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Free ISEE Math Practice Test — Grade 7

Math only, deliberately — the real ISEE (published by ERB) also has verbal and reading sections, which we don't cover.

20 real practice questions at ISEE Middle Level difficulty, drawn from the same calibrated bank our adaptive practice uses. Work through them right here — every question has the answer and a step-by-step explanation one tap away.

Question 1 · Pre-AlgebraIntro
A flower shop has 30 roses. The shop owner puts an equal number of roses into 5 vases. Then 3 more roses are added to each vase. How many roses are in each vase now?
A8
B11
C7
D9
Show answer & explanation
Let's work it out
1.Step 1: Divide the roses equally into 5 vases.
2.30 / 5 = 6 roses per vase.
3.Step 2: Add 3 more roses to each vase.
4.6 + 3 = 9 roses per vase.
Answer: D) 9
Why the other choices are tempting: The answer is 9.
Question 2 · ProbabilityIntro
A fair coin is flipped 5 times. What is the probability of getting EXACTLY 3 heads?
A316\frac{3}{16}
B132\frac{1}{32}
C14\frac{1}{4}
D516\frac{5}{16}
Show answer & explanation
Let's work it out
1.The total number of equally likely outcomes when flipping a coin 5 times is 25 = 32.
2.The number of ways to get exactly 3 heads is C(5,3) = 5!/(3! x 2!) = 5x42x1\frac{5 x 4}{2 x 1} = 10.
3.So the probability = 1032\frac{10}{32} = 516\frac{5}{16}.
Answer: D) 516\frac{5}{16}
Question 3 · Equations & InequalitiesEasy
To model negative integers in math class, Ms. Rao uses one red counter for each unit below zero. She has the same number of cards labeled -6 as cards labeled -9. Modeling every card uses 180 red counters altogether. How many cards of each label does she have?
A60
B12
C15
D20
Show answer & explanation
Let's work it out
1.Let n be the number of cards of each label.
2.The counter total gives 6n + 9n = 180, so 15n = 180.
3.Dividing by 15 gives n = 12 cards of each label.
Answer: B) 12
Question 4 · Fractions & DecimalsEasy
Maya is making decorative banners for a craft fair. She cuts two pieces of ribbon from an 8-yard spool: one piece that is 1 and 34\frac{3}{4} yards long and another piece that is 2 and 34\frac{3}{4} yards long. How many yards of ribbon remain on the spool after both cuts?
A4 and 14\frac{1}{4}
B4 and 12\frac{1}{2}
C3 and 12\frac{1}{2}
D3 and 14\frac{1}{4}
Show answer & explanation
Let's work it out
1.First, find the total ribbon used by adding 1 and 34\frac{3}{4} and 2 and 34\frac{3}{4}.
2.Add the whole-number parts: 1 + 2 = 3.
3.Add the fraction parts: 34\frac{3}{4} + 34\frac{3}{4} = 64\frac{6}{4} = 1 and 24\frac{2}{4} = 1 and 12\frac{1}{2}.
4.Combine: 3 + 1 and 12\frac{1}{2} = 4 and 12\frac{1}{2} yards used.
5.Subtract from the full 8-yard spool: 8 − 4 and 12\frac{1}{2} = 3 and 12\frac{1}{2} yards remain.
Answer: C) 3 and 12\frac{1}{2}
Question 5 · Pre-AlgebraEasy
One quantity, p, is 0.4 times another quantity, q. Which statement must be true about q?
A0.4 times p
B0.6 times p
C2.5 times p
D4 times p
Show answer & explanation
Let's work it out
1.The relationship can be written as p = 0.4q.
2.Dividing by 0.4 gives q = 2.5p, so q is 2.5 times p.
Answer: C) 2.5 times p
Question 6 · Data & StatisticsEasy
Six friends each counted the number of stickers they own: 12, 8, 15, 8, 17, and one unknown number. If the mean number of stickers for all six friends is 12, what is the unknown number?
A8
B10
C12
D13
Show answer & explanation
Let's work it out
1.The mean of 6 numbers is 12, so the total sum must be 6 x 12 = 72.
2.The known numbers sum to 12 + 8 + 15 + 8 + 17 = 60.
3.The unknown number = 72 - 60 = 12.
Answer: C) 12
Why the other choices are tempting: The answer is C.
Question 7 · Arithmetic & Number SenseStandard
Overnight Low Temperatures at the Sanctuary
NightTemperature (degrees C)
Monday-4
Tuesday-2
Wednesday3
Thursday7
Friday-4
A wildlife researcher recorded the overnight low temperature (in degrees Celsius) at an animal sanctuary for five nights. The table shows the data. What was the mean (average) overnight low temperature for the five nights?
A0
B2
C-2
D-1
Show answer & explanation
Let's work it out
1.Add all five temperatures: -4 + (-2) + 3 + 7 + (-4).
2.Grouping the negatives and positives: (-4 - 2 - 4) + (3 + 7) = -10 + 10 = 0.
3.Divide by 5 days: 0 / 5 = 0.
4.The mean overnight low temperature was 0 degrees Celsius.
Answer: A) 0
Question 8 · Fractions & DecimalsStandard
Wildlife Park Animal Distribution
SectionFraction of All Animals
Lions Enclosure38\frac{3}{8}
Bird Sanctuary14\frac{1}{4}
A wildlife park is home to 1200 animals in total. The table shows the fraction of all the animals found in two of the park's sections. How many more animals are in the Lions Enclosure than in the Bird Sanctuary?
A300
B600
C450
D150
Show answer & explanation
Let's work it out
1.Start by finding the number of animals in each section.
2.The Lions Enclosure contains 38\frac{3}{8} of all 1200 animals: (38\frac{3}{8}) × 1200 = 450 animals.
3.The Bird Sanctuary contains 14\frac{1}{4} of all 1200 animals: (14\frac{1}{4}) × 1200 = 300 animals.
4.To find how many more animals are in the Lions Enclosure than in the Bird Sanctuary, subtract: 450 − 300 = 150 animals.
Answer: D) 150
Question 9 · GeometryStandard
Highway Rest Stop Dimensions
Rest StopLength (m)Width (m)
A300150
B400200
C500250
A state park system is planning a series of highway rest stops along a long road trip route. The table shows the planned dimensions for three rest stops, each shaped as a rectangle. The park service needs to install a fence all the way around the outside of Rest Stop B. How many meters of fencing are needed?
A600 m
B3,600 m
C1,200 m
D800 m
Show answer & explanation
Let's work it out
1.The perimeter of a rectangle equals 2 times the sum of its length and width.
2.For Rest Stop B, which measures 400 m by 200 m, the perimeter is 2 times (400 plus 200), which equals 2 times 600, or 1,200 meters of fencing.
Answer: C) 1,200 m
Question 10 · IntegersStandard
Quiz-Bowl Round Results
RoundPoints
1+1,200
2+800
3-500
4-600
5+900
A classroom quiz-bowl team earns or loses points in each round of a competition. The table shows the team's results. What is the team's total score after all five rounds?
A2,400
B3,400
C4,000
D1,800
Show answer & explanation
Let's work it out
1.Add all five point values together, keeping track of signs.
2.The positive rounds contribute 1200 + 800 + 900 = 2900.
3.The penalty rounds contribute (−500) + (−600) = −1100.
4.The total score is 2900 + (−1100) = 1800.
Answer: D) 1,800
Question 11 · ProportionsStandard
Weaving Rate
Yarn (yards)Fringe (inches)
800500
1,200?
A craft table shows that a weaver uses 800 yards of yarn to produce 500 inches of decorative fringe. At the same rate, how many inches of fringe can she produce with 1,200 yards of yarn?
A1,000
B900
C333
D750
Show answer & explanation
Let's work it out
1.Set up a proportion that keeps inches of fringe over yards of yarn consistent: 500800\frac{500}{800} = x1200\frac{x}{1200}.
2.Cross-multiplying gives 800x = 500 × 1200 = 600,000, so x = 600,000 ÷ 800 = 750 inches.
Answer: D) 750
Question 12 · Ratios & ProportionsStandard
Floor Boards Laid by 6-Worker Crew
DaysBoards Laid
62160
10?
A construction crew of 6 workers lays 2,160 floor boards in 6 days. Working at the same rate, how many floor boards will the same crew of 6 workers lay in 10 days?
A21,600
B360
C2,160
D3,600
Show answer & explanation
Let's work it out
1.First, find the unit rate by dividing the total boards by the number of workers and the number of days: 2,160 ÷ 6 workers ÷ 6 days = 60 boards per worker per day.
2.Then multiply this rate by the crew size and the new number of days: 60 boards/worker/day × 6 workers × 10 days = 3,600 boards.
Answer: D) 3,600
Question 13 · Data & StatisticsStandard
ScoreNumber of Games
1003
2008
3005
4002
5002
Luke recorded his scores from 20 arcade games in the table shown. What is the mean score per game?
A200
B208
C300
D260
Show answer & explanation
Let's work it out
1.To find the mean from a frequency table, multiply each score by its frequency, sum those products, then divide by the total number of games.
2.First, confirm the total number of games: 3 + 8 + 5 + 2 + 2 = 20.
3.Next, compute the weighted sum: (100 × 3) + (200 × 8) + (300 × 5) + (400 × 2) + (500 × 2) = 300 + 1600 + 1500 + 800 + 1000 = 5200.
4.Finally, divide by the total number of games: 5200 ÷ 20 = 260.
Answer: D) 260
Question 14 · Ratios & ProportionsStandard
Observation Periods (sunny : cloudy)
DayMorning SunnyMorning CloudyAfternoon SunnyAfternoon Cloudy
Day 14254
Day 25346
Day 32448
A school weather club tracked sunny and cloudy observation periods during the morning and afternoon of three days in a row. Their results are shown in the table. Which day had the greatest ratio of total sunny periods to total cloudy periods, and what is that ratio written in simplest form?
A5:4
B3:2
C2:1
D2:3
Show answer & explanation
Let's work it out
1.First, find the total sunny and cloudy periods for each day by adding morning and afternoon together.
2.Day 1: sunny = 4 + 5 = 9, cloudy = 2 + 4 = 6, giving a ratio of 9:6.
3.Day 2: sunny = 5 + 4 = 9, cloudy = 3 + 6 = 9, giving a ratio of 9:9.
4.Day 3: sunny = 2 + 4 = 6, cloudy = 4 + 8 = 12, giving a ratio of 6:12.
5.Comparing the three ratios as fractions: Day 1 is 96\frac{9}{6} = 32\frac{3}{2}, Day 2 is 99\frac{9}{9} = 1, and Day 3 is 612\frac{6}{12} = 12\frac{1}{2}.
6.Day 1 has the greatest ratio.
7.Simplifying 9:6 by dividing both parts by 3 gives 3:2.
Answer: B) 3:2
Question 15 · Arithmetic & Number SenseHard
A warehouse stores 3,456 cans in equal stacks on shelves. Each shelf holds 8 stacks, and each stack contains 12 cans. How many shelves are needed to store all the cans?
AA) 32
BB) 48
CC) 36
DD) 24
Show answer & explanation
Let's work it out
1.Step 1: Find how many cans fit on one shelf: 8 stacks x 12 cans per stack = 96 cans per shelf.
2.Step 2: Find the number of shelves: 3,456 / 96 = 36 shelves.
3.Check: 36 x 96 = 36 x 100 - 36 x 4 = 3,600 - 144 = 3,456.
4.Correct.
Answer: C) C) 36
Why the other choices are tempting: The answer is 36 shelves.
Question 16 · Algebraic ExpressionsHard
Two remote-control cars start at the same point and travel in the same direction. Car A moves at a speed of 12\frac{1}{2} mile per minute and Car B moves at 13\frac{1}{3} mile per minute. A student writes an expression for the total combined distance, in miles, traveled by both cars after t minutes, and then evaluates it when t = 4. What is the total combined distance traveled by both cars when t = 4 minutes?
A43\frac{4}{3}
B83\frac{8}{3}
C103\frac{10}{3}
D85\frac{8}{5}
Show answer & explanation
Let's work it out
1.Car A travels (12\frac{1}{2})t miles and Car B travels (13\frac{1}{3})t miles, so the combined distance expression is (12\frac{1}{2})t + (13\frac{1}{3})t.
2.To add the coefficients, find a common denominator: 12\frac{1}{2} + 13\frac{1}{3} = 36\frac{3}{6} + 26\frac{2}{6} = 56\frac{5}{6}, giving the simplified expression (56\frac{5}{6})t.
3.Substituting t = 4 yields (56\frac{5}{6})(4) = 206\frac{20}{6} = 103\frac{10}{3} miles.
Answer: C) 103\frac{10}{3}
Question 17 · IntegersHard
Artist Streaming Bonus Balance
MonthChange (dollars)
January (start)-1,200
February+800
March-500
April+1,400
May-300
A record label tracks a streaming bonus balance (in dollars) for an artist. The table shows the artist's starting balance and monthly changes. Starting balance (January): -$1,200 February: +$800 March: -$500 April: +$1,400 May: -$300 What is the artist's bonus balance, in dollars, at the end of May?
A200
B1400
C-200
D1000
Show answer & explanation
Let's work it out
1.Begin with the starting balance of -1200.
2.Apply each monthly change sequentially: -1200 + 800 = -400; then -400 + (-500) = -900; then -900 + 1400 = 500; then 500 + (-300) = 200.
3.The artist's bonus balance at the end of May is $200.
Answer: A) 200
Question 18 · PercentagesHard
Game-Store Wallet Activity
TransactionChange in Balance
Initial load+$75
Game purchase-$50
Reload+$45
Headset purchase-$35
Accessory purchase-$25
Refund+$30
The table shows every change to a game-store wallet used by Nia. A positive amount adds money to the wallet, and a negative amount removes money. The initial load and reload are the only amounts Nia put into the wallet, while the refund reverses part of a purchase. After all the transactions, the net amount spent is what percent of the current wallet balance?
A20%
B66 23\frac{2}{3}%
C200%
D275%
Show answer & explanation
Let's work it out
1.The purchases total 110 dollars, and subtracting the 30-dollar refund gives net spending of 80 dollars.
2.The wallet contains 120 - 80 = 40 dollars, so the required ratio is 8040\frac{80}{40} = 2.
3.Written as a rate per hundred, 2 equals 200%.
Answer: C) 200%
Question 19 · ProbabilityHard
Music Genre Survey (500 students)
CategoryNumber of Students
Pop only180
Jazz only120
Both pop and jazz50
Neither150
A music streaming survey of 500 students recorded which genres each student likes. The results show: 180 students like only pop, 120 students like only jazz, 50 students like both pop and jazz, and 150 students like neither. If one student from the survey is chosen at random, what is the probability that the student likes pop or jazz (or both)?
A110\frac{1}{10}
B410\frac{4}{10}
C2350\frac{23}{50}
D710\frac{7}{10}
Show answer & explanation
Let's work it out
1.First, identify the total number of students who like pop or jazz (or both) using the inclusion-exclusion principle.
2.The number of students who like pop includes those who like only pop and those who like both: 180 + 50 = 230.
3.The number of students who like jazz includes those who like only jazz and those who like both: 120 + 50 = 170.
4.Applying inclusion-exclusion: students who like pop or jazz = 230 + 170 − 50 = 350, where 50 is subtracted to avoid double-counting the students who like both genres.
5.The probability that a randomly chosen student likes pop or jazz (or both) is 350500\frac{350}{500}, which simplifies by dividing numerator and denominator by 50 to give 710\frac{7}{10}.
Answer: D) 710\frac{7}{10}
Question 20 · ProportionsHard
Snail Travel
Distance (feet)Time (minutes)
54
108
1512
35?
A garden snail travels 5 feet in 4 minutes. At this same speed, how many minutes will it take the snail to travel 35 feet?
A35 minutes
B24 minutes
C44 minutes
D28 minutes
Show answer & explanation
Let's work it out
1.The ratio is 5 feet per 4 minutes.
2.Find how many groups of 5 feet fit in 35 feet: 35 divided by 5 = 7 groups.
3.Multiply the time by the same number: 4 times 7 = 28 minutes.
Answer: D) 28 minutes

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