12 multiple-choice questions, progressively harder.
A census divides 2,160 residents by a district area of 18 square kilometers. What does the result describe?
Solution
Correct answer: C
Divide population by the whole district area.
The units are residents per square kilometer. This whole-region average does not give the population of an individual square kilometer.
Pine and Cedar districts each cover 8 square kilometers. Pine has 760 residents and Cedar has 920. How do their average population densities compare?
Correct answer: B
The two areas are equal, so divide the difference in population by their common area.
Cedar averages 20 more residents per square kilometer.
A solid sample occupies 90 cubic centimeters and has mass 225 grams. What is its average mass density?
Correct answer: D
Divide mass in grams by volume in cubic centimeters.
A 12-cubic-centimeter piece of modeling wax has a mass density of 0.85 grams per cubic centimeter. What is its mass?
Correct answer: A
Multiply density by volume. The cubic centimeters cancel.
A batch of liquid has a mass of 270 g. Its density is 1.5 grams per cubic centimeter. How much space does it occupy?
Divide mass by density. Grams cancel and cubic centimeters remain.
The inside of a rectangular tray is 24 cm long and 15 cm wide. The tray is filled to a depth of 3 cm. What volume is in the tray?
Use the three inside dimensions, including the fill depth.
One centimeter on a paper map represents 75 meters on the ground. A straight route on the map measures 6 cm. How long is the actual route?
Each map centimeter represents 75 actual meters.
On a paper plan, 1 cm represents 2.5 m. An actual fence segment is 17.5 m long. How long is the segment on the plan?
Divide actual meters by the number represented by one plan centimeter.
Every length of a similar model is one sixth of the corresponding actual length. What factor takes model area to actual area?
Apply the model-to-actual length factor in both area directions.
Each inside length of an actual bin is three times the matching length of its model. What factor takes model capacity to actual capacity in the same volume unit?
Capacity is the inside volume. Each of its three dimensions has factor 3.
A district averages 500 residents per square kilometer. What extra assumption makes that rate appropriate for estimating the population of a selected 2-square-kilometer part?
Multiplying by the district rate estimates the population of the part only to the extent that the rate represents that part. Equal areas or a map unit cannot establish how people are distributed.
A jug has a capacity of 2.75 L. What is the same capacity in cubic centimeters?
Use 1,000 cubic centimeters per liter.
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