Unit 5 and 6 Exam (Modules 11 through 15)

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Class: Date: Unit 5 and 6 Exam (Modules 11 through 15) Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the value of x. Classify the triangle by its angles. a. 92; right b. 41; right c. 88; acute d. 47; acute 2. Find the value of x. (The figure may not be drawn to scale.) a. 57 b. 66 c. 33 d. 147 3. Find the length of the hypotenuse. Round your answer to the nearest hundredth. a. 10.82 c. 15.00 b. 11.62 d. 3.87 4. Find the length of the unknown side. Round your answer to the nearest tenth. a. 6.3 ft c. 40 ft b. 14.2 ft d. 2 ft 1

5. A community is building a square park with sides that measure 145 meters. To separate the picnic area from the play area, the park is split by a diagonal line from opposite corners. Determine the approximate length of the diagonal line that splits the square. If necessary, round your answer to the nearest meter. a. 42,050 meters c. 290 meters b. 205 meters d. 145 meters 6. Firefighters just arrived at the Farquand building with a rescue truck. Mr. Farquand is stuck on a window ledge 44 feet directly above the top of the truck. The base of the ladder is a horizontal distance of 33 feet away from the building. Using the Pythagorean Theorem, determine how long the ladder must extend to reach Mr. Farquand. a. 77 feet b. 44 feet c. 3025 feet d. 55 feet 7. A community is building a square park with sides that measure 65 meters. To separate the picnic area from the play area, the park is split by a diagonal line from opposite corners. Determine the approximate length of the diagonal line that splits the square. Round your answer to the nearest tenth. a. 130 meters c. 91.9 meters b. 65 meters d. 8,450 meters 8. Find the distance, to the nearest tenth, from T(7, 1) to V( 5, 4). a. 0.0 units c. 13.0 units b. 7.0 units d. 3.0 units 2

9. Find the volume of the figure. Use 3.14 for π. If necessary, round your answer to the nearest tenth. a. 16.7 cm 3 c. 401.9 cm 3 b. 33.5 cm 3 d. 134 cm 3 10. A county has constructed a conical building to store sand. The cone has a height of 171 ft and a diameter of 303 ft. Find the volume of this building to the nearest hundredth. a. 4,107,993.71 ft 3 c. 12,323,981.12 ft 3 b. 1,308,278.25 ft 3 d. 27,115.47 ft 3 11. A cylindrical barrel has a radius of 5.8 m and a height of 15 m. Tripling which dimension(s) will triple the volume of the barrel? a. height c. both height and radius b. radius d. neither height nor radius 12. Tell whether x and y have a positive association, a negative association, or no association. Explain your reasoning. a. positive; the slope is positive c. no correlation; the slope is close to zero b. negative; the slope is negative d. cannot determine 3

13. Tell whether x and y have a positive association, a negative association, or no association. Explain your reasoning. a. positive; the slope is positive c. negative; the slope is negative b. no correlation; the slope is close to zero d. cannot determine 4

14. There are five animal shelters in Casco County. Every week, each shelter reports the number of dogs and cats that are adopted. Use the data to make a scatter plot. Shelter Number of Number of Dogs Cats North County 28 69 Midtown 75 135 Fuzzy Friends 12 59 Garcia Street 56 110 Tri-Cities 35 86 a. c. b. d. 5

15. In the scatter plot, a line has been drawn to show the trend in a population of box turtles over a period of twelve months. Estimate the population of box turtles after 17 months. a. 380 turtles b. 160 turtles c. 80 turtles d. 200 turtles 6

16. The two-way table shows the results of a survey about which of two new television series people prefer. Complete the two-way table by finding the cumulative frequencies and the percentages. Program A Program B Total Women 20 20 Men 5 35 Total a. P rogram A P rogram B Total Women 20 (50%) 20 (50%) 40 (50%) Men 5 (12.5%) 35 (87.5%) 40 (50%) Total 25 (100%) 55 (100%) 80 (100%) b. P rogram A P rogram B Total Women 20 (20%) 20 (20%) 40 (100%) Men 5 (5%) 35 (35%) 40 (100%) Total 25 (31.25%) 55 (68.75%) 80 (100%) c. d. P rogram A P rogram B Total Women 20 (50%) 20 (50%) 40 (50%) Men 5 (12.5%) 35 (87.5%) 40 (50%) Total 25 (31.25%) 55 (68.75%) 80 (100%) P rogram A P rogram B Total Women 20 (50%) 20 (50%) 40 (100%) Men 5 (12.5%) 35 (87.5%) 40 (100%) Total 25 (62.5%) 55 (137.5%) 80 (100%) 7

17. The two-way table shows the results of a survey about whether people of different ages prefer to get their news online or through newspapers and/or television news. Complete the two-way table by finding the cumulative frequencies and the percentages. Does the table show any differences in the preferences? Online Newspapers/Television Total 45 years old or less 45 5 Over 45 years old 25 25 Total a. b. c. d. Online Newspapers / Television Total 45 years old or less 45 (90%) 5 (10%) 50 (100%) Over 45 years old 25 (50%) 25 (50%) 50 (100%) Total 70 (100%) 30 (100%) 100 (100%) Of the people surveyed, older people were more likely to get their news online than from newspapers and/or television. Online Newspapers / Television Total 45 years old or less 45 (90%) 5 (10%) 50 (50%) Over 45 years old 25 (50%) 25 (50%) 50 (50%) Total 70 (140%) 30 (60%) 100 (100%) Of the people surveyed, younger people were more likely to get their news online than from newspapers and/or television. Online Newspapers / Television Total 45 years old or less 45 (45%) 5 (5%) 50 (100%) Over 45 years old 25 (25%) 25 (25%) 50 (100%) Total 70 (70%) 30 (30%) 100 (100%) Of the people surveyed, older people were more likely to get their news online than from newspapers and/or television. Online Newspapers / Television Total 45 years old or less 45 (90%) 5 (10%) 50 (50%) Over 45 years old 25 (50%) 25 (50%) 50 (50%) Total 70 (70%) 30 (30%) 100 (100%) Of the people surveyed, younger people were more likely to get their news online than from newspapers and/or television. 8

18. Melanie is making a piece of jewelry that is in the shape of a right triangle. The two shorter sides of the piece of jewelry are 12 mm and 5 mm. Find the perimeter of the piece of jewelry. a. 28 mm c. 24 mm b. 30 mm d. 26 mm 19. Find the length of the hypotenuse of the triangle. a. 14.32 b. 17.12 c. 22.02 d. 3.61 20. A cylindrical pond has a 10 ft diameter, and the water in the pond is 3 ft deep. Water is being drained from the pond at a rate of 1 cubic foot per minute. How long will it take to drain the pond? Use 3.14 for π. a. 30 min c. 235.5 min b. 94.2 min d. 942 min 9

21. A travel agency surveys its customers to find out the average cost of a vacation compared to the miles traveled during the vacation. The results of the survey are shown in the table. Use the data to make a scatter plot.. Miles Traveled Vacation Cost 401 $475 102 $266 181 $330 291 $402 54 $238 a. c. b. d. 10

22. The population of a once-endangered animal species has been increasing. Create a scatter plot that represents the data in the table. Year (t) 1 388 2 406 3 538 4 1650 5 2440 6 3740 Population (P) a. c. b. d. 11

23. Write an equation for the trend line on the scatter plot. What is a reasonable interpretation for the slope in this context? a. y = x + 80; The number of students decreases by 1 student per year. b. y = 10x + 80; The number of students decreases by 10 students per year. c. y = x + 80; The number of students decreases by 10 students per year. d. y = 10x + 80; The number of students decreases by 1 student per year. 12

24. Compare the given scatter plots of data to the lines of best fit. Tell which model better fits the data. Explain your answer. Graph A Graph B a. Both scatter plots show data with a strong positive correlation. The linear model in Graph A fits the data better than the linear model in Graph B. b. Both scatter plots show data with a strong positive correlation. The linear model in Graph B fits the data better than the linear model in Graph A. c. Both scatter plots show data with a strong negative correlation. The linear model in Graph B fits the data better than the linear model in Graph A. d. Both scatter plots show data with a strong negative correlation. The linear model in Graph A fits the data better than the linear model in Graph B. 25. What is the approximate length of the diagonal from point A to point B in the right rectangular prism shown? Round your answer to the nearest centimeter. a. 8 cm b. 9 cm c. 10 cm d. 11 cm 13

Unit 5 and 6 Exam (Modules 11 through 15) Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 REF: MLC30553 NAT: NT.CCSS.MTH.10.8.8.EE.7 NT.CCSS.MTH.10.8.8.G.5 STA: MACC.8.EE.3.7 TOP: Angles and Triangles KEY: measure angle triangle classify DOK: DOK 1 2. ANS: C PTS: 1 REF: MCT80109 NAT: NT.CCSS.MTH.10.8.8.EE.7 NT.CCSS.MTH.10.8.8.G.5 STA: MACC.8.EE.3.7 TOP: Angles and Triangles KEY: angle triangle sum interior exterior DOK: DOK 1 3. ANS: A PTS: 1 REF: 9bf2a915-9631-11dd-8a40-001185f11039 OBJ: Finding the Length of a Hypotenuse NAT: NT.CCSS.MTH.10.8.8.G.7 STA: MACC.8.G.2.7 TOP: The Pythagorean theorem DOK: DOK 1 4. ANS: A PTS: 1 REF: 9bf2d025-9631-11dd-8a40-001185f11039 OBJ: Finding the Length of a Leg in a Right Triangle NAT: NT.CCSS.MTH.10.8.8.G.7 STA: MACC.8.G.2.7 TOP: The Pythagorean theorem KEY: hypotenuse Pythagorean theorem right triangle DOK: DOK 1 5. ANS: B PTS: 1 REF: 9bf53283-9631-11dd-8a40-001185f11039 OBJ: Application NAT: NT.CCSS.MTH.10.8.8.G.7 STA: MACC.8.G.2.7 TOP: Applying the Pythagorean theorem and Its Converse KEY: Pythagorean theorem right triangle diagonal DOK: DOK 1 6. ANS: D PTS: 1 REF: ANYA0049 NAT: NT.CCSS.MTH.10.8.8.G.7 STA: MACC.8.G.2.7 TOP: The Pythagorean theorem KEY: side Pythagorean word triangle DOK: DOK 2 7. ANS: C PTS: 1 REF: 9935d831-9631-11dd-8a40-001185f11039 OBJ: Problem-Solving Application NAT: NT.CCSS.MTH.10.8.8.G.7 STA: MACC.8.G.2.7 TOP: The Pythagorean theorem KEY: Pythagorean theorem right triangle problem solving DOK: DOK 2 8. ANS: C PTS: 1 REF: 9bf76dd1-9631-11dd-8a40-001185f11039 OBJ: Finding Distance on the Coordinate Plane NAT: NT.CCSS.MTH.10.8.8.G.8 STA: MACC.8.G.2.8 TOP: Applying the Pythagorean theorem and Its Converse KEY: distance DOK: DOK 1 9. ANS: D PTS: 1 REF: 9de78141-9631-11dd-8a40-001185f11039 OBJ: Finding the Volume of Pyramids and Cones NAT: NT.CCSS.MTH.10.8.8.G.9 STA: MACC.8.G.3.9 TOP: Volume of Pyramids and Cones KEY: volume pyramid cone DOK: DOK 2 10. ANS: A PTS: 1 REF: 9deea85b-9631-11dd-8a40-001185f11039 OBJ: Using a Calculator to Find Volume NAT: NT.CCSS.MTH.10.8.8.G.9 STA: MACC.8.G.3.9 TOP: Volume of Pyramids and Cones KEY: volume pyramid cone DOK: DOK 2 1

11. ANS: A PTS: 1 REF: 9dddf7c9-9631-11dd-8a40-001185f11039 OBJ: Exploring the Effects of Changing Dimensions NAT: NT.CCSS.MTH.10.8.8.G.9 STA: MACC.8.G.3.9 TOP: Volume of Prisms and Cylinders KEY: volume prism cylinder DOK: DOK 2 12. ANS: C PTS: 1 REF: f9e15b9c-6ff9-11df-9c81-001185f0d2ea NAT: NT.CCSS.MTH.10.8.8.SP.1 STA: MACC.8.SP.1.1 KEY: association relationships scatter plots DOK: DOK 1 13. ANS: C PTS: 1 REF: f9e182ac-6ff9-11df-9c81-001185f0d2ea NAT: NT.CCSS.MTH.10.8.8.SP.1 STA: MACC.8.SP.1.1 KEY: association relationships scatter plots DOK: DOK 1 14. ANS: D PTS: 1 REF: 97379d9d-9631-11dd-8a40-001185f11039 OBJ: Making a Scatter Plot NAT: NT.CCSS.MTH.10.8.8.SP.1 STA: MACC.8.SP.1.1 TOP: Scatter Plots KEY: construct scatter plots DOK: DOK 2 15. ANS: D PTS: 1 REF: MCT80230 NAT: NT.CCSS.MTH.10.8.8.SP.1 NT.CCSS.MTH.10.8.8.SP.2 STA: MACC.8.SP.1.1 TOP: Scatter Plots KEY: linear graph estimate scatter plots equation slope intercept DOK: DOK 2 16. ANS: C PTS: 1 REF: 91311bce-6ab2-11e0-9c90-001185f0d2ea OBJ: Constructing a Two-Way Table NAT: NT.CCSS.MTH.10.8.8.SP.4 STA: MACC.8.SP.1.4 TOP: Patterns in Two-Way Tables KEY: two-way tables DOK: DOK 2 17. ANS: D PTS: 1 REF: 913142de-6ab2-11e0-9c90-001185f0d2ea OBJ: Constructing a Two-Way Table NAT: NT.CCSS.MTH.10.8.8.SP.4 STA: MACC.8.SP.1.4 TOP: Patterns in Two-Way Tables KEY: two-way tables DOK: DOK 2 18. ANS: B PTS: 1 REF: 9dc5f90d-9631-11dd-8a40-001185f11039 OBJ: Multi-Step Application NAT: NT.CCSS.MTH.10.8.8.G.7 STA: MACC.8.G.2.7 TOP: Perimeter and Area of Triangles and Trapezoids DOK: DOK 2 19. ANS: C PTS: 1 REF: HMAL0388 NAT: NT.CCSS.MTH.10.8.8.G.8 STA: MACC.8.G.2.8 TOP: The Pythagorean theorem KEY: points right triangle coordinate geometry DOK: DOK 2 20. ANS: C PTS: 1 REF: 9e170989-9631-11dd-8a40-001185f11039 OBJ: Application NAT: NT.CCSS.MTH.10.8.8.G.9 STA: MACC.8.G.3.9 TOP: Scaling Three-Dimensional Figures KEY: scale factor DOK: DOK 2 21. ANS: B PTS: 1 REF: 9e90a243-9631-11dd-8a40-001185f11039 NAT: NT.CCSS.MTH.10.8.8.SP.1 STA: MACC.8.SP.1.1 TOP: Scatter Plots KEY: scatter plots data set DOK: DOK 2 22. ANS: D PTS: 1 REF: MCT80506 NAT: NT.CCSS.MTH.10.8.8.SP.1 STA: MACC.8.SP.1.1 TOP: Scatter Plots KEY: equation regression data plots scatter plots DOK: DOK 2 23. ANS: B PTS: 1 NAT: NT.CCSS.MTH.10.8.8.SP.2 STA: MACC.8.SP.1.2 DOK: DOK 2 2

24. ANS: B PTS: 1 REF: 912c5718-6ab2-11e0-9c90-001185f0d2ea OBJ: Assessing the Line of Best Fit NAT: NT.CCSS.MTH.10.8.8.SP.2 STA: MACC.8.SP.1.2 TOP: Linear Best Fit Models KEY: line of best fit correlation DOK: DOK 2 3

25. ANS: D First, find the diagonal along the base of the prism. Let b be the diagonal along the base. 8 2 + 6 2 = b 2 64 + 36 = b 2 100 = b 2 10 = b Then, let d be the diagonal from point A to point B. b 2 + 5 2 = d 2 10 2 + 5 2 = d 2 100 + 25 = d 2 125 = d 2 125 = d 11 d So, the length of the diagonal from point A to point B is approximately 11 cm. A B C D Feedback This is the approximate length of the diagonal along the left and right sides of the prism. This is the approximate length of the diagonal along the front and back sides of the prism. This is the length of the diagonal along the base of the prism. That s correct! PTS: 1 NAT: NT.CCSS.MTH.10.8.8.G.7 STA: MACC.8.G.2.7 KEY: Pythagorean theorem three dimensions DOK: DOK 2 4

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