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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
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 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
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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
The graphs of y = 0.5x - 2 and y = 1.5x - 4 intersect at a single point. What is that point?
A(3, -0.5)
B(2, -1)
C(0, -2)
D(6, 1)
Show answer & explanation
Let's work it out
1.To find where the two lines meet, set their right-hand sides equal: 0.5x - 2 = 1.5x - 4.
2.Subtracting 0.5x from both sides gives -2 = x - 4, and adding 4 gives x = 2.
3.Substituting back into either equation yields y = 0.5(2) - 2 = -1, so the intersection point is (2, -1).
Answer: B) (2, -1)
Question 4 · MathEasy
Which of the following correctly classifies 900\sqrt{900} and explains why?
ARational, because 900\sqrt{900} = 90
BIrrational, because the product of two irrational numbers is always irrational
CRational, because 900\sqrt{900} = 30
DIrrational, because any expression written with a square root symbol is irrational
Show answer & explanation
Let's work it out
1.To classify 900\sqrt{900}, first check whether 900 is a perfect square.
2.Since 30 x 30 = 900, we have 900\sqrt{900} = 30.
3.The number 30 can be written as 301\frac{30}{1}, a ratio of two integers, so it is rational.
4.Therefore 900\sqrt{900} is rational.
Answer: C) Rational, because 900\sqrt{900} = 30
Question 5 · 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 6 · Arithmetic & Number SenseStandard
A math teacher asks students to find a fraction, from a list of candidates, whose numerator is a prime number and whose value is already in simplest form (the GCF of its numerator and denominator is 1). Which fraction satisfies both conditions?
A1421\frac{14}{21}
B711\frac{7}{11}
C915\frac{9}{15}
D49\frac{4}{9}
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Let's work it out
1.For a fraction to satisfy both conditions, its numerator must be prime and the GCF of the numerator and denominator must equal 1.
2.Checking 711\frac{7}{11}: 7 is prime, and GCF(7, 11) = 1 since 11 is also prime and shares no common factor with 7 — both conditions are met.
3.The fraction 711\frac{7}{11} is the unique option satisfying both requirements.
Answer: B) 711\frac{7}{11}
Question 7 · 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
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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 8 · 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
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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 9 · PercentagesStandard
For a quilting project, a digital pattern is enlarged by 50%, or one-half of its current width, in each of two rounds. Which candidate starting width will result in a final width of 10 18\frac{1}{8} inches?
A9 18\frac{1}{8}
B6 34\frac{3}{4}
C2 1732\frac{17}{32}
D4 12\frac{1}{2}
Show answer & explanation
Let's work it out
1.Each enlargement multiplies the current width by 32\frac{3}{2}.
2.If x is the starting width, then x times 32\frac{3}{2} times 32\frac{3}{2} equals 10 18\frac{1}{8}, so x = 818\frac{81}{8} times 23\frac{2}{3} times 23\frac{2}{3} = 92\frac{9}{2}.
3.The starting width is 4 12\frac{1}{2} inches.
Answer: D) 4 12\frac{1}{2}
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
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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
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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
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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 shows selected values of g(x). What is g(-2)?
A1
B-2
C-7
D-10
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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 · Fractions & DecimalsHard
A research balloon records a temperature of -4 7/8 degrees Celsius at an altitude of 1 1/3 kilometers and -19 1/4 degrees Celsius at an altitude of 3 5/6 kilometers. The average temperature change per kilometer is the temperature change over the altitude change. About how many degrees Celsius per kilometer is this average change?
A-7
B-10
C-3
D-6
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Let's work it out
1.The temperature changes by -19 1/4 - (-4 7/8) = -14 3/8 degrees, while the altitude changes by 3 5/6 - 1 1/3 = 2 1/2 kilometers.
2.The resulting complex fraction is (-14 3/8)/(2 1/2) = -5 3/4, which is closest to -6.
Answer: D) -6
Question 16 · 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 17 · 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
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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 18 · Ratios & ProportionsHard
For a set of handmade bracelets, Nia has one bead mix that is 13\frac{1}{3} metallic beads and another that is 34\frac{3}{4} metallic beads. She begins with 1 18\frac{1}{8} cups of the first mix but uses 38\frac{3}{8} cup on a different project. She combines all of the remaining first mix with some of the second mix so that exactly 12\frac{1}{2} of the finished blend is metallic beads. How many cups of the second mix does she use?
A98\frac{9}{8}
B16\frac{1}{6}
C34\frac{3}{4}
D12\frac{1}{2}
Show answer & explanation
Let's work it out
1.After the other project, 34\frac{3}{4} cup of the first mix remains, containing 14\frac{1}{4} cup of metallic beads.
2.If x is the amount of the second mix, equating the metallic portion to half of the finished blend gives 14\frac{1}{4} + 3x/4 = 12\frac{1}{2} times the quantity 34\frac{3}{4} + x.
3.Solving this equation gives x = 12\frac{1}{2} cup.
Answer: D) 12\frac{1}{2}
Question 19 · Data & StatisticsHard
Set P contains half as many numbers as Set Q, and the mean of Set P is 34\frac{3}{4}. One-fourth of the numbers in Set Q, with a mean of 12\frac{1}{2}, are removed. The mean of the numbers in Set P together with the numbers remaining in Set Q is 710\frac{7}{10}. What was the original mean of Set Q?
A710\frac{7}{10}
B58\frac{5}{8}
C12\frac{1}{2}
D23\frac{2}{3}
Show answer & explanation
Let's work it out
1.Let Set Q contain 8 numbers, so Set P contains 4 and 2 are removed from Set Q.
2.The combined sum after removal is 10 times 710\frac{7}{10}, or 7; subtracting the sum of Set P leaves 4 for the remaining part of Set Q.
3.Restoring the removed sum gives an original Set Q total of 5, so its mean is 58\frac{5}{8}.
Answer: B) 58\frac{5}{8}
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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