: 6-3 Similar Figures and Scale Drawings

OBJ: 6-3.1 Using Similar Figures

STA: CA 7.MG.1.2

TOP: 6-3 Example 1

KEY: similar figures | corresponding angles | corresponding sides | solving a proportion | proportion

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13. ANS: C

PTS: 1

DIF: L2

REF: 6-3 Similar Figures and Scale Drawings

OBJ: 6-3.1 Using Similar Figures

STA: CA 7.MG.1.2

TOP: 6-3 Example 1

KEY: corresponding angles | corresponding sides | proportion | similar figures | solving a proportion

14. ANS: A

PTS: 1

DIF: L2

REF: 6-3 Similar Figures and Scale Drawings

OBJ: 6-3.1 Using Similar Figures

STA: CA 7.MG.1.2

TOP: 6-3 Example 2

KEY: problem solving | proportion | similar figures | solving a proportion | corresponding angles |

corresponding sides | indirect measurement | word problem

15. ANS: D

PTS: 1

DIF: L3

REF: 6-3 Similar Figures and Scale Drawings

OBJ: 6-3.1 Using Similar Figures

STA: CA 7.MG.1.2

TOP: 6-3 Example 2

KEY: problem solving | proportion | solving a proportion | indirect measurement | similar figures | word

problem

16. ANS: D

PTS: 1

DIF: L2

REF: 6-3 Similar Figures and Scale Drawings

OBJ: 6-3.2 Using Scale Drawings

STA: CA 7.MG.1.2

TOP: 6-3 Example 3

KEY: scale drawing | scale | problem solving | proportion | solving a proportion | word problem

17. ANS: B

PTS: 1

DIF: L2

REF: 6-3 Similar Figures and Scale Drawings

OBJ: 6-3.2 Using Scale Drawings

STA: CA 7.MG.1.2

TOP: 6-3 Example 3

KEY: scale | problem solving | proportion | scale drawing | solving a proportion | word problem

SHORT ANSWER

18. ANS:

To find whether the two ratios form a proportion, write them as a proportion and then check the cross

products.

1 ?8 12 96

Test by writing as a proportion.

1 96 ? 8 12

Write cross products.

96 = 96

Simplify.

The ratios form a proportion since the cross products are equal.

PTS: 1

DIF: L2

OBJ: 6-2.1 Solving Proportions

KEY: ratio | proportion | cross products

REF: 6-2 Proportions TOP: 6-2 Example 2

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19. ANS:

To find whether the two ratios form a proportion, write them as a proportion and then check the cross

products.

9 ? 11 4 5

Test by writing as a proportion.

9 5 ? 11 4

Write cross products.

45 z 44

Simplify.

The ratios do not form a proportion since the cross products are not equal.

PTS: 1

DIF: L2

REF: 6-2 Proportions

OBJ: 6-2.1 Solving Proportions

TOP: 6-2 Example 2

KEY: ratio | proportion | cross products

20. ANS:

a. To find the dimensions for the model, write and solve a proportion using the scale for each dimension.

model (in.) o 1 h m model (in.)

actual (ft) o 5 82 m actual (ft)

1 82 5 h

82 5h

5 5

16.4 h

model (in.) o 1 d m model (in.) actual (ft) o 5 26 m actual (ft)

1 26 5 d 26 5d 5 5 5.2 d

The model is 16.4 inches tall and 5.2 inches in diameter. b. You need to find the scale of the model as a ratio of 1 inch to some number of feet. Write and solve a

proportion using the height of the new model and the height of the actual tower.

model (in.) o 1 20 m model (in.) actual (ft) o f 82 m actual (ft)

1 82 20 f 82 20f 20 20 4.1 f

The scale is 1 inch : 4.1 feet.

Write a proportion.

PTS: 1

DIF: L4

REF: 6-3 Similar Figures and Scale Drawings

OBJ: 6-3.2 Using Scale Drawings

STA: CA 7.MG.1.2

KEY: cross products | multi-part question | problem solving | proportion | scale drawing | solving a proportion

| writing in math | word problem

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ESSAY

21. ANS:

[4] a. To find the perimeter of the smaller garden, you must add the lengths of the sides. The

trapezoids are similar, so write and solve proportions to find the lengths of the missing

sides.

63

63

63

10 a

4 b

4 c

6a 30

6b 12

6c 12

a 5

b 2

c 2

The perimeter of the smaller garden is 3 m + 5 m + 2 m + 2 m, or 12 meters.

[3] correct procedure with one mathematical error

[2] correct procedure with two mathematical errors

[1] correct answer with no explanation

PTS: 1

DIF: L4

REF: 6-3 Similar Figures and Scale Drawings

OBJ: 6-3.1 Using Similar Figures

STA: CA 7.MG.1.2

TOP: 6-3 Example 1

KEY: corresponding sides | extended response | problem solving | proportion | rubric-based question | similar

figures | solving a proportion | writing in math | word problem

22. ANS:

[4] a. 646 miles 40.4 mi/h 16 hours

Her average speed was about 40.4 miles per hour.

b. Methods may vary. Sample: Write and solve a proportion to find the speed needed to

shorten the trip from 16 hours to 15.5 hours:

40.4 r

16 15.5

16r 40.4 15.5

r

40.4 15.5 16

r 41.6774

Susan should drive at an average speed of approximately 41.7 mi/h to reduce her trip time by one half hour. [3] one computational error [2] two computational errors OR one error in method [1] correct answers with no work shown

PTS: 1

DIF: L3

REF: 6-1 Ratios and Unit Rates

OBJ: 6-1.1 Finding Rates and Unit Rates

STA: CA 7.MG.1.1 | CA 7.MG.1.3 | CA 7.AF.4.2

KEY: problem solving | rate | ratio | unit rate | multi-part question | writing in math

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OTHER

23. ANS: No, the ratios are not the same. Solution methods may vary. Sample: To determine whether the ratios are the same, test them by writing a proportion. If the cross products of the proportion are equal, then the ratios are equal. If the cross products of the proportion are not equal, then the ratios are not equal. 11 ? 23 29 33 11 33 ? 29 23 363 z 667 Since the cross products are not equal, the ratios are not the same for both classes.

PTS: 1

DIF: L3

REF: 6-2 Proportions

OBJ: 6-2.1 Solving Proportions

TOP: 6-2 Example 2

KEY: cross products | problem solving | proportion | ratio | writing in math | word problem

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