Grade 6 Math Practice Test: Dependent and Independent Variables
- Dependent and Independent Variables
- 10 questions
- 12 minutes
This test covers telling dependent and independent variables apart, writing an equation from a table or a story, and using the equation to find values. Tip: the dependent variable is the one that changes because of the other.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
A plumber charges $45 for each hour of work. The total charge is c dollars for h hours.
Which is the independent variable?
Correct answer: C
The number of hours worked decides the charge, so h is the independent variable and c depends on it. 45 does not change, so it is not a variable.
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Question 2
A plumber charges $45 for each hour of work. The total charge is c dollars for h hours.
Which equation shows the relationship?
Correct answer: A
Each hour adds $45, so the charge is 45 times the number of hours: c = 45h. c = 45 + h would add only one dollar per hour.
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Question 3
x 1 2 3 4 y 7 14 21 28 Which equation fits every pair in the table?
Correct answer: B
Each y-value is 7 times its x-value, for example 7 × 3 = 21. y = x + 6 works only for the first pair (1, 7).
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Question 4
Mia is always 4 years older than her brother. Let b be her brother's age and m be Mia's age.
Which equation shows Mia's age?
Correct answer: D
Mia is 4 years older, so add 4 to her brother's age: m = b + 4. b = m + 4 would make the brother the older one.
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Question 5
The more tickets a school sells for its play, the more money it raises.
Which is the dependent variable?
Correct answer: A
The money raised depends on how many tickets are sold, so it is the dependent variable. The number of tickets sold is the independent variable.
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Question 6
Sam saves $12 every week. The equation s = 12w gives his savings s after w weeks.
After how many weeks will he have $132?
Correct answer: B
Solve 12w = 132: w = 132 ÷ 12 = 11 weeks. 144 adds 12 to 132 instead of dividing.
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Question 7
Use the equation y = 8x. What is y when x = 2.5?
Correct answer: C
y = 8 × 2.5 = 20. 10.5 adds 8 and 2.5 instead of multiplying.
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Question 8
A car travels at a steady 55 miles per hour. The distance is d miles after t hours, so d = 55t.
How far does the car travel in 3.5 hours?
Correct answer: A
d = 55 × 3.5 = 192.5 miles. 165 miles uses only 3 hours and leaves out the half hour.
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Question 9
The time it takes to fill a pool depends on how many hoses are used.
Which is the dependent variable?
Correct answer: D
The sentence says the time "depends on" the number of hoses, so the time is the dependent variable. The number of hoses is the independent variable.
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Question 10
x 2 4 6 8 y 1 2 3 4 Which equation fits every pair in the table?
Correct answer: D
Each y-value is half of its x-value, for example 6 ÷ 2 = 3, so y = x ÷ 2. y = x − 1 works only for the first pair (2, 1), and y = 2x doubles x instead of halving it.
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