Dependent and Independent Variables: math test, Grade 6 – download the PDF

1 Identify the variables / 3 pts

For each situation, name the independent variable and the dependent variable (1 point each).

1. The number of hours a faucet runs and the gallons of water used.
2. The number of players on a team and the number of water bottles needed.
3. The speed of a car and the distance it has traveled in one hour.

2 Smoothie bar / 4 pts

A smoothie costs 7 dollars. Let \( n \) be the number of smoothies and \( c \) the cost in dollars.

1. Write an equation for \( c \). (1 pt)
2. Complete the table. (1 pt)
3. Find the cost of 11 smoothies. (1 pt)
4. A bill is 91 dollars. How many smoothies were bought? (1 pt)

3 Find the rule / 3 pts

Look at the table.

1. Write the rule. (1 pt)
2. Find \( y \) when \( x = 20 \). (1 pt)
3. What is the rate of change? Is the graph a line through the origin? (1 pt)

4 Planting tulips / 4 pts

A gardener plants bulbs at a steady pace. The graph shows the number of bulbs \( b \) planted after \( n \) hours.

1. Which variable is independent, and on which axis is it? (1 pt)
2. What is the constant rate of change? (1 pt)
3. Write an equation. (1 pt)
4. How many bulbs are planted in 6 hours? (1 pt)

5 Constant rate or not? / 3 pts

Look at the two tables.

1. Find the rate of change in Table A. (1 pt)
2. Show that the rate in Table B is not constant. (1 pt)
3. Which table can be written as \( y = kx \)? Give \( k \). (1 pt)

6 Renting a bus / 3 pts

A club rents a bus. The cost is a 40 dollar fee plus 12 dollars for each rider. Let \( r \) be the number of riders and \( c \) the total cost in dollars.

1. Write an equation. (1 pt)
2. Find the cost for 5 riders. (1 pt)
3. The total is 172 dollars. How many riders are there? (1 pt)