ISEE Middle Level Quiz: Situations To Expressions
20 questions · exam conditions
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Situations To ExpressionsQuestion 1 of 20

To build a straight fence, a post is needed at the beginning and the end, and a post is needed every f feet in between. If a fence is to be built that is L feet long, and L is a multiple of f, which expression represents the number of posts required?

Lf\frac{L}{f}
Lf+1\frac{L}{f} + 1
Lf−1\frac{L}{f} - 1
L⋅f+2L \cdot f + 2
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ISEE Middle Level Quiz

ISEE Middle Level Quiz: Situations To Expressions

Practice Situations To Expressions in ISEE Middle Level 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 Situations To Expressions, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Middle Level.

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

To build a straight fence, a post is needed at the beginning and the end, and a post is needed every f feet in between. If a fence is to be built that is L feet long, and L is a multiple of f, which expression represents the number of posts required?

  1. Lf\frac{L}{f}
  2. Lf+1\frac{L}{f} + 1 (correct answer)
  3. Lf−1\frac{L}{f} - 1
  4. L⋅f+2L \cdot f + 2
Explanation: A fence of length L with posts every f feet is divided into L/f sections. For example, a 24-foot fence with posts every 8 feet has 3 sections. The number of posts needed is one more than the number of sections, because there is a post at the start of each section plus one final post at the very end. Therefore, the number of posts is Lf+1\frac{L}{f} + 1.

Question 2

A baker sells cupcakes for $3 each and cookies for $2 each. The cost to make each cupcake is c dollars, and the cost to make each cookie is k dollars. On a given day, the baker sells 70 cupcakes and 120 cookies. Which expression represents the baker's total profit for that day?

  1. 70(3)+120(2)70(3) + 120(2)
  2. 70c+120k70c + 120k
  3. 70(3−c)+120(2−k)70(3-c) + 120(2-k) (correct answer)
  4. 450−(c+k)450 - (c+k)
Explanation: Profit is calculated as (Revenue - Cost). A more direct way is to find the profit per item and multiply by the number of items sold. The profit on one cupcake is (3−c)(3-c). The profit on one cookie is (2−k)(2-k). For 70 cupcakes, the profit is 70(3−c)70(3-c). For 120 cookies, the profit is 120(2−k)120(2-k). The total profit is the sum of the profit from cupcakes and cookies: 70(3−c)+120(2−k)70(3-c) + 120(2-k).

Question 3

On a science test, a student earns 5 points for each correct answer, loses 2 points for each incorrect answer, and gets 0 points for unanswered questions. The test has 40 questions in total. If a student answers c questions correctly and i questions incorrectly, which expression represents the student's score?

  1. 5c−2(40−c)5c - 2(40 - c)
  2. 5c+2i5c + 2i
  3. 5c−2i5c - 2i (correct answer)
  4. 5(c)−2(40−c−i)5(c) - 2(40 - c - i)
Explanation: The student's score is based on the points gained from correct answers minus the points lost from incorrect answers. The points gained are 5c. The points lost are 2i. The total score is 5c−2i5c - 2i. The total number of questions (40) is extra information not needed to write the expression for the score, as the number of unanswered questions does not affect the score.

Question 4

A jar contains only dimes and quarters. Let d be the number of dimes. The number of quarters is 3 more than twice the number of dimes. Which expression represents the total value of the coins in the jar, in cents?

  1. 3d+33d + 3
  2. 35d+7535d + 75
  3. 60d60d
  4. 60d+7560d + 75 (correct answer)
Explanation: First, express the number of each coin in terms of d. Number of dimes = d. Number of quarters = 2d + 3. Next, find the value of each set of coins in cents. Value of dimes = 10d. Value of quarters = 25(2d+3)=50d+7525(2d + 3) = 50d + 75. The total value is the sum: 10d+50d+75=60d+7510d + 50d + 75 = 60d + 75.

Question 5

Jordan has jj dollars and buys a game for 1515 and a snack for 33. How can the remaining balance be expressed algebraically?

  1. j−(15+3)j-(15+3) (correct answer)
  2. (j−15)+3(j-15)+3
  3. j−(15⋅3)j-(15\cdot3)
  4. j+15+3j+15+3
Explanation: This question tests middle school quantitative reasoning skills by translating situations into algebraic expressions. The core concept involves understanding how real-world quantitative data can be represented using variables and operations in mathematics. In this specific stimulus, Jordan starts with j dollars and makes two purchases: a game for $15 and a snack for $3, requiring us to find the remaining balance. Choice A is correct because it accurately models the situation by subtracting the total cost of both items (15+3 = $18) from the initial amount j, giving j-(15+3). Choice B is incorrect because it subtracts only the game cost first, then adds 3, which would increase rather than decrease the balance after the second purchase. To help students, encourage practice in identifying key quantitative relationships and expressing them algebraically. Teach them to group multiple expenses together before subtracting from the initial amount, and watch for the importance of proper parentheses usage.

Question 6

A corporation pledges to donate $10,000 plus 5% of its annual profits to a charity. The 5% donation only applies to the portion of profits that exceeds $1 million. If the corporation's annual profit is P dollars, and P > 1,000,000, which expression represents the total donation?

  1. 10,000+0.05P10,000 + 0.05P
  2. 0.05(P−1,000,000)0.05(P - 1,000,000)
  3. 10,000+0.05(P−1,000,000)10,000 + 0.05(P - 1,000,000) (correct answer)
  4. 10,000(0.05)+(P−1,000,000)10,000(0.05) + (P - 1,000,000)
Explanation: The donation has two components: a fixed amount and a variable amount. The fixed amount is $10,000. The variable amount is 5% of the profits exceeding $1,000,000. This amount is P−1,000,000P - 1,000,000. The donation on this portion is 0.05(P−1,000,000)0.05(P - 1,000,000). The total donation is the sum of the two components: 10,000+0.05(P−1,000,000)10,000 + 0.05(P - 1,000,000).

Question 7

A library charges a fine for an overdue book of $0.50 for the first day it is late and $0.15 for each additional day. If a book is d days overdue, where d > 1, which expression represents the total fine in dollars?

  1. 0.50+0.15d0.50 + 0.15d
  2. 0.65d0.65d
  3. 0.50d+0.15(d−1)0.50d + 0.15(d-1)
  4. 0.50+0.15(d−1)0.50 + 0.15(d - 1) (correct answer)
Explanation: The total fine consists of the charge for the first day and the charge for the additional days. The first day costs $0.50. If the book is d days late, there are d−1d - 1 additional days. The charge for these days is 0.15(d−1)0.15(d - 1). The total fine is the sum: 0.50+0.15(d−1)0.50 + 0.15(d - 1).

Question 8

The temperature of a chemical reaction starts at x degrees Celsius and increases by d degrees every minute for m minutes. The final Celsius temperature is then converted to Fahrenheit using the formula F=95C+32F = \frac{9}{5}C + 32. Which expression represents the final temperature in Fahrenheit?

  1. 95(x+d)+32\frac{9}{5}(x + d) + 32
  2. 95x+32+dm\frac{9}{5}x + 32 + dm
  3. 95(x+dm)+32\frac{9}{5}(x + dm) + 32 (correct answer)
  4. 95(x)+dm+32\frac{9}{5}(x) + dm + 32
Explanation: First, find the final temperature in Celsius. The initial temperature is x. The total increase is d degrees/minute times m minutes, which is dm. The final Celsius temperature, C, is x+dmx + dm. Now, substitute this expression for C into the conversion formula: F=95(x+dm)+32F = \frac{9}{5}(x + dm) + 32.

Question 9

A family phone plan costs $90 per month for the first two lines. For each additional line, the cost is $15. The family uses n lines, where n is greater than 2. Which expression represents the total monthly cost for the lines?

  1. 90+15n90 + 15n
  2. 90n+15(n−2)90n + 15(n - 2)
  3. 90+15(n−2)90 + 15(n - 2) (correct answer)
  4. (90+15)n(90+15)n
Explanation: The total cost is the sum of the base cost for the first two lines and the cost for the additional lines. The base cost is a flat $90. The number of additional lines is n - 2. The cost for these additional lines is 15(n−2)15(n - 2). Therefore, the total monthly cost is 90+15(n−2)90 + 15(n - 2).

Question 10

A rectangular garden has a length that is 5 feet longer than twice its width. If the width is represented by w feet, which expression represents the perimeter of the garden?

  1. 3w+53w + 5
  2. 6w+106w + 10 (correct answer)
  3. 2w2+5w2w^2 + 5w
  4. 4w+104w + 10
Explanation: First, express the length in terms of the width w. "Twice its width" is 2w. "5 feet longer than that" is 2w + 5. The perimeter of a rectangle is 2(length + width). Substituting the expressions gives 2((2w+5)+w)2((2w + 5) + w). Simplifying inside the parentheses gives 2(3w+5)2(3w + 5). Distributing the 2 gives 6w+106w + 10.

Question 11

A bouncing ball is dropped from a height of H feet. On each bounce, it returns to a height that is r times its previous height. Which expression represents the height of the ball after its third bounce?

  1. H+3rH + 3r
  2. H(3r)H(3r)
  3. Hr2Hr^2
  4. Hr3Hr^3 (correct answer)
Explanation: We need to track the height after each bounce. The starting height is H. After the first bounce, the height is H×r=HrH \times r = Hr. After the second bounce, the ball reaches a height of r times the previous height, so (Hr)×r=Hr2(Hr) \times r = Hr^2. After the third bounce, the height is again r times the previous height, so (Hr2)×r=Hr3(Hr^2) \times r = Hr^3.

Question 12

A car is rented for d days at a rate of $35 per day. This rate includes 100 free miles per day. For each mile driven over the total number of free miles, there is a charge of $0.20. If the total miles driven is m, and m is greater than 100d, which expression shows the total cost?

  1. 35d+0.20m35d + 0.20m
  2. 35d+0.20(m−100)35d + 0.20(m - 100)
  3. 35d+0.20(m−100d)35d + 0.20(m - 100d) (correct answer)
  4. 35+d+0.20(m−100d)35 + d + 0.20(m - 100d)
Explanation: The cost has two parts: the daily fee and the mileage charge. The total daily fee is 35d35d. The total number of free miles is 100d100d. The number of miles charged is the total miles minus the free miles, which is m−100dm - 100d. The cost for these miles is 0.20(m−100d)0.20(m - 100d). The total cost is the sum of these two parts: 35d+0.20(m−100d)35d + 0.20(m - 100d).

Question 13

A museum sells tickets for a special exhibit. The first ticket costs $25. Each additional ticket purchased in the same transaction costs $18. If a group buys t tickets, where t > 1, which expression represents the total cost for the group?

  1. 25+18(t−1)25 + 18(t - 1) (correct answer)
  2. 25+18t25 + 18t
  3. 25t+18(t−1)25t + 18(t - 1)
  4. (25+18)t(25 + 18)t
Explanation: The total cost is the price of the first ticket plus the price of the additional tickets. The first ticket is $25. If there are t tickets in total, there are t−1t - 1 additional tickets. The cost of these additional tickets is 18(t−1)18(t - 1). So, the total cost is 25+18(t−1)25 + 18(t - 1).

Question 14

A salesperson earns a monthly salary of $2,500 plus a 6% commission on all sales. For sales exceeding $40,000 in a month, an additional bonus of 3% is paid on the portion of sales above $40,000. If total monthly sales are S dollars, and S > 40,000, which expression represents the total monthly earnings?

  1. 2,500+0.09S2,500 + 0.09S
  2. 2,500+0.06S+0.03S2,500 + 0.06S + 0.03S
  3. 2,500+0.09(S−40,000)2,500 + 0.09(S - 40,000)
  4. 2,500+0.06S+0.03(S−40,000)2,500 + 0.06S + 0.03(S - 40,000) (correct answer)
Explanation: Total earnings are the sum of the base salary, the regular commission, and the bonus commission. The base salary is $2,500. The regular commission is 6% of total sales, or 0.06S0.06S. The bonus is 3% on the amount of sales over $40,000, which is represented by S−40,000S - 40,000. So the bonus is 0.03(S−40,000)0.03(S - 40,000). Adding all parts gives 2,500+0.06S+0.03(S−40,000)2,500 + 0.06S + 0.03(S - 40,000).

Question 15

A taxi company charges an initial fee of $3.00, plus $1.80 per mile traveled. There is also a surcharge of $0.50 for each passenger after the first one. Which expression represents the cost for a group of p people traveling m miles, where p > 1?

  1. 3.00+1.80m+0.50p3.00 + 1.80m + 0.50p
  2. 3.00+1.80m+0.50(p−1)3.00 + 1.80m + 0.50(p - 1) (correct answer)
  3. 3.00p+1.80m3.00p + 1.80m
  4. (3.00+1.80)m+0.50p(3.00 + 1.80)m + 0.50p
Explanation: The total cost is composed of three parts: the initial fee, the mileage cost, and the passenger surcharge. The initial fee is $3.00. The mileage cost is (1.80m). The surcharge applies to passengers after the first, so there are p−1p-1 such passengers. The surcharge cost is 0.50(p−1)0.50(p-1). The total cost is 3.00+1.80m+0.50(p−1)3.00 + 1.80m + 0.50(p - 1).

Question 16

Leo opens a savings account with an initial deposit of $500. Each week, he deposits $40. After w weeks of making deposits, he withdraws one-fourth of the total amount in the account. Which expression represents the amount remaining in his account?

  1. 34(500+40w)\frac{3}{4}(500 + 40w) (correct answer)
  2. 34(500)+40w\frac{3}{4}(500) + 40w
  3. 500+40w−14500 + 40w - \frac{1}{4}
  4. 500+34(40w)500 + \frac{3}{4}(40w)
Explanation: First, find the total amount in the account before the withdrawal. This is the initial deposit plus the weekly deposits: 500+40w500 + 40w. If Leo withdraws one-fourth of this total, then three-fourths of the total remains. The remaining amount is 34\frac{3}{4} of the total, which is 34(500+40w)\frac{3}{4}(500 + 40w).

Question 17

Maria is y years old. Her brother, Sam, is 4 years younger. Their father is 1 year more than twice the sum of Maria's and Sam's ages. Which expression represents the father's age?

  1. 3y−33y - 3
  2. 4y−34y - 3
  3. 4y−74y - 7 (correct answer)
  4. 2(2y−4)2(2y - 4)
Explanation: First, find the ages of Maria and Sam: Maria is y, Sam is y - 4. The sum of their ages is y+(y−4)=2y−4y + (y - 4) = 2y - 4. Twice the sum of their ages is 2(2y−4)=4y−82(2y - 4) = 4y - 8. The father is 1 year more than this, so his age is (4y−8)+1=4y−7(4y - 8) + 1 = 4y - 7.

Question 18

A student has taken n tests and has an average score of 88. On the next test, the student scores a 96. Which expression represents the student's new average score for all n+1 tests?

  1. 88+962\frac{88 + 96}{2}
  2. 88n+96n\frac{88n + 96}{n}
  3. 88+96n+188 + \frac{96}{n+1}
  4. 88n+96n+1\frac{88n + 96}{n + 1} (correct answer)
Explanation: The average is the total sum of scores divided by the number of tests. The sum of the scores for the first n tests is 88n. After scoring 96 on the next test, the new total sum is 88n + 96. The new number of tests is n + 1. Therefore, the new average is the new sum divided by the new number of tests: 88n+96n+1\frac{88n + 96}{n + 1}.

Question 19

Let k be the smallest of three consecutive even integers. Which expression represents the sum of these three integers?

  1. 3k+63k + 6 (correct answer)
  2. 3k+33k + 3
  3. (3k)
  4. k(k+2)(k+4)k(k+2)(k+4)
Explanation: If k is the smallest of three consecutive even integers, the next even integer is k + 2, and the one after that is k + 4. The sum of these three integers is k+(k+2)+(k+4)k + (k + 2) + (k + 4). Combining like terms gives 3k+63k + 6.

Question 20

The original price of a jacket is p dollars. It is on sale for 30% off. A sales tax of 7% is then applied to the discounted price. Which expression represents the final cost of the jacket?

  1. 1.07(0.70p)1.07(0.70p) (correct answer)
  2. 0.70p+0.070.70p + 0.07
  3. 0.77p0.77p
  4. 0.70(1.07p)0.70(1.07p)
Explanation: First, calculate the discounted price. A 30% discount means the price is 70% of the original, so the discounted price is 0.70p. Next, calculate the 7% sales tax on this new price. An increase of 7% is equivalent to multiplying by 1.07. So, the final cost is 1.07×(0.70p)1.07 \times (0.70p). Choice D is equivalent, but the order in A better reflects the sequence of operations described.