Units, Quantities and Modeling: Algebra 1 Math Test – PDF Download

Question 1: Two conversions (2 points)

1. Convert \(3.25\text{ mi}\) to feet. (1 point)
2. Convert \(252\text{ min}\) to hours. (1 point)

Question 2: Speed in feet per second (3 points)

A race car travels at \(55\text{ mi/h}\). Write the conversion to feet per second as a product of fractions and find the speed to the nearest tenth. (3 points)

Question 3: Units of a quotient (2 points)

A truck uses fuel at a constant rate. It travels \(60\text{ mi/h}\) and gets \(30\text{ mi/gal}\). Find the quotient \(\frac{60\text{ mi/h}}{30\text{ mi/gal}}\), including its units, and explain what it measures. (2 points)

Question 4: Filling a container (3 points)

A container is a rectangular box \(3\text{ ft}\) long, \(2\text{ ft}\) wide and \(1.5\text{ ft}\) tall. A hose fills it at \(8\text{ gal/min}\), and \(1\text{ ft}^{3}\) holds \(7.48\) gallons.

1. Find the volume in cubic feet. (1 point)
2. Find the capacity in gallons. (1 point)
3. Find the filling time in minutes, to the nearest tenth. (1 point)

Question 5: Scale of a graph (3 points)

The graph shows enrollment at Lincoln High School, in students, over five school years (Year 1 is 2020).

1. Find the increase from Year 1 to Year 5. (1 point)
2. Find what percent of the graph’s vertical axis height this increase covers. (1 point)
3. Find what percent it would cover if the vertical axis ran from 0 to 1250, and state which graph makes the change look larger. (1 point)

Question 6: Defining a quantity (2 points)

A courier charges \(\$20\) plus \(\$0.50\) per mile. Define variables with units and write an equation for the cost (1 point), then find the cost of an \(18\)-mile delivery (1 point).

Question 7: Accuracy of a poster (3 points)

A rectangular poster measures \(24.5\text{ in}\) by \(18.2\text{ in}\), each measured to the nearest tenth.

1. Find the area and report it with an appropriate level of accuracy. (2 points)
2. Write an inequality for the actual width \(w\). (1 point)

Question 8: Trip planning (2 points)

Sofia’s car gets \(25\text{ mi/gal}\) and gas costs \(\$4.00\) per gallon. Find the gas needed for a \(350\text{-mile}\) trip, the cost of that gas, and the cost per mile. (2 points)

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