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Free ISEE Math Practice Test — Grade 8

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 · MathEasy
A store is selling a specialty board game for $28. A shopper wants to estimate the square root of the price in dollars to decide how to split a group discount evenly. Which whole-dollar amount is closest to the square root of 28?
A6
B14
C4
D5
Show answer & explanation
Let's work it out
1.To estimate the square root of 28, identify the perfect squares on either side: 5 squared equals 25 and 6 squared equals 36.
2.Since 28 is between 25 and 36, the square root of 28 is between 5 and 6.
3.Because 28 is only 3 away from 25 but 8 away from 36, the square root of 28 is much closer to 5 than to 6, making 5 the best whole-dollar estimate.
Answer: D) 5
Question 2 · MathEasy
A linear function is defined by f(x) = 2.5x + 1.5. What is the rate of change of this function?
A2.5
B1.0
C4.0
D0.4
Show answer & explanation
Let's work it out
1.A linear function written in the form f(x) = mx + b has a constant rate of change equal to m, the coefficient of x.
2.In f(x) = 2.5x + 1.5, the coefficient of x is 2.5, so the rate of change is 2.5.
Answer: A) 2.5
Question 3 · Coordinate GraphsEasy
A music streaming app tracks how a newly released song is trending. The number of new listeners per hour (in hundreds) follows a linear pattern over the days since release. On day 2, the song is gaining 5 hundred new listeners per hour. On day 6, it is losing 3 hundred listeners per hour (a value of -3 hundred). Assuming this trend is perfectly linear, how many hundred new listeners per hour was the song projected to gain at the moment of release (day 0)?
A6
B1
C9
D17
Show answer & explanation
Let's work it out
1.To find the projected value at day 0, write the equation of the line through the two known points (2, 5) and (6, -3), then evaluate it at x = 0 (which means finding the y-intercept).
2.The slope is (-3 - 5) divided by (6 - 2), which equals -8 divided by 4, or -2.
3.Substituting the point (2, 5) into y = -2x + b gives 5 = -2(2) + b, so 5 = -4 + b, and b = 9.
4.The y-intercept is 9, meaning the song was projected to be gaining 9 hundred new listeners per hour at the moment of release.
Answer: C) 9
Question 4 · Data & StatisticsEasy
At a craft club, a student makes bracelets over two sessions. In the first session, the student completes 4 bracelets using an average of 3 beads each. In the second session, the student completes 2 bracelets using an average of 9 beads each. Which of the following is the overall average number of beads per bracelet across both sessions?
A15
B5
C6
D12
Show answer & explanation
Let's work it out
1.Find the total number of beads in each session by multiplying the number of bracelets by that session mean: 4 × 3 = 12 beads in session 1 and 2 × 9 = 18 beads in session 2.
2.The grand total is 12 + 18 = 30 beads across 4 + 2 = 6 bracelets, giving an overall average of 30 ÷ 6 = 5 beads per bracelet.
Answer: B) 5
Question 5 · MathEasy
What is the cube root of 512?
A9
B16
C7
D8
Show answer & explanation
Let's work it out
1.To find the cube root of 512, identify the integer n such that n cubed equals 512.
2.Testing 8: 8 times 8 equals 64, and 64 times 8 equals 512.
3.Therefore the cube root of 512 is 8.
Answer: D) 8
Question 6 · Fractions & DecimalsStandard
Price Ratio (Sale Price to Original Price)
Numerator of Complex FractionDenominator of Complex Fraction
34\frac{3}{4}54\frac{5}{4}
A clothing store is having a two-stage promotion on a jacket. The ratio of the jacket's sale price to its original price is given by the complex fraction shown in the table. If the jacket's sale price after both stages of the promotion is $1,800, what was the jacket's original price?
A$1,080
B$3,000
C$2,400
D$1,920
Show answer & explanation
Let's work it out
1.The complex fraction 3454\displaystyle \frac{\frac{3}{4}}{\frac{5}{4}} represents the ratio of the sale price to the original price.
2.To simplify it, multiply the numerator by the reciprocal of the denominator: (34\frac{3}{4}) * (45\frac{4}{5}) = 1220\frac{12}{20} = 35\frac{3}{5}.
3.So the sale price is 35\frac{3}{5} of the original price.
4.Setting up the equation: (35\frac{3}{5}) * O = 1800, and dividing both sides by 35\frac{3}{5} (or multiplying by 53\frac{5}{3}) gives O = 1800 * (53\frac{5}{3}) = 3000.
5.The original price was $3,000.
Answer: B) $3,000
Question 7 · MathStandard
A long-distance driver uses the function f(x) = 3x + 300 to estimate total trip mileage, where x is the number of miles driven on the current day and the constant accounts for miles already logged on previous days. If the driver covers 400 miles today, what is f(400)?
A2100
B1000
C1500
D900
Show answer & explanation
Let's work it out
1.To find f(400), substitute x = 400 into f(x) = 3x + 300.
2.First, multiply: 3 × 400 = 1200.
3.Then add the constant: 1200 + 300 = 1500.
4.The correct answer is C.
Answer: C) 1500
Question 8 · Coordinate GraphsStandard
A school district tracked its enrollment over time. In 2010, the district had 800 students enrolled. By 2015, enrollment had grown to 1,800 students. When the enrollment data is graphed as a straight line on a coordinate plane, with the year (starting from 2010) on the horizontal axis and number of students on the vertical axis, the line can be used to determine enrollment in any year. According to that graph, how many students were enrolled in 2013?
A600
B1,400
C1,550
D2,000
Show answer & explanation
Let's work it out
1.The two known points on the graph are (0, 800) and (5, 1800), where the horizontal axis counts years after 2010.
2.The line rises 1800 - 800 = 1000 students over 5 years, a rate of 200 students per year.
3.The year 2013 corresponds to t = 3 on the horizontal axis.
4.Reading the graph at t = 3 gives 800 + 200(3) = 800 + 600 = 1,400 students.
Answer: B) 1,400
Question 9 · PercentagesStandard
A quantity begins at 125.00. What is the difference after 3 periods between increasing it by 20% of its new value each period and increasing it by 20% of its starting value each period?
A216.00
B16.00
C5.00
D91.00
Show answer & explanation
Let's work it out
1.There are two growth methods to compare over 3 periods, starting from 125.00.
2.Method 1 – Compound (percentage of new value each period): Each period, multiply the current value by 1.20.
3.After 3 periods: 125.00 × 1.20³ = 125.00 × 1.728 = 216.00.
4.Method 2 – Linear (percentage of starting value each period): Each period, add 20% of the original 125.00, which is 25.00.
5.After 3 periods: 125.00 + 3 × 25.00 = 200.00.
6.Difference: 216.00 − 200.00 = 16.00.
Answer: B) 16.00
Question 10 · ProbabilityStandard
Wildlife Classification Categories
TraitNumber of Options
Activity Period?
Habitat4
Diet3
A field ecology team records each local animal using three traits: Activity Period, Habitat, and Diet. The table shows the number of classification options for Habitat and Diet. The team determined there are exactly 36 distinct animal profiles possible when all three traits are combined using the Fundamental Counting Principle. How many Activity Period options are there?
A4
B9
C2
D3
Show answer & explanation
Let's work it out
1.The Fundamental Counting Principle states that the total number of distinct profiles equals the product of the number of options in each trait category.
2.The table shows 4 Habitat options and 3 Diet options, so their product is 4 × 3 = 12.
3.Because all three traits together produce exactly 36 distinct profiles, the number of Activity Period options is 36 ÷ 12 = 3.
Answer: D) 3
Question 11 · Data & StatisticsStandard
School Supply Shop Sales (in dollars)
MonthOnlineIn-Store
September1,200800
October1,5001,000
November2,100900
December1,8001,500
The table shows monthly sales figures (in dollars) for a school supply shop, broken down by online and in-store purchases over four months. What fraction of the shop's total four-month sales came from online purchases?
A29\frac{2}{9}
B718\frac{7}{18}
C1625\frac{16}{25}
D1118\frac{11}{18}
Show answer & explanation
Let's work it out
1.Add the online sales across all four months: 1,200 + 1,500 + 2,100 + 1,800 = 6,600 dollars.
2.Then add every month's total to get the grand total: (1,200 + 800) + (1,500 + 1,000) + (2,100 + 900) + (1,800 + 1,500) = 2,000 + 2,500 + 3,000 + 3,300 = 10,800 dollars.
3.The fraction of total sales that came from online purchases is 6,60010\frac{600}{10},800, which simplifies by dividing both numerator and denominator by 600 to give 1118\frac{11}{18}.
Answer: D) 1118\frac{11}{18}
Question 12 · MathStandard
Daily Low Temperature
DayLow Temp (degrees C)
12.0
23.3
34.6
5?
A meteorologist records the daily low temperature (in degrees C) for three consecutive days. The temperatures follow a linear pattern, as shown in the table. If the pattern continues, what will the low temperature be on Day 5?
A2.0
B5.9
C6.5
D7.2
Show answer & explanation
Let's work it out
1.The table shows temperatures of 2.0, 3.3, and 4.6 degrees C on Days 1, 2, and 3.
2.The temperature increases by 1.3 degrees each day, so the rate of change is 1.3.
3.Writing the linear function as T(x) = 1.3x + b and substituting Day 1 gives 2.0 = 1.3(1) + b, so b = 0.7.
4.The function is T(x) = 1.3x + 0.7.
5.Evaluating at Day 5 gives T(5) = 1.3(5) + 0.7 = 6.5 + 0.7 = 7.2 degrees C.
Answer: D) 7.2
Question 13 · PercentagesStandard
Arin Bonus Challenge
Gate costBonus per roundNumber of bonus roundsFinal coins
850%272
In a game, Arin pays the gate cost once before entering the bonus rounds. At the end of each bonus round, the current coin total increases by the rate shown in the table. How many coins did Arin have before paying the gate cost?
A26
B40
C56
D44
Show answer & explanation
Let's work it out
1.Undo each 50% bonus by dividing the later coin total by 1.5.
2.Dividing 72 by 1.5 twice gives 32 coins immediately after the gate.
3.Restoring the 8 coins spent at the gate gives 40 coins.
Answer: B) 40
Question 14 · MathStandard
Values of g(x)
xg(x)
-4-13
-3-10
-2-7
-1-4
0-1
12
25
Maya is knitting scarves and tracks her progress using a function g(x), where x represents the number of days before her deadline (negative values mean days already past). The table below shows selected values of g(x). What is g(-2)?
A1
B-2
C-7
D-10
Show answer & explanation
Let's work it out
1.The function g(x) gives the number of rows Maya has knitted, where x is the number of days before her deadline.
2.The question asks for g(-2), meaning we need the output of g when the input x equals -2 (two days past the deadline).
3.Locating the row in the table where x = -2 and reading the corresponding g(x) value gives g(-2) = -7, so the answer is C.
Answer: C) -7
Question 15 · Equations & InequalitiesHard
The eighth grade sold 500 tickets to the winter dance, adult tickets at 20 dollars each and student tickets at 10 dollars each. After paying 500 dollars for the DJ, the class had 5,500 dollars left from the ticket money. Which pair below could be the number of adult tickets and the number of student tickets sold?
A300 adult, 200 student
B250 adult, 250 student
C100 adult, 400 student
D200 adult, 200 student
Show answer & explanation
Let's work it out
1.Ticket sales brought in 5,500 + 500 = 6,000 dollars, so a correct pair must satisfy both a + s = 500 and 20a + 10s = 6000.
2.Substituting s = 500 - a into the money equation gives 20a + 5000 - 10a = 6000, so 10a = 1000 and a = 100, which makes s = 400.
3.Checking 100 adult and 400 student tickets: the count is 100 + 400 = 500 tickets and the money is 2000 + 4000 = 6,000 dollars, so both conditions hold.
Answer: C) 100 adult, 400 student
Question 16 · Fractions & DecimalsHard
Which value is equal to 134+12+13\displaystyle \frac{1}{\frac{3}{4} + \frac{1}{2 + \frac{1}{3}}}?
A3328\frac{33}{28}
B113\frac{11}{3}
C2833\frac{28}{33}
D1219\frac{12}{19}
Show answer & explanation
Let's work it out
1.Evaluate from the innermost fraction outward: 2 + 13\frac{1}{3} = 73\frac{7}{3}, so 12+13\displaystyle \frac{1}{2 + \frac{1}{3}} = 37\frac{3}{7}.
2.Then 34\frac{3}{4} + 37\frac{3}{7} = 3328\frac{33}{28}, and taking the outer reciprocal gives 2833\frac{28}{33}.
Answer: C) 2833\frac{28}{33}
Question 17 · GeometryHard
For a school festival, a cooking club prepares 180,000 cubic centimeters of cake batter and sets aside 45,000 cubic centimeters for cupcakes. The rest exactly fills a giant cake mold consisting of a cylindrical lower section and a hemispherical dome. Both sections have radius 30 centimeters. Using 3 for pi, what is the height, in centimeters, of the cylindrical section?
A46 23\frac{2}{3}
B30
C10
D50
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Let's work it out
1.After the cupcake batter is removed, the mold receives 135,000 cubic centimeters of batter.
2.The hemispherical dome holds 54,000 cubic centimeters, leaving 81,000 cubic centimeters for the cylinder.
3.Since the cylinder has base area 2,700 square centimeters, its height is 81,000 divided by 2,700, or 30 centimeters.
Answer: B) 30
Question 18 · ProbabilityHard
A swim meet replay station can create a clip by choosing one of 5 race recordings, one camera angle, one of 4 playback speeds, and one starting point. The playback speeds are 0.5, 0.75, 1.0, and 1.25 times normal speed. Starting points occur every 0.8 second from 0.0 through 2.4 seconds, inclusive. If the station offers about 610 distinct clips, which is closest to the number of camera angles available?
A6
B38
C8
D10
Show answer & explanation
Let's work it out
1.There are 4 starting points: 0.0, 0.8, 1.6, and 2.4 seconds.
2.Each camera angle therefore produces 5 × 4 × 4 = 80 possible clips.
3.Since 610 ÷ 80 = 7.625, the number of camera angles is closest to 8.
Answer: C) 8
Question 19 · Equations & InequalitiesHard
A meteorologist checks a forecast model in which the morning low x and the afternoon high y (in degrees Celsius) must satisfy all three relations 3x - 2y = -16, x + y = 3, and 5x + y = -5. Which pair (x, y) satisfies every one of the three relations?
A(-2, 1)
B(5, -2)
C(-1, 0)
D(-2, 5)
Show answer & explanation
Let's work it out
1.Solve two of the relations together.
2.Subtracting x + y = 3 from 5x + y = -5 eliminates y and gives 4x = -8, so x = -2, and then y = 3 - (-2) = 5.
3.Testing this pair in the remaining relation confirms it: 3(-2) - 2(5) = -6 - 10 = -16.
4.So (-2, 5) satisfies all three relations.
Answer: D) (-2, 5)
Question 20 · GeometryHard
In a puzzle game, a token advances only if the three selected lengths form a right triangle whose hypotenuse is also a leg of a second right triangle with other leg 12.0 and hypotenuse 15.0. Which set of lengths advances the token?
A7.2, 9.6, 12.0
B1.8, 2.4, 3.0
C48.6, 64.8, 81.0
D5.4, 7.2, 9.0
Show answer & explanation
Let's work it out
1.The shared side satisfies h² + 12.0² = 15.0², so h² = 81 and h = 9.0.
2.Since 5.4² + 7.2² = 29.16 + 51.84 = 81, the required set is 5.4, 7.2, 9.0.
Answer: D) 5.4, 7.2, 9.0

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