Pre-Algebra Practice Test: Variables and Expressions
- Variables and Expressions
- 10 questions
- 12 minutes
This test covers evaluating and writing algebraic expressions, like terms and the distributive property. Tip: "6 less than n" means you start with n and take 6 away, so it is n − 6.
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
What is the value of 4x − 7 when x = 5?
Correct answer: D
4x means 4 × 5 = 20, and 20 − 7 = 13. Reading 4x as the two-digit number 45 gives 38.
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Question 2
Which expression means "6 less than a number n"?
Correct answer: B
"Less than" reverses the order: start with n and subtract 6. The expression 6 − n means n less than 6.
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Question 3
Simplify: 3x + 5 + 2x − 8
Correct answer: A
Combine like terms: 3x + 2x = 5x and 5 − 8 = −3. The answer 5x + 13 adds 8 instead of subtracting it.
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Question 4
Which expression is equivalent to 4(2y − 3)?
Correct answer: C
Multiply 4 by each term: 4 × 2y = 8y and 4 × (−3) = −12. The answer 8y − 3 forgets to multiply the second term.
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Question 5
What is the value of a2 + 2b when a = −3 and b = 4?
Correct answer: B
(−3)² = 9 and 2 × 4 = 8, so 9 + 8 = 17. The answer −1 squares only the 3 and keeps the minus sign.
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Question 6
A phone plan costs $25 per month plus $4 for each gigabyte (GB) of data. Which expression gives the monthly cost for g GB?
Correct answer: D
The $25 is charged once, and $4 is charged for each of the g gigabytes: 25 + 4g. The expression 4 + 25g swaps the fixed and per-GB amounts.
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Question 7
Which pair shows like terms?
Correct answer: A
Like terms have exactly the same variables with the same exponents; the coefficients may differ. 5x² and 5x have different exponents.
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Question 8
Simplify: −2(x − 5) + 3x
Correct answer: C
−2 × x = −2x and −2 × (−5) = +10, so −2x + 10 + 3x = x + 10. The answer x − 10 misses that a negative times a negative is positive.
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Question 9
What is the coefficient of y in the expression 9 − 6y + x?
Correct answer: D
The coefficient includes the sign in front of the term: −6y has coefficient −6. The number 9 is a constant term.
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Question 10
A rectangle has width w and length 3w + 2. Which expression gives its perimeter?
Correct answer: A
Perimeter = 2(length + width) = 2(3w + 2 + w) = 2(4w + 2) = 8w + 4. The expression 3w² + 2w is the area.
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