Context-Based Multiple-Choice Questions
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1 UNIT3 Chapters BUILDING 8 10 Strategies for Answering Context-Based Multiple-Choice Questions Some of the information you need to solve a context-based multiple-choice question may appear in a table, a diagram, or a graph. Problem 1 Joe s pool has a deck around it. The outer edge of the deck has twice the radius of the pool. Find the area of the deck. 4 ft deck A ft 2 B ft 2 C ft 2 D. 512 ft 2 Solution Read the problem carefully. Decide how you can use the information you are given to solve the problem. Find the areas of the two circles. 1) You know that the radius of the pool is 4 feet and the radius of the deck is double the radius of the pool, or 8 feet. You can use the areas of both circles to find the area of the deck. 2) Area of inner circle: Area of outer circle: radius 4 ft radius 8 ft A πr 2 A πr 2 πpr 2 πpr 2 16π 64π Use the areas of the circles to find the area of the deck. 3) Area of deck Area of outer circle Area of inner circle A 64π 16π 48π The area of the deck is about ft 2. The correct answer is B. Use one of the strategies on pages ) Check to see that the answer is reasonable. Estimate that 64π is about 200 and 16π is about 50. Because , B is the most reasonable choice. 67
2 Problem 2 Karen walked diagonally across a parking lot. Tom walked along the length and width of the parking lot. The lot is 300 feet wide and 500 feet long. How much farther did Tom walk than Karen? F. 800 ft G. 600 ft H. 200 ft I. 100 ft Solution Read the problem carefully. Remember that the parking lot is a rectangle. 1) Use the information in the problem to make a sketch. 500 ft Karen s path 300 ft Use the Pythagorean theorem to find the length of Karen s path. Add to find the length of Tom s path. 2) a 2 b 2 c 2 Pythagorean theorem c 2 Substitute for a and b. 90, ,000 c 2 360,000 c 2 Solve. 600 c Evaluate positive square root. The length of Karen s path is 600 feet. The length of Tom s path is feet. Find the difference of the two distances. Watch Out! Be sure that you know what question you are asked to answer. Some choices given may be intended to distract you. 3) Tom s distance Karen s distance Tom walked 200 feet more than Karen. The correct answer is H. Your turn now 1. In Problem 2, Karen and Tom both walk at the rate of 200 ft/min. How many minutes more does Tom walk than Karen? A. 2 min B. 1 min C. 0.5 min D min In Exercises 2 3, use the diagram. 2. How tall is the flag pole? F. 10 feet G. 12 feet H. 18 feet I. 24 feet 3. How long will the flag pole s shadow be when the sign s shadow is 12 feet long? 6 ft A. 32 feet B. 36 feet 3 ft 9 ft C. 40 feet D. 42 feet 68 PASS Keys for the Oklahoma Core Curriculum Test, Course 3
3 UNIT3 Chapters 8 10 Multiple Choice PRACTICING In Exercises 1 and 2, use the diagram below. 1. Which angles are complementary? A. a2 and a3 B. a3 and a1 C. a1 and a2 D. a4 and a How long is side a? F ft G ft H ft I ft a 10 ft 7 ft 2. Which angles are vertical angles? F. a3 and a5 G. a1 and a4 H. a4 and a5 I. a2 and a4 In Exercises 3 and 4, use the diagram below. y 7. What is the area of the parallelogram? 15 cm 20 cm A. 300 ft 2 B. 150 ft 2 C. 25 ft 2 D. 5 ft 2 In Exercises 8 and 9, use the diagram below. 3 ft 3. What is the value of y? A. 360 B. 120 C. 60 D How many lines of symmetry does the figure have? F. 10 G. 6 H. 4 I. 2 5 ft 8. What is the surface area of the cylinder? F ft 2 G ft 2 H ft 2 I ft 2 5. ax and ay are complementary. If max 57, what is may? A. 33 B. 43 C. 123 D What is the volume of the cylinder? A. 35.5π ft 3 B. 45π ft 3 C ft 3 D. 149π ft 3 69
4 Short Response 10. What is the value of y? Explain A laser on the ground is aimed at a building at a 60 angle. The beam s length is 100 feet. How many feet from the building is the laser? 62 y 14. Darren s new patio is a perfect circle with a diameter of 20 feet. Find the area of the patio to the nearest square foot. 11. The base of a right triangle is 10 feet long. The triangle s height is 8 feet. How long is the third side? 15. A circular lake has an area of about 154 square miles. What is the diameter of the lake? 12. A tree fort is 20 feet up in the tree. A rope extends from the ground to the tree fort at a 45 angle. What is the length of the rope? Draw a diagram and explain. Extended Response 16. A water ski show uses two large ramps. Each ramp is 50 feet long. The first ramp is pitched at a 22 angle. The second ramp is at a 26 angle. How much taller is the second ramp than the first? Draw a diagram and explain. 17. A new roller skating rink has been built. Write an equation that you can use to find area of the rink. Explain your reasoning. Solve the equation to find the area of the rink. 100 ft 200 ft 1 If you use gallon of paint for each square foot of the rink, how many 1 2 gallons of paint will be needed to paint the entire rink? 70 PASS Keys for the Oklahoma Core Curriculum Test, Course 3
5 UNIT3 Chapters PRACTICING 8 10 Cumulative Practice for Chapters 8 10 Chapter 8 Multiple Choice In Exercises 1 7, choose the letter of the correct answer. 1. a2 and a3 are supplementary, and ma2 39. What is ma3? (Lesson 8.1) A. 41 B. 90 C. 141 D Which transformation is shown? (Lessons ) F. dilation G. rotation H. reflection I. translation x y 2. What is the value of z? (Lesson 8.2) z 7. You reduce a 27-inch by 24-inch photo to 2 of its original dimensions. What are the 3 new dimensions of the photo? (Lesson 8.8) 46 A. 18 inches by 16 inches F. 40 G. 44 H. 224 I. 314 B. 21 inches by 18 inches 3. Which quadrilateral has only one pair of parallel sides? (Lesson 8.3) A. rhombus B. parallelogram C. trapezoid D. rectangle 4. What is the value of x? (Lesson 8.4) F. 103 G. 92 H. 78 I Quadrilateral ABCD c EFGH. What is the maf? (Lesson 8.5) A. 126 B. 155 C. 111 D A 110 D 11 cm B C H E x F 5 cm G C. 24 inches by 21 inches D. 16 inches by 12 inches 8. Short Response Quadrilateral ABCD has vertices A( 5, 1), B( 5, 3), C( 3, 4), and D( 1, 1). Reflect quadrilateral ABCD in the x-axis. What are the vertices of the image? (Lesson 8.6) 9. Extended Response The hexagon below has two acute angles and four obtuse angles. (Lesson 8.4) a. Find the sum of the angle measures of the hexagon. b. Write an equation that you can use to find the measure of each obtuse angle. c. Solve the equation to find the measure of each obtuse angle. 71
6 Chapter What is the value of x? (Lesson 9.5) Multiple Choice In Exercises 10 17, choose the letter of the correct answer. 10. A soccer field has an area of 45,000 square feet. What are the dimensions of the field? (Lesson 9.1) A B. 2 C. 2 2 D in. 45 x x A. 200 ft by 200 ft B. 300 ft by 150 ft 17. In TEFG, what is the cosine of E? (Lesson 9.6) C. 90 ft by 400 ft D. 350 ft by 150 ft 11. What are the values of n in the equation n ? (Lesson 9.1) F. n 19.2 G. n 10.5 F G H. 1 5 J E 17 in. 15 in. F 6 in. G H. n 14 I. n Which list shows the numbers in order from least to greatest? (Lesson 9.2) A. 5, 3, 5, 4 B. 2, 3, 4, Short Response A skateboard ramp rises from the ground at a 35 angle. The part of the ramp that the skateboarders ride on is 6 feet long. What is the height of the ramp to the nearest foot? Draw a diagram and explain your steps. C. 3, 5, 3, 10 D. 4, 4, 5, What is the value of h? (Lesson 9.3) F. 24 feet G. 22 feet H. 20 feet I. 18 feet 12 ft h 16 ft 19. Extended Response An airplane takes off at an angle of 35 with the ground. The airplane s speed is 200 feet per second. d One side of a right triangle is 6 centimeters long. Another side is 8 centimeters long. What is the length of the third side? (Lesson 9.4) A. 14 cm B. 12 cm C. 10 cm D. 9 cm 15. Which set of numbers is a Pythagorean triple? (Lesson 9.4) a. How far does the airplane travel in 5 seconds? b. Find the height of the airplane 5 seconds after takeoff. c. Find the horizontal distance the airplane travels after 5 seconds. F. 2, 4, 8 G. 8, 15, 17 H. 13, 15, 22 I. 7, 12, PASS Keys for the Oklahoma Core Curriculum Test, Course 3
7 Chapter 10 Multiple Choice In Exercises 20 26, choose the letter of the correct answer. 20. What is the area of the trapezoid? (Lesson 10.1) 8 cm A. 234 cm 2 B. 117 cm 2 C. 81 cm 2 D. 63 cm The circular wading pool has a diameter of 24 feet. What is the area of the pool? Use 3.14 for π. (Lesson 10.2) F ft 2 G. 117 ft 2 H ft 2 I. 1, ft Identify the solid. (Lesson 10.3) A. triangular prism B. cylinder C. cone D. pyramid 23. What is the approximate surface area of the cylinder? (Lesson 10.4) F cm 2 G cm 2 H cm 2 I cm 2 9 cm 18 cm 4 cm 7 cm 25. What is the volume of the prism? (Lesson 10.6) F. 95 m 3 G. 285 m 3 H. 570 m 3 I. 855 m What is the approximate volume of the cone? (Lesson 10.7) A. 128 cm 3 B. 134 cm 3 C. 402 cm 3 D. 516 cm Short Response Identify the solid. Then count the number of faces, edges, and vertices. (Lesson 10.3) 28. Extended Response A grocery store sells a small size of ice cream in a cylindrical container and a large size of ice cream in a conical container. (Lessons 10.6, 10.7) Ic Large e C re a m 19 m 4 in. 7 in. 3 m 5 m Small Ic e re C 2 in. 4 cm 8 cm 5 in. 24. What is the surface area of the square pyramid? (Lesson 10.5) A. 49 cm 2 B. 70 cm 2 C. 119 cm 2 D. 189 cm 2 7 cm 5 cm 7 cm $6.00 $3.00 a. What is the volume of the small container? b. What is the volume of the large container? c. Which container gives you more ice cream for your money? Explain your reasoning. 73
A. 180 B. 108 C. 360 D. 540
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