FOM 11 Practice Test Name: Ch.8 Proportional Reasoning Block: _ Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A 454 g block of butter costs $4.37. What is the price per 100 g? a. $0.96/100 g b. $1.04/100 g c. $0.10/100 g d. $1.09/100 g 2. The graph shows how a cyclist travels over time. Over which interval is the cyclist travelling at 4.5 km/h? a. AB b. BC c. CD d. FG 3. A 4.5 kg package of wild Pacific salmon costs $108. Which equation determines the amount of salmon, A, in kilograms, you could buy for $8? a. b. c. d.
4. The original pushpin for these scale diagrams was 24 mm long. Which diagram was drawn using a scale factor of 3.5? a. b. (8.4 cm long) c. (9.6 cm long) d. (4.9 cm long) (6.1 cm long) 5. A billboard is 5.0 m by 2.5 m. A scale diagram of the billboard must fit in a space that is 18 cm by 15 cm. Which scale would be the most reasonable one to use for the scale diagram?? a. 3.6 % b. 6 % c. 4 % d. 300 %
6. Data for rectangle ABCD is shown on the first line of the table. Rectangle ABCD is enlarged by a scale factor of 250%. Which rectangle is the enlargement of rectangle ABCD? Rectangle Name Length (cm) Width (cm) Scale Factor Area (cm2) ABCD 9.0 13.0 1 117.00 1.00 EFGH 22.5 32.5 250% 731.25 6.25 JKLM 19.0 28.0 250% 532.00 4.25 NOPQ 18.0 29.0 250% 522.00 5.25 RSTU 32.5 22.5 250% 713.25 7.25 a. EFGH b. JKLM c. NOPQ d. RSTU 7. Which one of the following right cones is similar to a right cone that is 15 cm high and has a diameter of 9 cm? Choose the best answer. a. a right cone 30 cm high and 18 cm in diameter b. a right cone 10 cm high and 5 cm in diameter c. a right cone 20 cm high and 11 cm in diameter d. all of the above 8. A 1:25 scale model of a garbage truck is 0.5 ft tall, 0.32 ft wide, and 1.4 ft long. What are the dimensions of the actual garbage truck? a. 25 ft by 12.5 ft by 50 ft b. 9 ft by 6.4 ft by 25 ft c. 15 ft by 7.4 ft by 33.5 ft d. 12.5 ft by 8 ft by 35 ft 9. An ocean kayak is 5.5 m long, with a beam (width) of 54.0 cm and a depth of 34.0 cm. What are the dimensions of a scale model built using a scale of 1 : 5? a. 1.4 m long, 8.0 cm beam, 7.2 cm deep b. 1.5 m long, 9.0 cm beam, 8.0 cm deep c. 1.1 m long, 10.8 cm beam, 6.8 cm deep d. 1.2 m long, 11.0 cm beam, 7.6 cm deep
10. A stage director needs a large chess pawn for a scene. The pawn in her chess set is 35 mm tall and she estimates that the height of the enlarged pawn must be 700 mm. How many times greater will the surface area of the larger pawn be? a. 800 b. 400 c. 200 d. 1600 11. Cylinder A has a radius of 5 mm and a height of 30 mm. Cylinder B has a radius of 20 mm and a height of 120 mm. These two cylinders are similar. By what factor is the volume of cylinder B greater than the volume of cylinder A? a. 64 b. 8 c. 16 d. 32 Short Answer 12. A reindeer can run 133.25 km in 2.5 h. A grizzly bear can run 12.5 km in 15 min. Determine the speed of each animal in kilometres per hour. Which animal can faster? 13. Jamia is deciding between two long-distance telephone plans: Plan A charges $5 per month plus 6 /min. Plan B charges $20 per month plus 1 /min. Jamia usually makes about 200 min of long distance calls each month. Which plan costs less? Show your calculations.
14. It takes 35 min to inflate 73 helium balloons. How many balloons can be inflated in 50 min? 15. Today, crude oil is worth $77.84/barrel (1 barrel is about 159 L). What is the value of 45 L of crude oil? 16. Anna reduces this figure by a scale factor of. Determine the area of the reduced figure, to the nearest tenth of a square unit.
Problem 17. The floor plan for a small industrial company is drawn as shown, using a scale factor of 0.002. a) What are the actual dimensions for the office area and the storage areas? Show your work. b) What is the actual area, in square metres, of the work area? Show your work. (Remember 1 m 2 = 10000 cm 2 ) 18. A window in a clothing store is 6.00 ft high and 15.00 ft long. Lee has been asked to paint a mural on the window. The mural must be the area of the window and the mural and window must be similar. The mural must also be centred on the window. Draw a scale diagram that shows the dimensions of the window, the dimensions of the mural, and where the mural should be placed.
FOM 11 - Practice Test Ch.8 Proportional Reasoning Answer Section MULTIPLE CHOICE 1. A 5. A 9. C 2. B 6. A 10. B 3. B 7. A 11. A 4. A 8. D SHORT ANSWER 12. Reindeer s speed: Grizzly bear s speed:... The reindeer is faster. 13. The cost of Plan A for 200 min is: $5 + 200($0.06) = $17 = 53.3 km/h = 50.0 km/h PROBLEM 17. a) Office Area Dimensions: = 2500 cm or 25 m; = 500 cm or 5 m. The office area is 25 m by 5 m. Storage area #1: = 1500 cm or 15 m; = 1000 cm or 10 m. Storage area #2 has the same dimensions as storage area #1: 15 m by 10 m. b) = 2500 m or 25 m; = 1500 cm or 15 m. The actual area of the kitchen and work area is (25 m)(15 m) = 375 m 2. The actual dimensions of the kitchen are = 1000 cm or 10 m and = 500 cm or 5 m. 14. The cost of Plan B for 200 min is: $20 + 200($0.01) = $22 Plan A costs less. 2.0857 50 = 104 balloons Its actual area is (10 m)(5 m) = 50 m 2. Subtract the area of the kitchen. 375 m 2 50 m 2 = 325 m 2 The work area covers 325 m 2. OR Work area on Diagram = 15 cm 2 2 cm 2 = 13 cm 2 15. $. $0.4895 45 = $22.03 for 45 L. 16. Area IMAGE = (Area OBJECT) x (SF) 2 13 units 2 x (1/16) = 0.8 units 2 Area OBJECT = Area IMAGE SF 2 = 13 (0.002) 2 = 3250000 cm 2 3250000 1 10000 325 18. The dimensions of the mural must be onehalf the dimensions of the window because that would make the area of the mural onequarter the area of the window. To centre the mural, have it take up the middle two quarters of the height and the middle two quarters of the length of the window.