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Variable Substitution 2 - 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=no-exp

Evaluate.

1.   Evaluate: - 2x - 2y + x + y - 2x
where x=2,y=4.
2.   Evaluate: - 2x + 3x + y + x + x
where x=3,y=4.

Complexity=1, Mode=pos-num

Evaluate.

1.   Evaluate: 3y - y 3 - x 2 - 2z
where x=1,y=2,z=2.
2.   Evaluate: y 2 + 3y + x + z
where x=2,y=2,z=6.

Complexity=1, Mode=neg-num

Evaluate.

1.   Evaluate: -z + 2x 2 + 3z 3 + 2y 2
where x=-2,y=3,z=1.
2.   Evaluate: 2x 2 + 2z 3 + 3z + 2y 2
where x=2,y=3,z=-2.

Answers

Complexity=1, Mode=no-exp

Evaluate.

#ProblemCorrect AnswerYour Answer
1Evaluate: - 2x - 2y + x + y - 2x
where x=2,y=4.
Solution
Combine and arrange terms: - 3x - y

Substitute the values:
- 3(2) - 4

Compute the answer: - 10

#ProblemCorrect AnswerYour Answer
2Evaluate: - 2x + 3x + y + x + x
where x=3,y=4.
Solution
Combine and arrange terms: 3x + y

Substitute the values:
3(3) + 4

Compute the answer: 13

Complexity=1, Mode=pos-num

Evaluate.

#ProblemCorrect AnswerYour Answer
1Evaluate: 3y - y 3 - x 2 - 2z
where x=1,y=2,z=2.
Solution
Combine and arrange terms: -x 2 - y 3 + 3y - 2z

Substitute the values:
- 1 • 1 2 - 2 3 + 3(2) - 2(2)

Compute the answer: - 7

#ProblemCorrect AnswerYour Answer
2Evaluate: y 2 + 3y + x + z
where x=2,y=2,z=6.
Solution
Combine and arrange terms: y 2 + x + 3y + z

Substitute the values:
2 2 + 2 + 3(2) + 6

Compute the answer: 18

Complexity=1, Mode=neg-num

Evaluate.

#ProblemCorrect AnswerYour Answer
1Evaluate: -z + 2x 2 + 3z 3 + 2y 2
where x=-2,y=3,z=1.
Solution
Combine and arrange terms: 2x 2 + 2y 2 + 3z 3 - z

Substitute the values:
2(( - 2) 2) + 2(3 2) + 3(1 3) - 1

Compute the answer: 28

#ProblemCorrect AnswerYour Answer
2Evaluate: 2x 2 + 2z 3 + 3z + 2y 2
where x=2,y=3,z=-2.
Solution
Combine and arrange terms: 2x 2 + 2y 2 + 2z 3 + 3z

Substitute the values:
2(2 2) + 2(3 2) + 2(( - 2) 3) + 3(- 2)

Compute the answer: 4

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