Pre-Algebra Unit 8 Practice Test: Ratios, Rates, & Proportions Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: L2 REF: -1 Ratios and Unit Rates STA: CA 7.MG.1.1 CA 7.MG.1.3 CA 7.AF.4.2 TOP: -1 Example 1 KEY: rate unit rate problem solving ratio word problem 2. ANS: C PTS: 1 DIF: L2 REF: -1 Ratios and Unit Rates STA: CA 7.MG.1.1 CA 7.MG.1.3 CA 7.AF.4.2 TOP: -1 Example 2 KEY: rate ratio unit rate 3. ANS: A PTS: 1 DIF: L2 REF: -1 Ratios and Unit Rates STA: CA 7.MG.1.1 CA 7.MG.1.3 CA 7.AF.4.2 TOP: -1 Example 2 KEY: rate ratio unit rate 4. ANS: B PTS: 1 DIF: L3 REF: -1 Ratios and Unit Rates STA: CA 7.MG.1.1 CA 7.MG.1.3 CA 7.AF.4.2 TOP: -1 Example 1 KEY: problem solving rate ratio unit rate word problem 5. ANS: D PTS: 1 DIF: L2 REF: -2 Proportions. ANS: D PTS: 1 DIF: L2 REF: -2 Proportions 7. ANS: C PTS: 1 DIF: L3 REF: -2 Proportions 8. ANS: A PTS: 1 DIF: L2 REF: -2 Proportions KEY: cross products problem solving proportion solving a proportion word problem 9. ANS: D PTS: 1 DIF: L2 REF: -2 Proportions KEY: problem solving proportion ratio word problem 10. ANS: A PTS: 1 DIF: L3 REF: -2 Proportions KEY: cross products problem solving proportion ratio solving a proportion word problem 11. ANS: B PTS: 1 DIF: L3 REF: -2 Proportions KEY: cross products problem solving proportion rate solving a proportion word problem 12. ANS: B PTS: 1 DIF: L2 STA: CA 7.MG.1.2 TOP: -3 Example 1 KEY: similar figures corresponding angles corresponding sides solving a proportion proportion 1
13. ANS: C PTS: 1 DIF: L2 STA: CA 7.MG.1.2 TOP: -3 Example 1 KEY: corresponding angles corresponding sides proportion similar figures solving a proportion 14. ANS: A PTS: 1 DIF: L2 STA: CA 7.MG.1.2 TOP: -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 STA: CA 7.MG.1.2 TOP: -3 Example 2 KEY: problem solving proportion solving a proportion indirect measurement similar figures word problem 1. ANS: D PTS: 1 DIF: L2 OBJ: -3.2 Using Scale Drawings STA: CA 7.MG.1.2 TOP: -3 Example 3 KEY: scale drawing scale problem solving proportion solving a proportion word problem 17. ANS: B PTS: 1 DIF: L2 OBJ: -3.2 Using Scale Drawings STA: CA 7.MG.1.2 TOP: -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 12? 8 Test by writing as a proportion. 9 1 9? 8 12 Write cross products. 9 = 9 Simplify. The ratios form a proportion since the cross products are equal. PTS: 1 DIF: L2 REF: -2 Proportions KEY: ratio proportion cross products 2
19. ANS: To find whether the two ratios form a proportion, write them as a proportion and then check the cross products. 9 4? 11 5 Test by writing as a proportion. 9 5? 11 4 Write cross products. 45 44 Simplify. The ratios do not form a proportion since the cross products are not equal. PTS: 1 DIF: L2 REF: -2 Proportions 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. actual (ft) 5 h model (in.) 82 actual (ft) 1 82 5 h 82 5 5h 5 1.4 h actual (ft) 5 d model (in.) 2 actual (ft) 1 2 5 d 2 5 5d 5 5.2 d The model is 1.4 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. 20 model (in.) actual (ft) f 82 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 OBJ: -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 3
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. 10 3 a a 30 a 5 4 3 b b 12 b 2 4 3 c c 12 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 STA: CA 7.MG.1.2 TOP: -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] 4 miles a. 40.4 mi/h 1 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 1 hours to 15.5 hours: 40.4 1 r 15.5 1r 40.4 15.5 r 40.4 15.5 1 r 41.774 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: -1 Ratios 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 4
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 29? 23 33 11 33? 29 23 33 7 Since the cross products are not equal, the ratios are not the same for both classes. PTS: 1 DIF: L3 REF: -2 Proportions KEY: cross products problem solving proportion ratio writing in math word problem 5