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Practice ISEE #2: 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.

Upper Level ISEE Prep Guide

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Verbal Reasoning - Synonyms 1. APEX = the highest or most successful point of something A. abyss B. average C. nadir D. peak endless chasm or gorge typical amount or degree

of something the lowest possible point of something

the highest point of something

2. ANTEDILUVIAN = extremely old-fashioned or outdated A. augmented B. contemporary C. outdated D. warped increased to make it more substantial

of same age or modern in style

no longer in fashion twisted or deviated from course

3. PLACATE = please somebody to make them less angry, hostile, or upset A. anger B. improve C. seal D. soothe make someone feel strong displeasure

make something better in quality or condition

close something firmly or make something airtight

calm someone to make them less angry or upset

4. ENMITY = hostility or extreme ill will or hatred that exists between enemies A. apathy B. calamity C. hostility D. love lack of enthusiasm or energy in anything

disastrous situation or event

intense aggression or anger towards someone

intense feeling of tender affection and compassion

5. AMBIGUOUS = having more than one meaning or causing uncertainty or confusion A. benevolent B. capable C. lucid D. unclear showing kindness or goodwill

doing something well or able to do something

rational or clear and easily understood

uncertain or vague

6. FATIGUE = mental or physical exhaustion A. generosity B. lethargy C. military D. ponderousness willingness to give money or help freely

physical and mental tiredness

armed forces or its high-ranking officers

state of lumbering or laborious in movement

7. SAVVY = shrewd and well informed A. clueless B. knowledgeable C. tasty D. unskilled incompetent or ignorant knowing a great deal

about something having a pleasant or full flavor

lacking skill or the basic or proper skills

8. MAIL = flexible armor made of interlocking metal rings or overlapping metal plates A. armor B. electricity C. iron D. knight protective clothing or metal or leather

energy created by moving charge particles

metallic element with symbol Fe

medieval mounted soldier of low rank

9. VILIFY = to make malicious and abusive statements about someone to malign them A. package B. praise C. slander D. uphold promote or present something

express admiration for somebody or something

say false and malicious things about someone

maintain or support something

10. VIGNETTE = short essay or descriptive piece of literary writing A. compilation B. dressing C. novel D. short essay collection or gathering of things

sauce used on salads long story with a complex plot

short piece of literary or journalistic prose


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11. PREDECESSOR = previous holder of a job or a thing previously in use that has been replaced A. carnivore B. descendant C. hunter D. precursor animal that eats other animals

something related to one that lived in the past

predator or somebody who seeks out something

previous holder of a job or thing that came before

12. ADEQUATE = sufficient in quality or quantity to meet a need or qualify for something A. disappointing B. intelligent C. passable D. probable not as good or satisfactory as expected

mentally able or able to think and understand

good enough or suitable likely to exits, occur or be true

13. ALLAY = relieve pain or a painful emotion, such as fear A. alleviate B. graft C. hesitate D. unite lessen the pain or hardship of something

join together two dissimilar things

be slow to act or pause because of uncertainty

bring things together to act as a unit

14. PALPABLE = obvious or easily observed; so intense as to be almost able to be felt physically A. ambiguous B. delicious C. obvious D. tender having more than one meaning

having an enjoyable taste or smell

easy to see or understand

sensitive and caring towards others

15. BELITTLE = to reduce or dismiss the importance or quality of something of somebody A. demean B. enlarge C. praise D. shrink humiliate and degrade someone

make or become larger express admiration for somebody or something

make or become smaller

16. FLAGELLATE = to whip somebody A. embrace B. mark C. spur D. whip hug somebody or make use of something

put sign or symbol on something

encourage somebody to try harder

lash somebody or something

17. SERVILE = too willing to agree with somebody or to do anything that somebody wants A. commanding B. jobless C. personable D. subservient able to control or dominate

unemployed or without a job

pleasant and polite too eager to obey or follow others' wishes

18. MALFORMED = misshapen, deformed, or twisted A. distorted B. moldable C. pleasant D. proper bent or twisted out of its usual or natural shape

able to be shaped into something else

bringing feelings of enjoyment or satisfaction

appropriate or correct

19. ENTHRALL = enslave someone or engage someone’s attention completely A. captivate B. pardon C. pester D. release attract and hold someone’s attention

exempt guilty party from punishment

annoy somebody constantly

let somebody or something go

20. DIGRESS = move away from the central topic or line of argument, usually temporarily A. continue B. disrobe C. narrate D. stray keep going or start something again

remove clothing from yourself or someone else

tell story or give an account of something

wander away from the correct place or course

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Verbal Reasoning - Sentence Completions 21. We find our younger sister too quarrelsome, so we prefer to spend time with our

more amiable cousins. C

Explanation

The second part of the sentence indicates that the cousins are better than the younger sister with which to spend time, so the blank is a negative word. The definition of quarrelsome is having a tendency to argue with people, and it is our only negative choice.

22. An indescribable languor fell over Jonathan as he reclined into the plush softness of

the divan. D

Explanation

“plush” and “softness” indicate that the divan, a backless sofa, is very relaxing; thus, the word for the blank would be the resulting feeling of sitting in something so relaxing. The definition of languor is a pleasant feeling of weariness or weakness and would be felt after sitting in a relaxing chair.

23. Unlike long-term sleeplessness, acute insomnia can strike without warning and be

quite severe. A

Explanation

“Unlike” indicates the blank is an adjective that is opposite from “long-term.” The definition of acute is severe and of short duration. Answer choices B, C, and D would not occur without warning, though “degenerate” does mean becoming more severe that before.

24. The unscrupulous lawyer did not hesitate to extort money from his unwitting

clients. D

Explanation

“extort” and “unwitting” indicate the lawyer is taking advantage of his clients; thus, the blank is a negative word that describes the type of person who would do this. The definition of unscrupulous is someone who is not restrained by moral or ethical principles

25. Because no comprehensive scholarly works on the origins of the game exist, we

had to cobble together our report from a variety of sources A

Explanation

“Because” indicates the sentence is a cause and effect relationship. The group could not find a definitive source of information for their report, so they had to pull bits of information from many sources. A definition of cobble is to roughly assemble something from various parts or elements.

26. The professor’s overly pedantic tone bored even the most enthusiastic student.

D

Explanation

“bored” juxtaposed (compared side by side) with “enthusiastic” indicates that the blank is a negative word, since the professor is boring the students who most want to be there. The definition of pedantic is too concerned with the details or rules of something, which shows that the professor is spending too much time on the little details in his lecture. In other words, when you spend too much time on the little things in a speech, the audience’s interest in what you have to say wanes.


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27. Unable to gratify his desire for a teddy bear, Geoffrey had to make do with a building set.

B

Explanation

Geoffrey wants a teddy bear, and the “Unable” indicates he was wasn’t able to make this happen. The definition of gratify is to satisfy a desire. Geoffrey would have received the teddy bear if he was unable to “debunk” or “refuse” his desire for one, and we do not have enough information to say if “comprehend” affects whether or not he would get the teddy bear.

28. A small portion of bread and a cup of weak tea comprised our daily subsistence

during the way. D

Explanation

A bit of bread and weak tea is not very much food and drink, which indicates that our blank is a word that reflects this scenario. The definition of subsistence is the condition of managing to stay alive, especially when there is barely enough food or money for survival.

29. Having taken a solemn oath to uphold the ideal of honesty, Benjamin found himself

unable to prevaricate about his whereabouts the night of the incident. C

Explanation

The first part of the sentence states that Benjamin will not break from honesty and lie, and the second part of the sentence states Benjamin was unable to do something about where he was that night. If Benjamin took an oath to not lie, then he cannot lie about where he was the night of the incident. The definition of prevaricate is to get out of telling the truth by being deliberately misleading.

30. Unused to the effervescent beverage, Gladys found herself slightly intoxicated by

the champagne. B

Explanation

While the definition of effervescent is producing gas in the form of tiny bubbles, you do not need to know beforehand that champagne is bubbly. A drink cannot be “apathetic” or “miserable” as a drink does not have feelings, and “Unused” indicates that champagne has predictable effects to which Gladys is not used to feeling. Only answer choice B works.

31. We found it highly ironic that our usually compliant sister-in-law had amassed so

many parking tickets. A

Explanation

“usually” indicates that the second blank is an expectation for the sister-in-law that contrasts the large number of parking tickets he amassed. The first blank is a word that reflects this contrast. If getting a parking ticket is in contrast with how the sister-in-law normally behaves, then she must usually obey or be compliant with the law. A definition of ironic is involving a surprising or apparently contradictory fact, which represents this scenario.

32. My brother used to be quite tentative about standing up to our parents, but

recently he has begun to assert himself more often. A

Explanation

“but” indicates that the first blank and second blank will be opposite in meaning, and “often” suggests the brother is standing up to his parents more. The definition of tentative is said or done in a hesitant way that reveals a lack of confidence, and assert is to exercise your power and influence in an obvious way. The relationships between the other answer choices to no match the scenario played out in the sentence.

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33. The duke’s munificence and the luxury of the palace surroundings made Evelyn envy the life of a wealthy aristocrat.

C

Explanation

“envy” indicates that the first blank and “luxury” work well enough together that Evelyn very much wants them. The second blank is someone who is able to make the first blank and “luxury” happen. The definition of munificence is very generous in giving a lot of money, and an aristocrat is a member of the nobility or the highest social class (such as a duke).

34. Gregory was such a purist when it came to grammar that his students’ errors

struck him as nearly obscene. A

Explanation

“struck” indicates that his students’ errors strongly affect him in some way; thus, the first blank is a positive word towards grammar, and the second blank is a negative word towards Gregory. The definition of purist is one who seeks to maintain the pure or traditional form of something, and obscene is offensive to conventional standards or disgusting.

35. Because the dry, windy climate often left the earth parched, the farmer selected

particularly hardy varieties of plants to cultivate. B

Explanation

“dry” indicates that the first blank will be somewhat similar to it. If the weather is “often” harsh, the farmer will select plants he can cultivate that can stand up to this kind of weather. The definition of parched is lacking moisture because of hot conditions or lack of rainfall, and hardy is sufficiently robust to withstand hardship or adverse physical conditions.

36. Although his beard and spectacles lent him a sagacious air, it turned out that Karl

knew very little of the world and was actually quite naïve. C

Explanation

“Although” indicates a shift will occur between the first part of the sentence and the second part. If Karl knows very little of the world in the second part, the first part will be the opposite of this. The definition of sagacious is wise or shrewd, and naïve is inexperienced and not shrewd.

37. Jerome’s iniquitous ways led to his being driven out of the village, and he lived the

rest of his days as a pariah, unwelcome in anyone’s home. D

Explanation

“unwelcome” and “driven out” indicate that Jerome’s ways were not good ways, and both blanks will be negative words. The second blank will be a word that means the last portion of the sentence (“unwelcome in anyone’s home”). The definition of iniquitous is utterly harmful and wrong, and pariah is an outcast who is despised and avoided.

38. The magnanimity of the victorious army, even in the aftermath of the brutal

conflict, left an indelible impression on the national consciousness. C

Explanation

“even” suggest that the first blank will be in contrast with “brutal,” and this contrast will define what type of impression is left on the nation. The definition of magnanimity is great generosity or noble-spiritedness, and indelible is unforgettable. The fact that the army was so generous is in sharp contrast the brutality of the conflict, and the impression left on the nation will be unforgettable.


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39. The brilliance of the sun’s rays shining over the frozen precipice forced the travelers to avert their eyes.

D

Explanation

“brilliance” and “forced” indicate that the travelers cannot look at the object reflecting the sun’s rays. The definition of a precipice is a high, vertical, or very steep rock face, and avert is to turn your eyes away from something. A frozen precipice would shine sunlight directly into the traveler’s eyes.

40. The lakes and rivers were replete with fish and other aquatic wildlife, attracting

the notice of many a hungry carnivorous bird. C

Explanation

If hungry bird’s notice is attracted to the lakes and rivers, then the lakes and rivers must have a source of food to negate the bird’s hunger. The definition of replete is amply or fully supplied with something, and carnivorous is feeding mainly on the flesh of other animals. While answer choice D’s first word meets the first criteria, the sentence does not provide enough information to say whether or not a nomadic bird would feed on fish and other aquatic life.

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Quantitative Reasoning 1. -7 A

Tools: functions Steps: (1) The star before the q represents a function where q is the input for the

expression on the right hand side of the equation (2) Since the value of 7 replaces the q in , then we input the value of 7 for q in

the right hand expression (3) ( )

Quick Tips: If a series of strange symbols appear that are coupled with variables and set equal to an algebraic expression, then it is a function

The variables coupled with the strange symbols are the inputs for the function

2.

C

Tools: balancing algebraic equations Steps: (1) You are looking to get n by itself and set equal to everything else

(2) Multiply both sides by 3 to cancel out the 3 on the left, and multiply both sides by 2 to cancel out the 2 on the right

(3)

(4) Balance the equation until n is by itself (5) (6)

(7)

Quick Tips: Start with eliminating the denominators of rational algebraic expressions so they are no longer fractions

3.

C

Tools: probability Steps: (1) We are looking for the probability of removing two animals from the cage that

are only mice and hamsters (2) There are a total of 9 creatures in the cage, six of those 9 creatures are mice

and hamsters

(3)

Quick Tips: Since we removed a creature and didn’t return it, the total number of creatures in the cage changed as did the total number of mice and hamsters

4. 8p B

Tools: perimeter Steps: (1) Two of the sides are p and two of the sides are 3p

(2) Find the sum of the four sides: Quick Tips: Draw the rectangle and mark the sides with the appropriate algebraic

expressions so that you can visualize how to solve the problem


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5. 4 C Tools: distributive property Steps: (1) Distribute the 2 and 7 into their accompanying parentheses

(2) ( – ) ( – ) ( ) ( )

(3) Balance the equation until x is by itself (4) ( ) ( )

Quick Tips: You can also input the answer choices in for x if you can quickly solve the equation in your head

6. 360 C

Tools: permutations Steps: (1) Order matters, so we use permutations. Louise has six letters in her name, so

our set has 6 elements from which we are making 4 choices

(2) nPr

( )

( )

(3)

Quick Tips: The number of values in the factorial you ultimately multiply is dependent on the number of choices being made

For example, if you have 5 elements and you are making 2 choices, then you only multiply two values or

7. 75 B

Tools: mean Steps: (1) Find the sum of Lawrence’s five test scores and subtract the unknown value of

his lowest test score from that sum (2) To find the sum of Lawrence’s five test scores, set the sum equal to x

(3)

(4) Subtract the unknown value of his lowest score from this sum, divide by 4 (the number of test scores remaining) and set all of it equal to 85 (the new mean)

(5)

(6) Quick Tips: If you are unsure of where to start, see if you can find as many values that you

don’t know as possible, such as the sum of Lawrence’s five test scores

8. A

Tools: number types, deciphering word problems Steps: (1) The first part is stating that t is

(2) The second part is looking for the value of (3) Notice that the second part does not include the addition of 219 and 220, so

we are looking for a value that does not include those integers (4) Since we know t includes 219 and 220, we can remove these integers from t by

subtracting them (5)

Quick Tips: Compare the information provided in word problems to find solutions

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9. B Tools: rules for triangles Steps: (1) If triangles are similar, then their angle measurements are the same

(2) The value of angle R is the same as angle B, and angle M is the same as angle A (3) Since angle A is the same as angle M, we can subtract from ( ) (4) Now we need to subtract the value of angle B from the remaining , which

would be (5) Though this answer is not strictly in the answer choices, the value of z is the

same as k, so we may interchange them Quick Tips: You can start questions like these by writing out how you would find the value

of angle C normally without any additional information ( ) You can replace the values in your first equation with their counterparts from

the other similar triangle

10. 10.5% B

Tools: percent of change, area Steps: (1) Though the object is a rectangle, we can use whatever values we want for the

original length and width of the rectangle (such as 10 for both) (2) Increase the length by 30%: ( ) (3) Decrease the width by 15%: ( ) (4) Find the area of the original rectangle: (5) Find the area of the new rectangle:

(6) Use the percent of change formula to solve:

Quick Tips: With percentages, the actual lengths of the sides of a polygon do not matter since the percent of change will be the same regardless

11.

B

Tools: balancing algebraic equations Steps: (1) We need b by itself on one side of the equation

(2) Subtract 123 from both sides:

(3) Divide both sides by ac:

Quick Tips: To eliminate a value from one side of the equation, we must perform the opposite operation of what the value is currently performing to that side (such as subtraction for addition and division for multiplication)

12. The speed at which Cowboy A was traveling C

Tools: deciphering arithmetic word problems Steps: (1) We know the time Cowboy A and B spent riding west on I-10

(2) We know the distance between Cowboy A and B after riding for 10 minutes (3) We don’t know the speeds for Cowboy A and B, and the question is asking for

Cowboy B’s speed (4) We need to know Cowboy A’s speed to find Cowboy B’s speed

Quick Tips: Write out to the side of the problem the information you know, so you can find what is missing


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13. B Tools: inequalities, powers Steps: (1) Since the value of w is between 0 and -1, w is a negative decimal number

(2) Select a negative decimal number to test out the correct ordering (such as -0.5) (3) ; ; (4)

Quick Tips: The closer the negative number is to zero, the greater its value Any negative number squared will result in a positive number

14. 8 D

Tools: multiplying polynomials Steps: (1) g is positioned as the coefficient of the variable x on the right hand side

(2) Find the result of squaring the binomial (3) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) (4) ( )( ) ( )( ) ( )( ) ( )( ) (5)

Quick Tips: If terms are the same on both sides of the equation, then their coefficients are related as well

15.

B

Tools: balancing algebraic equations Steps: (1) We need x by itself on one side of the equation

(2) Multiply both sides by 12: (3) Subtract 3 from both sides:

(4) Divide both sides by 4:

Quick Tips: To eliminate a value from one side of the equation, we must perform the opposite operation of what the value is currently performing to that side (such as subtraction for addition and division for multiplication)

16. 3 B

Tools: ratios Steps: (1) The ratio is stating that for every four walruses there are seven sea lions

(2) There are a total of 11 aquatic mammals in this ratio (3) To equal 33 aquatic mammals, the ratio must occur three times (4) Multiply 3 to the number of walruses and to the number of sea lions to find the

total number of each animal (5) There are 12 walruses and 21 sea lions (6) The ratio of 2 walruses to 3 sea lions can be met if the total number of aquatic

animals is divisible by 5, or the total number of animals in the ratio (7) If we subtract 3 sea lions, we have 12 walruses and 18 sea lions, or 30 animals

in total (8) 30 is divisible by 5 and thus meets the criteria for a 2 to 3 ratio

Quick Tips: The ratio of walruses to sea lions is a part to a part ratio, and the sum of the parts makes up the whole that governs the parts

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17. 120 D

Tools: fundamental counting principle Steps: (1) The types of crust, types of sauce, and toppings are all independent sets

(2) Since we are choosing two distinct toppings, the number of elements in the toppings set decreases by one after we choose the first topping

(3) Multiply the number of types of crusts by the number of types of sauce by the number of toppings by the number of toppings minus one

(4) Quick Tips: Focus on what is stated in the word problem

Had the word problem not mentioned needing two different toppings, we would have multiplied the set of toppings to the other values twice

18.

B

Tools: absolute value Steps: (1) Solve the equation normally (without the absolute value signs)

(2)

(3) Solve the equation a second time with the right hand side of the equation all multiplied by negative one (without the absolute value signs)

(4) Quick Tips: Plug your solutions back into the original equation, including the absolute

value signs, to see if the values work

19. 3.33% B

Tools: percent of change, perimeter Steps: (1) An equilateral triangle has three equal sides, so we must be sure to use the

same value for all sides (such as 10) (2) Increase one side by 30%: ( ) (3) Decrease two of the sides by 20%: ( ) (4) Find the perimeter of the original triangle: (5) Find the perimeter of the new triangle:

(6) Use the percent of change formula to solve:

Quick Tips: If you find a repeating decimal as your answer and none of the answer choices is a repeating decimal, look for decimal value that best matches your result

20. ( ) is the greater value B

Tools: powers, decimals Steps: (1) Find the value of ( ) ( )( )( )( )

(2) Find the value of ( ) ( )( ) (3)

Quick Tips: A positive decimal squared will result in a decimal value that is smaller than the original

Since 0.2 is multiplied to itself many more times than 0.4, the resulting decimal of 0.2’s will be much smaller than 0.4’s


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21. The values are equal C

Tools: evaluating algebraic expressions Steps: (1) Input the value of 2 for each instance of x in the expressions

(2) ( ) ( ) ( ) (3) ( ) ( ) ( )

Quick Tips: Be sure to follow the order of operations, as you can easily miscalculate values in these types of questions

22. Excluding 1, the sum of the prime factors of 36 is the greater value A

Tools: factors Steps: (1) Find the prime factors of 36

(2) (3) Find the sum of the prime factors of 36 (4) (5) Find the prime factors of 24 (6) (7) Find the sum of the prime factors of 24 (8)

Quick Tips: The larger the number the more larger value factors it will have

23. The sale price of the coat is the greater value B

Tools: percentages Steps: (1) Find the sale price of the coat

(2) ( ) (3) You can also compare the difference between 105 and 127 to the discount (4) and (5) 22 is the greater difference so the discounted price results in a number that is

greater than 105 Quick Tips: For some mental math, you can multiply parts of a percentage to a number and

find the sum of those parts after the fact For example, 15% is the same thing as 10% + 5% of a value

24. is the greater value B

Tools: powers, roots Steps: (1) Find the value of √ via factoring by finding two of the same values, with no

remainders, multiplied together that result in the value under the radical (2) (3) ( )( )

(4) ( )( ) ( )( ); thus, √ (5) Find the value of (6)

Quick Tips: Notice that the value of 12 was reached by and that more multiplication is occurring with

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25. The height of the giraffe that casts an 11-foot shadow is the greater value B Tools: deciphering word problems Steps: (1) This question requires that you carefully read the description of each quantity

(2) All other information provided by the problem suggests that the taller giraffe in Column A will create a longer shadow than the giraffe that creates an 11-foot shadow in Column B

(3) However, Column A is referring to the height of the shadow and not its length (4) A shadow does not have any height and in no way can be a greater value than

the height of a giraffe that creates an 11-foot shadow Quick Tips: Do not let your mind assume how the problem will play out

Carefully read all of the details about the quantities

26. The relationship cannot be determined from the information given D

Tools: area, perimeter Steps: (1) The problem does not give us exact values for the length and width of the

rectangle, but we are given the rectangles perimeter (2) Our two lengths and two widths of the rectangle will add up to 28 in some way (3) If we try a length of 12, our width is 2 and the area of this rectangle is 24; thus,

Column B is greater (4) If we try a length of 8, our width is 6 and the area of this rectangle is 48; thus,

Column A is greater (5) Since our answer has changed, the only possible solution is D

Quick Tips: For testing questions like these, try out a very long length first and then scale it back to being closer to the measurement of the width

27. 120% of 12 more than 85 is the greater value B

Tools: deciphering word problems, percentages Steps: (1) Find the value of 85% of 12 less than 120

(2) ( ) ( ) (3) Find the value of 120% of 12 more than 85 (4) ( ) ( )

Quick Tips: You can stop calculating once you realize that 97 is greater than 91.8 and that 97 will be increased by multiplying it to 1.2

28. 1/3 is the greater value B

Tools: probability, fractions Steps: (1) Find the probability of obtaining heads in each of three consecutive coin tosses

(2) Event 1: probability of obtaining one head is



(5) The product of these three events is the probability of the stated outcome

(6)

Quick Tips: Even if Column A was looking for two heads in a row, 1/3 would be greater


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29. The number of students who received higher than the median score is greater A Tools: analyzing charts and graphs Steps: (1) Find the median and mode of the data

(2) 76, 76, 78, 80, 80, 80, 80, 84, 86, 86, 92, 92, 92 (3) 80 is the median and the mode (4) 3 students scored lower than the mode (5) 6 students scored higher than the median

Quick Tips: Pay attention to both the x-axis and y-axis when analyzing data, since the y-axis shows multiple students scoring the same score on the test in some cases


Tools: area, perimeter Steps: (1) Input the positive values in for q and p

(2) If you try 1 for q and 2 for p, then the value of Column A is 1 and the value of Column B is 4; thus, Column B is greater

(3) If you try 1 for q and 8 for p, then the value of Column A is 4 and the value of Column B is 4; thus, the values are equal

(4) Since our answer has changed, the only possible solution is D Quick Tips: Basic geometry does not include negative numbers, so only input positive

values for testing out the quantities

31. kilograms is the greater value B

Tools: measurement Steps: (1) grams expanded is 2,400,000 grams or 2,400 kilograms

(2) kilograms expanded is 24,000,000 kilograms or 24,000,000,000 grams

Quick Tips: You must know metric system measurements for the ISEE There are 1000 grams in a kilogram, so even if the amounts listed were the

same Column B would still be the greater value

32. √ is the greater value A Tools: roots Steps: (1) Find the value of √

(2) √ ( )

(3) Find the value of √

(4) √ √( )( ) (√ )(√ ) ( )( )(√ ) √

(5) The square root of 4 is a larger value than the square root of 2; thus, the product of 6 and the square root of 4 is larger than the product of 6 and the square root of 2

Quick Tips: Though you are not allowed a calculator on the ISEE, you can determine the value of a root of a number by comparing it to the roots of numbers you can calculate without a calculator.

For example, the square root of 11 would be between the square root of 9 and the square root of 16

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33. is the greater value A Tools: evaluating algebraic expressions Steps: (1) Input the value of 3 for m in both algebraic expressions

(2) ( ) ( ) ( ) (3) ( ) ( ) ( )

Quick Tips: Be sure to follow the order of operations as you can easily make a miscalculation for the types of problems

34. The quantities are equal in value C

Tools: probability Steps: (1) Find the probability of rolling two even numbers

(2) 3 even numbers out of 6 numbers on a dice:

(3) Find the probability of rolling an even number and then an odd number

(4) 3 even numbers and 3 odd numbers out of 6 on a dice:

Quick Tips: While you could reduce these fractions, it is sometimes best to leave the fractions in their original forms for easier comparison


Tools: ratios Steps: (1) Though the setup for this question is similar to other ratio questions, we are

not provided with the total number of animals in the store (2) We are not told how the addition of the 3 cats affects the ratio between cats

and dogs in the store (3) We cannot find the difference between the number of dogs and cats in the

store because we cannot find the total number of dogs and the total number of cats

Quick Tips: Focus on the information provided and do not just to conclusions based on previously attempted problems

36. The probability of drawing one blue and one red marble is the greater value B

Tools: probability Steps: (1) Find the probability of drawing two red marbles:

(2) Find the probability of drawing one blue and one red marble:

Quick Tips: If the problem does not state the marbles were returned, then the marble was removed from the bag and the total number of marbles in the bag changed

37. The absolute distance from -2 to 2 is the greater value A

Tools: absolute value, number lines Steps: (1) The absolute value of -2 is 2, and the absolute value of 2 is 2; thus, the distance

between these two values is 4 (2) The absolute value of 3 is 3, which is less than 4

Quick Tips: The absolute value of a number refers to how far away it is from zero


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Reading Comprehension - Passage 1 1. The author would agree that although the United States did not win every battle of

the War of 1812, the conflict yielded important benefits for the United States. C

Explanation

Look to lines 8 to 18, “In spite of defeats and disappointments this war was, in the large, enduring sense, a victory…the world was to respect these States, not as so many colonies bitter wrangling among themselves, but as a sovereign and independent nation.” The United States emerged from the war with the recognition from the world and overcame “Greaten Britain and the wooden walls of her invincible navy.”

2. The Constitution and the Guerrière (lines 30-31) are most likely military ships.

C

Explanation

Look to lines 29 and 30, “…sons of the tarry seamen…” and to the last paragraph of the passage. Seamen are sailors and sailors occupy ships. Also, the last paragraph is discussing that the War of 1812 began in part because Great Britain was assaulting US ships. This indicates that some of the War of 1812 occurred on the sea.

3. The phrase “welding of the nation” (line 7) means the political unification of the

colonies. A

Explanation

Look to lines 15 to 18, “Henceforth the world was to respect these States, no as so many colonies bitterly wrangling among themselves, but as a sovereign and independent nation.” The War of 1812 “welded” the colonies into a unified entity that could withstand the likes of Great Britain on its own terms.

4. The need to secure the United States’ border with Canada is not stated as a reason

for fighting the War of 1812. D

Explanation Securing the border with Canada is not mentioned in the passage. The focus of the passage is the United States need to assert itself to Great Britain and the world by defending the freedom of its ships and its sovereignty.

5. The tone of this passage is descriptive.

B

Explanation

The passage does not pine for things in the past (nostalgic), nor does it passionately argue in favor of something (polemic). The passage does not celebrate the many victories of the United States, nor does it praise the War of 1812 as a shining moment in the United States’ history. However, the passage is descriptive of the effects of the War of 1812 and the lead up to it.

6. In lines 24-31, the author provides examples of the descendants of people who

fought in the War of 1812. B

Explanation

The author of this passage remarks that the War of 1812, “…was a valiant context for survival on the part of spirit of freedom. It was essentially akin to the world-wide struggle of a century later, when the sons of the old foeman of 1812…” The foemen are those who participated in the War of 1812. Thus, the sons of these foemen are their descendants.

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Reading Comprehension - Passage 2 7. The main purpose of the first paragraph is to introduce the author’s premise.

B

Explanation

The first paragraph discusses the fact that people’s understanding of something or their “concept” of something is vastly different from others people’s understanding of something. According to the passage, this divide is due to the fact, “…that very few of our concepts are nearly perfect; the majority of them are quite imperfect and complete.” The author then goes on to discuss how to fix this divide through study. Thus, the first paragraph introduces his premise.

8. The author includes the quotation (“My idea…image”, lines 10-22) primarily in

order to support an earlier claim. C

Explanation

Compare lines 3 to 6 and lines 10 to 22. The author states, “Each has his or her own concept of a the particular thing.” His quote from Green states, “My idea or image is mine alone.” The quote is meant to support the author’s statement that we perceive things differently, but we attach the same words to the same things.

9. The author does not claim that it is probably not worthwhile to try to improve our

mental concepts. C

Explanation

Answer choice C is in contradiction with the whole of the passage. The author states that we have different interpretations of concepts and that this is due to the incompleteness of our concepts. The author then goes onto to prescribe study to improve our knowledge and thus our understanding of things so that our concepts are completely formed.

10. The author uses anecdotal evidence to support his claim that self-study is effective.

B

Explanation

Look to lines 51 to 61, “We have heard of a man who made a practice…” The definition of anecdotal is consisting of or based on secondhand accounts rather than firsthand knowledge or experience or scientific investigation. The author is recounting something that has been heard of happening and not any sort of research. A synecdoche is a figure of speech in which part of something is used to mean the whole, and the man’s effort is not metaphoric language.

11. The overall tone of the passage is instructive.

B

Explanation The purpose of the passage is to explain the differences in people’s concepts of things and how those concepts are incomplete. The author also describes a way to improve upon our concepts. In this, the author is being instructive.

12. The author would agree the most effective method for accomplishing a large goal is

to divide it into small tasks. C

Explanation

Look to lines 65 to 69, “We shrink at the idea of a general course of instructive reading, little realizing that we can take our study in small installments and at a very little cost in time or labor.” The author is stating that the idea of improving our general knowledge is daunting, but that we can actually accomplish it by dividing it up in small study sessions.


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Reading Comprehension - Passage 3 13. The Casa de Palatos is located in Seville.

B

Explanation Looks to lines 8 and 9, “…which, on completion of his edifice at Seville, he established,” which refer to the location of Casa de Palatos. The definition of edifice is a building, especially a large or impressive one.

14. In line 12, “lofty” most nearly means tall.

D

Explanation

“A lofty wall, filling the side of the small square, called the Plaza de Pilatos, and surmounted by a balustrade, forms the outer enclosure of the palace.” The definition of lofty is very high or tall. A wall cannot be educated (erudite) or idealistic. A wall might be imposing, but we do not have enough information in the passage to say whether or not the wall is large and stately (expressing grandeur).

15. The Alcazar has an inferior fountain to the one at Casa de Palatos.

B

Explanation

Look to lines 21 to 26, “Here you might imagine yourself still in Alcazar. The ornament is in the same style; only the arcades are inferior in lightness and beauty. It contains, however, a fountain very superior to that of the principal court of the Alcazar.” The fountain at Casa de Palatos is superior to Alcazar’s fountain.

16. The Casa de Palatos was built by an ancestor of the Duke of Medina Coeli.

B

Explanation

Look to the first paragraph, “The Casa de Palatos is a palace belonging to the Duke of Medina Coeli. One of his ancestors is said to have built it in exact imitation of Pontius Pilate’s palace.” The ancestor of the Duke of Medina Coeli built Casa de Palatos.

17. It can be inferred from the passage that the author is an expert in the history of

Spanish architecture. B

Explanation

The whole of the passage is a very detailed description of the architecture or makeup of Casa de Palatos. The author provides examples of other buildings to compare certain aspects of Casa de Palatos, and give specific measurements for many parts of the palace.

18. The author mentions that candles used to be burned in the chapel at all times in

order to explain the placement of the painting of the Madonna. B

Explanation

Very little light enters the chapel and the Madonna is placed directly across from the cross. Either this is because it must be placed directly across from the cross or the painting must be placed at a high altitude. Since many people used the chapel at the time, there would need to be a light source so that people could use the ladder to examine the painting of the Madonna. Without the light, they would not be able to see it.

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Reading Comprehension - Passage 4 19. The best title for this passage is “Our Feline Dynasty.”

A

Explanation The passage as a whole concerns discussing the attributes and personalities of several cats and not one or two cats. The passage does not discuss the tale of two dogs, and Bobinette and Mr. McGinty are only parts of the passage.

20. The author primarily describes her pets using personification.

C

Explanation

Look to the descriptions of each cat, particularly lines 57 to 63, “For instance, if we…but purr and evince the greatest pride in it.” Pride and prancing are certainly human qualities, if not animal qualities. The author does not use exaggeration (hyperbole), statistics, or irony to describe the cats.

21. In line 63, “evince” most nearly means demonstrate.

B

Explanation The cat is prancing around showing his pride in the yellow ribbon; thus, Bobinette is demonstrating his pride. The definition of evince is to show clearly a feeling for something.

22. It is most likely that the Bobinette’s “intelligence was rewarded” (lines 82-83) with

another game with the tape measure. C

Explanation

Look to the paragraph containing lines 82 to 83. The author is describing Bobinette’s fascination with the tape measure and that he would not play with anything else. Plus, the fact that he continually would search for the tape measure indicates that in previous attempts he was allowed to play with it upon discovering it again and again.

23. Mr. McGinty can be best described as demonstrative and intelligent.

A

Explanation

Look to the second paragraph. Mr. McGinty is described as a cat that showed his affection and remembered the author and her particular way of petting him. Because he showed his affection to the author and the family, he is demonstrative. Because he remembered the author and her particular way of petting him, he is intelligent. He is not fixed in a bad habit (inveterate), uncaring (apathetic), distant (aloof), or demanding (fastidious), and he is not given to sudden, unexpected changes (capricious).

24. The author mentions that Old Pomp was stolen on two or three occasions in order

to underscore the superior characteristics of Old Pomp. C

Explanation

Look to lines 47 to 50, “…and that somebody envied us the possession of him was evident, as he was stolen two or three times during the last summer of his life.” The word “envied” indicates that someone is jealous the author possesses such a great cat. In this case, Old Pomp is stolen because his superior characteristics made him incredibly appealing to the thief. The passage does not state anything about the dangers of letting a cat outside, or that the theft caused his pneumonia.


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Reading Comprehension - Passage 5 25. The primary purpose of this passage is to instruct the reader in how to play a

game. B

Explanation

The author details the roles of all the players (Hares, Hounds, Huntsman, Whipper-in) and the tools used in the game (white paper, flags). The author then describes in great detail the rules for the game and the preparation necessary to play the game successfully. The passage does not state the game is the author’s favorite childhood pastime.

26. The game requires all of the following of the Hare except being the best runner.

B

Explanation Look to lines 15 to 18, “The Hare should not be the best runner, but should be daring, and at the same time prudent…” Daring refers to courage, and prudence is, in a nutshell, wisdom in caution.

27. In line 33, “grace” most nearly means head start.

C

Explanation

While the definition of grace is normally smoothness of form or movement, the passage is using grace to describe a period of time given the Hare to start his part of the chase. A grace period refers to a period of time given a person to perform an action safe from consequence.

28. When the Huntsman rediscovers the Hare’s trail, the Hounds form a line between

two flags. C

Explanation

Look to lines 52 to 58, “When the track is found…the Hounds form in line between the two flags, and off they go again.” “Tally Ho” is the indicator used by one of the Hounds to bring the Huntsman over to examine the trail to ascertain whether or not it really is the trail of the Hare. A different action occurs when the trail is lost, and the author does not state what action occurs when the Hare is caught.

29. The minimum number of players required for this game is four.

C

Explanation While not explicitly stated, the passage states that a Hare, a Huntsman, and a Whipper-in are chosen, while the rest of the players are the Hounds. Thus, the game requires a Hare, a Huntsman, a Whipper-in, and a Hound, or four people.

30. It can be inferred from the passage that the author played this game in the past.

C

Explanation

Since the passage provides a very detailed explanation of how to play the game, it is apparent that the author has played the game before. However, look to lines 7 to 9, “When we were at school in the north, this game was extensively played,” and lines 63 to 65, “We used often to make our chases fourteen or fifteen miles in length.” The “we” in both parts indicate the author has played the game in the past.

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Reading Comprehension - Passage 6 31. In line 3, “remarkable” most nearly means conspicuous.

A

Explanation

The definition of remarkable is worthy of notice, particularly because it is unusual. The place the author is visiting is “remarkable” in that it seems larger than it probably is and it is a place one would never miss noticing if one were awake. In this case, remarkable most closely matches conspicuous, which means attracting attention by being remarkable or unusual.

32. The phrase “frowning walls” (lines 29-30) is an example of metaphor.

C

Explanation

The author is describing how his voice will not penetrate through the aspects of the building, in particularly the “frowning walls.” The walls are not literally frowning, but the author is describing them in such a way that makes the walls seem inhospitable towards the author and his voice. Thus, the “frowning walls” are a metaphor. The goal of adding “frowning” before walls is meant to describe how the author’s voice will not carry through the wall and is not meant to give the wall human qualities (personification).

33. A recurring image in the passage is darkness.

B

Explanation The author frequently references a lack of light in the passage, such as “gloom,” “dim light,” “dark openings,” “dark window,” “nightmare,” and “wait the coming of morning.” The author is surrounded by dark objects and uncertainty.

34. The series of questions in lines 33-39 (“What sort…foreigner”) primarily serves to

represent the narrator’s thought process. D

Explanation

These lines reflect what the author is thinking about the current situation. The author is trying to figure out why he is there and if it’s a routine part of becoming a solicitor. The questions do not recall an incident from his past. The author has no dialogue with the driver. The questions do not introduce the subject matter for the next part of the passage since the passage is still talking about the author standing in the dark courtyard.

35. The narrator’s state of mind can best be described as fearful.

D

Explanation

The author’s description of the courtyard, the driver, and everything else depicts a terrifying place or at least a place that is not cheerful or receptive to visitors. Look to lines 45 to 46, “It all seemed like a horrible nightmare to me.” This line indicates that the author is fearful of his current situation.

36. The passage is likely an excerpt from a novel.

C

Explanation

The passage is very descriptive of the author’s surroundings, including metaphors, and contains inner dialogue. It is not in the style of an informative booklet. It is not describing a proposal or theory (expository essay). It is not review any sort of book.


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Mathematics Achievement

1. √

D Tools: number types, powers, roots Steps: (1) We are looking for the answer choice that does not result in an integer, or a

whole number that can be positive or negative or zero

(2) √

results in 3 and √

results in 2 (3) Answer choice A results in 1; Answer choice B and C both result in 6 and are

actually the same expression

(4) Answer choice D results in √

, which does not have a perfect third root and would not result in an integer

Quick Tips: If addition or subtraction is occurring underneath a radical, like in Answer choice D, you must complete that operation first before performing the radical

2. 7 C

Tools: order of operations, balancing algebraic equations Steps: (1) Balance the equation according to the rules of order of operations

(2) ( ) (3) (4) (5)

Quick Tips: Once you’ve achieved your result, input the answer back into the equation and check your answer for accuracy

3. A

Tools: triangles, vertical angles Steps: (1) The line crossing the two rays that form angle w creates vertical angles and a

triangle (2) The unknown angle adjacent to angle is the same degree value as the top

angle in the triangle, or (3) The angle is the same degree value as the bottom right angle in the

triangle, or (4) To find the value of w, subtract the sum of and from (5) ( )

Quick Tips: When two lines intersect, they form vertical angles, with adjacent angles adding up to and opposing angles being equal in value

4. 90 B

Tools: data analysis, mean Steps: (1) Determine the average grades for each month: 93 (September), 89 (October),

91 (November), and 87 (December) (2) Find the sum of the values and divide by the number of values to find the mean

(3)

Quick Tips: Note that each marking on the graph is an even number and is not consecutive

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5.

B

Tools: probability Steps: (1) While the word problem lists two events, the first event is fixed with Sonia

eating a red apple (2) We can subtract one red apple from the total red apple count (now 2 apples) (3) Find the sum of the total number of fruits:

(4) Find the probability of drawing a green apple:

Quick Tips: Pay attention to how the events play out in a word problem and in what order they occur

6. Irrational number C

Tools: number types Steps: (1) If X and Y are rational numbers, they are numbers that can be represented as

fractions, such as 2 and 1 (2) The difference between rational numbers results in a rational number, such as

the difference between 5 and 2 is 3 (3) Integers and Prime numbers are rational numbers, such as 3 is both an integer

and a prime number (4) The difference between two rational numbers cannot be irrational

Quick Tips: Test out values using the guidelines set by the word problem to see which answer choices work or don’t work

7. -12 A

Tools: multiplying binomials Steps: (1) The right side of the equation is as simplified as possible, so we must multiply

the left side of the equation to evaluate the value of q (2) ( ) ( )( ) (3) (4) q is located in the same place as -12 and is the result after balancing

the equation Quick Tips: While you can balance the equation to determine the value of q, you will know

the value of q if it is in the same place and in the same setup as its counterpart on the other side of the equation

8. 3.5 B

Tools: linear equations, slope-intercept Steps: (1) Since lines c and d are parallel they share the same slope

(2) Find the slope of line c by inputting the known values in for

(3) ( ) ( )

(4) The slope of line c is the slope for line d, so we input the known values in for to find w

(5)

( )

Quick Tips: Parallel lines share the same slope because the lines never intersect


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9. 26.25 minutes B Tools: proportion Steps: (1) Set up the proportion with the two ratios equal to one another

(2)

(3) Cross-multiply and solve for x to find out how long it will take to run 3.5 miles

(4)

minutes

Quick Tips: Make sure that the relationship between the ratios makes sense, as in the types of values in the numerators match (miles to miles)

10. 21% C

Tools: data analysis, percentages Steps: (1) Find the sum of the known percentages and subtract this sum from 100%

(2) (3) 28% reflects the sum of Sci-fi and Horror books in the library (4) The ratio of Sci-fi books to Horror books is 3:1, or a total of 4 books (5) Divide 28% by the total number of books in the ratio: (6) Multiply this value by the number of Sci-fi books:

Quick Tips: If you estimate the percentage of Sci-fi books in the library, you can eliminate answer Choice A for being too low and Answer choice D for being too high

11. A

Tools: probability Steps: (1) A cat crossing your path and your mirror breaking are two independent events

(2) The problem is asking you the probability of a cat crossing your path AND your mirror breaking, so this is the probability of independent events

(3) In these cases, you multiply the probability of the first event to the probability of the second event

(4) The product is the probability of these two events occurring as one event Quick Tips: If the events are independent and the question asks for the probability of one

event OR the other event happening, you use probability of mutually exclusive events

If the events are independent and the question asks for the probability of one event AND the other event happening, you use probability of independent events

12. C

Tools: least common multiple Steps: (1) The least common multiple of , , and would be a value in which each

of these expressions can evenly divide into (2) While and can evenly divide into Answer choice A, cannot (3) While and can evenly divide into Answer choice B, cannot (4) , , and can all evenly divide into Answer choice C

Quick Tips: Think of a multiple as a product of the original number and some other number

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13. 117 C Tools: functions Steps: (1) ( ) indicates that h is the input for the function or equation

(2) ( ) means that every instance of h in the equation is replaced with 12 (3) ( ) ( ) ( ) ( )

Quick Tips: ( ) is the same thing as ( ), which is the same thing as (output)

14. 40 B

Tools: volume Steps: (1) A marble, or sphere, is not an object that, when stacked with many more

marbles, will fit and fill perfectly into the volume of another object (there will be some open space the stacked marbles will not fill)

(2) You must imagine each marble as a cube to get an accurate count of how many marbles will fit into this rectangular box

(3) Since the diameter of the marble is 1.5 cm, it would be the same distance of 1.5 cm from the bottom of the cube to the top of the cube (height of the cube)

(4) The height of a cube is the same as the width and length of the cube (5) The volume for these cubes would be: (6) The volume of the rectangular box is: (7) Divide the volume of the “cube” into the volume of the box:

Quick Tips: You can also set up the problem this way:

15. 9 cm B

Tools: surface area Steps: (1) A rectangular solid has six faces, just like a cube, and has a specific length,

width, and height (2) The area of two of the faces will be defined by the length and the width of the

box: and (3) The area of two of the faces will be defined by the length and the height of the

box: ( )( ) and ( )( ) (4) The area of the remaining two faces will be determined by the width and the

height of the box: ( )( ) and ( )( ) (5) The surface area of the box is determined by the sum of the areas of the faces:

(6) Solve for x (height):

Quick Tips: It helps to visualize the problem by drawing out the box and placing the known and unknown quantities in their respective places on the box

16. 75 B

Tools: mean Steps: (1) Find the mean of the first four test scores:

(2) Set the sum of all five tests scores, divided by 5, equal to two less from 85

(3)

Quick Tips: Answer choices C and D would not lower the mean from the first four tests


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17.

D

Tools: probability Steps: (1) The probability of a square occurring in the first event is

(2) The probability of a triangle occurring in the second event is

(3) The probability of a triangle occurring in the third event is

(4) The probability of a circle occurring in the fourth event is

(5) The probability of the sequencing occurring in this order is

Quick Tips: The object is not removed when generated, so the probability remains

for

each event

18. $0.30 B

Tools: arithmetic word problems Steps: (1) Find the cost per red toothbrush in the first package:

(2) Find the cost per green toothbrush in the second package: (3) Find the difference between the two costs:

Quick Tips: You can also set up this question with algebraic equations and

19. B

Tools: balancing equations, roots, powers Steps: (1) Find y by placing it by itself on one side of the equation

(2) (√ ) √

(3) √ (√ )(√ ) ( )( )

(4) Quick Tips: If you take the square root of a squared number, the result is the original

number

√ ; √ ; √

20. D

Tools: imaginary numbers, roots Steps: (1) Solve for m: √

(2) √ (3) The square root of a negative number is an imaginary number, since the

square of a negative and the square of a positive number is always positive

(4) Break down √ √( )( ) (√ )(√ ) (√ )( ) √

(5) √ can be represented as 12i, since i represents √ (6) However, and , so we must include both options if the

answer choices include them (which they do): Quick Tips: If the square of a number results in a negative number (as m did), then the

original number is an imaginary number or square root of a negative number

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21. 37 C Tools: perimeter Steps: (1) The questions should be stating, “Which of the following is NOT a possible

value for the perimeter of the rectangle if the values for its length and width are integers?”

(2) If the length and width of the rectangle are both integers, these values cannot be a decimal number or a fraction

(3) Answer choices A, B, and D result in integers for the values of the length and the width

(4) Answer choice C results in the width being

and the length being

Quick Tips: If the measurements of a four-sided polygon are integers, then the perimeter of the polygon cannot be odd

22. 1.2 hours C

Tools: work word problems Steps: (1) Jake completes one job in 3 hours and Emily completes one job in 2 hours

(2) Using the work word problem formula:

(3) Cross-multiply the values to find T

(4)

hours

Quick Tips: An easy common denominator to find for adding and subtracting fractions is by multiplying the two values together, such as

23. 2 C

Tools: mean, number types Steps: (1) We only need to find the sum of the original consecutive integers (label it x)

and not their original values

(2)

( )( )

(3) Since each integer is decreased by 2, we are reducing the sum of the original consecutive integers by 2 six times:

(4) Find the mean of this new sum:

(5) Find the difference between the old mean and the new mean: Quick Tips: If you change the value of every value in a set of data by the same amount, the

mean will also change by the same amount

24. D

Tools: number line, powers Steps: (1) S is the negative equivalent of Q, such as -0.5 and 0.5

(2) Use the values of -0.5 and 0.5 to test the answer choices (3) For A: (4) For B: (5) For C: (6) For D:

Quick Tips: While S and Q look more like -0.8 and 0.8, you can use any decimal for testing


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25. 13 C Tools: factors Steps: (1) Factor out 96 into its parts to find its prime factors

(2) (3) (4) Find the sum of these primes factors (5)

Quick Tips: 1 is not prime, but many problems state “excluding 1” to make sure you do not accidentally count it when you factor out a number

Even if the problem does not state “excluding 1,” you do not count it since 1 is not prime

26. and B

Tools: quadratic equations Steps: (1) In evaluating the numerator, we determine that several values may be

inputted in for n to achieve the value of 0 (since 0 divided by any number is 0) (2) In evaluating the denominator, we determine there may be some values

inputted in for n that can result in 0 (which make the solution undefined) (3) Find the values that would result in the denominator equaling 0 (4) Factor out and use the zero product property to solve for n (5) ( )( ) (6) and (7) and 2 would make the denominator 0, so we must exclude them

Quick Tips: If your mental math is quick, you can test out the answer choices before performing any math

27. 6, 8, 10 D

Tools: triangles Steps: (1) The measurement of the hypotenuse does not matter, as all we need are the

measurements for the base and the height of the right triangle

(2) The formula for the area of a triangle is

, so we need a base and a height

whose product divided by 2 equals 24 or simply 48

(3) Answer choice D’s measurements work: and

Quick Tips: Write out the formula for the area of a triangle and quickly place values in their appropriate spots on the triangle so you may visualize the problem

28. orange, orange, green B

Tools: probability Steps: (1) Three events occur with a ball drawn from the box and it is not returned

(2) The probability for Answer choice A is

(3) The probability for Answer choice B is

(4) We do not need to calculate Answer choices C and D Quick Tips: In many cases, you may stop testing answer choices once you’ve found an

answer that fits the criteria of the word problem

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29. 2.16 C Tools: data analysis, mean Steps: (1) The problem is only looking at the players who scored 1 goal or more, so we

can ignore the first part of the graph (the tall bar over 0 goals) (2) 2 players scored 1 goal, 2 players scored 2 goals, 1 player scored 3 goals, and 1

player scored 4 goals (3) Find the sum of the goals:

(4) Find the mean of this sum:

2.16666667 (only Answer choice C matches)

Quick Tips: Make sure you understand what data each axis represents

30. 5 D

Tools: deciphering word problems Steps: (1) While the question seems like it is asking us to find the amount of pennies in

the jar after Erica takes out three of each, it is not (2) We need only be concerned with the “original” number of pennies in the jar (3) A penny is worth $0.01, so we look to the one’s place of the dollar amount (4) The current amount of money in the jar is $12.47, but this was after Erica took

out 3 quarters, 3 dimes, and 3 pennies (5) If we add back in three pennies, the dollar amount is $12.50, and the one’s

place is technically 10, or a multiple of 5 Quick Tips: Consider the least number of pennies possible in the jar

If the new amount is $12.47, then there are at least 2 pennies in the jar If we put three pennies back into the jar, there are at least 5 pennies

31. C

Tools: scientific notation Steps: (1) in standard notation is 750,000,000,000,000

(2) in standard notation is 1,200,000,000,000 (3) The sum of these two values is (4) in scientific notation is

Quick Tips: Since the second value is two full place values less than the larger value, the sum of these two values will not change the exponent of the first value (eliminating Answer choices A and D)

32. √ C Tools: triangles Steps: (1) The diagonal of the base of the cube is the base of the triangle formed from line

d and its opposite edge l (2) The diagonal of the base forms a triangle with edges l and

measures √ according to the triangle ratios

(3) Use Pythagoreans Theorem to solve for d: ( √ )

(4) ( √ ) √ Quick Tips: Though the object is 3-dimensional, the cube is made up of various 2-

dimensional objects, all of which have sides that can be solved with formulas


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33. Kilometers D Tools: measurement Steps: (1) The units of measure used for measuring the distance between two towns

have to do with length (2) Answer choices B and C are measurements of weight (3) Answer choices A and D are measurements of length (4) Answer choice A is a smaller unit of measurement of Answer choice D (5) Meters are not a practical measurement since the distance between two towns

would result in thousands upon thousands of meters, or a very large value (6) Kilometers are a practical measurement since the distance between two towns

would result in tens upon tens of kilometers, or a small value Quick Tips: Focus on what measurement would result in a value that is easy to understand

and work with

34. ( ) A

Tools: factoring polynomials Steps: (1) Since and every term in the algebraic expression is multiplied by q, you

can factor out the 4 from the expression with ( ) remaining (2) Factor out the remaining expression (3) ( )( ) or ( ) (4) The expression is now ( )

Quick Tips: If every term in a polynomial can be divided by the same value, such as 4 or q, you can place the value outside of the expression

35. 70% C

Tools: probability, percentages Steps: (1) The probability of replacing a burnt out bulb is the same as 30% or

(2) The percentage of working bulbs is

(3) The probability of replacing a working bulb is the same as 70% or

(4) The percentage of working bulbs is a fraction, the same format as probability;

thus, the probability of replacing a working bulb is

or 70%

Quick Tips: You can test this out by finding the actual number of working bulbs

Set up the proportion:

If you multiply each value of the actual probability by

36.

D

Tools: volume Steps: (1) Find the radius using the Circumference formula:

(2) Convert the height to inches and find the volume of the cylinder

(3) (

) ( )

( )( )( )

( )( )

Quick Tips: can be treated like a variable and you can leave it as the symbol

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37. 9 B Tools: area Steps: (1) All of the information in the word problem indicates that the two triangles are

similar (same degree values but different side lengths) (2) Because the two triangles are similar, there is a ratio between the triangle’s

side lengths, such as AB : AD and AC : AE (3) The ratio of AB and AD is 8 : 10 and the ratio of AC and AE is 4: x

(4) Set these two ratios equal to each in a proportion:

(5) Solve for x:

(6) Find the area of triangle BAC (non-shaded triangle): ( )( )

(7) Find the area of triangle DAE (shaded triangle): ( )( )

(8) Find the difference between the areas of the triangles: Quick Tips: The measurements of the hypotenuses do not matter for this problem

38. D

Tools: inequalities, balancing equations Steps: (1) Solve the left part of the compound inequality:

(2) (3) Solve the right part of the compound inequality: (4) (5) Create a new compound inequality for x:

Quick Tips: Answer choice D is the only answer with ; thus, you can stop your calculations once you’ve found

39. C

Tools: operations on algebraic expressions Steps: (1) Add like terms together

(2) and are like terms; and are like terms (3) (4) (5) Thus,

Quick Tips: For like terms, the type and number of variables and their accompanying exponents must match

40.

A

Tools: slope Steps: (1) Find the slope using the slope formula:

(2) Select one point as your first set and another point as your second set (it doesn’t matter which one you select)

(3)

( )

Quick Tips: The slope of this line heads in a downward direction; thus, the slope of this line will be negative (eliminating Answer choices B and D)


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41. A

Tools: absolute value, inequalities Steps: (1) The solution set for the number line is written as or and

(2) Start with Answer choice A and solve the absolute value to see if it matches the

solution set (3) (4)

Quick Tips: You can quickly test the answer choices by only performing the first solution for the absolute value

Answer choice B results in and Answer choices C and D result in

42. 5 B

Tools: mean, data analysis Steps: (1) Find the mean of the parking tickets in the North:

(2) Find the mean of the parking tickets in the South:

(3) Find the mean of the parking tickets in the West:

(4) Find the sum of the means of the South and West:

(5) Find the difference between the North’s mean and the combined mean of the South and the West:

Quick Tips: Indicate with shapes which parts of the graph you are analyzing, as we never touch the East’s data

43. 10 cm D

Tools: volume, circumference Steps: (1) Find the radius of the cylinder’s base using the formula for the volume of a

cylinder: (2) (3) Find the circumference of the base: ( ) (4) ( )

Quick Tips: Eliminating from one formula does not subsequently eliminate it from other formulas, so make sure all the parts of a formula are included

44. 7 C

Tools: balancing equations Steps: (1) Look at what can be factored out from the left part of the equation

(2) ( ) (3) Look at what can be factored out from the right part of the equation (4) ( ) (5) Set the newly factored expressions equal to one another (6) ( ) ( ) (7) If you divide by sides by , you are left with

Quick Tips: If a variable and a value share the same location in an equation, they are equal

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45. 50% B

Tools: probability Steps: (1) The product of two odd numbers is an odd number

(2) (3) The product of an odd and even number is an even number (4) (5) The probability of rolling an odd number multiplied by three remains the

same:

(6)

is the same as

or 50%

Quick Tips: Don’t assume that changing the result will alter the original probability If each result had been multiplied by an even number, every roll would have

been an even number and the probability would have changed

46. 8 B

Tools: deciphering word problems, systems of equations Steps: (1) The key factor for this problem is that Stephen has $112 to spend on

doodledads and thingamajigs and not a penny more (2) You can set up two equations for this word problem (3) and (since Stephen needs an equal number of each) (4) Substitute the value of x for y in the first equation, since they are equal (5) ( ) (6) However, you cannot purchase a part of each item from a store, you must buy

the whole item, and Stephen cannot spend more than $112 (7) If Stephen purchases 8 of each item ($28 and $72 respectively), he purchases

as many doodledads and thingamajigs as possible without going over $112 Quick Tips: You may also input the answer choices into the first equation to see which one

gets as close to $112 without going over

47. 10 miles C

Tools: triangles, deciphering word problems Steps: (1) Assume the hikers head west and east from their camp, they each travel 3

miles in their respective directions (

)

(2) If both hikers turn right at 90 degrees, they are heading north (for west) and south (for east)

(3) Traveling for an hour, they are each 4 miles away from their right turn

(

)

(4) Draw a line connecting the top of the line going up to the bottom of the line going down (you’ll have created two right triangles connected by a vertex, or the camp)

(5) Find the measurement of the hypotenuses (they’ll be the same) (6) (7) Find the sum of the hypotenuses for the distance between the hikers (8) miles

Quick Tips: Draw out actions and events in a word problem to visualize it


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Essay

Who was your most important role model as a child? Describe this person and his or her influence on you.

Brainstorming The prompt is asking you about the most important individual that you have modeled yourself and/or the things you do in some way and their influence on you. This individual does not need to be someone you have actually met, nor does his or her influence have to have had that great of an impact on you. However, role models are usually those individuals who have changed or shaped your life in an effective way. Your choice does not necessarily have to be serious, but you should be serious in making your choice, since the admissions department reads your ISEE Essay. For example, your role model can be a/an:

family member (parent, grandparent, aunt/uncle, sibling, cousin) friend teacher leader author actor/actress sports figure historical figure fictional character (book, television, comic, video game, etc.) Outline

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Section 5 – Essay (EXAMPLE) 30 Minutes

Please write your essay prompt here.

Who was your most important role model as a child? Describe this person and his or

her influence on you.

My most important role model as a child was Batman. Even though he is a fictional

person, I have always looked up and admired the good things that he does in the comics,

on TV, and in the movies. Growing up, many of my birthday parties were Batman-

themed, and I regularly dressed up as Batman for Halloween (including this past

Halloween). I would watch the Batman cartoon series over and over again, and I’m sure

my parents could even quote several episodes now. Batman is a great role model as he

always tries to do the right thing as a person and as a crime-fighter, he is incredibly

charitable to those in need, and he has persevered through a very difficult life.

Although I realize that Batman goes above the law with how he fights crime, I know

that his heart is in the right place. When Batman lost his parents as a child at the

hands of a criminal, he made it his mission to battle crime in Gotham City. Batman

utilizes his intelligence and vast wealth to stop criminals such as the Joker at every turn,

all the while trying to minimize the damage the criminals cause. For example, Batman

thwarted the efforts of Ra’s al Ghul, a man determined to destroy Gotham City. Ra’s

al Ghul decided that Gotham City needed to be destroyed because it was too corrupt, but

Batman knew that it could be saved. Though Ra’s al Ghul managed to wreak havoc on

a portion of Gotham City, Batman was able to stop it from spreading. Batman’s crime-

fighting inspires me to stop violence and other destructive actions whenever I can. Once,

I saw one of my classmates bullying another in the hall. Without thinking, I got

between them and was shoved by the bully in the process. I stood back up and staid

between them, and eventually the bully walked away. Thinking about it later, I realized

that Batman always puts himself in danger to help others, so why can’t I risk a little

injury to do the same? In the end, I felt I had done the right thing.

Batman and Bruce Wayne are one in the same person, as Batman is Bruce Wayne’s


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crime-fighting alter ego. However, the actions of one are in the same spirit as the other.

Bruce Wayne is incredibly wealthy because of his parents’ businesses and investments.

Bruce Wayne uses this wealth to help those in need in Gotham City. For example, Bruce

Wayne and his family set up the Wayne Foundation Building, which works on several

social projects like soup kitchens and funds scientific research. The Thomas Wayne

Foundation funds medicine and medical help and manages several free clinics across

Gotham City. Along with these two foundations and many others like it, Bruce Wayne,

or Batman, seeks to improve the quality of life for everyone in Gotham City. To that

end, I am inspired to perform whatever charitable work that I can. Every holiday season,

I work in soup kitchens to help those who can’t feed themselves. I regularly participate in

food and clothing drives with my church, and I perform community service with Small

Steps, an organization that helps underprivileged young people.

Aside from his acts of charity and crime-fighting, Batman has led a very difficult

life. Both of his parents were killed one night when he was very young, and he had no

other family except Alfred, the family butler. However, Batman made the most of it, and

found a father figure in Alfred. He selflessly seeks to help those in need, even though

he could not claim any credit for himself. He is a vigilante, you see, since he fights

crime without the approval of the police. Batman has to forever remain in the shadows

and cannot claim any credit for his actions because he would be locked away for it.

Whenever I feel down about how life is treating me, I think of all the hardships that

Batman has faced. I realize that I should make the most of the situation, because there

are many people who have it worse than I do. I also realize that, like Batman, I should

help these people.

All in all, Batman was, and still is, the most important role model to me as a child.

He inspires me to stop violence and wrongdoing whenever I can, strive to help as many

people as possible, and to overcome hardships with optimistic thinking. Although he is

fictional, Batman demonstrates what it really means to be a good person.

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