Answer Key

Level 1

1. $60\text{ mi per h}$
2. $\$3\text{ per pen}$
3. $60\text{ words per min}$
4. $3\text{ laps per min}$
5. $\$7\text{ per h}$
6. $30\text{ pages per day}$
7. $5\text{ gal per min}$
8. $\$1.50\text{ per apple}$

Grade 8 Algebra: Rate of Change and Unit Rates

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Rate of change between two points

1. Solve:
$\text{After}$ $\text{2}$ $\text{hours}$ $\text{a}$ $\text{car}$ $\text{has}$ $\text{gone}$ $\text{100}$ $\text{miles.}$ $\text{After}$ $\text{5}$ $\text{hours}$ $\text{it}$ $\text{has}$ $\text{gone}$ $\text{250}$ $\text{miles.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
2. Solve:
$\text{A}$ $\text{plant}$ $\text{is}$ $\text{4}$ $\text{cm}$ $\text{tall}$ $\text{on}$ $\text{day}$ $\text{1}$ $\text{and}$ $\text{10}$ $\text{cm}$ $\text{tall}$ $\text{on}$ $\text{day}$ $\text{4.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
3. Solve:
$\text{It}$ $\text{is}$ $\text{20}$ $\text{degrees}$ $F\text{}$ $\text{at}$ $\text{6}$ $\text{am}$ $\text{and}$ $\text{8}$ $\text{degrees}$ $F\text{}$ $\text{at}$ $\text{10}$ $\text{am.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
4. Solve:
$\text{A}$ $\text{phone}$ $\text{battery}$ $\text{is}$ $\text{at}$ $\text{90\%}$ $\text{at}$ $\text{1}$ $\text{pm}$ $\text{and}$ $\text{60\%}$ $\text{at}$ $\text{4}$ $\text{pm.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
5. Solve:
$\text{Savings}$ $\text{are}$ $\text{\$50}$ $\text{after}$ $\text{2}$ $\text{weeks}$ $\text{and}$ $\text{\$110}$ $\text{after}$ $\text{6}$ $\text{weeks.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
6. Solve:
$\text{A}$ $\text{tank}$ $\text{holds}$ $\text{40}$ $L\text{}$ $\text{after}$ $\text{3}$ $\text{minutes}$ $\text{and}$ $\text{16}$ $L\text{}$ $\text{after}$ $\text{9}$ $\text{minutes.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$
7. Solve:
$\text{A}$ $\text{3}$ $\text{mile}$ $\text{taxi}$ $\text{ride}$ $\text{costs}$ $\text{\$10}$ $\text{and}$ $\text{a}$ $\text{7}$ $\text{mile}$ $\text{ride}$ $\text{costs}$ $\text{\$18.}$ $\text{Find}$ $\text{the}$ $\text{cost}$ $\text{per}$ $\text{extra}$ $\text{mile.}$
8. Solve:
$\text{An}$ $\text{elevator}$ $\text{is}$ $\text{at}$ $\text{floor}$ $\text{12}$ $\text{at}$ $\text{0}$ $\text{seconds}$ $\text{and}$ $\text{at}$ $\text{floor}$ $\text{2}$ $\text{at}$ $\text{20}$ $\text{seconds.}$ $\text{Find}$ $\text{the}$ $\text{rate}$ $\text{of}$ $\text{change.}$

Answer Key

Level 2

1. $50\text{ mi per h}$
2. $2\text{ cm per day}$
3. $-3\text{ degrees per h}$
4. $-10\%\text{ per h}$
5. $\$15\text{ per week}$
6. $-4\text{ L per min}$
7. $\$2\text{ per mi}$
8. $-0.5\text{ floors per s}$

Answer Key

Level 3

1. $\text{Ben (32 vs 30 pages per h)}$
2. $\text{Store 2 (\$0.70 vs \$0.75 per can)}$
3. $\text{cyclist (6 vs 5 m per s)}$
4. $20\text{ min}$
5. $256\text{ mi}$
6. $-1.5\text{ ft per day; 8 more days}$
7. $\text{Printer 2 (35 vs 30 pages per min)}$
8. $200\text{ m per h}$