This test covers writing and using equations of proportional relationships, standard 7.RP.A.2c. It has 8 questions worth 20 points in total. Calculators are not needed. Show all work, write equations in the form \(y=kx\) where possible, and include units. Allow about 45 minutes.
- Grade: Grade 7
- Chapter: Equations of Proportional Relationships
- Common Core: 7.RP.A.2c
- Time: 45 minutes
- Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 3 pts; Question 5: 2 pts; Question 6: 3 pts; Question 7: 3 pts; Question 8: 3 pts)
Question 1: Constant from a table (2 points)
The table shows a proportional relationship.
- Find the constant of proportionality. (1 point)
- Write an equation for \(y\) in terms of \(x\). (1 point)
Question 2: Equation from a graph (2 points)
The graph shows a proportional relationship.
- Find the constant of proportionality. (1 point)
- Write the equation of the line. (1 point)
Question 3: Notebooks (2 points)
Noah buys notebooks that cost $1.85 each.
- Write an equation for the total cost \(t\), in dollars, of \(n\) notebooks. (1 point)
- Find the cost of 12 notebooks. (1 point)
Question 4: Two tables (3 points)
Table A and Table B each show values of \(x\) and \(y\).
- Decide whether each table shows a proportional relationship. Justify each answer. (2 points)
- Write an equation for the table that is proportional. (1 point)
Question 5: Hourly pay (2 points)
Aisha’s pay is given by \(p=13.5h\), where \(h\) is the number of hours worked and \(p\) is her pay in dollars.
- Find her pay for 18 hours. (1 point)
- Find how many hours she must work to earn $202.50. (1 point)
Question 6: Two printers (3 points)
Printer A prints \(p=18m\) pages in \(m\) minutes. Printer B is described in the table.
| Minutes | 2 | 5 | 8 |
|---|---|---|---|
| Pages | 40 | 100 | 160 |
- Write an equation for the number of pages Printer B prints in \(m\) minutes. (1 point)
- Which printer prints faster? Explain. (1 point)
- How many more pages does the faster printer print in 15 minutes? (1 point)
Question 7: Dog walking (3 points)
The graph shows Ethan’s earnings \(y\), in dollars, for walking dogs \(x\) hours. His friend Mei earns \(y=7.5x\).
- Write the equation for Ethan’s earnings. (1 point)
- Explain what the point \((1,8)\) means in this situation. (1 point)
- Who earns more in 6 hours, and how much more? (1 point)
Question 8: Filling a tank (3 points)
A hose fills a tank at a constant rate. After 8 minutes it has delivered 30 gallons.
- Write an equation for the number of gallons \(g\) delivered after \(m\) minutes. (1 point)
- How many gallons are delivered in 25 minutes? (1 point)
- How long does it take to deliver 150 gallons? (1 point)
See every chapter on the Grade 7 math page.