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

Question 1: Two conversions (2 points)

1. \(3.25\times 5280=17{,}160\text{ ft}\).
2. \(252: 60=4.2\text{ h}\).

Scoring: 1 point for each correct converted value with its unit.

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

\(55\,\frac{\text{mi}}{\text{h}}\times \frac{5280\text{ ft}}{1\text{ mi}}\times \frac{1\text{ h}}{3600\text{ s}}=\frac{290{,}400}{3600}\,\frac{\text{ft}}{\text{s}}\approx 80.7\,\frac{\text{ft}}{\text{s}}\).

About 80.7 ft/s

Scoring: 1 point for each correct conversion factor (2), 1 point for the value rounded correctly.

Question 3: Units of a quotient (2 points)

\(\frac{60\text{ mi}}{1\text{ h}}\times \frac{1\text{ gal}}{30\text{ mi}}=2\,\frac{\text{gal}}{\text{h}}\).

The truck uses 2 gallons of fuel per hour.

Scoring: 1 point for the value 2 with units gal/h, 1 point for the interpretation.

Question 4: Filling a container (3 points)

1. \(3\times 2\times 1.5=9\text{ ft}^{3}\).
2. \(9\times 7.48=67.32\text{ gal}\).
3. \(67.32: 8=8.415\approx 8.4\text{ min}\).

9 ft³; 67.32 gal; about 8.4 min

Scoring: 1 point for each part, with units.

Question 5: Scale of a graph (3 points)

1. \(1230-1180=50\) students.
2. Axis height: \(1250-1150=100\). \(\frac{50}{100}=50\%\).
3. \(\frac{50}{1250}=0.04=4\%\). The graph that starts at 1150 makes the change look larger.

50 students; 50%; 4%

Scoring: 1 point per part.

Question 6: Defining a quantity (2 points)

Let \(m\) be the distance in miles and \(C\) the cost in dollars: \(C=20+0.5m\). For \(m=18\): \(C=20+9=29\).

\(C=20+0.5m\); \(\$29\)

Scoring: 1 point for variables with units and the equation, 1 point for the cost.

Question 7: Accuracy of a poster (3 points)

1. \(24.5\times 18.2=445.9\). Each measurement has three significant digits, so the area is reported as \(446\text{ in}^{2}\).
2. The measurement is within \(0.05\) of \(24.5\): \(24.45\le w< 24.55\).

Scoring: (a) 1 point for 445.9, 1 point for rounding to 3 digits; (b) 1 point for both bounds with correct inequality signs.

Question 8: Trip planning (2 points)

Gallons: \(350: 25=14\). Cost: \(14\times \$4.00=\$56\). Per mile: \(\$56: 350=\$0.16\).

14 gal; \(\$56\); \(\$0.16\) per mile

Scoring: 1 point for the gallons and cost, 1 point for the cost per mile with units.

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