12 multiple-choice questions, progressively harder.
Brook has 1,260 residents across 9 square kilometers. Harbor has 1,520 residents across 8 square kilometers. By how much does Harbor’s average population density exceed Brook’s?
Solution
Correct answer: B
Find each whole-region rate, then subtract.
Harbor averages 50 more residents per square kilometer.
A survey recorded 450 plants in a rectangular plot 12 m by 25 m. A second plot has the same average plant density and an area of 184 square meters. How many plants does the second plot contain?
Correct answer: D
The first plot covers 12(25)=30012(25)=30012(25)=300 square meters. Use its average rate for the second plot as stated.
An island has 840 residents. A 3-square-kilometer reserve with no residents makes up one quarter of the island’s area. What is the average population density of the part outside the reserve?
Correct answer: A
The reserve is one quarter of the whole area, so the island covers 4(3)=124(3)=124(3)=12 square kilometers. All 840 residents live in the other 12−3=912-3=912−3=9 square kilometers.
The average is in residents per square kilometer.
A storage tub with a rectangular interior measures 50 cm by 36 cm along its inside base. The inside rim is 28 cm above the bottom and a fill mark is 22 cm above it. How many liters can the tub hold up to the fill mark?
Correct answer: C
Use the 22 cm fill depth. Convert the cubic centimeters to liters.
A mixture has a mass density of 1.6 grams per cubic centimeter. What is the mass of 2.5 liters of the mixture?
Convert 2.5 L to 2,500 cubic centimeters. Then multiply by the density and convert grams to kilograms.
On a site plan, a 5 cm scale bar represents 120 m. A rectangular pen on the plan is 4 cm by 3 cm. What actual area does the pen cover?
One plan centimeter represents 120÷5=24120\div5=24120÷5=24 actual meters. Apply this factor in both area directions.
A field covers 3,136 square meters. On a map, 1 cm represents 28 m. What is the field’s area on the map?
One map square centimeter represents 282=78428^2=784282=784 square meters. Divide the actual area by that area per map square centimeter.
A model reservoir and its full-size version have similar interiors at model-to-actual length scale 1:5. If the full-size version holds 40 liters to the rim, how many cubic centimeters does the model hold to the rim?
Convert 40 liters to 40,000 cubic centimeters. Since the full-size length is five times the model length, divide the actual capacity by the cube of five.
A park map uses 1 cm for 200 m. A fenced nesting area covers 15 square centimeters on that map. What is its average nesting density if the full area contains 48 nests? Give the answer per square kilometer.
One map centimeter represents 0.2 km. Square that factor, then divide the nest count by the actual area.
The average is 80 nests per square kilometer.
A model shows a 2 cm depth. In the actual installation, the depth is 50 cm. The actual installation is similar to the model. A model volume is 4 cubic centimeters. What is the matching actual volume in liters?
The actual-to-model depth ratio is 50÷2=2550\div2=2550÷2=25. Multiply the model volume by its cube.
A foam model and a solid plaster sculpture are similar. The model occupies 80 cubic centimeters and each sculpture length is four times the corresponding model length. The plaster density is 1.25 grams per cubic centimeter. What mass does the model predict for the sculpture?
Scale the model volume by 434^343. Apply the density of the actual plaster.
A map is reprinted at three times its original width and three times its original height. It represents the same town and the same 900 residents. How does the number of residents represented per square centimeter of paper change?
The paper area grows by 32=93^2=932=9 while the represented population remains the same. If the original map area is AAA, the new paper-based rate is
The population and the actual town density do not change.
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