Middle School Math Quiz: Evaluate Expressions With Variables
20 questions · exam conditions
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Evaluate Expressions With VariablesQuestion 1 of 20

The expression 4n2−3n+74n^2 - 3n + 7 gives the number of tiles needed for a mosaic pattern when nn represents the row number. How many tiles are needed for row 5?

92 tiles
85 tiles
112 tiles
77 tiles
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Middle School Math Quiz

Middle School Math Quiz: Evaluate Expressions With Variables

Practice Evaluate Expressions With Variables in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Evaluate Expressions With Variables, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

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Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

The expression 4n2−3n+74n^2 - 3n + 7 gives the number of tiles needed for a mosaic pattern when nn represents the row number. How many tiles are needed for row 5?

  1. 92 tiles (correct answer)
  2. 85 tiles
  3. 112 tiles
  4. 77 tiles
Explanation: Substitute n=5n = 5: 4(5)2−3(5)+7=4(25)−15+7=100−15+7=924(5)^2 - 3(5) + 7 = 4(25) - 15 + 7 = 100 - 15 + 7 = 92 tiles.

Question 2

A rectangular garden has length (3w+4)(3w + 4) feet and width (2w−1)(2w - 1) feet. The expression for its perimeter is 2(3w+4)+2(2w−1)2(3w + 4) + 2(2w - 1). What is the perimeter when w=7w = 7?

  1. 78 feet
  2. 70 feet
  3. 84 feet
  4. 76 feet (correct answer)
Explanation: Substitute w=7w = 7: 2(3(7)+4)+2(2(7)−1)=2(21+4)+2(14−1)=2(25)+2(13)=50+26=762(3(7) + 4) + 2(2(7) - 1) = 2(21 + 4) + 2(14 - 1) = 2(25) + 2(13) = 50 + 26 = 76 feet.

Question 3

Marcus is saving money for a gaming console. He starts with $45 and saves $12 each week. After some number of weeks, he spends $30 on a game controller. The expression $45+12w−3045 + 12w - 30 representshowmuchmoneyMarcushasafterrepresents how much money Marcus has after ww weeks.Whatisthevalueofthisexpressionwhenweeks. What is the value of this expression when w=7w = 7 $?

  1. $99 (correct answer)
  2. $84
  3. $69
  4. $114
Explanation: Substitute w=7w = 7 into the expression: 45+12(7)−30=45+84−30=129−30=9945 + 12(7) - 30 = 45 + 84 - 30 = 129 - 30 = 99.

Question 4

The expression 2x2+5x−32x^2 + 5x - 3 represents the profit in dollars from selling xx items. When x=4x = 4, what is the value of this expression?

  1. $29
  2. $45
  3. $37
  4. $49 (correct answer)
Explanation: Substitute x=4x = 4: 2(4)2+5(4)−3=2(16)+20−3=32+20−3=492(4)^2 + 5(4) - 3 = 2(16) + 20 - 3 = 32 + 20 - 3 = 49.

Question 5

Evaluate 2x+3y2x + 3y when x=5x = 5 and y=2y = 2.

  1. 10+3y10 + 3y
  2. 2525
  3. 2222
  4. 1616 (correct answer)
Explanation: This problem tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=5 and y=2 in expression 2x+3y, write 2(5)+3(2) replacing x with 5 and y with 2, use parentheses for clarity). To evaluate 2x+3y when x=5 and y=2, substitute: 2(5)+3(2), then evaluate: 2×5=10 and 3×2=6 (multiply first), then 10+6=16 (add). The correct answer is 16. Common errors include not substituting all variables (leaving answer as 10+3y), concatenation (reading 2x as 25), or arithmetic mistakes. Process: (1) write expression with variables (2x+3y), (2) substitute all given values (x=5, y=2: write 2(5)+3(2)), (3) evaluate using order (multiply: 2×5=10 and 3×2=6, add: 10+6=16), (4) verify reasonable (2×5=10, 3×2=6, sum=16✓).

Question 6

Evaluate x2+2yx^2 + 2y when x=3x = 3 and y=4y = 4.

  1. 25
  2. 20
  3. 17 (correct answer)
  4. 15
Explanation: This question tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=3 and y=4 in expression x²+2y, write 3²+2(4) replacing x and y, use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: x²+2y at x=3, y=4 becomes 3²+2(4), exponent: 9, multiply: 8, add: 9+8=17. Two variables: track separately, substitute all. Specific evaluation: x²+2y at x=3, y=4, substitute: 3²+2(4), evaluate: 9+8=17. Common error: treating exponent as multiplication, like 3×2+8=14, but wrong.

Question 7

Evaluate x+62\dfrac{x+6}{2} when x=8x=8.

  1. 11
  2. 14
  3. 7 (correct answer)
  4. 8
Explanation: Tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=8 in (x+6)/2, write (8+6)/2, use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: (x+6)/2 at x=8 becomes (8+6)/2, parentheses: 14, divide: 14/2=7. For this specific question, evaluate (x+6)/2 at x=8: substitute (8+6)/2, parentheses first: 8+6=14, then divide: 14/2=7. Correct substitution and evaluation yield 7, which matches choice C. Common errors include ignoring parentheses (8+6/2=8+3=11) or arithmetic mistakes (14/2=6). Process: (1) write expression (x+6)/2, (2) substitute x=8 to get (8+6)/2, (3) evaluate using order (parentheses then divide to get 7), (4) verify reasonable (8+6=14, half is 7 makes sense).

Question 8

A snack shop charges $2 per item plus a $3 one-time bag fee. The total cost is 2n+32n + 3, where nn is the number of items. What is the total cost when n=7n = 7?

  1. $27
  2. $73
  3. $17 (correct answer)
  4. $14
Explanation: This question tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if n=7n=7 in expression 2n+32n+3, write 2(7)+32(7)+3 replacing n with 7, use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: 2n+32n+3 at n=7n=7 becomes 2(7)+32(7)+3, multiply: 14, add: 14+3=1714+3=17. With exponent: x2−5x^2-5 at x=4x=4 becomes 16−5=1116-5=11. Real-world: cost formula 2n+32n+3 at n=7n=7 items gives 2(7)+3=172(7)+3=17 dollars (substitute n, evaluate, interpret as cost). Specific evaluation: 2n+32n+3 at n=7n=7, substitute: 2(7)+32(7)+3, evaluate: 14+3=1714+3=17.

Question 9

A science experiment measures temperature changes using the formula T=20+5t−2t2T = 20 + 5t - 2t^2, where TT is temperature in degrees Celsius and tt is time in minutes.

According to the formula in the passage, what is the temperature after 3 minutes?

  1. 17°C (correct answer)
  2. 21°C
  3. 35°C
  4. 53°C
Explanation: Substitute t=3t = 3: T=20+5(3)−2(3)2=20+15−2(9)=20+15−18=17T = 20 + 5(3) - 2(3)^2 = 20 + 15 - 2(9) = 20 + 15 - 18 = 17°C. Choice B results from calculating 20+5(3)−2(3)=20+15−6=2920 + 5(3) - 2(3) = 20 + 15 - 6 = 29, not squaring the 3. Choice C results from 20+5(3)=3520 + 5(3) = 35, forgetting the −2t2-2t^2 term. Choice D results from 20+5(3)+2(3)2=5320 + 5(3) + 2(3)^2 = 53, adding instead of subtracting the 2t22t^2 term.

Question 10

Evaluate x2−5x^2-5 when x=4x=4.

  1. 3
  2. 8
  3. 15
  4. 11 (correct answer)
Explanation: This problem is all about substitution—that means we swap the letter xx for the number it equals, then do the math. Here's how it works, one step at a time: First, write the expression: x2−5x^2 - 5. Next, replace xx with 44:
42−54^2 - 5 Now handle the exponent. Remember, 424^2 means 4×44 \times 4, which is 1616:
16−516 - 5 Finally, subtract:
16−5=1116 - 5 = 11 So the answer is D) 11. Think of xx like a labeled box. The label says "x=4x = 4," so whenever you see xx, you reach in and pull out a 44. Easy swap! Try this at home: Pick your own number for xx, like x=3x = 3, and evaluate x2−5x^2 - 5 again. Do the exponent first, then subtract. You've got this! 🎯

Question 11

Evaluate the expression 3x+53x+5 when x=4x=4.

  1. 27
  2. 16
  3. 39
  4. 17 (correct answer)
Explanation: Tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=4 in expression 3x+5, write 3(4)+5 replacing x with 4, use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: 3x+5 at x=4 becomes 3(4)+5, multiply first: 12, then add: 12+5=17. For this specific question, evaluate 3x+5 at x=4: substitute 3(4)+5, evaluate 3×4=12 (multiply), then 12+5=17 (add). Correct substitution and evaluation yield 17, which matches choice C. Common errors include concatenation (3x with x=4 as 34 instead of 3×4=12) or violating order by adding before multiplying (3+5=8, then 8×4=32). Process: (1) write expression 3x+5, (2) substitute x=4 to get 3(4)+5, (3) evaluate using order (multiply then add to get 17), (4) verify reasonable (3×4=12, +5=17 makes sense).

Question 12

A store's daily profit is modeled by 150+25h−5h2150 + 25h - 5h^2, where hh is the number of hours past noon. What is the profit at 2:00 PM (when h=2h = 2)?

  1. $190
  2. $170
  3. $180 (correct answer)
  4. $160
Explanation: When you encounter a problem involving a mathematical model or formula, your job is to substitute the given values and carefully perform the calculations step by step. Here, you need to find the profit when h=2h = 2 (since 2:00 PM is 2 hours past noon). Substitute h=2h = 2 into the profit formula 150+25h−5h2150 + 25h - 5h^2: 150+25(2)−5(2)2150 + 25(2) - 5(2)^2 Work through this systematically: 25(2)=5025(2) = 50 and 5(2)2=5(4)=205(2)^2 = 5(4) = 20. So you have: 150+50−20=180150 + 50 - 20 = 180 The profit at 2:00 PM is $180, which is answer choice C. Let's see where the wrong answers might come from. Choice A ($190) likely results from forgetting to subtract the $5h25h^2 termentirely,givingyouterm entirely, giving you 150+50=200150 + 50 = 200 ,ormakinganarithmeticerror.ChoiceB($170)mightoccurifyoumiscalculate$, or making an arithmetic error. Choice B ($170) might occur if you miscalculate $5(2)^2as10insteadof20,givingyouas 10 instead of 20, giving you150 + 50 - 10 = 190, or make another computational mistake. Choice D ($160) could result from incorrectly calculating $$25(2) as 30 instead of 50, leading to 150+30−20=160150 + 30 - 20 = 160. Remember: when substituting into algebraic expressions, follow the order of operations carefully. Calculate exponents first, then multiplication, and finally addition and subtraction from left to right. Double-check each arithmetic step to avoid careless errors.

Question 13

Evaluate 2x+y3−x\frac{2x + y}{3} - x when x=6x = 6 and y=9y = 9.

  1. −3-3
  2. 11 (correct answer)
  3. 33
  4. 77
Explanation: Substitute the values: 2(6)+93−6=12+93−6=213−6=7−6=1\frac{2(6) + 9}{3} - 6 = \frac{12 + 9}{3} - 6 = \frac{21}{3} - 6 = 7 - 6 = 1.

Question 14

Verify: Is 3x+2=203x + 2 = 20 when x=6x = 6?

  1. Yes, because 3(6)+2=203(6) + 2 = 20. (correct answer)
  2. Yes, because 3+6+2=203 + 6 + 2 = 20.
  3. No, because 3(6)+2=163(6) + 2 = 16.
  4. No, because 36+2=2036 + 2 = 20.
Explanation: This problem tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=6 in expression 3x+23x+2, write 3(6)+23(6)+2 replacing x with 6, use parentheses for clarity). To verify if 3x+2=203x+2=20 when x=6, substitute: 3(6)+23(6)+2, then evaluate: 3×6=183 \times 6 = 18 (multiply first), then 18+2=2018 + 2 = 20 (add). Since 3(6)+2=203(6)+2=20, the equation is true when x=6, so the answer is "Yes, because 3(6)+2=203(6)+2=20". Common errors include concatenation (reading 3x as 36, giving 36+2=3836+2=38), wrong order (adding before multiplying), or arithmetic mistakes (18+2=1918+2=19). Process: (1) substitute x=6 into 3x+23x+2, (2) evaluate 3(6)+2=18+2=203(6)+2=18+2=20, (3) compare to given value 20, (4) they match, so verification is correct.

Question 15

Evaluate the expression x+62\dfrac{x + 6}{2} when x=8x = 8.

  1. 7 (correct answer)
  2. 8
  3. 11
  4. 14
Explanation: This question tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=8x=8 in expression (x+6)/2(x+6)/2, write (8+6)/2(8+6)/2 replacing x with 8, use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: (x+6)/2(x+6)/2 at x=8x=8 becomes (8+6)/2(8+6)/2, parentheses: 14, divide: 14/2=714/2=7. With exponent: x2−5x^2 - 5 at x=4x=4 = 16−5=1116-5=11. Two variables: 2x+3y2x+3y at x=5x=5, y=2y=2 = 10+6=1610+6=16. Specific evaluation: (x+6)/2(x+6)/2 at x=8x=8, substitute: (8+6)/2(8+6)/2, evaluate: 14/2=714/2=7.

Question 16

Evaluate the expression 3x+53x + 5 when x=4x = 4.

  1. 39
  2. 16
  3. 27
  4. 17 (correct answer)
Explanation: This question tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=4 in expression 3x+5, write 3(4)+5 replacing x with 4, use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: 3x+5 at x=4 becomes 3(4)+5, multiply first: 12, then add: 12+5=17. With exponent: x²-5 at x=4 becomes 4²-5, exponent first: 16, subtract: 16-5=11. Two variables: 2x+3y at x=5, y=2 becomes 2(5)+3(2)=10+6=16. Specific evaluation: 3x+5 at x=4, substitute: 3(4)+5, evaluate: 3×4=12 (multiply), 12+5=17 (add).

Question 17

Evaluate x2−5x^2 - 5 when x=4x = 4.

  1. 11 (correct answer)
  2. 3
  3. 8
  4. 25
Explanation: This question tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=4 in expression x²-5, write 4²-5 replacing x with 4). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: x²-5 at x=4 becomes 4²-5, exponent first: 16, subtract: 16-5=11. With multiplication: 3x+5 at x=4 becomes 3(4)+5=12+5=17. Two variables: 2x+3y at x=5, y=2=10+6=16. Specific evaluation: x²-5 at x=4, substitute: 4²-5, evaluate: 16-5=11.

Question 18

A rectangle has length x+2x+2 inches and width 33 inches. The area is A=3(x+2)A=3(x+2). What is the area when x=6x=6?

  1. 11
  2. 20
  3. 24 (correct answer)
  4. 18
Explanation: Tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=6x=6 in A=3(x+2)A=3(x+2), write 3((6)+2)3((6)+2), use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: 3(x+2)3(x+2) at x=6x=6 becomes 3(6+2)3(6+2), parentheses: 88, multiply: 3×8=243 \times 8=24. For this specific question, evaluate A=3(x+2)A=3(x+2) at x=6x=6: substitute 3(6+2)3(6+2), parentheses: 6+2=86+2=8, multiply: 3×8=243 \times 8=24. Correct substitution and evaluation yield 24, which matches choice A. Real-world: rectangle area 3(x+2)3(x+2) at x=6x=6 gives 3(8)=243(8)=24 square inches (substitute x, evaluate, interpret as area). Process: (1) write expression 3(x+2)3(x+2), (2) substitute x=6x=6 to get 3(6+2)3(6+2), (3) evaluate using order (parentheses then multiply to get 24), (4) verify reasonable (6+2=86+2=8, times 3=243=24 makes sense).

Question 19

A rectangle's area is A=lwA = lw. If the length is l=9l = 9 cm and the width is w=4w = 4 cm, what is the area?

  1. 13 cm213\text{ cm}^2
  2. 36 cm236\text{ cm}^2 (correct answer)
  3. 94 cm294\text{ cm}^2
  4. 324 cm2324\text{ cm}^2
Explanation: Tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if l=9, w=4 in expression lw, write 9×4 replacing them, use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). Example: lw at l=9, w=4 becomes 9×4=36. Specific evaluation: lw at l=9, w=4: substitute 9×4, evaluate 36 cm². Correct substitution and evaluation leads to 36 cm², which matches choice B. Common errors include adding instead of multiplying (9+4=13 as in A), or wrong operations like 9×4=36 but then extra (maybe 929^2×4=324 as in D).

Question 20

Evaluate 18−2x218-2x^2 when x=3x=3.

  1. 12
  2. 0 (correct answer)
  3. 144
  4. 36
Explanation: Tests evaluating expressions by substituting variable values and applying order of operations (PEMDAS). Substitution: replace variables with given values (if x=3 in 18-2x², write 18-2(3)², use parentheses for clarity). Order of operations: evaluate following PEMDAS (parentheses first, exponents, multiply/divide, add/subtract). With exponent: 18-2x² at x=3 becomes 18-2(3)², exponent: 9, multiply: 2×9=18, subtract: 18-18=0. For this specific question, evaluate 18-2x² at x=3: substitute 18-2(3)², exponent: 3²=9, multiply: 2×9=18, subtract: 18-18=0. Correct substitution and evaluation yield 0, which matches choice A. Common errors include order violations like subtracting before exponent (18-2=16, then 16×3²=144) or exponent wrong (3²=6). Process: (1) write expression 18-2x², (2) substitute x=3 to get 18-2(3)², (3) evaluate using order (exponent, multiply, subtract to get 0), (4) verify reasonable (2×9=18, 18-18=0 makes sense).