Math 11F



Math 11F Proportional Reasoning Review Name:_________________

1) Olga drove 346 km and used up 28.7 L of gas. What is her car's fuel efficiency?

a. 8.29 L/100 km b. 12 mL/km c. 12 km/L d. 0.083 L/km

2) Maureen ran 15 km in 1.25 h. What is her running speed?

a. 12 km/h b. 15 km/h c. 120 m/min d. 200 m/s

3) It takes 7.5 h to fill a 6000 L ornamental pond. What is the rate in litres per second?

a. 800 L/s b. 13.3 L/s c. 0.22 L/s d. 0.125 L/s

4) The graph shows how a cyclist travels over time. Over which interval is the cyclist travelling the slowest?

a. BC b. DE c. EF d. FG

5) The graph shows how a cyclist travels over time.

What does a zero slope mean in the context of this graph?

a. The cyclist is travelling very fast.

b. The cyclist is travelling parallel to the starting point.

c. The cyclist is travelling on a flat surface.

d. The cyclist is not moving.

7) 15 kg of Yukon gold potatoes costs $32.70. Which equation determines the price, P, in dollars, of 4 lb of potatoes?

a. [pic] b. [pic] c. [pic] d. [pic]

8) Which scale factor(s) will produce an image that is larger than the original? I. 0.86 II. 116% III. [pic]

a. I only b. I and II only c. II and III only d. I, II, and III

9) Cashews cost $8.72 for 350 g. Peanuts cost $19.80 for 2 kg. Jack buys 750 g of cashews. Which equation determines

the number of kilograms of peanuts, A, Jack could buy for the same cost?

a. [pic] c. [pic] b. [pic] d. [pic]

10) It costs $2.25/lb, plus a loading fee of $30, to send freight by airplane around the Yukon and the Northwest Territories. Which equation determines the amount of fresh fruit, A, you can ship from Vancouver to Whitehorse for $81, in pounds?

a. [pic] b. [pic] c. [pic] d. [pic]

11) A photograph is 6 cm by 11 cm. A copy is made using a scale factor of 140%. What are the dimensions of the copy?

a. 4.3 cm by 7.9 cm b. 8.4 cm by 15.4 cm c. 24 cm by 44 cm d. 43 mm by 79 cm

12) A room in a floor plan is 8.4 cm by 9.12 cm. The floor plan was made using a scale factor of 0.024. What are the dimensions of the actual room?

a. 2 m by 2.19 m b. 20.16 m by 21.9 m c. 3.5 m by 3.8 m d. 202 cm by 219 cm

13) The distance between two towns on a map is 5.4 cm. The map was made using a scale of 1 cm to 300 km. What is the actual distance between the two towns?

a. 1600 km b. 1550 km c. 1620 km d. 1520 km

14) Which one of the following cylinders is similar to a cylinder that is 8 cm long and 2.5 cm in diameter? Choose the best answer.

a. a cylinder 4 cm long and 1.5 cm in diameter b. a cylinder 12 cm long and 3.5 cm in diameter

c. a cylinder 16 cm long and 5 cm in diameter d. all of the above

18) 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

19) 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. What scale factor must she apply to create the enlarged pawn?

a. 30 b. 10 c. 20 d. 40

20) A sideboard cabinet is 90 cm tall, 176 cm wide, and 65 cm deep. What are the dimensions of a scale model built using a scale of 1 : 4?

a. 18 cm tall, 35.2 cm wide, 13 cm deep b. 22.5 cm tall, 44 cm wide, 16.25 cm deep

c. 24 cm tall, 45 cm wide, 17.5 cm deep d. 20.25 cm tall, 42 cm wide, 12.5 cm deep

22) A pool in the shape of a rectangular prism is filled with 15 m3 of water. A similar pool has dimensions that are increased by a scale factor of [pic]. What volume of water will fill the larger swimming pool?

a. 27 m3 b. 19 m3 c. 47 m3 d. 36 m3

23) A large city map book will be changed so that it can be used as a street guide. To keep the same number of pages, the page dimensions will be halved and the maps will be less detailed. The area of each page in the original book is 3000 cm2. What is the area of each page in the smaller map book?

a. 1500 cm2 b. 750 cm2 c.  425 cm2 d. 375 cm2

24) The butcher shop sells a 3 lb package of chicken legs for $9.57. The supermarket sells chicken legs for $7.68/kg.

Determine the price per kilogram that each store charges. Which store has the lower price per kilogram?

25) Wayne and Steve work at a photocopy shop. They have an order to print and bind 500 copies of a business report.

Steve finished 125 reports in 8.5 h and Wayne finished the remaining 375 reports in 22 h. Who worked at a faster rate?

26) 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?

27) A 4.0 L can of Coloura paint will cover 45 m2. A 2.5 L can of Brights paint will cover 30 m2. Determine the area that one litre of each type of paint will cover. Which brand of paint will cover a greater surface area?

30) A medic administers a vaccine that comes in a 15 mL bottle. The adult dosage is 0.6 cc (1 cc is equivalent to 1 mL).

How many adults can the medic vaccinate before the bottle is empty?

33) Jean wants to defrost a frozen turkey that weighs 9 kg in his refrigerator. His cookbook says to allow 24 h of thawing time for every 5 lb of turkey. How many days will it take to thaw the turkey?

36) Dortea is grilling chicken for a school reunion. Her barbecue sauce recipe is one fifth molasses, and she needs 200 mL of sauce per pound of chicken. She is grilling 18 kg of chicken legs. How many milliliters of molasses does she need?

Leo has a microscope with a lens that magnifies by a factor of 80. He was able to capture the image of a slide containing human skin cells. In the image, the cell was about 5.6 mm long. Determine the length of the actual human skin cell, to nearest hundredth of a millimetre.

43) The gas tank of Salma's van holds about 110 L. She can either buy gas in her town at $1.18/L or travel across the U.S. border to fill up at $3.03 U.S./gal (1 U.S. gallon = 3.79 L). The current exchange rate is $1 U.S./$1.05 Cdn. Salma will use less than 1 L of gas to drive 5 min to her local gas station and one third of a tank to make the 2 h round trip to the nearest gas station across the U.S. border. Which option makes more sense? Justify your decision.

44) Lamar jogs at 11 km/h. When Lamar jogs at this rate for 15 min, he burns 276 Cal. Angela jogs at a slower rate, 9 km/h, burning 641 Cal in 60 min. If Lamar jogs for 2 h, how much longer will Angela have to jog to burn the same amount of Calories as Lamar?

45) A cargo jet leaves an airport that is 3000 ft above sea level at 7.15 p.m. The jet climbs steadily to a cruising altitude of 35 000 ft, at a rate of 4000 ft/min. After cruising at this altitude for 70 min, the jet descends steadily at a rate of 5500 ft/min to an airport that is 1500 ft above sea level. What time does the jet land? Show your work.

46) 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 of the area for the office area and the storage areas?

b) What is the actual area, in square metres, of the work area?

47) This scale diagram, drawn on 0.5 cm grid paper, shows the plan of a swimming pool, drawn using a scale factor of 1:250.

a) Determine the perimeter of the pool.

b) Determine the area of the bottom of the pool.

48) The diagram of an amusement park and the attached parking area was drawn with a scale of 1:1500. On the diagram, the area of the amusement park is 32 cm2 and the area of the parking lot is 8 cm2.

a) Determine the area of the actual amusement park in square metres.

b) Determine the area of the actual parking area in square metres.

49) Yield signs on city, town, and rural roads are equilateral triangles pointing downward. Describe how you would create a similar yield sign that is one-ninth the area of a typical yield sign to use as a collectable novelty.

50) A scale model of a Boeing 747 passenger jet is 14.12 cm long and has a wingspan of 11.92 cm. The model was made at a scale of [pic]. What are the dimensions of a hangar that could fit three of these passenger jets side by side, if each jet needs 10 m clearance around it on all sides?

51) A cook has a set of four mixing bowls with lids. Each bowl is a half sphere. The bowls stack inside each other and are similar to each other. The diameters of the two largest bowls are 30 cm and 26 cm. The scale factor is the same from each bowl to the next smaller bowl. The cook estimates that the largest bowl has a capacity of about 7400 cm3.

Estimate the capacity of the smallest of the four bowls.

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