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## Independent and Dependent Variables - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=1, Mode=txt

Do not put multiplication signs between a variable and its coefficient. (e.g., Use "5m" instead of "5 × m")

1.   You drive at a rate of 40 miles per hour for t
hours.

A. Which variable(s) are independent?
(Check all that apply.)
 distance you drive
 rate of miles per hour
 hours you drive

B. Which variable(s) are dependent?
(Check all that apply.)
 hours you drive
 distance you drive
 rate of miles per hour

C. Write an equation that expresses the situation.
Let d be the distance you drive.
Let t be the hours you drive.
2.   You burn 14 calories every minute you exercise.

A. Which variable(s) are independent?
(Check all that apply.)
 calories burned per minute
 number of calories you burn
 number of minutes you exercise

B. Which variable(s) are dependent?
(Check all that apply.)
 number of calories you burn
 calories burned per minute
 number of minutes you exercise

C. Write an equation that expresses the situation.
Let c be the number of calories you burn.
Let m be the number of minutes you exercise.

### Complexity=1, Mode=eq

Do not put multiplication signs between a variable and its coefficient. (e.g., Use "5m" instead of "5 × m")

 1.   7h - 2z = k Which variable(s) are independent?        k        z        hWhich variable(s) are dependent?        h        z        k 2.   9u - 4v = r Which variable(s) are independent?        u        r        vWhich variable(s) are dependent?        u        v        r

### Complexity=2, Mode=eq

Do not put multiplication signs between a variable and its coefficient. (e.g., Use "5m" instead of "5 × m")

 1.   5n - 2v - w = x Which variable(s) are independent?        w        n        x        vWhich variable(s) are dependent?        n        x        v        w 2.   k = (t)9u + 4z Which variable(s) are independent?        z        u        t        kWhich variable(s) are dependent?        z        u        t        k

### Complexity=1, Mode=txt

Do not put multiplication signs between a variable and its coefficient. (e.g., Use "5m" instead of "5 × m")

1You drive at a rate of 40 miles per hour for t
hours.

A. Which variable(s) are independent?
(Check all that apply.)
 distance you drive
 rate of miles per hour
 hours you drive

B. Which variable(s) are dependent?
(Check all that apply.)
 hours you drive
 distance you drive
 rate of miles per hour

C. Write an equation that expresses the situation.
Let d be the distance you drive.
Let t be the hours you drive.
Solution
The distance you drive depends on the hours you drive,
but the hours you drive does not depend on the distance you drive.

Therefore, the distance you drive is the dependent variable
and the hours you drive is the independent variable.
The rate of miles per hour is a constant - it is neither independent nor dependent.

 distance you drive = rate of miles per hour × hours you drive d = 40 × t
2You burn 14 calories every minute you exercise.

A. Which variable(s) are independent?
(Check all that apply.)
 calories burned per minute
 number of calories you burn
 number of minutes you exercise

B. Which variable(s) are dependent?
(Check all that apply.)
 number of calories you burn
 calories burned per minute
 number of minutes you exercise

C. Write an equation that expresses the situation.
Let c be the number of calories you burn.
Let m be the number of minutes you exercise.
Solution
The number of calories you burn depends on the number of minutes you exercise,
but the number of minutes you exercise does not depend on the number of calories you burn.

Therefore, the number of calories you burn is the dependent variable
and the number of minutes you exercise is the independent variable.
The calories burned per minute is a constant - it is neither independent nor dependent.

 number of calories you burn = calories burned per minute × number of minutes you exercise c = 14 × m

### Complexity=1, Mode=eq

Do not put multiplication signs between a variable and its coefficient. (e.g., Use "5m" instead of "5 × m")

17h - 2z = k

Which variable(s) are independent?
k        z        h
Which variable(s) are dependent?
h        z        k
Solution
In the equation, the variable k depends on the variables h and z.

So k is the dependent variable and
h and z are independent variables.
29u - 4v = r

Which variable(s) are independent?
u        r        v
Which variable(s) are dependent?
u        v        r
Solution
In the equation, the variable r depends on the variables u and v.

So r is the dependent variable and
u and v are independent variables.

### Complexity=2, Mode=eq

Do not put multiplication signs between a variable and its coefficient. (e.g., Use "5m" instead of "5 × m")

15n - 2v - w = x

Which variable(s) are independent?
w        n        x        v
Which variable(s) are dependent?
n        x        v        w
Solution
In the equation, the variable x depends on the variables n, v and w.

So x is the dependent variable and
n, v and w are independent variables.
2k = (t)9u + 4z

Which variable(s) are independent?
z        u        t        k
Which variable(s) are dependent?
z        u        t        k
Solution
In the equation, the variable k depends on the variables t, u and z.

So k is the dependent variable and
t, u and z are independent variables.