Middle School Math Quiz: Writing Algebraic Expressions
9 questions · exam conditions
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Writing Algebraic ExpressionsQuestion 1 of 9

Maya has xx stickers. She gives away 55 stickers to each of her 44 friends, then receives 1212 more stickers from her teacher. Which expression represents the number of stickers Maya has now?

x−5⋅4+12x - 5 \cdot 4 + 12
x−5+4+12x - 5 + 4 + 12
x+5⋅4−12x + 5 \cdot 4 - 12
x−(5+4)+12x - (5 + 4) + 12
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Middle School Math Quiz

Middle School Math Quiz: Writing Algebraic Expressions

Practice Writing Algebraic Expressions 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 Writing Algebraic Expressions, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

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.

All questions

Question 1

Maya has xx stickers. She gives away 55 stickers to each of her 44 friends, then receives 1212 more stickers from her teacher. Which expression represents the number of stickers Maya has now?

  1. x−5⋅4+12x - 5 \cdot 4 + 12 (correct answer)
  2. x−5+4+12x - 5 + 4 + 12
  3. x+5⋅4−12x + 5 \cdot 4 - 12
  4. x−(5+4)+12x - (5 + 4) + 12
Explanation: Maya starts with xx stickers, gives away 55 stickers to each of 44 friends (5⋅4=205 \cdot 4 = 20 stickers), then receives 1212 more. This gives x−5⋅4+12=x−20+12x - 5 \cdot 4 + 12 = x - 20 + 12. Choice B incorrectly adds the number of friends instead of multiplying. Choice C has the wrong signs. Choice D adds the stickers per friend and number of friends instead of multiplying.

Question 2

The perimeter of a rectangle is 66 units less than 44 times its width. If the width is ww units and the length is 33 units more than twice the width, which expression represents the perimeter?

  1. 4w−64w - 6 (correct answer)
  2. 2w+2(2w+3)2w + 2(2w + 3)
  3. 6w+66w + 6
  4. 4w+34w + 3
Explanation: The problem states that the perimeter IS 66 units less than 44 times the width, so perimeter = 4w−64w - 6. Choice B represents the actual perimeter formula using the given dimensions (2w+2(2w+3)=6w+62w + 2(2w + 3) = 6w + 6), but this doesn't match the given relationship. Choice C equals 6w+66w + 6, which would be 66 more than 44 times the width plus 66. Choice D represents 44 times the width plus 33.

Question 3

In a science experiment, the temperature of a solution decreases by 2°C2°C every 55 minutes. If the initial temperature is T°CT°C and mm represents the number of 55-minute intervals that have passed, which expression represents the current temperature after 3030 minutes?

  1. T−2mT - 2m
  2. T−12T - 12 (correct answer)
  3. T−60T - 60
  4. T−2(30)T - 2(30)
Explanation: After 3030 minutes, there have been 305=6\frac{30}{5} = 6 five-minute intervals. The temperature decreases by 2°C2°C per interval, so the total decrease is 2×6=12°C2 \times 6 = 12°C. The current temperature is T−12T - 12. Choice A gives the general formula for mm intervals but doesn't substitute m=6m = 6. Choice C incorrectly uses 3030 instead of 66 intervals. Choice D multiplies the rate by the total time instead of the number of intervals.

Question 4

In a basketball game, Alex scored 22 fewer three-point shots than twice the number of two-point shots he made. If he made ff two-point shots and rr three-point shots, which equation correctly represents this relationship?

  1. r=2f+2r = 2f + 2
  2. f=2r−2f = 2r - 2
  3. r=2(f−2)r = 2(f - 2)
  4. r=2f−2r = 2f - 2 (correct answer)
Explanation: When you encounter word problems involving relationships between variables, the key is to translate the English description into mathematical symbols step by step, staying true to the order and meaning of the words. Let's break down the given information: Alex scored "2 fewer three-point shots than twice the number of two-point shots." Start with "twice the number of two-point shots" - since he made ff two-point shots, this gives us 2f2f. Then the phrase "2 fewer than" means we subtract 2 from that amount. So the number of three-point shots rr equals 2f−22f - 2, giving us r=2f−2r = 2f - 2. Looking at the wrong answers: Choice A gives r=2f+2r = 2f + 2, which would mean Alex scored 2 more three-point shots than twice his two-point shots - the opposite of what the problem states. Choice B has f=2r−2f = 2r - 2, which incorrectly makes the number of two-point shots depend on three-point shots, reversing the relationship. Choice C gives r=2(f−2)r = 2(f - 2), which means "twice the quantity of 2 fewer two-point shots" - this changes the meaning entirely by putting the subtraction inside the parentheses first. The correct answer is D: r=2f−2r = 2f - 2. Study tip: When translating word problems, work through the phrase in the exact order given, and watch out for answers that flip the relationship between variables or change the order of operations with parentheses.

Question 5

A recipe calls for 13\frac{1}{3} cup of flour for every 22 servings. Sarah wants to make enough for ss servings, but she only has 23\frac{2}{3} the amount of flour the recipe requires. Which expression represents the amount of flour Sarah has, in cups?

  1. 23⋅13⋅s2\frac{2}{3} \cdot \frac{1}{3} \cdot \frac{s}{2}
  2. 23⋅s6\frac{2}{3} \cdot \frac{s}{6}
  3. 13⋅s2⋅23\frac{1}{3} \cdot \frac{s}{2} \cdot \frac{2}{3} (correct answer)
  4. s6−23\frac{s}{6} - \frac{2}{3}
Explanation: For ss servings, the recipe requires 13⋅s2=s6\frac{1}{3} \cdot \frac{s}{2} = \frac{s}{6} cups of flour. Sarah has 23\frac{2}{3} of this amount, so she has 23⋅s6=s9\frac{2}{3} \cdot \frac{s}{6} = \frac{s}{9} cups. This can be written as 13⋅s2⋅23\frac{1}{3} \cdot \frac{s}{2} \cdot \frac{2}{3} (order of multiplication doesn't matter). Choice A has an extra 13\frac{1}{3} factor. Choice B is equivalent to the correct answer but not in the same form as choice C. Choice D subtracts 23\frac{2}{3} instead of multiplying.

Question 6

A parking garage charges a flat fee plus an additional amount for each hour parked. If the total cost is $8 more than $33 timesthenumberofhoursparked,whichexpressionrepresentsthetotalcostindollarsforparkingtimes the number of hours parked, which expression represents the total cost in dollars for parking hh $ hours?

  1. 3h+83h + 8 (correct answer)
  2. 8h+38h + 3
  3. 3(h+8)3(h + 8)
  4. 8(h+3)8(h + 3)
Explanation: The phrase '$8 more than $33 timesthenumberofhours′meanswestartwithtimes the number of hours' means we start with 33 timesthehours( times the hours ( 3h3h )andadd) and add 88 toit,givingusto it, giving us 3h+83h + 8 .ChoiceBincorrectlyreversesthecoefficients.ChoiceCdistributesincorrectly,representing. Choice B incorrectly reverses the coefficients. Choice C distributes incorrectly, representing 3h+243h + 24 .ChoiceDrepresents. Choice D represents 8h+248h + 24 $, which misinterprets both parts of the problem.

Question 7

A cell phone plan charges $25 per month plus $0.15 for each text message over $200200 .If. If tt representsthetotalnumberoftextmessagessentinamonth,whichexpressionrepresentsthemonthlycostwhenrepresents the total number of text messages sent in a month, which expression represents the monthly cost when t>200t > 200 $?

  1. 25+0.15t25 + 0.15t
  2. 25+0.15(t−200)25 + 0.15(t - 200) (correct answer)
  3. 25+0.15(t+200)25 + 0.15(t + 200)
  4. 25(t−200)+0.1525(t - 200) + 0.15
Explanation: When you encounter word problems involving tiered pricing or charges that apply only above a certain threshold, you need to carefully identify what triggers the additional cost and how to calculate it. This cell phone plan has two components: a fixed monthly fee of $25 and an overage charge of $0.15 per text beyond the 200-message allowance. The key insight is that you only pay extra for messages that exceed 200, not for all $tt $ messages. If you send t messages where t > 200 , the number of messages you pay extra for is (t - 200) . For example, if you send 250 messages, you pay extra for 250 - 200 = 50 messages. The total cost becomes: fixed fee plus overage charge, or 25 + 0.15(t - 200) . This matches answer choice B. Looking at the wrong answers: Choice A ( 25 + 0.15t ) incorrectly charges $0.15 for every single text message, ignoring the 200-message allowance. Choice C (25+0.15(t+200)25 + 0.15(t + 200)) mistakenly adds 200 to your total messages, which would mean paying for 200 extra messages you never sent. Choice D (25(t−200)+0.1525(t - 200) + 0.15) confuses the structure entirely, multiplying the fixed fee by the overage amount and treating the per-message rate as a fixed charge. Study tip: In tiered pricing problems, always identify the threshold carefully. The phrase "over 200" means you subtract 200 from the total to find the amount subject to extra charges. Look for this subtraction pattern in similar problems.

Question 8

A delivery service charges $3.50 for the first pound and $1.25 for each additional pound or fraction thereof. If a package weighs $ww poundswherepounds where w>1w > 1 $, which expression represents the total shipping cost in dollars?

  1. 1.25w+3.501.25w + 3.50
  2. 3.50+1.25w3.50 + 1.25w
  3. 3.50w+1.25(w−1)3.50w + 1.25(w - 1)
  4. 3.50+1.25(w−1)3.50 + 1.25(w - 1) (correct answer)
Explanation: When you encounter a shipping cost problem with a base fee plus additional charges, break down the pricing structure carefully. This delivery service has two components: a fixed charge for the first pound and a variable charge for everything beyond that. The cost structure is $3.50 for the first pound, then $1.25 for each additional pound. If a package weighs $ww poundswherepounds where w>1w > 1 ,youneedtodeterminehowmanypoundsarechargedattheadditionalrate.Sincethefirstpoundisalreadycoveredbythe, you need to determine how many pounds are charged at the additional rate. Since the first pound is already covered by the 3.50 fee, the remaining (w−1)(w - 1) pounds are charged at $1.25 each. The total cost is: Base fee + (Additional pounds × Additional rate per pound) = 3.50 + 1.25(w - 1) . This is answer choice D. Looking at the incorrect options: Choice A, 1.25w + 3.50 , charges the additional rate for all w pounds plus adds the base fee, essentially double-charging. Choice B, 3.50 + 1.25w , also charges the additional rate for all pounds instead of just the additional ones beyond the first. Choice C, 3.50w + 1.25(w - 1) , incorrectly applies the base fee to every pound rather than just once. Remember this pattern for multi-tier pricing problems: identify what's included in the base fee, then only apply additional charges to quantities beyond that base amount. Always subtract the base quantity from the total when calculating additional charges.

Question 9

The number of bacteria in a petri dish triples every hour. If there are initially bb bacteria, which expression represents the number of bacteria after the population has tripled nn times?

  1. 3bn3bn
  2. b+3nb + 3n
  3. b⋅3nb \cdot 3^n (correct answer)
  4. 3bn3b^n
Explanation: When a quantity triples nn times, it's multiplied by 3n3^n. Starting with bb bacteria and tripling nn times gives b⋅3nb \cdot 3^n. Choice A represents linear growth (33 times nn times bb). Choice B represents adding 3n3n to the original amount. Choice D has the exponent on the wrong factor, representing 33 times bb raised to the nnth power.