ISEE Practice Questions (2026) — Free Sample Questions with Answers

14 free ISEE questions from our 150-question bank, grouped by content domain. Each answer explains why the right option is right — and why every wrong option is wrong.

Verbal Reasoning (3)Quantitative Reasoning (4)Reading Comprehension (3)Mathematics Achievement (4)

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Verbal Reasoning

Question 1

Select the word or word pair that best completes the sentence.

Far from being -------, the economist's forecast was hedged with so many conditions and exceptions that it committed her to almost nothing.

Show answer & explanation

Answer: A

categorical: Correct. Categorical means absolute and without qualification; "Far from being" reverses it, and a forecast full of conditions is the opposite of categorical.

pessimistic: Pessimistic describes outlook, which hedging neither confirms nor denies.

tentative: Tentative describes the forecast as it actually was; "Far from being" needs the opposite of the description that follows.

unfounded: Unfounded (baseless) is unrelated to how qualified the forecast was.

"Far from being X" means the truth is the opposite of X; hedged and noncommittal is the opposite of categorical.

Question 2

Select the word or word pair that best completes the sentence.

Although the new footbridge looked -------, engineers showed that its thin cables could support far more weight than the heavy steel trusses they replaced.

Show answer & explanation

Answer: C

antiquated: Antiquated (old-fashioned) does not contrast with strength; the bridge is new.

durable: Durable agrees with the strength described, so it cannot follow "Although."

flimsy: Correct. Flimsy means weak or easily broken; "Although" sets up the contrast between how thin cables look and how much weight they hold.

symmetrical: Symmetrical describes shape, which has no contrast with the bridge's strength.

"Although" signals that the blank opposes the rest of the sentence: looks weak, is strong.

Question 3

Select the word that is most nearly the same in meaning as the word in capital letters.

MUNIFICENT:

Show answer & explanation

Answer: C

affluent: Affluent (wealthy) fits a donor who could give a great deal, but it describes having money, not giving it away.

flamboyant: Flamboyant suggests a showy, lavish style, but it describes display, not generosity.

generous: Correct. Munificent means very liberal in giving, lavishly generous: "a munificent gift to the hospital."

pompous: Pompous (self-important) matches the grand sound of the word, but it criticizes vanity, while munificent praises giving.

Munificent = lavishly generous in giving.

Quantitative Reasoning

Question 4

Column A: $17 + 19$

Column B: $17 + 19$

Show answer & explanation

Answer: B

Column A: $36 = 6$ .
Column B: $17 > 16 = 4$ and $19 > 4$ , so the sum is greater than 8.
$8 > 6$ , so Column B is greater.

The quantity in Column A is greater.: Would need $36 = 6$ to beat a sum of two roots that are each more than 4.

The quantity in Column B is greater.: Correct. Column A is $36 = 6$ . In Column B, $17 > 4$ and $19 > 4$ , so the sum is more than 8.

The two quantities are equal.: Splits the root over the sum; $a + b$ is not $a + b$ .

The relationship cannot be determined from the information given.: Both quantities are fixed numbers, so the relationship can be determined.

The square root of a sum is less than the sum of the square roots of positive numbers; estimate with nearby perfect squares.

Question 5

Column A: $(x + 2)^{2} - (x - 2)^{2}$

Column B: $8 x$

Show answer & explanation

Answer: C

$(x + 2)^{2} = x^{2} + 4 x + 4$ .
$(x - 2)^{2} = x^{2} - 4 x + 4$ .
Subtract: $8 x$ , the same as Column B.
Another way: test $x = 1$ : $9 - 1 = 8$ ; and $x = - 1$ : $1 - 9 = - 8$ . Both match $8 x$ .

The quantity in Column A is greater.: Expanding $(x - 2)^{2}$ as $x^{2} - 4 x - 4$ makes Column A $8 x + 8$ ; the constant term of $(x - 2)^{2}$ is $+ 4$ .

The quantity in Column B is greater.: Squaring term by term ( $(x + 2)^{2} = x^{2} + 4$ ) drops the middle terms and makes Column A 0; with them kept, A is exactly $8 x$ .

The two quantities are equal.: Correct. $(x^{2} + 4 x + 4) - (x^{2} - 4 x + 4) = 8 x$ , so the two quantities are equal for every $x$ .

The relationship cannot be determined from the information given.: The variable seems to make the answer depend on $x$ , but the expressions are equal for every real $x$ .

Expand before deciding "cannot be determined"; an identity makes the columns equal for every value.

Question 6

Each edge of a cube is increased by 50%. By what percent does the volume of the cube increase?

Show answer & explanation

Answer: C

Scale factor for edges: 1.5.
Volume scale factor: $1. 5^{3} = (\frac{3}{2})^{3} = \frac{27}{8} = 3.375$ .
Increase $= 3.375 - 1 = 2.375 = 237.5%$ .
Another way: a cube of edge 2 has volume 8; edge 3 has volume 27; increase $19 \div 8 = 2.375$ .

50%: Applies the linear scale factor to volume; volume scales by the cube of the factor.

125%: Uses the square of the scale factor ( $1. 5^{2} = 2.25$ ), which gives the change in area, not volume.

237.5%: Correct. One way: the new volume is $1. 5^{3} = 3.375$ times the old, an increase of $3.375 - 1 = 2.375$ , or 237.5%.

337.5%: This is the new volume as a percent of the old; the increase is 100% less.

If lengths are multiplied by $k$ , areas multiply by $k^{2}$ and volumes by $k^{3}$ ; percent increase is (new ÷ old) − 1.

Question 7

Which of the following describes all values of $x$ for which $- 3 < 5 - 2 x \leq 7$ ?

Show answer & explanation

Answer: B

Subtract 5 from all three parts: $- 8 < - 2 x \leq 2$ .
Divide all three parts by $- 2$ and flip both inequality signs: $4 > x \geq - 1$ .
Rewrite from least to greatest: $- 1 \leq x < 4$ .
Check the endpoints: $x = - 1$ gives 7 (included); $x = 4$ gives $- 3$ (excluded).

$- 4 < x \leq 1$ : Divides by 2 instead of $- 2$ , so the signs of the bounds and the direction of the inequalities are both wrong.

$- 1 \leq x < 4$ : Correct. Subtract 5: $- 8 < - 2 x \leq 2$ . Dividing by $- 2$ flips both signs: $4 > x \geq - 1$ , that is, $- 1 \leq x < 4$ .

$- 1 < x \leq 4$ : Swaps the endpoints but not the strict and inclusive signs; $x = - 1$ gives $5 - 2 (- 1) = 7$ , which is allowed.

$1 \leq x < 4$ : Comes from a sign slip, writing $7 - 5$ as $- 2$ , so the left bound becomes 1 instead of $- 1$ .

Dividing a compound inequality by a negative number flips every inequality sign and swaps which end is strict.

Reading Comprehension

Question 8

Which of the following best describes the main focus of the passage?

Read the passage, a memoir-style narrative. Then answer the questions that follow.

The Tuner's Apprentice

¹ The summer I turned fifteen, my uncle Teodor hired me to carry his

²tool case. He tuned pianos for a living, driving from town to town in a

³van that smelled of felt and coffee, and he claimed he needed someone to

⁴hold the flashlight. I suspected my mother had arranged the job to keep

⁵me out of trouble, but I took it anyway, mostly because he paid in cash

⁶at the end of each week.

⁷ The first house we visited belonged to a retired music teacher whose

⁸piano had not been played in years. Uncle Teodor lifted the lid, struck

⁹a single key, and winced as if someone had stepped on his foot. Then he

¹⁰struck it again and listened, his head tilted, for a long time. I heard

¹¹nothing wrong at all. To me, the note sounded like every other note I

¹²had ever heard: loud, then quieter, then gone.

¹³ "Listen for the wobble," he said. He played two keys together, and

¹⁴this time I caught it: a faint throbbing inside the sound, like a moth

¹⁵fluttering behind a curtain. As he turned the tuning pin with his

¹⁶wrench, a fraction of a turn at a time, the throbbing slowed, and

¹⁷slowed, and then simply stopped. The two notes melted into one clean

¹⁸tone. I must have looked astonished, because he laughed. "It was always

¹⁹there," he said. "You just never had a reason to hear it."

²⁰ By August I could hear the wobble in nearly every piano we opened, and

²¹in other places, too: in the hum of the refrigerator, in two car horns

²²sounding at once. It was not always a pleasant gift. Some evenings the

²³whole world seemed slightly out of tune.

²⁴ On our last day, the teacher played a hymn on her repaired piano and

²⁵cried a little at the end. Uncle Teodor packed his tools without a word,

²⁶but in the van he handed me the wrench to hold, not the flashlight, and

²⁷I understood that something between us had changed.

Show answer & explanation

Answer: C

a teenager's dislike of a summer job: The narrator takes the job willingly (line 5) and comes to value it; dislike is not the focus.

the process of repairing an old piano: Too narrow: the tuning is the setting, but the story centers on what the narrator learns.

how a summer job taught the narrator a new way of listening: Correct. The narrator first hears "nothing wrong" (lines 10–11), learns to hear the wobble (lines 13–19), and keeps hearing it everywhere (lines 20–23).

the narrator's attempt to persuade the teacher to start playing her piano again: The narrator never tries to persuade the teacher; she plays on her own at the end (line 24).

In a narrative, the main focus is usually the change a character undergoes.

Question 9

The passage is primarily concerned with

Read the passage. Then answer the questions that follow.

The Golden Seam

¹ When a favorite bowl cracks, most of us do one of two things. We throw

²it away, or we glue it back together and hope no one notices the line.

³Centuries ago, Japanese craftspeople developed a third option called

⁴kintsugi, which means "golden joinery." In kintsugi, broken pottery is

⁵rejoined with lacquer, a sticky sap from the lacquer tree, and the seams

⁶are then dusted with powdered gold. The repaired object does not hide

⁷its injury. Instead, a bright line runs exactly where the break once

⁸was.

⁹ The technique is slow. Each layer of lacquer must cure for days in a

¹⁰warm, humid space before the next can be applied, and a single bowl may

¹¹take weeks to finish. That patience is part of the point. A kintsugi

¹²repair cannot be rushed, and the mender must study every crack before

¹³deciding how the gold should travel across the surface.

¹⁴ Admirers often connect kintsugi to wabi-sabi, a Japanese way of seeing

¹⁵that finds beauty in things that are imperfect, aging, or incomplete.

¹⁶From this point of view, a mended tea bowl is not a damaged copy of the

¹⁷original. It is a new object with a history, and the gold seam is the

¹⁸record of that history. Some collectors have even prized repaired pieces

¹⁹above unbroken ones.

²⁰ In recent years, the word has drifted far from the workshop. Self-help

²¹books invoke kintsugi as a symbol of recovering from hardship, and

²²stores sell home kits that rely on quick-setting glue and gold-colored

²³powder. Some traditional craftspeople find this troubling. A kit that

²⁴finishes a bowl in an afternoon, they point out, skips the very patience

²⁵that gave the practice its meaning.

²⁶ Still, the popularity of the idea may tell us something worth hearing.

²⁷In a culture that often replaces what it could repair, kintsugi offers a

²⁸quiet argument: that the marks of use and mending are not flaws to be

²⁹erased, but part of what makes an object, or a life, worth keeping.

Show answer & explanation

Answer: B

explaining how to repair a bowl at home: Home kits are one detail (lines 22–23), and the passage gives no instructions.

describing an art of repair and the ideas behind it: Correct. The passage defines kintsugi (lines 1–8), describes its method (lines 9–13), explains its link to wabi-sabi (lines 14–19), considers modern uses (lines 20–25), and ends with its lesson (lines 26–29).

arguing that home kintsugi kits should no longer be sold: Overstatement: some craftspeople find the kits "troubling" (line 23), but no one argues for a ban, and the author ends on a positive note.

comparing Japanese pottery with the pottery of other cultures: No other culture's pottery is discussed.

Check each answer against the whole passage: an answer that fits only one paragraph is too narrow.

Question 10

The primary purpose of the passage is to

Read the passage. Then answer the questions that follow.

A Brainless Problem Solver

¹ In a laboratory dish, a bright yellow blob spreads slowly across a

²layer of damp gel. It has no eyes, no nerves, and no brain. It is, in

³fact, a single cell, though one large enough to see without a microscope

⁴and containing many nuclei. Biologists call it Physarum polycephalum,

⁵and over the past few decades this humble slime mold has become an

⁶unlikely celebrity in the study of how living things solve problems.

⁷ Its fame began with a maze. In 2000, a team led by the Japanese

⁸biologist Toshiyuki Nakagaki let pieces of Physarum fill every corridor

⁹of a small maze. The researchers then placed oat flakes, a favorite

¹⁰food, at the maze's two exits. Over the next several hours, the

¹¹organism withdrew from the dead ends and from the longer routes, leaving

¹²a single thick tube that stretched along the shortest path between the

¹³two meals.

¹⁴ How does a creature without a brain manage this? The answer seems to

¹⁵lie in feedback. The slime mold moves by pumping its fluid interior back

¹⁶and forth through a network of tubes. Tubes that carry more flow grow

¹⁷thicker, and thicker tubes carry still more flow, while little-used

¹⁸tubes shrink and disappear. No part of the cell "knows" where the food

¹⁹is; the efficient route simply wins out over the inefficient ones, much

²⁰as a footpath across a lawn deepens wherever the most people choose to

²¹walk.

²² A later experiment pushed the idea further. In 2010, researchers

²³arranged oat flakes on a dish to match the locations of cities around

²⁴Tokyo and let the slime mold grow among them. The network it built

²⁵looked strikingly similar to the region's actual rail system, which

²⁶engineers had spent years designing. Some scientists now study the

²⁷organism's simple rules in hopes of designing transport and computer

²⁸networks that adjust themselves as conditions change.

²⁹ None of this means that the slime mold is thinking. But it does

³⁰suggest that intelligent-looking behavior does not always require a

³¹brain, and that a few simple rules, repeated across a whole body, can

³²sometimes accomplish what we might expect only a mind to do.

Show answer & explanation

Answer: B

praise researchers for designing better rail networks: The rail comparison (lines 22–26) is one example; the passage praises no one for rail design.

explain how a brainless organism can still solve problems: Correct. The passage introduces Physarum (lines 1–6), shows it solving a maze and a network problem, explains the feedback behind it (lines 14–21), and concludes that problem-solving behavior does not always need a brain (lines 29–32).

trace the growth of the slime mold from one cell into many: Misreads lines 3–4: the slime mold stays a single cell that contains many nuclei; its growth is not the subject.

prove that slime molds think in the same way that animal brains do: Overstatement contradicted by line 29: "None of this means that the slime mold is thinking."

For primary-purpose questions, choose the answer that covers every paragraph, including the conclusion, without going beyond what the author claims.

Mathematics Achievement

Question 11

The table shows how many students in Grades 9 and 10 belong to the robotics club. One of the 60 students is chosen at random. What is the probability that the student is in Grade 10 or is not in the club?

Robotics Club Membership
Grade	In club	Not in club	Total
Grade 9	10	30	40
Grade 10	15	5	20
Total	25	35	60

Show answer & explanation

Answer: C

Grade 10: 20 students. Not in the club: 35 students.
Both in Grade 10 and not in the club: 5 students, counted in each group.
P = $\frac{20 + 35 - 5}{60} = \frac{50}{60} = \frac{5}{6}$ .
Another way: the only students in neither group are the 10 Grade 9 club members, so P = $1 - \frac{10}{60} = \frac{5}{6}$ .

$\frac{1}{12}$ : This is $\frac{5}{60}$ , the probability of being in Grade 10 and not in the club; "or" includes everyone in either group.

$\frac{7}{12}$ : This is $\frac{35}{60}$ , only the students not in the club; the 15 Grade 10 club members are left out.

$\frac{5}{6}$ : Correct. Grade 10 has 20 students and 35 students are not in the club, but 5 students are in both groups: $\frac{20 + 35 - 5}{60} = \frac{50}{60} = \frac{5}{6}$ .

$\frac{11}{12}$ : Adds 20 and 35 without subtracting the 5 students counted twice: $\frac{55}{60} = \frac{11}{12}$ .

P(A or B) = P(A) + P(B) − P(A and B); subtract the overlap so no one is counted twice.

Question 12

The figure shows a garden made of a 12-foot-by-8-foot rectangle and a semicircle whose diameter is one 8-foot side of the rectangle. What is the area of the garden, in square feet?

Garden plan

Show answer & explanation

Answer: B

Rectangle: 12 × 8 = 96 square feet.
The semicircle's diameter is 8 feet, so r = 4.
Semicircle: $\frac{1}{2} π (4^{2}) = 8 π$ square feet.
Total: $96 + 8 π$ square feet.

$96 + 2 π$ : Uses r instead of r² for the semicircle: $\frac{1}{2} π (4)$ .

$96 + 8 π$ : Correct. The rectangle is 12 × 8 = 96, and the semicircle has radius 4, so its area is $\frac{1}{2} π (4^{2}) = 8 π$ .

$96 + 16 π$ : Uses the area of a full circle instead of a semicircle.

$96 + 32 π$ : Uses the diameter, 8, as the radius: $\frac{1}{2} π (8^{2})$ .

Split a composite figure into familiar shapes, and halve the radius before using a circle formula.

Question 13

Which of the following is a factor of $2 x^{2} + 5 x - 12$ ?

Show answer & explanation

Answer: A

Look for $(2 x + p) (x + q)$ with $pq = - 12$ and $2 q + p = 5$ .
Try q = 4 and p = −3: $2 (4) + (- 3) = 5$ , and $(- 3) (4) = - 12$ .
So $2 x^{2} + 5 x - 12 = (2 x - 3) (x + 4)$ .
Check by expanding: $2 x^{2} + 8 x - 3 x - 12 = 2 x^{2} + 5 x - 12$ .

$2 x - 3$ : Correct. $2 x^{2} + 5 x - 12 = (2 x - 3) (x + 4)$ ; the middle term is $8 x - 3 x = 5 x$ .

$2 x + 3$ : Comes from $(2 x + 3) (x - 4) = 2 x^{2} - 5 x - 12$ , which has the wrong sign on the middle term.

$x - 4$ : Also from $(2 x + 3) (x - 4)$ : both signs are reversed, so the middle term is $- 5 x$ , not $5 x$ .

$x + 3$ : From $(2 x - 4) (x + 3) = 2 x^{2} + 2 x - 12$ : the constants multiply to −12, but the middle term is $2 x$ , not $5 x$ .

To factor $a x^{2} + b x + c$ , the outer and inner products must add to $b x$ ; check the middle term, not just the constants.

Question 14

If $f (x) = x^{2} - 3 x$ and $g (x) = 2 x + 1$ , what is the value of $f (g (2))$ ?

Show answer & explanation

Answer: B

Work from the inside out: g(2) = 2(2) + 1 = 5.
Then f(5) = 5² − 3(5) = 25 − 15 = 10.

−3: This is g(f(2)): the functions were applied in the reverse order.

10: Correct. g(2) = 5, and f(5) = 25 − 15 = 10.

19: Substitutes 5 only into the $x^{2}$ term and keeps x = 2 in $- 3 x$ : 25 − 6 = 19.

40: Computes f(5) as 25 + 15, a sign error on −3x.

In f(g(x)), apply g first and then apply f to the result.

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