General Academic
Practice ISEE #5:
Answer Explanations
By Stephen Hayes and the Staff of General Academic
® ISEE is a registered trademark of the Educational Records Bureau, which does not endorse this
book.
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Upper Level ISEE Prep Guide
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General Academic
Verbal Reasoning - Synonyms
1. AMBROSIAL = exceptionally pleasing to taste or smell
A. cloying
B. dangerous
C. divine
sickly sweet in taste or
smell
able or likely to cause
physical injury
godlike or pleasing in
taste or smell
D. hellish
of, like, or suitable to hell
2. CHICANERY = the use of trickery to achieve a political, financial, or legal purpose
A. charity
B. deception
C. proverb
D. wisdom
the voluntary giving of
help to those in need
the action of deceiving
someone
stating a general truth or
piece of advice
having experience and
good judgment
3. EPITAPH = a phrase or statement written on a tombstone
A. cremation
B. dirge
C. headstone
D. inscription
4. ARDENT = feeling great passion, or felt very passionately
A. fluid
B. haphazard
C. passionate
D. resilient
5. RAMBUNCTIOUS = uncontrollably active
A. childlike
B. energetic
D. professional
the incineration of a dead
body
flowing or smoothly
carried out
having qualities
associated with a child
a passionate expression
of grief for the dead
happening or done in a
way that is not planned
showing or involving
great activity
a slab of stone set up at
the head of a grave
showing intense emotion
or feeling
C. hazardous
something risky or
dangerous
words inscribed, as on a
monument or in a book
able to recover quickly
from setbacks or elastic
following conduct as if it
were a profession
6. ELOQUENCE = the ability to speak or write well and in an effective way
A. articulateness
B. deviousness
C. electricity
D. inertness
clearly expressed and
easily understood
willing to lie in order to
get what is wanted
energy created by
moving charged particles
quality of not moving or
acting
7. EGALITARIAN = aiming for equal wealth, status, etc., for all people
A. democratic
B. equestrian
C. imperial
D. partisan
8. CYNICAL = believing that people are generally selfish and dishonest
A. apathetic
B. optimistic
C. pessimistic
D. truant
9. MERCURIAL = changing moods quickly and often
A. planetary
B. poisonous
C. steady
D. unpredictable
10. ABATE = to become weaker or become less
A. amplify
B. distract
D. muddle
the idea that all people
should be treated equally
not having or showing
much emotion or interest
of or relating to planets
to increase the strength
representing a person on
horseback
belief that good things
will happen in the future
causing sickness by
touching the body
to stop thinking about or
paying attention
of or relating to an
empire or an emperor
having or showing a lack
of hope for the future
direct or sure in
movement
C. minimize
to make something as
small as possible
one exhibiting blind and
unreasoning allegiance
one who misses school
without permission
not being able to say
what will happen
to mix up something in a
confused way
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Upper Level ISEE Prep Guide
11. ABRIDGE = to shorten something by leaving out some parts
A. condense
B. connect
C. cross
D. expand
12. CLANDESTINE = secret or done in a private place or way
A. antagonizing
B. caring
C. overt
D. secretive
13. ADULATE = praise someone excessively or obsequiously
A. cheat
B. compromise
C. flatter
D. humiliate
14. INIMICAL = tending to obstruct or harm.
A. banal
B. hostile
D. vast
to make shorter by
removing parts
to cause someone to feel
hostile or angry
act dishonestly in order
to gain an advantage
lacking in originality as
to be obvious and boring
to join two or more
things together
displaying kindness and
concern for others
settle a dispute by
mutual concession
of or being unfriendly or
antagonistic
a figure or mark formed
by two intersecting lines
done or shown openly
lavish insincere praise
and compliments
C. tactful
having good judgment
with delicate situations
to increase in size, range,
or amount
inclined to conceal
feelings and intentions
make someone feel
ashamed and foolish
of very great extent or
quantity
15. PENURIOUS = extremely poor and poverty-stricken
A. aggressive
B. bountiful
C. impoverished
D. literate
16. GANGLING = tall, thin, and awkward in movements
A. brawny
B. haughty
C. lanky
D. tawny
17. LOFTY = of a noble or exalted nature
A. economical
B. exalted
D. truncated
ready or likely to attack
or confront
physically strong;
muscular
careful not to waste
money or resources.
large in quantity
arrogantly superior and
disdainful
placed at a high or
powerful level
a person or place that is
poor
of a person ungracefully
thin and tall
C. middling
moderate or average in
size, quantity, or quality
of a person able to read
and write
of an orange-brown or
yellowish-brown color
shortened by cutting off
the top or the end
18. OFFICIOUS = meddlesome and interfering, usually giving unwanted help or advice
A. meddlesome
B. palpable
C. sanctioned
D. subdued
fond of interfering in
other people's affairs
able to be touched or felt
to give official approval
for something
quiet and rather
reflective or depressed
19. LANGUID = lazy or lacking vigor and energy; sluggish or moving slowly
A. animated
B. indolent
C. robust
D. watery
full of life or excitement
lazy or wanting to avoid
activity or exertion
strong and healthy
20. WINSOME = attractive or appealing in appearance or character
A. charming
B. mediocre
C. repulsive
pleasant or attractive
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of only moderate quality;
not very good
arousing intense distaste
or disgust
consisting of, containing,
or resembling water
D. victorious
having won a victory
General Academic
Verbal Reasoning - Sentence Completions
21. The dramatic film was meant to be the young man’s debut into the acting world.
Explanation
B
“into the acting world” indicates that the man was out of the acting world before
the film. This rules out exodus (departure) as an answer choice and leaves debut
(first appearance or performance) as the only viable answer.
22. Loathing small town life, Charles knew he would flourish in a more metropolitan
B
environment.
Since Charles loathes (intense dislike or disgust) a small town, we need to find a
word that is the opposite of a small city. The definition of metropolitan is
Explanation
something constitutes a large urban area, one that usually includes a city and its
suburbs and outlying areas.
23. In accordance with the wealthy woman’s will, her favorite charities were awarded
D
largesse to help them grow.
In order for a charity to grow, they do not need calliopes (steam powered organ)
or insolvencies (inability to pay ones debt). Also, since we do not know the types
Explanation
of charities, we cannot assume they will need apothecaries (the selling of
medicines). The only logical answer is largesse (bestowing money).
24. She jumped for joy at the sight of the elaborate buffet filled with epicurean
B
delights.
The only answer choice that can describe joy and a buffet (meal consisting of
several dishes) is epicurean (devoted to sensual enjoyment of fine food and drink).
Explanation
A droll (oddly amusing), ghoulish (hideous or morbid), or spartan (frugal) buffet
would not elicit joy.
25. Aside from the head priest, people are not allowed into inner sanctum of the
C
temple as it would profane its sanctity.
The key words here are “head priest.” Those that are not a head priest are not
Explanation
seen as being holy or saintly. Therefore, they will profane (treat with irreverence)
the sanctity (state of being holy) of the temple.
26. Ms. Brisby’s bake sale to save the local children’s park disproved her neighbor’s
C
assumption she was a misanthropic crone.
The keyword here is “disproved”. We are looking for a word that will describe a
person that would normally not give to a children’s park. The word reeking (smell
Explanation
unpleasantly) may describe an uncharitable person, but misanthropic (disliking
humankind) is a better answer.
27. Though only a prototype, the machine performed beyond the expectations of its
A
creators and sponsors.
The key words here are “machine” and “beyond the expectations.” Both
stereotype and whimsicality do not describe a machine. A replica (an exact copy)
Explanation
should function just as good as the original, so the only answer we are left with
will have to be a prototype (preliminary model).
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Upper Level ISEE Prep Guide
28. Frank decided it would be better to retire at the zenith of his sports career instead
D
of leaving when he no longer had the skill to play.
The keyword here is “instead.” The answer choice we are looking for must
describe a player that still has his skills. The words nadir (lowest point in
Explanation
fortunes), nascence (being born), and conclusion (end) will describe a very low
level of skill.
29. Her vast and diverse library demonstrated to her guests that she was a prolific
C
reader.
A person who has a “vast” and “diverse” collection of books would seem to be an
active reader. She will not seem to be dawdling (slow) or slothful (lazy) when it
Explanation
comes to reading. Instead she will seem to be prolific (plentiful) in her knowledge
of books.
30. Far from ostentatious, the home was furnished with simple furniture and only a
A
few decorations.
We can tell from the words “Far from” that the answer should be the opposite of
what comes after the coma. Therefore we are looking for a word that is the
Explanation
opposite of “simple.” Ostentatious is defined as a vulgar display that attracts
notice or rich and showy.
31. Lance avoided exacerbating his friend’s heartbreak by remaining mum about his
A
friend’s ex and her activities.
The keyword here is “avoided,” which will make the first blank a negative action
and the second blank a positive way of stopping that action. Exacerbating means
Explanation
make worse, and mum means silent. Placating (make less angry) may work as the
first blank, but you cannot avoid it by being surly (bad-tempered).
32. It was clear our military base was sabotaged by our supposed ally, and our
D
president quickly sought to annul that alliance.
The word “supposed” implies that something negative happened with the ally,
which then caused the president to respond. This implies that both blanks are
Explanation
negative. Sabotaged means to deliberately destroy, and annul means to declare
invalid.
33. The young man was a nefarious thief who pilfered many homes of family heirlooms
C
to bury them in the woods.
Since a thief is seen as someone who is negative and does negative things, both
blanks should be negative. Nefarious means wicked or criminal, and pilfered
Explanation
means to steal. Lambasted means to criticize harshly and is not something a thief
would do to a house.
34. The gravity of bankruptcy had not yet donned on Tina as she remained
B
effervescent throughout the day.
The keywords here are “bankruptcy had not yet donned,” which indicates that the
Explanation
first blank is negative and the second blank is positive. Gravity means seriousness
or importance, and effervescent means enthusiastic.
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General Academic
35. Though the child’s decision to tell the truth was laudable, he was reprimanded for
B
disobeying his parents in the first place.
The keyword here is “though,” this tells us that the two blanks will be opposite
from each other. The second blank must be negative, since it is something that
Explanation
happens when a child disobeys their parents. Laudable means deserving praise,
and reprimanded means to reprove or rebuke.
36. After years of displaying jingoism for his home nation, the diplomat’s defection to a
C
foreign government was an utter shock.
The word “shock” indicates that the action the diplomat took was irregular and
Explanation
that the first blank will be opposite from the second blank. Defection means
desertion of one’s country, and jingoism means extreme patriotism.
37. Kurt’s pilgrimage to pray at one-hundred monasteries proved to be an arduous but
D
fulfilling endeavor.
The keyword is “but,” which indicates that the second blank will be negative in
relation to the word fulfilling. The word “proved” implies that anyone who travels
Explanation
to one-hundred monasteries will feel the second blank. The word arduous means
requiring strenuous effort.
38. When traveling, it is important that you not loiter in areas considered precarious to
A
foreign visitors.
The key phrase here is “important that you not,” which indicates that the verb has
Explanation
to be negative inside the location. Loiter means to stand around idly, and
precarious means dangerously unsafe or unstable.
39. We could not move from our chairs as we were quite torpid after eating the
D
smorgasbord of food provided by our generous hosts.
The keyword here is “generous,” which implies that the food provided was a
positive thing. Since they could not move from their chairs, we can assume that
Explanation
the first blank is negative. Torpid means mentally or physically inactive, and
smorgasbord means a wide range of something (food).
40. My mother’s sprightly nature proved to be expedient in managing the infinite
B
energy of my children on our family vacations.
The keyword here is “proved,” which implies that the two blanks must be positive
or both negative. Since the sentence states the mother manages the infinite energy
Explanation
of the speaker’s children, then the blanks are positive as good comes from her
mother’s nature. Sprightly means full of energy, and expedient means practical.
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Upper Level ISEE Prep Guide
Quantitative Reasoning
1.
D
Tools: functions, order of operations
)
indicates that whenever
occurs, then (
(
)
Steps: (1)
happens
(2) With
, plug in 5 for every m value and 4 for every n value
(
)
(
)
( )
(3)
( )
(4)
Quick Tips:  Don’t forget your order of operations or PEMDAS
 The symbol is not a particular operation, but is instead used to signify the
output from the two variables m and n
2.
B
Tools: deciphering word problems
Steps: (1) Since there are 5 times as many volleyball players as Frisbee players, we can
write the value for volleyball players as 5F and Frisbee players as F
(2) The total number of players at a recreation park is the sum of volleyball
players and Frisbee players, so add the two values and set them equal to 72
(3)
Quick Tips:  Answer choices A and C are the same, just written differently
3. 35
A
Tools: deciphering word problems
Steps: (1) The project group contains two subgroups, with 5 people working in both
subgroups
(2) Since the 5 people are only counted once as part of the whole group, you must
only count them on one of the subgroups amounts
(3) The idea is that
(4)
Quick Tips:  You can also visualize the problem by drawing out a Venn Diagram
 Both signifies the number people working in both groups
 Neither signifies the number of people working in neither group (essentially a
third group)
4. {1, 2, 3, 4, 6, 12}
C
Tools: factors
Steps: (1) Break each number down into its factors
(2) 60 
(3) 72 
(4) Match the similar factors together: {1, 2, 3, 4, 6, 12}
Quick Tips:  You can also test the answer choices by dividing the largest value from each
set into the two numbers, and then the next largest (and so on)
 20, 10, and 5 do not work for 72, so answer choices A, B, and D do not work
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General Academic
5. 5 hours
B
Tools: deciphering word problem
Steps: (1) The ratio between the two velocities will be 1 : 2 (East : West)
(2) West traveled 50 miles and East traveled 25 miles; thus, West’s rate is 50 mph
(3) Subtract the 50 miles already traveled from the total 300 miles in order to
obtain the distance remaining (250 miles)
(4) Divide the remaining distance from the rate to find the time remaining to
travel the distance:
hours
Quick Tips:  Draw a line to visualize the distance traveled by the two family members
6. 9. 12 inches2
C
Tools: area of circle, area of square
Steps: (1) Find the diameter of the circle using the 45-45-90 triangle rule (4√ )
(2) Find the radius by dividing the diameter in half (2√ )
(3) Find the area of the circle (
( √ )
(4) Find the area of the Square (
)
(5) Subtract the area of the square from the circle (9.12)
Quick Tips:  If you forget the 45-45-90 rule (x-x-x√ ), then just estimate the diameter of
the circle and choose the closest answer
7.
D
Tools: number line, negative numbers
Steps: (1) The letters to the left of the 0 will be negative
(2) Solve each answer choice and see which value will give you the lowest
negative value
(3)
is a negative multiplied by a negative and will give you a positive value
(4)
is a higher positive value subtracted by a lower positive value. This will
give a positive value.
(5)
is a low negative number multiplied by a low positive number. This will
give you a low negative value.
(6)
is a high negative number multiplied by a high positive number. This
will give you the lowest negative value.
Quick Tips:  A negative value multiplied by another negative value will always give you a
positive value
8.
A
Tools: exponent rules
Steps: (1) When we multiply numbers with the same base, we add the powers together
(2)
(3) Place 81 in the same terms as 3:
(4) Thus,
, and since a, b, and c are whole numbers, two of the
variables are 1 and the third variable is 2 (it doesn’t matter which)
(5)
Quick Tips:  If many of the numbers are the same and the question is working with
exponents, try to have all of the numbers in the same terms
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Upper Level ISEE Prep Guide
9. 240 miles
D
Tools: deciphering word problems, cross multiplying fractions
Steps: (1) Convert the 2 hours into minutes (120 minutes)
(2) Set up your fractions in terms of
(
)
(3) Cross multiply (
)
(4) Solve for
Quick Tips:  It doesn’t matter if you put minutes on top of the fraction or the distance. Just
make sure you keep the order the same on the other fraction.
A
Tools: exponent rules
Steps: (1) We want to get by itself, so we need to eliminate the exponent. We do this by
taking the 13th root of
.
10.
√ . We can rewrite it as
(2) This leaves us with
(3) We then can reduce the fraction, giving us
Quick Tips:

( )
The root of a value with a power can be rewritten to be: √
11. 50
C
Tools: deciphering word problems
Steps: (1) The ratio of pairs of socks to pairs of shoes is 8 : 3, or 11 pairs of items in total
(2) The ratio can also be written as 16 : 6, or 22 items in total (double the original
ratio since each pair has two socks and two shoes)
(3) If there are 110 items in total in the closet, divide this amount by the number
of total items in the ratio:
(the ratio occurs 5 times)
(4) Multiply each value in the 16 : 6 ratio by 5 to determine the total number of
socks and the total number of shoes
(5)
and
(80 : 30)
(6) To make the ratio equal, subtract the number of shoes from the number of
socks to see how many shoes need to be added
(7)
shoes (80 : 80)
Quick Tips:  Pay attention to the wording such as “pairs,” which signifies two items in a set
12. {0, 2, 4}
C
Tools: deciphering word problems, set notation
Steps: (1) Write out all possible integers for both sets
(2) Set A = {0, 1, 2, 3, 4, 5} and Set B = {0, 2, 4, 6, 8, 10}
(3) The stands for the intersection of the two sets, or what values are shared
between the two sets
(4) Both Set A and B contain 0, 2, and 4
(5)
Quick Tips:  Pay attention to the wording for Set A and Set B
 Set A is basically stating
 “inclusive” indicates that Set B includes 0 and 10 in the set
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General Academic
13. 5.5
B
Tools: distance formula
Steps: (1) Notice that the x values do not change for line NM and the y values do not
change for line JK
(2) Find the absolute distance between the x values on line JK by subtracting the
values and taking the absolute value of that difference
|
(3) |
(4) Line NM is half the length of line JK, so the length of line NM is
(5) Find the difference between the y values for line JK and set it equal to 8.5
(6)
Quick Tips:  You can also find the lengths of line NM and JK by using the distance formula
)
√(
(
)
14. 0
B
Tools: algebraic equations
Steps: (1) We want to simplify the first equation by subtracting
from both sides.
(
.)
(2) Now divide both sides by 17. (
)
(3) This tells us that and must be opposite but equal (absolute value)
( )
(4) We can just pick 1 and -1 to test this: ( )
( )
( )
(5)
Quick Tips:  Don’t make it hard for yourself and choose the lowest possible number to plug
in to formulas, like 0 or 1
15.
C
Tools: deciphering word problems
Steps: (1) We need to first multiply the percent to the total amount of sales (
)
(2) We then divide that between the seven charities (
)
Quick Tips:  Some word problems add unnecessary information to try and trick you.
 If you find yourself reading the question multiple times, skip it and come back
16.
A
Tools: perpendicular lines
Steps: (1) We first need to reorganize the equation into a
format (slopeintercept)
(2)
(3) When two lines are perpendicular to each other they will have negative
reciprocal slopes
(4) The negative reciprocal of 4 is
or
Quick Tips:  When we convert the equation into
form, the number in front of
the will be your slope
 If the slope of the first line is a whole number, the slope of the second line that
is perpendicular to the first line will be a fraction or decimal
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Upper Level ISEE Prep Guide
17. .75
B
Tools: area of circle
Steps: (1) Since the circle is inscribed perfectly in the square, we can use the side length
of the square for the diameter of the circle (2)
(2) Split the diameter in half and insert it in the area formula for a circle
(
( )
)
(3) The lines forming the triangle in the square meet at the origin point of the
circle and form a 90° angle
(4) If the sector of the non-shaded area of the circle has a 90° angle, it is onefourth of the circle, and the shaded regions make up three-fourths of the circle
(5) Multiply the area of the circle by three-fourths or .75 to find the area of the
shaded region:
Quick Tips:  Never assume that the shape is a square unless the question states it
 Sometimes it helps to redraw the shapes
18.
C
Tools: exponent rules
Steps: (1) When we put a negative exponent on a number, it changes the number to its
reciprocal (
)
(2) Focus on the answer choices that result in a value that is not an integer
(3) Answer choice A and B result in integers in both cases (9 and 1, 32 and 2)
̅ and ̅ )
(4) Answer choice D results in non-integers in both cases (
(5) Answer choice C results in 54 and 1.5 (an integer and non-integer)
Quick Tips:  A value that is a multiple of another number will result in an integer when
divided by that value, such as 2 and 4 or 3 and 3
19. 5
D
Tools: absolute values, inequalities
Steps: (1) The question is asking for which input would result in its output being less
than the input
(2) Input the answer choices and see which works
| |
| | |
(3) Answer choice D: | ( )
Quick Tips:  Try picking a number in the middle. From there you can see whether to pick a
lower or higher number next
20. The two quantities are equal
C
Tools: balancing equations
Steps: (1) Start simplifying the equation by multiplying each side by (
)
(2) Then distribute the
and you will get (
)
(3) Now move like terms to one side by adding (-20b) and subtracting (5) from
both sides (
)
(4) Now divide both sides by 25 to get the value of (3)
Quick Tips:  Do not forget to distribute the negative to each term inside the parentheses
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General Academic
21. y is the greater value
B
Tools: systems of linear equations
Steps: (1) Use the elimination method and subtract the two equations to eliminate the y
variable (
)
(2) Solve for x:
( )
(3) Then plug in the value for x into one of the equations (
)
(4) If
, then
and
Quick Tips:  If you do not remember the elimination method, you can just substitute the
value of y in the first equation into the second equation
22. The distance between points (1,2) and (4,6) is greater
Tools: distance formula, midpoint formula
Steps: (1) Plug in the
values into the distance formula:
)
√(
(
)
)
)
(2) √(
(
)
√(
(
)
√( )
(3) √
√
(
)
(4) Plug in the values into the midpoint formula:
(5)
Quick Tips:  Pay attention to order of operations
A
( )
√
23. The relationship cannot be determined from the information given.
D
Tools: multiplying with exponents
Steps: (1) Simplify each column
(2) Column A is
and Column B is
(3) If you input 0 for all three variables, both columns are 0 (Answer choice C)
(4) If you input -1 for all three variables, Column A is -1 and Column B is 1
(Answer choice B)
(5) Since our answer changed, we must choose D since we must know the values
for the three variables to answer the question
Quick Tips:  If a negative number is taken to an even power, its product is positive
 If a negative number is taken to an odd power, its product is negative
24. The two values are equal
C
Tools: simplifying, order of operations
Steps: (1) Multiply the numbers inside the parentheses for Column A
) (
) ( )
(2) (
( )
(3)
( )
(4) Now we need to simplify Column B
(5)
Quick Tips:  Watch out for the last parenthesis in Column A, as the exponent is outside of
the parenthesis
 Your eye might play a trick on you and assume that the exponent is actually
inside of the parenthesis
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Upper Level ISEE Prep Guide
25.
is the greater value
Tools: intersecting lines, vertical angles
Steps: (1) If we add up all the angles (
), we will get 360°
(2) If we subtract C from all the angles, only A, B, and D will be left
(3)
, since all angles are positive values
Quick Tips:  Do not over think some of the problems
 Sometimes you can solve problems visually instead of formulaically
A
26. y is the greater value
B
Tools: inequalities
Steps: (1) We need to simplify the two inequalities by dividing the outer number by 3
and 2, respectively. (
)
(2) Compare the greatest value limit for x and the least value limit for y
(3) Since is greater than , y must be greater than x
Quick Tips:  If you cannot see which fraction is greater, then just use the common
denominator method
27. The probability of getting three heads up is the greater value
Tools: probability
Steps: (1) The probability of one coin flipping to head is
A
(2) Since we have three coins flipping all at once, we need to multiply by itself
three times. (
)
(3) .166>.124
Quick Tips:  If you are having trouble converting from fraction to decimal, try converting
from decimal to fraction. (
)
28.
is the greater value
B
Tools: triangles rules
Steps: (1) The two smaller sides of a triangle must be larger than the largest side.
(2) Column B adds up all of the smaller sides so it will have to be larger than
Column A, which is adding up the two larger sides.
Quick Tips:  When there are no numbers in a problem, they will likely be testing you on
theory or rules.
29. 1 inch is the greater value
B
Tools: linear problem solving
Steps: (1) IJ (3 inches) is between HK (4 inches) which means HI and JK will have to
share 1 inch
(2) Since there has to be some distance between two points, 1 inch must be
greater than HI
Quick Tips:  Collinear means passing through or lying on the same straight line
P a g e | 14
General Academic
30. The smallest of the three consecutive numbers is the greater value
B
Tools: consecutive numbers, number types
)
Steps: (1) For Column A: ( )(
)
(2) ( )(
(
)(
)
(3)
(4) Thus, the even numbers can be -6 and -4 or 4 and 6 (6 is the greatest value)
) (
)
(5) For Column B: ( ) (
) (
)
(6) ( ) (
(7, 8, and 9)
(7)
Quick Tips:  When the numbers are low like 24, you should be able to answer this question
without the equation (
) to find consecutive numbers
 For even consecutive numbers use the equation (
)
31. M is the greater value
A
Tools: functions, trends
Steps: (1) We can see that as increases, the ( ) increases as well
(2) While we do not know the function, we can see the output increases by an
amount that is consecutive odd integers (5  8 is +3, and 8  13 is +5)
( )
( )
( )
(3) Following this pattern, L is 29 (
( ))
(
)
(4)
(
)
(
)
(5) If we continue the pattern, then
(
)
(6)
so
Quick Tips:  Coming up with a function might take up too much of your time, so look for
patterns instead
32. The relationship cannot be determined from the information given
Tools: math properties, quadratic equations, functions
Steps: (1) ( ) indicates that every x will be replaced with -2, but focus on the
denominator first
( )
(2)
( )
D
(3) With Column A, the denominator is 0:
(4) When the denominator is 0, the value is undefined, and we cannot determine
the relationship between the two values when one is undefined
Quick Tips:  In functions that are rational equations, focus on the denominator first
33. The two values are equal
C
Tools: set notation, median
; thus, the sum of the lowest and greatest elements, 14 and
Steps: (1)
24, is 38
(2)
; thus the median is 19, and
( )
Quick Tips:  For , you are looking for elements found in both sets (no repeats)
 For , you joining all of the elements into a single set (no repeats)
P a g e | 15
Upper Level ISEE Prep Guide
34. The value of x is the greater value
B
Tools: arc length of sector, triangles
( )) and multiply it by the fraction
Steps: (1) Find the circumference of the circle (
of the circle shaded ( ):
(6.28)
(2) To find the value of x, we can use the Pythagorean Theorem (
)
(3)
√
(√ )(√ )
(4)
√
√
√
(5) The square root of 3 is somewhat less than the square root of 4 but more than
the square root of 2.25 (1.5). Because of this, the square root of 3 multiplied to
6 will result in a number larger than 6.28
Quick Tips:  You can find the value of x in this problem more quickly using the
ratios (
)
√
35. The difference between
and
is the greater value
A
Tools: operations on algebraic expressions, exponents
) (
)
Steps: (1) Find the difference for Column A: (
(2) We need to simplify 64 to have a base of 2. This way we can cancel the base
and set the exponents equal to each other:
(3) Now set the two exponents equal to each other (
) and solve for
(4)
(5)
Quick Tips:  When solving for variables in exponents, try to have all non-exponents in the
same terms, such as 2 for every base
36. 725 is the greater value
Tools: permutations
Steps: (1) Order matters, so we must use the permutations formula (
(
(2) There are ten elements in the set, so n is 10, and r is 3 ((
(3)
(4)
Quick Tips:  You can also use the formula (
)(
)
(
B
)
)
)
) to solve
37. The two values are equal
C
Tools: multiplying exponents
Steps: (1) Since the bases of the exponents are the same, we can add the exponents in
(
)
(2) We now need to simplify 125 to have the same base (
)
(3) Both sides of the equation have the same base, so now we can set the
exponents equal to each other:
(4) Compare the two fractions:
Quick Tips: 
P a g e | 16
( )
(
)
You can also reduce the fraction in Column B before doing anything with
Column A for an easier comparison
General Academic
Reading Comprehension - Passage 1
1. The main idea of this passage is to discuss factors that contribute to the decline of
B
peregrine falcon populations.
The author begins the passage stating the decline of the population and then
Explanation
discusses some of the factors that contribute to the decline. DDT and sonic booms
are just small details in the passage.
2. The author of this passage would likely recommend banning further development
D
in peregrine falcon nesting areas.
Banning further developments will help the falcons from avoiding prolonged
disturbance, which will allow them to incubate their eggs properly. DDT chemicals
Explanation
have already been banned since 1972, reintroduction efforts have been discovered
as a partial solution, and new roads will cause more disturbance.
3. In line 44, “aerie” most nearly means nest.
Explanation
Look at lines 57 to 58, “…the nest is deserted. Desertion of an aerie with eggs…”
The first sentence states the nest is deserted, followed by the second sentence
stating the aerie is deserted. The two terms are one in the same.
4. Peregrine falcon populations increased most during 1974 to 1985.
Explanation
B
D
Look at lines 19 to 20, “…increasing at a rate of 2.9% to 25% per year between
1974 and 2000…” The peregrine falcons were placed on the endangered species
list prior to 1974, so populations were in decline or stagnant before then.
5. According to this passage, “They are attracted to areas where shorebirds and
A
waterfowl live” is TRUE.
Look at lines 38 to 40, “…are often attracted to wetlands where shorebirds and
waterfowl are abundant.” Peregrine falcons are “global,” so their migration is not
Explanation
limited to the North America. Answer choices C and D are opposite of what is
stated in the passage.
6. We can infer from the fourth paragraph in this passage that the effects of jet overC
flights can vary among peregrine falcons.
The example was of one instance in California and cannot represent every
peregrine falcon. Look to lines 48 to 50, “However, effects of jet over-flights on
Explanation
nesting behavior were minimal in Alaska.” Since the falcons in Alaska were
unaffected by the sonic booms, it is safe to say that the effects will vary among the
falcons.
P a g e | 17
Upper Level ISEE Prep Guide
Reading Comprehension - Passage 2
7. In line 49, “obscurity” most nearly means anonymity.
Explanation
A
Obscurity is defined as the state of being unknown, inconspicuous, or unimportant.
Anonymity, the condition of being anonymous or unidentified, is the only answer
choice suitable to replace obscurity.
8. The purpose of the first three paragraphs is to describe daily life as it existed
B
before the war.
Look at lines 1 and 2, “Once upon a time there wasn’t any war.” This tells us that
Explanation
the author is writing about before the war.
9. The best title for this passage would be “Home Turned Battlefield.”
Explanation
The passage describes the effects of war on a small town. Even though the town is
in France, the passage describes only the small town and not what happened to the
bigger cities. Since the author claims to be from this town, it is seen as his home
turning into a battlefield.
10. According to the passage, a panorama of the village was painted by Corot.
Explanation
C
Look at lines 45 to 46, “…the very place where Corot painted his masterpiece.”
11. The overall tone of the passage suggests the author laments the state of his village.
Explanation
C
B
The definition of lament is a passionate expression of grief or sorrow. The author
spends the first half of the passage describing what the village was before the war.
He does not blame the Americans for the war, and he does not show anger
towards the village.
12. The author juxtaposes the state of the village before the war and during the war to
D
demonstrate the indiscriminately chaotic nature of war.
The author does not mention that his life had returned to normal, nor did he
discuss France’s allies. The author builds a village in our minds with the first three
Explanation
paragraphs, and then destroys it with lines 39 to 41, “…the station at ChâteauThierry is all of that city that remains in our hands.”
P a g e | 18
General Academic
Reading Comprehension - Passage 3
13. In line 6, “punctiliousness” most nearly means decorum.
Explanation
A
The definition of punctilious is showing great attention to correct behavior. Look
at line 8, “…it sustain no damage.” We are looking for a word that means to show
great attention in order to keep the book from damage. Decorum is defined as
proper behavior that shows respect and good manners.
14. The author does all of the following EXCEPT claim that one should never write in
B
books one owns.
Look to lines 18 to 19, “…you should own no book that you are afraid to mark up.”
Explanation
The author clearly states that one should write in their books.
15. The main purpose of this passage is to describe some of the pleasures afforded by
B
books.
Although the author does mention some of these answers, the overall purpose is to
Explanation
describe the pleasures that books bring. Look to lines 1 to 3, “reading is one of the
greatest resources of mankind; and we enjoy reading books that belong to us…”
16. We can infer from this passage that the author believes one can gain a deeper
D
understanding of the world through reading.
The overall passage describes books as a positive thing. Answer choices A, B, and
Explanation
C are all negative beliefs. Look to line 60, “Literature is the immortal part of
history.”
17. The author’s tone suggests that, overall, books are accessible.
Explanation
A
The author would agree that books are bountiful and colorful. However, due to
these attributes, books are very accessible to anyone. Look to lines 58 to 59,
“Books are of the people, by the people, for the people.”
18. The author compares the reader to an audience in order to show how authors rely
C
on readers to give their work purpose.
Look to lines 76 to 77, “They wrote for you.” If the audience was not present the
Explanation
actor would not perform. If the reader does not read the book, then why write the
book?
P a g e | 19
Upper Level ISEE Prep Guide
Reading Comprehension - Passage 4
19. The best title for this passage would be “A World of Uncertainty and Despair.”
Explanation
C
Look to lines 22 to 23, “Never has our future been more unpredictable,” and lines
48 to 51, “…not less effectively forgotten by those committed to a belief in an
unavoidable doom, than by those who have given themselves up to reckless
optimism.”
20. We can infer from this passage that the author does not see a way to conquer the
A
powerlessness paralyzing society.
Look to lines 33 to 34, “…whom powerlessness has become the major experience
Explanation
of their lives.” The author mentions these types of people but does not show us
how to stop them from paralyzing society.
21. In line 5, “respite” most nearly means breather.
Explanation
The definition of respite is a short period of rest or relief from something difficult
or unpleasant. After the first war the victors did not have a chance to take a
breather, a brief rest, before the second world war.
22. According to the passage, World War III will be fought between two world powers.
Explanation
B
D
Look to lines 6 to 7, “…a third World War between the two remaining world
powers.”
23. In lines 20-21, the author repeats the word “unprecedented” to bolster the author’s
D
argument that the state of the world has no parallels in history.
The definition of unprecedented is to have never done or known before. The
author is trying to say that the scale of homelessness and the depth of rootlessness
Explanation
have never been seen before in history. In other words, the result of the end of
World War II did not bring what previous wars brought.
24. The style of this passage is personal.
Explanation
P a g e | 20
B
A personal style of writing generally expresses the author’s ideals, personal
beliefs, or inner convictions. Look to lines 9 to 10, “We no longer hope for an
eventual restoration…” The author considers his viewpoint as everyone else’s
viewpoint.
General Academic
Reading Comprehension - Passage 5
25. The author will most likely follow up the passage with an example of a teacher
C
guiding a student in accordance with the author’s specifications for education.
Look to lines 4 to 5, “It is necessary for the teacher to guide the child…” The author
Explanation
does not mention any of the other answer choices as an example to better
education.
26. According to the passage, a child is superior to adults in that the child is innocent
C
and his future is filled with great possibilities.
Look to lines 56 to 58, “…superior to us by reason of their ‘innocence’ and of the
Explanation
greater possibilities of the future.”
27. We can infer from this passage that there should be no limitations on a child’s
A
learning.
Look to lines 18 to 19, “provided that he be left free in his movements and in his
experiences.” In subsequent sentences, the author describes what happens when
Explanation
a child is left unhindered. “There is therefore no need of intervention” because the
child will seek out experiences and learning and will want to share what he has
learned.
28. In line 49, “hindrances” most nearly means obstructions.
Explanation
The definition of hindrances is a thing that provides resistance, delay, or
obstruction to something or someone. The author states that the parent or
teacher hopes to have their efforts pay off and not be obstructed by something.
29. The overall tone of the passage is one of veneration.
Explanation
B
D
The definition of veneration is to have great respect or reverence. Look to lines 69
to 71, “Let us treat them, therefore, with all the kindness which we would wish to
help to develop in them.” The author has great respect for not only the children,
but also the parent and teacher.
30. The main purpose of this passage is to demonstrate a style of education that
C
focuses on freedom and respect.
Look to lines 13 to 19, which state that the child must be given respect and
Explanation
freedom in their education. The author only briefly discusses the disadvantages of
traditional education or the faults of adults when dealing with children.
P a g e | 21
Upper Level ISEE Prep Guide
Reading Comprehension - Passage 6
31. The best title for this passage would be “Chaos, Creation, and Sacrifice: P’an Ku.”
Explanation
The passage is split up into the three things mentioned in the title: Chaos, Creation,
and Sacrifice. The first paragraph mentions that P’an Ku “chiseled the universe out
of Chaos.” Furthermore, Line 12 states that he was the actual creator of the
universe and the third paragraph goes into detail of how P’an Ku sacrificed his
body for the universe.
32. According to this passage, P’an Ku crafted the universe in eighteen thousand years.
Explanation
B
Look to lines 39 to 40, “His task occupied eighteen thousand years…”
33. In line 2, “cosmogony” most nearly means study of a universe’s origin.
Explanation
D
B
The definition of cosmogony is the branch of science that deals with the origin of
the universe. The passage states that P’an Ku was the creator of the universe,
which include people, planets, and rivers.
34. We can infer from this passage that the author has studied many creation myths
D
from various cultures.
Look to lines 30 to 39, which state all of the forms and pictures of P’an Ku. In
order to find all of the different forms of P’an Ku, the author had to research the
Explanation
cosmogony of numerous cultures. Plus, the author mentions deities and
mythological creatures from other mythologies.
35. P’an Ku was 40,000,000 feet tall once the universe was completed.
Explanation
D
Look to lines 42 to 44, “…himself increasing in stature day by day, being daily six
feet taller than the day before, until, his labors ended…” If P’an Ku took eighteen
thousand years to finish and there are normally 365 days in a year, we must
multiply 18,000 by 365 by 6 feet tall. Thus roughly equaling to 40,000,000 feet
tall. (39,420,000)
36. In subsequent passages, the author will most likely discuss the Buddhist
D
interpretation of P’an Ku’s creation of the universe.
The last paragraph of the passage mentions that there are different accounts of
Explanation
P’an Ku in the Buddhist religion, but does not indicate what they are. Thus, leaving
the subsequent paragraph to do so.
P a g e | 22
General Academic
Mathematics Achievement
1. 6
C
Tools: roots, balancing equations
Steps: (1) First square both sides of the equation. (
)
(2) Next divide 4 on both sides. (
)
Quick Tips:  If we have √ then we will need to raise it to the 3rd power.
A
2.
Tools: substitution method, power rules
Steps: (1) We first insert in the place of
in the second equation. (
√
(2) Now simplify by converting the root into the exponent form. (
(3) Now simplify the powers by multiplying them. (
Quick Tips: 

( )
(
) )
( )
)
)
√
3. 15 miles
A
Tools: deciphering word problems,
Steps: (1) Add up all of the miles he ran during the week (
)
(2) Multiply the total by two (
)
(3) Subtract the total miles that Patrick wants to run by the miles he has run (15)
Quick Tips:  Pay attention to the wording, as Answer choice D is the right answer if he ran
for just one week
4. 23%
D
Tools: deciphering word problems, percentages
Steps: (1) To figure out what percent 700,000 is of 3,000,000, divide the two
(
)
(2) Multiply .233 by 100 to find the percentage. (23%)
Quick Tips:  If you are dividing two large numbers and you do not have a calculator, you
can move the decimal place to the left (
)
5.
D
Tools: parallelograms
Steps: (1) Answer choice A is true, because the angles diagonal from each other in a
parallelograms will always be equal
(2) Answer choice B is true, because angles opposite from each other are
complimentary angles
(3) Answer choice C is true, because a complimentary angle equals 180 degrees
and
Quick Tips:  The total internal angle of a polygon equals to
(
)
P a g e | 23
Upper Level ISEE Prep Guide
6. 50 bowls
B
Tools: deciphering word problems, cylinder
(
)
(
)
Steps: (1) Find the total volume of the pot (
)
(
)
(2) Find the volume of the smaller bowls (
)
(3) Now divide the two values to find how many bowls would fit (
)
Quick Tips:  If you forget the formula for the volume of a cylinder, just multiply the area of
the base by the height
7. {}
D
Tools: set notation
Steps: (1) Find the union of H and J:
)
(2) Find the intersection of the new set and I: (
(no shared values)
Quick Tips:  Avoid skipping numbers by writing them in numerical order
8. 104
A
Tools: averages
Steps: (1) Add the sixth test ( ) to all of the other tests
(2)
(3) Divide that by 6 (the number of total tests) and set it equal to 92 (
)
(4) Solve for by multiplying 6 on both sides and subtracting 424 (104)
Quick Tips:  Remember an average is the sum of all terms divided by the number of terms.
9. 7 hours
Tools: work word problem
Steps: (1) Max’s work time is and Julie’s
C
(or
)
(2) Use the work word problem formula to solve for x:
(3)
Quick Tips: 
Work word problems rely on time, so pay attention to how quickly or how
slowly workers complete the job
10. The range of the data is greater than the median of the data
B
Tools: median, range, data analysis
Steps: (1) The range of the data can be found by subtracting the lowest number of shoes
sold from the highest number of shoes sold. (
)
(2) The median of a number set is the number separating the higher half of the
data set from the lower half of the set (2, 4, 4, 5, 6, 7, 7, 8, 9, 9, 9)
(3) Since the set has an even number of values, we will need to take the average of
the two middle numbers. (
)
(4) The two values are the same.
Quick Tips:  Pay attention to the measurements and units for each axis
P a g e | 24
General Academic
11. 81
C
Tools: roots, balancing equations
Steps: (1) Since both roots in the equation are the same, we can add the two together
( √
√
√ )
(2) We then want to subtract 8 on both sides ( √
)
(3) Divide both sides by 15 ( √
)
(4) Raise both sides to the fourth power in order to get rid of the fourth root on
the left (
)
Quick Tips:  If the value underneath the radical is not the same then you cannot add them
12. 75.36 inches2
Tools: word problem, sphere
Steps: (1) Divide the diameter by two to get the radius (3)
(2) Plug in the radius into the surface area formula for a sphere (
(3) Multiply the total surface area by (75.36)
Quick Tips:  The formula for the surface area of a sphere is
 Watch out for unnecessary information (“hurls the shot 50 feet”)
13.
A
)
A
Tools: data analysis, quartile
Steps: (1) Expand and set the numbers in order {82, 82, 85, 85, 89, 89, 94, 94, 94, 94, 94,
98, 98, 98}
(2) Next split the numbers into 4 equal parts {82, 82, 85, 8 5, 89, 89, 94 94, 94,
94, 9 4, 98, 98, 98}
(3) The number that is split first is the first quartile (85)
Quick Tips:  If you have not heard of a quartile before you can use context clues to solve the
problem. Quartile sounds similar to quarter. 85 is the only answer choice
closest to the first quarter of the numbers
14. 50
C
Tools: perimeter, squares, triangles
Steps: (1) The top and bottom lines should equal to 10 each (definition of a square)
(2) Since the angles of the two points are 30 degrees each, we can calculate the
complementary angles to be 60 degrees
(3) If two angles of a triangle equal 60 degrees, then the last must equal 60
degrees (definition of an equilateral triangle)
(4) Since the base of the triangle equals to one of the sides of the square, we can
deduce that the base will equal 10
(5) If one side of the equilateral triangle is 10, then all of the sides must equal 10
(6) Add up all the sides (
)
Quick Tips:  Try redrawing the shapes if you are having a hard time visualizing the problem
P a g e | 25
Upper Level ISEE Prep Guide
15. 12
A
Tools: word problems
Steps: (1) Arrange the numbers in order (2, 3, 7, 8, 10, T)
(2) Now subtract the largest number by the smallest and set it equal to 10.
(
)
(3) Add 2 on both sides (
)
Quick Tips:  You can easily tell that the largest number will be T if you look at the answer
choices (17 makes the range 15, 18 makes it 16, and 20 makes it 18)
16. 27Π
B
Tools: area, circles, parallelogram
Steps: (1) We can form a triangle at the end of the parallelogram by connecting a
perpendicular line to the base from the top right corner.
(2) This will create a 30-60-90 triangle, with the side across from the 60 degree
angle being the height of the parallelogram. The height of the parallelogram
will also equal the diameter of the circle.
(3) Use the 30-60-90 formula to solve for the height (
√ )
( √ )
(4) Divide the height in half and plug into the area formula (
Quick Tips:  In a 30-60-90 triangle, the side across from 90 degrees will always be the
largest (2x)
)
17. 24 inches
B
Tools: proportions
Steps: (1) We need to set up our proportions by grouping the drawings on one side and
the actual heights on the other (
)
(2) Plug in the values (
(3) Divide both sides by 1.5. (
Quick Tips: 
) and cross multiply (
)
)
You can also set up the proportions by grouping the hawk on one side and the
finch on the other
18. 2
Tools: exponents
Steps: (1) Take the square root of both sides (( )
)
(2) Now take the square root again (
)
(3) Divide 3 on both sides(
)
(4) You can also simplify the left hand side
(5) ( ) )
(
)
(6) Balance the equation
(7)
Quick Tips:  Pay attention to the parentheses and where the exponent is located
P a g e | 26
A
General Academic
19.
D
Tools: scientific notation
Steps: (1) Reduce the second notation so that it has
(
)
(2) Now subtract the two numbers in front of the exponents (
)
(3) Multiply this number with the exponent (
)
Quick Tips:  If you forget this method, just multiply both numbers together and subtract,
and then put it in scientific notation to find the answer choice
20. 212 mpm
C
Tools: distance, rate, time
Steps: (1) Find the speed of the kayaker and river together by dividing the total meters
by the total time (
)
(2) Add the total speed to the speed of the river (
)
Quick Tips:  Answer choice A would be correct if the kayaker was going with the current
 Answer choice B would be correct if there were no current
21. $483.00
C
Tools: compound interest
(
)
Steps: (1) Plug in the information into the interest rate formula
(
) )
(
(2) Add the two numbers inside the parenthesis and square it (
(
))
(3) Divide both sides by 1.69 (
)
(4) Subtract the amount after two years by the principal (M) (
)
Quick Tips:  Just move the decimal place of the percentage to the left twice to get the
decimal value
22.
C
Tools: perpendicular lines
Steps: (1) Take the negative reciprocal of the slope on the given equation (
(2) Whichever answer choice has this slope is the right answer (
Quick Tips:  Two parallel lines will have the same slope
23.
)
)
D
Tools: absolute values, inequalities
Steps: (1) Solve for the positive value of the inequality by adding 7 and dividing by -3
(
)
(2) Solve for the negative value of the inequality by distributing the negative first
)
( (
)
(3) Subtract 7 and divide by 3 (
)
(4) Combine the simplified positive and negative inequalities together.
Quick Tips:  When dividing or multiplying a negative in an inequality, make sure to switch
the direction of the inequality
P a g e | 27
Upper Level ISEE Prep Guide
24. No solution
D
Tools: matrices
Steps: (1) If the number of rows and columns don’t match, then you cannot subtract or
add matrices
Quick Tips:  Multiplying matrices requires that the number of columns in the first matrix
match the number of rows in the second matrix
25. 200.96
B
Tools: triangles, circles
Steps: (1) The triangle has a 90 degree angle at K due to it being tangent to circle H as it
forms perpendicular lines with JK and KH
(2) With degree values 45° and 90°, the remaining angle is 45° (45-45-90 triangle)
(3) The ratio dictates that the values are JK and KH are x and are equal to 8 (based
off of the √ part of the ratio)
(4) We then plug in 8 into the area formula of a circle, since KH is also the radius of
the circle (
)
Quick Tips:  A tangent line forms a perpendicular line to the radius of the circle
 You can also find the values of JK and KH through Pythagorean’s Theorem
( )( )(√ )(√ )
( )( )

( √ )

26. $850
B
Tools: word problems, averages
Steps: (1) Add all of the sales earned each week with in the place of the 5th week
(
)
(2) Divide the sum by 5 and set it equal to 500 (
)
(3) Multiply both sides by 5 and subtract 1650 (
)
Quick Tips:  Don’t forget your order of operations (PEMDAS)
27.
(
)(
A
)
Tools: word problem, probability
Steps:
(1) The probability of picking the first book will be
(2) The probability of picking the second fiction book will be
(3) In order to find the probability of picking these two in a row we have to
multiply the two together. ((
Quick Tips: 

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)
(
)
(
)(
)
)
When multiplying fractions, you have to multiply the denominators together
and numerators together
When you pick another object without replacing the previous, you have to
subtract the first object from the set
General Academic
28. 30 inches
Tools: volume of cone
Steps: (1) Plug in the information into the formula (
(
D
) of a cone volume
)
( )(
)
(
(2)
(3) Multiply both sides by 3 (
30)
Quick Tips:  Just think of the volume of a cone as 1/3 of a cylinder
)
29. -.25
B
Tools: elimination method
Steps: (1) In order to eliminate the x value we need to multiply the second equation by 4.
(
)
(2) Now add both equations together in order to eliminate the value.
(
)
(3) Solve for y by dividing both sides by -12 (
)
( )
(4) Plug -7 in for the y value in the first equation. (
)
(5) Solve for by subtracting 49 and then dividing by 4. (
)
Quick Tips:  It does not matter which equation you plug back in, but pick the easier one
30.
C
Tools: quadratic functions
Steps: (1) Plug in 0 for ( ) ( ( )
)
(2) Factor the quadratic (
(
)(
))
(3) Set each factor to equal zero and solve by subtracting 4 and adding 7,
respectively (
)
Quick Tips:  The last number in the quadratic function must have two numbers that
multiply together that also add to give you the middle number of the quadratic
31. 10.535
B
Tools: squares, circles
Steps: (1) The side length of the square will equal to double the radius (
)
(2) Since there are two half circles with the same radius, we can just solve for the
( )
area of one circle (
)
(3) Find the area of the square (
)
(4) Subtract the area of the circle from the square (
)
Quick Tips:  You can estimate the answer by subtracting the value to the left of the decimal
in each answer choice (
)
 This picture would be the same as one complete circle with the radius of 3.5
inside a square
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Upper Level ISEE Prep Guide
A
32.
Tools: pie charts
Steps: (1) Since sleeping takes up 8 hours of her day and there are no other activities that
come close to that amount, the pie chart must have just one big slice. Answers
C and B must be eliminated because of this
(2) Answer D must be eliminated because there are only 4 slices
Quick Tips:  Start off by looking at which variables stand out
 If you can’t see the answer right away, try drawing the pie chart yourself and
match the answer closest to it
33. 6
A
Tools: probability
Steps: (1) Add up all the cards (
)
(2) Set up the probability of choosing a red card (R) and set it equal to
(
)
(3) Cross multiply (
(
))
(4) Subtract R from both sides (
)
(5) Divide by 9 (
)
Quick Tips:  Remember the order of operation (PEMDAS)
 The total amount of cards will always be in the denominator
34. 1020
B
Tools: deciphering word problems, proportions, direct variation
Steps: (1) Set up a proportion with the number of guests on the left and the number of
shrimp on the right (
)
(2) Cross multiply (
)
(3) Divide by 50 and simplify (
)
Quick Tips:  Remember to keep last year’s party on the top of the fractions and this year’s
on the bottom
35. 30 miles
Tools: distance formula
Steps: (1) Plug in the two points in the distance formula.
(
√(
)
(
)
√(
(
))
D
(
)
)
(2) Multiply the value by 3 (30)
Quick Tips:  If the ratio did not have 1 as a value, you must set up a proportion and cross
multiply.
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General Academic
36. 1
B
Tools: graphs, trends
Steps: (1) The trend of the “uhs” is decreasing at a rate of ½ per speech
(2) If we take half of the number of “uhs” from speech 3, then we will get a total of
1 “uhs”
Quick Tips:  If you just notice that the trend is decreasing you can eliminate half of the
answer choices (C and D)
37. 120
D
Tools: permutations
Steps: (1) Multiply the total possible choices of the first symbol, by the total possible
symbols of the second choice, by the total possible choices of the third
(
)
Quick Tips:  Remember that if you cannot repeat a symbol, which is why the total possible
choices always decrease as you pick
 If you could repeat, then your answer would be
38. 63
D
Tools: probability
Steps: (1) We need to find the lowest common denominator between the two
probabilities (63)
(2) The total number of pants must be a multiple of 63
Quick Tips:  Watch out for excess information
 Another method could be to multiply the answer choices to both probabilities
and the answer choice that gives you two whole numbers will be correct
39. 68
A
Tools: exponents
)
Steps: (1) Multiply on both sides of the first equation (
)
(2) Substitute this value in for the in the second equation ((
(3) Simplify by multiplying the constants and like terms together (
( )
(4)
and
will cancel each other out. (
Quick Tips:  You can also think of
as
40.
Tools: mean
Steps: (1) Add up all the values in the set (
)
(2) Divide that value by the number of terms (4) and set it equal to 8.5.
)
)
)
A
(
)
(3) Multiply both sides by 4 (
)
(4) Subtract 25 on both sides (
)
(5) Take the square root on both sides (
)
Quick Tips:  When you take the square root of a constant, it must represent both positive
and negative values
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Upper Level ISEE Prep Guide
41. (4,0)
C
Tools: quadratic equations, factoring
)(
))
Steps: (1) Factor the equation. ((
(2) Since both factors are the same, the parabola crosses the x axis at exactly one
place (the vertex)
( )
(3) Plug in 4 for the value and solve for the value ( ( )
)
(4) The vertex is at (4, 0)
Quick Tips:  If the factors are not the same, then you will need to pick the value that lies
exactly between your two factors
42. 26.9
A
Tools: cylinder, cube
Steps: (1) Since the cylinder is inscribed in the cube, the diameter of the cylinder is the
side length of the cube (5)
(2) Divide the diameter by 2 to find the radius (2.5)
(3) Plug that into the volume formula (
) and use the side length of the
( )
cube as the height (
)
(4) Find the volume of the cube (
)
(5) Subtract the volume of the cube by the volume of the cylinder
(
)
Quick Tips:  The volume of a rectangular prism is
 If the answer choices are far apart from each other, then you can just use 3 as
pi instead of 3.14. Make the calculations as easy as possible
43. 3
C
Tools: Pythagorean Theorem
Steps: (1) First find the diagonal of the rectangle facing the right (
√
√ )
(2) Now use that value as one of the sides of the triangle formed with the dotted
line and plug it into the Pythagorean Theorem again (
Quick Tips: 
44. 2
Remember the in the Pythagorean Theorem (
the hypotenuse of the triangle
√
√
)
) will always be
A
Tools: power rules
Steps: (1) Add up all the exponents of the first equation and set it equal to 30
(
)
(2) Solve for by subtracting 6 and 17 on both sides (
)
(3) Subtract the two exponents from the second equation and set it equal to 9
(
)
(4) Solve for by subtracting 15 and dividing by (-1) (
)
(5) Multiply the two exponents in the third equation and set it equal to 9
(
)
(6) Solve for by dividing both sides by 3 (
)
(7) Plug in the values of
and into the fourth equation and solve (2)
Quick Tips: 
;
;( )
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General Academic
45. 256
D
Tools: polynomials
Steps: (1) These types of questions can be solved with Pascal’s triangle, a geometric
concept, but you can also solve this problem through pattern recognition
(2) As with quadratic equations, look to the first and last terms in the expression
(3) If two parentheses are formed with and
in the quadratic expression,
then four parentheses are formed with the and
in this expression
(4) Four x’s are needed to make and four y’s are needed for
)(
)(
)(
)
(5) Thus, (
(6) Since
, we can rewrite what we just found as ( )( )( )( )
Quick Tips:  If the equation or expression seems outrageous, then there is likely a quick
solution to the problem
46. 25
B
Tools: area of triangle and square
Steps: (1) Find the area of one triangle (
( )( )
)
(2) There are four of these triangles, so multiply the area of one by 4 (24)
(3) Find the area of the larger square (
)
(4) Subtract the area of the larger square by the area of the four triangles
(
)
Quick Tips:  Try not to focus on the smaller square. Look at the shape as 4 triangle lined up
to create two squares
47.
D
Tools: domain
Steps: (1) Set the denominator equal to zero (
)
(2) Add 15 to both sides and solve for (
)
(3) The domain cannot equal to this value, because this will make the answer have
a zero as the denominator and undefined (
)
(4) Now, set the value under the radical equal to zero (
)
(5) Add 8 on both sides to solve for (
)
(6) The value for has to be equal or greater than 8, or else the number under the
radical will be negative and make it imaginary (
)
Quick Tips:  The domain equals to all possible values
 The range equals to all possible values

will be an undefined value, which cannot be included in the domain

will equal to an imaginary number, which cannot be included in the
√
domain.
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Upper Level ISEE Prep Guide
Essay
What aspect of high school interests you the most?
Brainstorming
The prompt is asking you about the things that you may hope to learn or do in high school. It is
something that may be exciting and interesting to you, but not to everyone else. You could talk
about sports, science, theater, or new friends. As long as it interests you. For example:





Being on the swim team
Acting in a high school play
Learning how to play a new instrument
Meeting new friends from other middle schools
Working in the science laboratory
Outline
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General Academic
Section 5 – Essay (EXAMPLE)
30 Minutes
Please write your essay prompt here.
What aspect of high school interests you the most?
A very big aspect of high school that interests me the most is the opportunity to learn
new things. My middle school did not have too many extracurricular opportunities
besides sports. I have been on the football team, basketball team , and even the swim
team. It is time to challenge myself with something new and exciting. What is more
different from sports than science and the arts? The three things that interest me the
most about high school are the opportunity to take more science classes, learn how to play
the trumpet, and act in a high school play.
The opportunity to learn new experiments and scientific principles excites me the
most. I have always loved my science classes growing up, and every year I enter an
experiment to the science fair. Last year I did my experiment on the effects of household
soaps on the human skin. My favorite subject is chemistry. I feel like it is one of the
few subjects that get over looked in middle school. My science class did not even have
the proper supplies when it came to performing a chemistry experiment. This will not be
the case for the high schools. My brother even told me that the chemistry classes are
equipped with Bunsen burners. Science has a very important part in our society. Some
of the things we love and cherish, like our smart phones and laptops, would not be here
today if it was not for science. The process to become a scientist starts in high school
and I cannot wait to start.
Science is not the only new and exciting subject I want to learn. I have this urge
to play a new instrument, and that instrument is the trumpet. My dad grew up in New
Orleans and played the trumpet when he was in high school. He always talks about the
days he would play at football games and in competitions. Growing up, he would play
his old jazz records for me, and sometimes even play along with his trumpet. Some of
the records are so old, the labels have fallen off. Once in high school, I hope to learn how
P a g e | 35
Upper Level ISEE Prep Guide
to play like these unnamed musicians. I am excited to think that, while in high school, I
can learn how to play as well as my dad. Maybe even I can play with him one day.
Along with learning to play the trumpet, I would also love to act in a play. I went
to my older brothers performance while he was in high school, and I want to follow in his
footsteps. Everything about theater is interesting to me. I want to learn how to create a
set from scratch. I want to play the villain and the hero. I want be in a comedy and in a
Shakespeare play. When it comes to theater, I feel like the sky is the limit. In middle
school, we just had the basic holiday performance. We would sing boring Christmas
songs and one lucky student would be picked to play Rudolph. My brother performed as
Ebenezer Scrooge in their high school rendition of a Christmas Carol. Even though I
may not play the Scrooge, the chance to become a new and exciting character is the most
interesting aspect of high school that I can think of.
High school is a time for a student to grow and develop into an adult. The adult I
want to become will need his high school science, music, and theater classes. With the
information I learn in my science classes, I can go on to get a degree in chemistry.
Learning the trumpet can give me a better appreciation for jazz. Maybe, my dad and I
can even play the trumpet together; Or my brother and I can perform in a play together.
High school seems like a very interesting and memorable place.
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