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Practice ISEE #1: 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. SPOOF = a light amusing satire, such as a parody of a song or movie, making fun of something A. climate B. injury C. satire D. wisp the prevailing weather or situation

damage or harm to something

the use of wit to criticize something

threadlike or delicate and slender

2. COAX = persuade gently A. advertise B. ignore C. persuade D. wear tell others about something

refuse to notice something or somebody

convince somebody of something

damage something by use or rubbing

3. WANE = become smaller or less A. clean B. diminish C. gather D. increase make something free of dirt or filth

make or become smaller or less

form into a group or collect something

make or become larger or greater

4. LITHE = flexible and supple A. nimble B. slothful C. sly D. white fast, agile, and light in movement

lazy or disliking physical exertion in any form

cleverly skillful and cunning

lacking color or pale-skinned

5. ACME = highest point of perfection or achievement A. breakable B. faulty C. pinnacle D. wily likely to be broken if not handled carefully

containing flaws that could cause malfunctions

highest or topmost point or level of something

skillful in using clever tricks to deceive people

6. PRUDENT = having good sense in dealing with practical matters A. ridiculous B. sophisticated C. stuffy D. wise unreasonable and not at all sensible or acceptable

knowledgeable and cultured

very old-fashioned or conventional

showing good sense of judgment

7. NYMPH = spirit of nature inhabiting natural beauty (woods, mountains, rivers, oceans) A. dragon B. fairy C. ocean D. wood mythical creature that breathes fire

small, magical being that inhabits nature

immense expanse of salt water

area of land covered by trees or bushes

8. VOLATILE = unstable and potentially dangerous, even explosive A. explosive B. fulfilling C. reliable D. stable likely to explode or erupt in violence

giving satisfaction to someone

dependable or likely to be accurate

steady and not liable to change or move

9. EPHEMERAL = lasting for only a short period of time A. complicated B. momentary C. perpetual D. spiritual difficult or having many interrelated parts

lasting for a very short period of time

lasting for an indefinitely long time

relating to the soul or spirit

10. RECOGNIZANCE = formal agreement or sum of money pledged by someone A. infiltration B. jeopardy C. lecture D. pledge enter organization to spy on it

the risk of loss, harm, death, or destruction

instructional speech made before an audience

solemn agreement or promise

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11. CUPIDITY = greed, especially for money or possessions A. archery B. avarice C. demigod D. matrimony activity of shooting with a bow and arrow

greed for wealth mythological being who is half man and half god

the state or condition of being married

12. IMPUGN = to suggest that something cannot be trusted, respected, or relied on A. benefit B. challenge C. collaborate D. honor give someone help or an advantage

call something into question

work with others to achieve something

show great respect to someone or something

13. PORTENTOUS = very serious and significant, especially with regard to the future A. corpulent B. futuristic C. significant D. trivial obese or somewhat overweight

suggesting the future in design or technology

meaningful or having a major or important effect

lacking in seriousness, importance, or value

14. APPROBATION = approval or official sanction of something A. admiration B. discrimination C. experimentation D. probation warm approval of something or someone

unfair treatment of others due to prejudice

use of repeated tests and trials

period of testing somebody’s suitability

15. ECLECTIC = made up of parts from various sources A. electrical B. topical C. singular D. varied full of tension or excitement

relating to something of current interest

especially great or remarkable

characterized by many different forms or kinds

16. VOLITION = the ability to make conscious choices or decisions A. choice B. combustion C. conundrum D. court the ability to choose between different things

the burning of fuel to provide power

something that is puzzling or confusing

meeting where legal judgments are made

17. ABSTEMIOUS = not indulging in or characterized by excessive eating or drinking A. chaotic B. extreme C. moderate D. quiet completely disordered and out of control

highest in intensity or farthest out

not excessive or unreasonable

making little to no noise or undisturbed

18. RANCOR = a bitter, deeply held, and long-lasting grudge or resentment A. annoyance B. ceremony C. destruction D. resentment something that causes a feeling of irritation

ritual for a formal occasion

the act or process of destroying something

ill feeling caused by a sense of poor treatment

19. APLOMB = confident poise, especially in difficult or challenging circumstances A. feather B. fedora C. insecurity D. poise part of a bird’s plumage or something trivial

a soft felt hat with a brim the length of its crown

insecure condition or unsafe feeling

composure or calm self-assured dignity

20. CAPITULATE = to give in to an argument, request, pressure, or something unavoidable A. bankrupt B. invest C. surrender D. surmount unable to pay debts or without qualities

contribute effort or money to something

relinquish control or possession of something

deal with a difficulty successfully

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Verbal Reasoning - Sentence Completions 21. The Marabou Stork mostly feeds on carrion, the dead or decaying flesh of animals.

A

Explanation The comma after the blank signifies that the following information will define the missing word. In this case, carrion is the dead or decaying flesh of animals.

22. The consultant, currently working in London, is an expatriate and greatly misses

his home in Kentucky. C

Explanation The consultant is from one country and lives and works in another, which is the definition of an expatriate.

23. The young man began his apprenticeship with a fervent wish to surpass his master.

D

Explanation

An apprentice learns a trade from a master tradesman, but the keyword here is fervent (passionate enthusiasm), which shows he wants to do well in his trade. An apprentice would not abase (demean), rebuke (scold), or elucidate (reveal the truth of something to) his master.

24. After much research and successful experimentation, the drug was finally

determined to be a viable cure for the common cold. D

Explanation “successful experimentation” indicates that the drug is a possible cure for the common cold. Of the answer choices, only viable means possible.

25. Living vicariously through others is a poor substitute for experiencing things

firsthand. B

Explanation We are looking for a word that is a substitute or the opposite of “experiencing things firsthand.” Living vicariously through someone means you experience life through the works and acts of someone else and none of your own.

26. While walking through the flea market, Paula found a very accurate facsimile of

Leonardo da Vinci’s Mona Lisa. B

Explanation The keyword here is “accurate.” When it comes to art, or anything for that matter, copies are valued at their level of accuracy. A facsimile is an exact copy of something else.

27. Martin has a capricious mind, adamantly refusing my advice one moment then

begging for my wisdom the next. A

Explanation The comma indicates that the following information will define the missing word. In this case, capricious refers to a mind that is given to sudden changes.

28. Christie felt nothing but animosity towards her sister, wishing that uncontrollable

acne would overtake her sister’s face. B

Explanation Since Christie wishes something terrible to happen to her sister, we know she bears hostility towards her sister. Animosity means hostility.

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29. Mosquito hawk, a common name for the crane fly, is actually a misnomer, since the crane fly does not feed on mosquitos at all.

C

Explanation Since the crane fly does not feed on mosquitos, the name mosquito hawk is not appropriate. A misnomer is an unsuitable name for something.

30. Usually organized and meticulous, Paul’s haphazard handling of the project

surprised his managers. A

Explanation The keyword here is “Usually,” which indicates that the second part of the sentence will be a contradiction to the first part. So, we are looking for the opposite of “organized and meticulous,” which is haphazard.

31. The querulous child raised the ire of everyone around him and was promptly

grounded upon his return home. B

Explanation

The first blank results in the second blank, and we know both words will be negative because the child is grounded. A querulous (complaining) child would raise someone’s ire (strong anger), and answer choice B is the only one with two negative words.

32. In order to satiate his voracious appetite for information, Patrick would visit

museums and libraries everywhere he went. C

Explanation Patrick has a large appetite for information as he constantly visits sources of information to satisfy that need. Satiate means to satisfy, and voracious means very hungry or especially eager.

33. The energy drink promised to revitalize you, but I felt enervated the whole

morning. C

Explanation The keyword is “but,” which indicates the second half of the sentence is opposite of the first. If the drink is supposed to revitalize, or refresh you, then the opposite of that would be something that saps your energy, or enervates you.

34. Her speech, though eloquent and fiery, did not rouse the populace to protest the

new laws put in place. A

Explanation

The keyword is “though,” which indicates the second half of the sentence will be the opposite of the blank and the word “fiery.” The first blank needs to match the context of fiery, while the second blank needs to be the appropriate reaction to a fiery speech if it actually worked. Thus, eloquent and rouse.

35. An advocate for human rights, she led numerous protests to oust tyrants and

strongmen. A

Explanation

Since a protest is expressing disagreement with something, our first blank is positive for human rights while the second blank is negative for tyrants and strongmen. An advocate supports something, and oust is to remove someone from power or force someone out.

36. The settlers searched for fecund land that could promise copious amounts of food

and natural resources. D

Explanation To settle somewhere, one needs food and resources to survive, and “promise” indicates the land promises these things. Thus, both blanks are positive. Fecund means fertile, and copious means abundant or existing in large amounts.

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37. Fresh out of college and replete with ideas, he began his new business with the

hopes of stimulating a stagnant economy. D

Explanation The keyword here is “hope,” which is a positive word. After gaining knowledge and skills in college, the man is set on improving the economy; thus, both blanks are positive. Replete means full, and stimulating means to encourage something.

38. She found the small café, located far from the cacophonous hustle and bustle of the

city, conducive to her studying habits. B

Explanation

The keywords here are “hustle and bustle,” or continual noisy activity. These words suggest she is looking for an escape from this so she can study in peace. Thus, the first blank is negative to describe the city, and the second blank is positive to describe the small café. Cacophonous means bad noise, and conducive means helpful.

39. Though he was a truant in his youth, Carl eventually became rather erudite and

earned two doctorates. C

Explanation

The keyword is “Though,” which indicates a switch in context between Carl’s youth and when he is older. If he earned two doctorates, Carl became interested in his education when he became older. Thus, the first blank is negative in describing his youth, and the second blank is positive in describing earning two doctorates. Truant means someone who is absent from school without permission, and erudite means very knowledgeable through study.

40. The warlord fell victim to chicanery, for his advisor was actually a spy sent to

sabotage the warlord’s conquest of the land. B

Explanation

The keyword here is victim, which indicates the warlord’s efforts to conquer the land were stopped. Thus, both blanks will be negative. Chicanery means deception (especially through language), and sabotage means to hinder the efforts of something.

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Quantitative Reasoning

1.

A

Tools: balancing equations, definition of division Steps: (1) We need D by itself, or D in the numerator and 1 in the denominator on one

side of the equation (2) Multiply D to both sides

(3) Multiply the reciprocal of

to both sides to achieve answer choice A

Quick Tips: You are essentially switching the places of D and

, with

flipping around

2. 7 C

Tools: squaring numbers, number types Steps: (1) The one’s place of any product results from the multiplication of the one’s

place of the two multipliers (2) The values for the one’s place can be 0 to 9 (3) Square each of these values to see the resulting one’s place for each product (4)

(5) Thus, the possible one’s place values for squared whole numbers are 0, 1, 4, 5,

6, and 9 Quick Tips: No squared whole number results in 2, 3, 7, and 8 for its one’s place value

3. C

Tools: number lines Steps: (1) Evaluate the possible values of A, B, U, and V

(2) A and B are left of zero and are negative numbers, possibly with decimals (3) U and V are right of zero and are positive decimals less than 1 (4) is the largest value subtracted from the smallest value and is the only

instance that goes farther left than A Quick Tips: Whichever instance results in a value that is less than A will be the least value

4. 8 B

Tools: ratios Steps: (1) Set up a ratio which defines how many red marbles are in the bag compared to

green marbles 5 : 3 (2) The red and green marbles are parts that make up a whole amount; thus, we

can say that one ratio or set of red marbles to green marbles is 8 marbles (3) Divide 32 marbles by 8, which indicates there are 4 groupings of 8 marbles (4) Multiply both values for red and green marbles by 4 to see how many of each

type of marble are in the bag (20 red and 12 green) (5) To make the ratio equal, we must subtract 8 red marbles from the bag to make

it 12 : 12 Quick Tips: Anytime a ratio is parts of a whole, add up the parts to see what the value of

the whole is for that ratio

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5. 25% D

Tools: perimeter, percentages, balancing equations Steps: (1) We need the formula for the perimeter of an octagon, which is or the

sum of the all the side lengths (2) If we increase the perimeter by 25%, me must increase the other side of the

equation by the same percentage to achieve balance (3) For example, if each side length is 1, then the perimeter of this octagon would

be 8 ( ) (4) 10 (5)

Quick Tips: When dealing with percentages, it does not matter what the values of a shape’s side lengths are

6. Number of Sci-Fi books sold in February versus Sci-Fi books sold in March C

Tools: percentages, data analysis Steps: (1) Evaluate the differences between the number of books sold for each answer

choice (2) ~210 books (A); ~30books (B); ~250 (C); ~230 books (D) (3) We do not even need to figure out the percentages as the difference in answer

choice C is larger than the other differences, which indicates the percent difference will be larger as well

Quick Tips: Look for ways to arrive at the answer without completely working out the math, such as with this problem

7.

B

Tools: fractions, squaring numbers, inequalities Steps: (1) Input a value for n that meets the criteria of , such as 0.5

(2) Find the values for the three expressions

(3)

;

; and

(4) Thus, Quick Tips: For variables in inequalities, input a value that is easy to work in all ways

8.

D

Tools: probability Steps: (1) Determine the total number of buttons in the bag (10 buttons)

(2) We are looking at the probability of drawing two green buttons in a row without replacing the first green button

(3) The probability of drawing a green button on the first draw is

(4) The probability of drawing a green button on the second draw is

(5) Multiply these two probabilities for the final probability

Quick Tips: Create a column for each drawing to keep your probabilities organized

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9. 30° B Tools: types of angles Steps: (1) The intersection of line B through parallel lines M and P creates vertical angles

(2) The third, unmarked line creates a triangle between the two parallel lines (3) Find the angle values for the remaining two angles in the triangle (4) A line contains 180°; thus, we subtract 100° from 180° for one angle (80°) (5) A triangle contains 180°; thus, we add 80° and 70° and subtract that value

from 180° (30°) (6) The 30° value is equal to the value of y° because vertical angles are equal (7) The value of y° and the value of x° are equal due to the rules for vertical angles

( Quick Tips: The vertical angles created by a line intersecting two parallel lines are equal

The vertical angles in the first line match the vertical angles in the second line

10. 6 A

Tools: multiplying polynomials, distributive property Steps: (1) Multiply the two polynomials

(2) (3) (4) Distribute the 6 throughout the polynomial (5) (6) z and 6 are located in the same place in both polynomials; thus, z is 6

Quick Tips: You can also simply distribute the 6 to one of the binomials and look to the parts of the binomials that create the middle term in the resulting trinomial

11. The difference between Patrick’s speed with and without the river’s current A

Tools: deciphering word problems Steps: (1) Since Patrick is swimming with the current, we can figure out his speed with

the current by dividing the distance he swam by the time it took him to swim the distance

(2) To find the speed of the river’s current, we would subtract Patrick’s speed without the current from Patrick’s speed with the current

(3) Thus, we need to know Patrick’s speed without the current Quick Tips: Act like you have all the pieces of the puzzle, and then try to solve the problem

As you progress, you will hit on what information you still need

12. 3.19 B

Tools: weighted averages, percentages Steps: (1) The actual number of students doesn’t matter since we’re working with

percentages. We can assume there are 100 students and it works. (2) Multiply each Avg. GPA by the number of students for each grade out of 100 (3) Find the sum of these products, and then divide by 100 (the number of

students in all grades) for the average GPA of all students Quick Tips: 2.94 and 3.45 cannot be averages since they are the lowest and highest values

in the set of data, so A and D can be eliminated at the start

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13. B Tools: graphing linear equations Steps: (1) A linear equation is perpendicular to another linear equation if the product of

their slopes is negative one (slopes are found in slope-intercept form) (2) The first equation is currently in standard form, so we need it to be in slope-

intercept form

(3) Set -1 equal to the known slope times the unknown slope (

) and

solve for m (4) (answer choice B is the only slope equal to 5)

Quick Tips: Ignore the y-intercepts for finding perpendicular linear equations

14. 32 C

Tools: sequences, deciphering word problems Steps: (1) Evaluate the definitions put forth by the sequence

(2) Each consecutive term is larger than the term before it and by the same increased amount (ex. 1, 3, 5, 7…all are increase of 2)

(3) The sequence has 8 terms and we know two of the terms (a, 8, b, c, 20, d, e, f) (4) Since the increase is the same for each value, we first need to find the

difference between the two known values ( ) (5) While there are two terms between 8 and 20, we must include 20 to figure out

how 12 is divided among the terms. Thus, there are three terms (think tick marks on a number line)

(6) ; each term is increased by four (7) There are three terms between 20 and f (including f), so we need to add 4 to

20 three times ( ) Quick Tips: Write out the sequence using variables so that you can visualize the sequence

15. 3750 C

Tools: data analysis Steps: (1) There are essentially three parts to this graph: the time between 0 and 20

minutes, the time between 20 minutes and 35 minutes, and the time between 35 minutes and 60 minutes

(2) The first part is a steady speed to reach 1000 meters (3) The second part is a sharp incline to reach about 4750 meters (4) The third part has 5 minutes of no movement followed by the same steady

pace as the first part (5) The second part, which is also the only part that is 15 minutes long, indicates

the hikers were chased from the 1000 meter mark to the 4750 meter mark, or for 3750 meters

Quick Tips: When analyzing charts and graphs, make sure you understand what values are being shown on the y-axis and the x-axis

Make notes and markings on the charts and graphs as these will help keep you focused on the important information

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16. -36 B Tools: functions, order of operations Steps: (1) While the left hand side of the algebraic equation looks strange and you may

not have seen those symbols before, all it represents is a function (2) The function states that when occurs, then

happens (3) Each of the values in are the inputs for each of the variables in

, so we simply input each value in for its corresponding variable in the right hand side of the equation

(4) Quick Tips: The symbols in the function are not operations and do not really mean

anything except to show that it is a function Always follow the order of operations

17. 7 A

Tools: mode, median Steps: (1) Put the values in order, which n somewhere in the mix (3, 3, 3, 3, 7, 7, 7, n, 9)

and note that there are 9 terms in the current list (2) Since the only mode is 3, then that means that it is the only value that appears

the most out of the list (3) If n were equal to 7, then the list would have two modes (3 and 7) (4) 8, 9, and 10 would not change the mode of the list

Quick Tips: For mean, median, mode, and range questions, input the answer choices to see how each value affects data

18. I and III C

Tools: functions Steps: (1) If , then we can replace a with b or b with a in the function

(2) If we replace a with b: (I) (3) If we replace b with a: (III) (4) The second function cannot be determined from the information provided, so

only I and III are true Quick Tips: Function questions can seem overwhelming, so it is best to save these kinds of

questions for later

19. Parabola intersects the 3 on the y-axis and cross points 1 and 3 on the x-axis D

Tools: quadratic equations and their graphs Steps: (1) This question requires that we remember the format of the quadratic equation

and what its parts mean ( ) (2) a defines the direction of the parabola. Since a is 1 for this equation, the

parabola is drawn like a smile (3) c defines where the equation crosses the y-axis. Since c is 3 for this equation,

the parabola crosses the y-axis at 3 (4) Answer choice D is the only parabola that crosses the y-axis at 3

Quick Tips: Look to a and c first when determining the graph of a quadratic equation

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20.

is the greater value A

Tools: powers Steps: (1) Complete the operation for each value

(2) (

)

(3)

√

(4) √ Quick Tips: You do not have a calculator when you take the ISEE, so you will not know the

actual value of √ . However, you know that it is a value that is less than 10, and 10 is less than 100

21. The measure of an interior angle of a regular octagon is the greater value B

Tools: angles in polygons Steps: (1) Using the equation provided, determine the sum of the interior angles for both

a rectangle and an octagon (2) A rectangle has 4 sides: (3) An octagon has 8 sides: (4) Now, divide each of those sums by the number of sides in each polygon (5) and (6)

Quick Tips: Draw a rectangle and octagon side by side and see that the rectangle’s interior angles are right angles and the octagon’s interior angles are obtuse angles

An obtuse angle will have a greater degree value than a right angle

22. The two values are equal C

Tools: commutative property, factors Steps: (1) You could figure out the products for these values, but it would take you a long

time without a calculator (2) Instead, determine what the factors are for some of the values and see if you

can eliminate similar values occurring in both columns (3) 450 is the same thing as , 180 is the same thing as , and 900 is

the same thing as . (4) All parts are the same, thus the product for each column will be the same

Quick Tips: If an operation appears in both columns, such as multiplied to both values, then that operation can be crossed out and ignored for the comparison

23.

is the greater value B

Tools: linear equations, fractions Steps: (1) Line h if parallel with line f, so their slopes are the same or

(2) Twice the slope of line h is

(3)

is the same thing as

, and

Quick Tips: Parallel linear equations share the same slope since they never meet

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24. The relationship cannot be determined from the information given D Tools: perimeter, area Steps: (1) We need to know the exact measurements for the length and width of the

rectangle in order to answer this question (2) If the width of the rectangle is 10 and the length is 19, which meet the

requirements for a perimeter of 58, the area would be 190 (greater than 144) (3) If the width of the rectangle is 2 and the length is 27, the area would be 54

(less than 144) (4) Since our answer changed from input to the next, the answer is D

Quick Tips: Do not automatically assume a quantitative comparison will be D if some information is missing. You must prove it is D first by inputting some values

25. is the greater value B

Tools: area, algebraic expressions Steps: (1) To find the area of the shaded region, we must find the area of the small square

and subtract it from the area of the larger square (2) and ; (3) The measurements for a geometric shape will not be negative, and we know

that the measurement for b is smaller than a (4) Input the values of 1 for b and 2 for a for both equations (5) and ( )

Quick Tips: occurs in both equations, so we can eliminate them ; a and b are positive values

26. The probability that both candies selected are blue is the greater value A

Tools: probability, fractions Steps: (1) There are eight candies in total

(2) The probability of drawing a purple candy is

(3) The probability of drawing two blues is

(4)

is the same thing as

and

Quick Tips: The candy is replaced, so the first drawing will match the probability of the second drawing

27. The sum of the prime factors of 30 is the greater value B

Tools: factors Steps: (1) Break each number down into its prime factors

(2) 27 (3) 30 (4) Find the sum of each number’s prime factors (5) and (6)

Quick Tips: The sum of a number’s prime factors includes repeats of a particular prime factor, such as 27’s three 3’s

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28. The two values are equal C Tools: roots Steps: (1) You can quickly solve for the columns’ values

(2) √

(3) √ √ √ Quick Tips: For column B, you can combine √ √ into √ as radicals follow

similar rules to variables or unknown quantities

29. c° is the greater value A

Tools: triangles and angles Steps: (1) The sum of a triangle’s interior angles is 180° ( )

(2) c° and d° make up the degree value for a line, which is also 180° (3) We subtract the value of d° from 180° to find c° ( ) (4) We can determine the value of b° by subtracting a° and c° from 180°

( ) (5)

Quick Tips: The sum of a° and b° is the same as d°, since the sum of two of the interior angles equals the exterior angle of the third angle

30. √

is the greater value A Tools: roots Steps: (1) Solve each quantity normally

(2) √

√

(3) √

√

(4)

Quick Tips: Use a factor tree to break a large number down to more manageable values

31. Area of the shaded region in Column B is the greater value B

Tools: circle, area of a sector Steps: (1) Find the area of the shaded region in column A

(2)

(3) Find the area of the shaded region in Column B by subtracting the area of the smaller circle from the area of the larger circle

(4) and ; (5) We can multiply each value to 3.14 to see what the final value will be (6) and (7)

Quick Tips: For questions that have , you can assume its value is 3.14 or estimate it more to be 3

You can quickly see that would not be as large as Also, since occurs in both columns, we can eliminate it and simply compare

16 and 56

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32. 10 is the greater value B Tools: distance formula (graph) Steps: (1) The origin of the circle is its center and the radius will originate from the point

(-5, 10) to the edge of the circle at (1, 4) (2) We must use the distance formula to figure out what the radius of the circle in

Column A is using the two points provided

(3) √ √

(4) √ √ √

(5) Though we do not have a calculator, we know that the square of 10 is 100. We

can compare the square root of 72 to the square root of 100 (√ √ ) Quick Tips: It does not matter which point set you pick for and , just make sure you

keep your choice true for both and

33. NO is the larger value A

Tools: deciphering word problems, algebraic expressions Steps: (1) Collinear means that points M, N, O, and P are in a row on the same line

(2) Draw a line with points M, N, O, and P (3) Mark the distance between M and N as x, the distance between O and P as 3x,

and the distance between N and O as 4.5x ( ) (4) Find the sum of MN and OP: (5) The distance between the points cannot be negative, so x is a positive number (6) If we input 1 for x: and

Quick Tips: Draw out the events in the word problem so that you can visualize what is happening

34. The smallest of the 4 consecutive integers is the greater value A

Tools: sequences Steps: (1) If you were to set up Column A as an algebraic expression, you would write

, which would result in a large polynomial (2) Instead, see what the product of four consecutive numbers would be if the

smallest integers was the value in Column B (3) (4) Since this product is much less than 1,680, then the value of Column A must be

a larger number (incidentally it’s 5: ) Quick Tips: You can use the value in one column to determine the value of the other

35. The two values are equal C

Tools: average of algebraic expressions, roots Steps: (1) For Column B, you are looking for the third root of 343

(2) √

√

(3) Find x by finding the average of the included information

(4)

Quick Tips: When a power is a fraction, the denominator is the root of the number 3 is the denominator in Column B, so we are looking for 343’s third root

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36. The relationship cannot be determined from the information given D Tools: number types, absolute value Steps: (1) x and y are rational numbers, which means that they can be represented as

fractions (2) However, we need to know the specific values to figure out the relationship (3) We can input any rational number for x and y and our answers will change

with each input Quick Tips: Try simple values when proving to yourself that the answer is D, such as -2, -1,

0, 1, and 2

37. The two values are equal C

Tools: factoring polynomials, multiplying polynomials Steps: (1) This question tests your ability to recognize patterns as well as your ability to

factor out polynomials (2) If we factor out the polynomial in Column A, we must first setup two empty

parentheses ( )( ) (3) Determine a possible set of factors for the first term in the polynomial (4) ; the first entry into the parentheses is (5) All of our signs are positive, so all of the signs in the parentheses are positive (6) Determine a possible set of factors for the third term in the polynomial (7) ; the second entry into the parentheses is (8) Notice that the binomials in each parentheses matches the binomial in the

given expression (9) Since the expression is equal to 9, we can replace each instance of the

expression with 9: Quick Tips: When factoring polynomials, start with the factors of the first term and then

the factors of the third term

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Reading Comprehension - Passage 1 1. The main purpose of this passage is to discuss the expansion of China.

C

Explanation Each paragraph of the passage includes information regarding the growth of China’s borders and/or population. Answer choices A, B, and D are only briefly mentioned in the passage.

2. “nuclei” most nearly means hubs.

B

Explanation The definition of nuclei (plural form of nucleus) is the center of something, which is the same thing as a hub. Nuclei is being used to define centers of population in early China.

3. The Tartars controlled all of china during the Yüan dynasty.

D

Explanation

Look to lines 44 to 46, “…and in the Yüan dynasty (1280-1368) they conquered the whole country.” The Tartars owned the northern half of China during the Southern Sung dynasty, and then conquered the whole of China during the Yüan dynasty.

4. China changed from the feudal system to the monarchial system in 221 B.C.

A

Explanation Look to lines 17 to 24, “…which in that year instituted the monarchial form of government.”

5. China expanded at a much greater rate under the monarchial form of government

than the feudal states. C

Explanation

The beginning part of the first paragraph discusses how the borders did not change much during the first two thousand years of China’s known history. After the feudal states became a single kingdom under a monarch, the passage describes China’s border growing at a much greater rate than previously described.

6. The change to China’s flag suggests many peoples make up China’s large

population. B

Explanation Look to lines 47 to 60, “At present the five chief component peoples of China are represented in the striped national flag…This flag was adopted on the establishment of the Republic in 1912…had increased to about 400,000,000 .”

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Reading Comprehension - Passage 2 7. The best title for this passage is “A New America Necessitates New Methodologies.”

B

Explanation

Woodrow Wilson’s speech brings up many examples of the old ways not fitting in with the new ways of America. Look to the last few lines, “…that a new nation seems to have been created which the old formulas do not fit or afford a vital interpretation of.” Wilson is calling for new methods that fit the new ways.

8. The author provides examples of breaking from the past to strengthen his

argument that current politics do not match the new America. C

Explanation

By providing multiple examples of old politics not working for the new America, Wilson is proving his point with evidence. Wilson does not deride the changes in America, nor does he provide examples of citizens being happy and prosperous. He also does not mention American culture in his speech.

9. “transcend” most nearly means surpass.

C

Explanation The definition of transcend is to go beyond a limit or range, which is the same as surpass. Wilson uses this word to suggest that the changes in America have moved beyond its borders and have influenced the world.

10. The author would most likely agree that the economy is the driving force behind

the new America. D

Explanation

Look to lines 11 to 15, “We have changed our economic conditions, absolutely, from top to bottom; and, with our economic society, the organization of our life.” The prosperity of the nation’s economy has completely altered how the average American now lives. Wilson does not state whether he would want the government to increase or decrease in size, and the whole of the passage is in contrast with answer choice C.

11. It may be inferred from the passage that the author is impressed with the

development of America. D

Explanation

Look to lines 37 to 49, “Our development has run so fast and so far along the lines sketched in the earlier day of constitutional definition…which transcend the boundaries of the country itself and fill the eyes of the world.” We can infer that Wilson is impressed with America’s development because we are influencing the rest of the world with our changes.

12. The next logical step for the author is to provide new political formulas that match

the new America. A

Explanation

The entirety of the passage discusses how old formulas do not fit the new America, so it is logical that Wilson will now talk about new formulas that fit in with the new America. While America may be influencing the world, there is nothing in the passage that suggests the rest of the world envies America’s changes, nor does Wilson give evidence to suggest America will not change in another twenty years. Answer choice B is in contrast with the point of the passage.

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Reading Comprehension - Passage 3 13. The author of this passage is infatuated with corgis.

A

Explanation

The definition of infatuated is to be captivated by something, which describes the author’s interest in corgis. Keywords such as “wonderfully” and “singular” indicate that the author likes corgis, and in lines 32 and 33, the author states, “Being the owner of a corgi, I can understand Queen Elizabeth’s the II’s obsession…”

14. The main purpose of this passage is to demonstrate the many facets of the corgi’s

nature. C

Explanation

In the passage, the author describes the corgi’s ability to work, its history, its character, and even shares a folktale about how the corgi came to be. Thus, the author is describing all the aspects, or parts, of the corgi’s nature or being. Answer choices A and B are only briefly mentioned. The definition of abhorrent is distasteful or repulsive, definitions that do not fit in with the author’s descriptions of the corgi.

15. “enthrall” most nearly means captivate.

A

Explanation

The definition of enthrall is to charm or delight someone thoroughly, which is the same as captivate. Look to lines 34 to 37, “The corgi commands an almost otherworldly presence…Even the action of sitting delights the eye.” The author uses enthrall to state that everyone will be delighted or charmed by anything the corgi does.

16. According to the passage, the corgi will instinctively chase a squirrel.

D

Explanation Look to lines 27 to 30, “The corgi will also instinctively chase anything that moves, so prepare for a run if a squirrel or other poor woodland creature crosses his path.”

17. We can infer from this passage that the author will likely own a second corgi.

B

Explanation

There is not any evidence presented in the passage for answer choices A, C, and D. Though the passage mentions a fairy or pixie helping the Queen by creating the two corgis, it does not say that the pixie rode them. Also, look to lines 33 and 34, “…(she owned 30 of them!)…,” which indicate that owning multiple corgis is a natural thing for someone obsessed with corgis.

18. The author does not mention Cardigan Welsh Corgis until the end of the passage

because Pembroke Welsh Corgis interest the author more than Cardigans. B

Explanation

There is no evidence stated in the passage to support answer choices A and D, and answer choice C is incorrect as the pixie made both corgis to help the Queen. Due to the language used by the author to describe Pembrokes and that the author only mentions the Cardigans in the folktale, it is clear the Pembrokes interest the author more than Cardigans.

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Reading Comprehension - Passage 4 19. The best title for this passage is “Bats - Flying Marvels.”

C

Explanation

The author only briefly discusses terror caused by bats or examples of bats being disgusting creatures. Lines 28 to 30 state that some bats feed on insects, some on fruit, and some on blood; thus, answer choice B does not work. The whole of the passage focuses on the abilities of the bat.

20. According to the passage, the statement “Bats have dull bites” is NOT true.

B

Explanation Look to lines 50 to 51, “The bite of all is extremely sharp.” All bats have sharp bites, so answer choice B is not true in stating bats have dull bites.

21. “locomotive peculiarities” refers to the bat’s ability to fly.

D

Explanation

Since bats are the only “creatures which suckle their young” that have the ability to fly, the bat’s movements can be considered peculiar in comparison to other animals. Lines 17 to 21 describe the makeup of the bat’s legs, tail, wing membrane, and breastbone in relation to helping the bat fly.

22. Bats who feed on insects clear the air of pests.

B

Explanation Look to lines 30 to 32, “The first help to clear the atmosphere of those insects which fly at twilight…” The “first” refers to bats that feed on insects, which fill the air at twilight.

23. The author mentions the Lemur Galeopithecus to support his claim about the bat’s

ability to fly. A

Explanation

In the first sentence, the author states that bats are the only “creatures which suckle their young” that can fly. One who is reading the passage might try to counter his claim by stating the Lemur can fly. However, the author counters this possibility by stating that the Lemur, though it can glide from tree to tree, cannot actually fly, thereby supporting his statement.

24. We can infer from this passage that bats intrigue the author.

D

Explanation

The author does not state he is afraid of bats in the passage (answer choice A). Though the author states that fruit eating bats damage crops and bats that feed on blood damage living creatures, the author clearly states that bats that eat insects are helpful (answer choice B). The author does not state that bats regularly bite thumbs. The author discusses the bat’s ability to fly, its makeup, its feeding habits, its habitats, and interesting characteristics of some of the types of bats. Thus, the author has demonstrated that he is intrigued (interested) by bats.

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Reading Comprehension - Passage 5 25. The main purpose of this passage is to show early perceptions and portrayals of

gods and other spirits. C

Explanation

The author begins with the Babylonian’s perception of spirits and gods, and then follows up with some examples of other cultures’ perceptions of their own spirits and gods. Answer choices A and D are only briefly mentioned, and the author is not praising the spirits of ancient cultures.

26. We can infer from the passage that early Sumerians believed gods and demons

looked the same. B

Explanation

Look to lines 30 to 33, “In the early stages of Sumerian culture, the gods and goddesses who formed groups were indistinguishable from demons.” Subsequent sentences continue the idea that Sumerian gods and demons looked the same by lumping them into the pronoun “they.”

27. “manifestation” most nearly means a visible form.

A

Explanation

One definition of manifestation is visible form of a spirit or divine being. The Babylonians believed that the statues and other art were inhabited by the spirits of their gods, and when an idol was stolen, they believed that their god had been physically taken from them.

28. The “dragon of Babylon” was depicted as a deity composed of various animal parts.

D

Explanation

Look to lines 39 to 43, “The ‘dragon of Babylon,’ for instance, which was portrayed on walls of temples, had a serpent’s head, a body covered with scales, the fore legs of a lion, hind legs of an eagle, and a long wriggling serpentine tail.” Each part of the “dragon of Babylon” is made up of different animal parts.

29. The tone of the passage suggests that the author believes art is not reality but

merely reflects it. C

Explanation

Look to lines 5 to 12, “Our painters and poets and sculptors are greatest when they symbolize their ideals and ideas and impressions…But what may seem poetic to us, was invariably a grim reality to the Babylonians.” The author is part of the “us” that believes art is symbolic and states that the Babylonians believed that art was reality.

30. The “producer of calamity” was Ra.

B

Explanation Look to lines 55 to 57, “In Egypt the sun god Ra was similarly a ‘producer of calamity,’…” In the previous sentence, the author describes Bel Enlil and Nergal as destructive forces, and likens Ra to them in the following sentence.

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Reading Comprehension - Passage 6 31. The author of this passage finds the Pilgrims landing to be unremarkable.

C

Explanation

Look to lines 17 to 28, “What was there remarkable about it, I would like to know? What can you be thinking of? Why, those Pilgrims had been at sea three to four months…” Twain is stating that the Pilgrims landed because they had been out at sea for a long time and it was freezing. To him, it was a natural choice to land at Plymouth Rock and not a remarkable one.

32. “pretext” most nearly means excuse.

D

Explanation The definition of pretext is a made-up excuse or a misleading reason given for doing something. Twain is stating that the celebration is misleading as the Pilgrims and their landing were nothing to celebrate.

33. The best title for this passage would be “Celebrating Natural Inevitabilities.”

B

Explanation

Twain states that the Pilgrim’s landing at Plymouth Rock was an inevitability due to them being out at sea for three to four months and that is was “deathly” cold outside. In lines 58 to 62, Twain is stating that is only natural that the Pilgrims were better than those who came before them because “People always progress.”

34. According to the passage, they had been celebrating the Pilgrim’s landing for two

hundred and sixty years. D

Explanation

Look to lines 37 to 42, “…a circumstance to be amazed at, and admired, aggrandized and glorified, at orgies like this for two hundred and sixty years--hang it, a horse would have known enough to land; a horse.” The “orgies” Twain is referring to are the celebrations of the Pilgrim’s landing.

35. We can infer from this passage that the author believes he is better than his

ancestors. A

Explanation

Look to lines 60 to 65, which state that people are always better than their ancestors or the people who came before them. Thus, Twain believes that he is better than his ancestors. Answer choice B is in contrast with lines 60 to 65, and answer choices C and D are pulling information from the passage and twisting it.

36. “aggrandized” most nearly means exaggerate greatness. A

Explanation

The definition of aggrandized is to exaggerate the greatness of something to make them appear bigger or better than it actually is. Twain uses this word to make a point that the celebrators of the Pilgrim’s landing are making something out of nothing.

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Mathematics Achievement 1. 4 miles C

Tools: deciphering word problems Steps: (1) Find the sum of the distance Sally bikes from Monday to Friday

(2) miles (3) Find the difference between how many miles she wants to bike and what she

has biked thus far (4) miles (5) Multiply this amount by ¼ or 0.25 to find the final result (6) miles

Quick Tips: When adding the distances traveled from Monday to Friday, write a single or two letter abbreviation of the day over its appropriate distance biked so that you do not miss any values

2.

A

Tools: number lines, roots Steps: (1) Note that there are three tick marks from zero to √ ; thus, every three tick

marks is an increase of √ and nine tick marks is equal to √

(2) Since nine tick marks are also equal to 1, we can set √ equal to 1 and solve for x

(3) √ √

√

Quick Tips: You can test your result by having each tick mark an increase of

3. 16 erasers C

Tools: proportions Steps: (1) 3 erasers costing $0.75 is a ratio (3 : 0.75), and $4.00 worth of erasers is a

second ratio (x : 4) (2) Since the ratios are related, we can set them up in a proportion and solve by

cross-multiplying the values

(3)

erasers

Quick Tips: The ratios are related because the quantity types are the same in both ratios

4. 30% C

Tools: percent of change Steps: (1) Since the seller bought the home at $500,000 and wants to make at least a

profit of $60,000, then the lowest he can sell the home for is $560,000 (2) Find the difference between the current cost of the home and the minimum

selling price ( ) (3) Divide the difference by the current cost of the home to find the percentage (4) or 30% decrease

Quick Tips: The current cost of the home is considered the original amount for the formula since we are making the change from that amount

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5. {3} D Tools: intersection (set notation) Steps: (1) Following the order of operations, we must find the intersection of sets A and

B and then find the intersection of that intersection and set C (2) (3)

Quick Tips: Technically, we are looking for the intersection of all three sets; thus, the only value shared by the three sets is 3

6. 72 A

Tools: permutations Steps: (1) Find the number of combinations possible with all five symbols, regardless of

where the symbol falls (2) (3) Since the is fixed for two scenarios, we need to figure out the number of

combinations possible for the other four symbols when the is at the front and at the end

(4) is at the front: (5) is at the end: (6) Subtract these two values from the total number of combinations possible (7) possible combinations

Quick Tips: Since order matters, we must use the permutations formula

7. 64 D

Tools: roots Steps: (1) Though there is a radical in front of the variable, the normal addition rules

apply and you can subtract the first variable from the second variable

(2) √

√

√

(3) Solve by taking each side to the power of 3

(4) √

√

Quick Tips: Treat a radical like an exponent when it is attached to a value or variable

8. B

Tools: triangle rules Steps: (1) The only information we are provided is that side length BC is less than side

length AC (2) Triangle rules state that if one side length is less than another side length, the

degree value opposite the shorter side length is also less than the degree value opposite the longer side length

(3) In this case, is the opposite degree value for BC and is the opposite degree value for AC

(4) Thus, and they are not equal, making answer choice B false Quick Tips: We do not have enough information to say whether or not the other answer

choices are true or false, and we can only prove that answer choice B is false

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9. 2.0 inches C Tools: area, perimeter Steps: (1) The perimeter of the object is the sum of all the outside side lengths or 12L

(2) The area of the object is the sum all of all the areas of the squares or (3) Since the area of the object is equal to the perimeter of the object, we can set

these values equal to each other and solve for L (4)

Quick Tips: Write out the formulas for area and perimeter of a square so that you can visualize the steps you need to take

10. 30 inches3 A

Tools: volume Steps: (1) We have all of the measurements necessary to find the volume of the

triangular prism, which is the area of its base (triangle) times its length (2) Find the area of its base (3) (4) Multiply this area to the prism’s length (5) inches3

Quick Tips: Don’t forget that the area of a triangle is

11. 16 mph B

Tools: distance, rate, and time Steps: (1) We have our values for distance and time, so we need to find the rate

(2) However, our answers are in miles per hour, so we need to convert the time from minutes into hours

(3)

hours

(4) Divide the distance by the time (in hours) to find the rate (5) mph

Quick Tips: Make sure that your measurements are the same as what the question is asking or what the answers are before you perform any operations

12. 45 minutes C

Tools: work word problem Steps: (1) Since Alan can clean twice as fast as Zack, we know he can clean a room in half

the time Zack can (ex. Alan: 15 minutes; Zack: 30 minutes) (2) Thus, Alan can complete two jobs in the time that Zack completes one (3) Use the work word problem with both times equal to x, but with one of the

fractions with 2 jobs completed in the numerator (symbolizing Alan)

(4)

(5) Cross-multiply the values in the proportion to find Zack’s cleaning time by himself ( )

(6) Divide Zack’s time by 2 to find Alan’s cleaning time by himself ( ) Quick Tips: If someone cleans twice as fast as another worker, you do not multiply his time

by 2 as that would mean he works twice as slow as the other worker

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13. 88.57 B Tools: data analysis, weighted average Steps: (1) We cannot take a blanket average of the scores shown on the graph since each

classroom has a different number of students (2) We need to multiply each average to its appropriate classroom’s number of

students, find the sum of those values, and then divide by the total number of students to find the true average of South Elementary’s 1st grade

(3) (4)

Quick Tips: Only one answer choice has the value of 88, so you could stop dividing Step 4 at that point

14. 21 D

Tools: probability Steps: (1) If there are 9 pink towels in Amanda’s closet and the probability of selecting a

pink towel is

, then that means the fraction has been reduced

(2) We need to bring the numerator in the fraction up to 9 to match the number of towels in the closet

(3) To do this, we multiply the numerator by 3; however, whatever we multiply the numerator by, we must multiply the denominator by the same amount

(4)

(5) Since the denominator of a probability is the total number of possible outcomes, the total number of towels in Amanda’s closet is 21 towels

Quick Tips: You could also solve this problem via a proportion:

15. 95° B

Tools: degrees in triangles, vertical angles Steps: (1) The points of the two triangles that touch form vertical angles; thus, the

unmarked angle in both triangle is the same value (2) Because the unmarked degree value is the same in both triangles, the sum of

the other two angles in the triangles is also the same (3) or

Quick Tips: You do not need to know the specific values of and , only that their sum is equal to the sum of and

16. -3 C

Tools: midpoint formula Steps: (1) To find the value of p, we need to set up the x-coordinates in the midpoint

formula

(2)

(3) Quick Tips: We do not even need to bother with the y-coordinates of the two points, since

they have no bearing on the x-coordinates

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17. 95 A Tools: direct variation or proportion Steps: (1) The word problem states that the values are directly proportional, so that

means we are looking at direct variation ( ) (2) We need to find the constant of the variation. We can input the guests for x

and the pizzas for y

(3)

(4) Now that we know the constant, we can figure out how many pizzas are needed for 400 people

(5) (

)

(6) However, the guests already ate 5 pizzas, so all that’s needed is 95 pizzas Quick Tips: You can also solve this problem using a proportion (

)

18. B

Tools: scientific notation Steps: (1) written normally is 5,256,000,000,000,000

(2) written normally is 9,250,000,000,000 (3) (4) written in scientific notation is

Quick Tips: Though both of these values are very large numbers, the second value is small enough to where adding it to the larger value will not change the total number of digits from the larger number to the sum

19. 12 A

Tools: roots and exponents Steps: (1) We are looking for the product of the third root of 64 and the fourth root of 81

(2) Find the third root of 64:

√

√

(3) Find the fourth root of 81: √

√

(4) Quick Tips: When the exponent is a fraction, the numerator is the power the number is

being taken to and the denominator is the root of the number

20. D

Tools: factoring polynomials Steps: (1) Factor out b from the polynomial, leaving you with

(2) Factor out the polynomial (3) (4) Thus, our answer is

Quick Tips: The is actually superfluous information since it is factored out from all of the answer choices

Answer choice C looks correct, but it is missing the coefficient of 2 from the second term

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21.

C

Tools: absolute value Steps: (1) With absolute value of an algebraic expression, we must solve the equation

twice (remove the | | signs for both)

(2) Once normally:

(3) Once with right hand side of the equation multiplied by negative one:

Quick Tips: For the second time you solve the equation, you may also multiply the left hand side by negative one. You will achieve the same result

22. D

Tools: graphing on number lines Steps: (1) The dot at the -4 on the number line is a closed circle, and the line extends to

the right of -4; thus, the value of C can be equal to -4 or greater than 4 (2) The dot at the -1 on the number line is an open circle, and the line extends to

the left of -1; thus, the value of C cannot be equal to -1 and is less than -1 (3) Answer choice D is the only inequality that represents these facts

Quick Tips: If the dot on the number line is an open circle, the value where the dot is located is not included in the set of values of the inequality

If the dot on the number line is a closed circle, the value where the dot is located is included in the set of values in the inequality

23. 7Π B

Tools: circles, area of a sector Steps: (1) We need the formula for the area of a sector (

)

(2)

Quick Tips: When looking for the area of a sector, look to the degree value of the sector to figure out what portion the sector is of the circle

The answer choices do not multiply the value of , so make sure that you do not take that unnecessary step

24.

B

Tools: probability Steps: (1) Find the total number of shirts in the drawer ( )

(2) We are looking for the probability of drawing two shirts in a row that are not green shirts, so we need the sum of the other two colors ( )

(3) The probability of drawing a non-green shirt on the first draw is

(4) On the second drawing, there is one less non-green shirt and one less shirt in

total in the drawer, so the probability is

or

(5) We multiply these values to find the final probability (

)

Quick Tips: Answer choice C is not being multiplied, so we can eliminate this answer

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25. Runner 2 began the run at a slower pace, and then finished at a much faster pace C Tools: data analysis Steps: (1) The x-axis refers to the distance traveled by the runners and the y-axis refers

to the time it takes each runner to reach a particular distance (2) In 10 minutes, Runner 1 has completed 1 mile and Runner 2 has completed 0.5

miles (3) In 55 minutes, Runner 1 has completed 4.7 miles, and Runner 2 has completed

5 miles (4) Runner 2 starts out slow and then picks up the pace after 25 minutes to finish

the 5 mile run before Runner 1 Quick Tips: Make sure you understand the values represented on each axis

26. 61 D

Tools: mean, number types Steps: (1) Algebraically:

(2)

(3) We can also solve this problem through reasoning that the mean of an odd number of integers will also be the median of the set

(4) If 57 is the median or middle of the set, then there are 4 integers that are less than 57 and 4 integers that are greater than 57

(5) Since we are looking for the greatest integer, we simply add 4 to 57 to get 61 Quick Tips: If a question seems difficult in the amount of work required to solve it, then

there is likely a faster way of answering the question

27. 40 mph B

Tools: weighted average Steps: (1) We can input whatever distance we want it takes Tommy to travel to work,

such as 120 miles (2) If Tommy travels at 60 mph for the 120 miles, it will take him 2 hours (3) If Tommy travels at 30 mph back home for 120 miles, it will take him 4 hours (4) Tommy’s total travel time for the round trip is 6 hours, but he spends less time

traveling to his office than traveling home; thus, we use the time as the weight

(5)

mph

Quick Tips: We cannot simply find the average of his rates because Tommy spends less time traveling 60 mph than he spends traveling 30 mph

28. $162.24 A

Tools: compound interest Steps: (1) We have the values needed for the compound interest formula ( )

(2) (3)

Quick Tips: Make sure you follow the rules for order of operations. Do not multiply the 150 to the 1.04 before squaring the 1.04

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29. 4500 mL D Tools: units of measurement Steps: (1) Find the sum of water Doug drank throughout the day

(2) liters of water (3) Convert liters to milliliters (1 L is 1000 mL) (4) mL

Quick Tips: Make sure you know your metric system units of measure

30.

C

Tools: probability Steps: (1) Though we are not given values for p and n, we know that their sum at least

equals 7 due to the denominator in the probability for negative numbers and the value of n is at least 4 due to the numerator in the same probability

(2) If and , then

(3) We input our values for p and n to find our answer (

)

Quick Tips: There may actually be more positive numbers and negative numbers than we’ve found, but the fraction will reduce down to the same number regardless

In other words, the ratio is stating that for every three positive numbers in the set, there are 4 negative numbers

31. 13 hours D

Tools: data analysis Steps: (1) Keira spends 13% of her day playing video games and 33% of her day sleeping

(2) If Keira spends 46% of her day playing video games and sleeping, then she spends 54% of her day doing other things

(3) 54% of 24 hours is 12.96 or 13 hours (rounded up) Quick Tips: Pay attention to words in all caps, as these indicate the question is asking for a

result that you may not be expecting

32. [

] A

Tools: matrix addition Steps: (1) Follow the rules for matrix addition

(2) Find the sum of the values in row 1, column 1 in both matrices ( ) (3) Find the sum of the values in row 1, column 2 in both matrices ( ) (4) Find the sum of the values in row 2, column 1 in both matrices ( ) (5) Find the sum of the values in row 2, column 2 in both matrices ( ) (6) Input each of these sums in the same location as their addends

Quick Tips: Be careful that you are adding the proper values to each other The resulting matrix from adding two matrices together will have the same

dimensions (2 by 2, in this case)

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33. 10 D Tools: linear equations, slope Steps: (1) Two lines are perpendicular when the product of their slopes is negative one

(2) Find the slope of line L:

(3) We can find the slope of line Q:

(4) To find T:

(5)

Quick Tips: Write out the formula for finding the slope so that you don’t get your x-coordinates and y-coordinates confused

34. 24 B

Tools: multiplying polynomials Steps: (1) Distribute throughout the other polynomial to see how it relates to

(2) (3) (4) (5) The polynomials are equal to one another, so they both equal 24

Quick Tips: Before distributing, you can look at the pattern of the products of the first and last terms in the polynomials ( and )

35. I and III only B

Tools: median Steps: (1) Observe that all of the known values are whole numbers and the list contains

an even number of values (2) If N is added to the list of whole numbers, then the list contains an odd number

of values (3) If a list contains an odd number of whole numbers, then one of the values will

be the median (4) If the value of N is less than 8, then the median could be 7 (5) If the value of N is greater than 7, then the median could be 8

Quick Tips: 7.5 is not located in the set of whole numbers and cannot be the median

36. C

Tools: quadratic equations and their graphs Steps: (1) a defines the direction and width of the quadratic’s parabola, so begin by

observing the direction of the parabola (2) The parabola goes in a downward direction, thus a is negative (3) c is the y-intercept, so observe where the parabola crosses the y-axis (4) The parabola crosses the y-axis in the negatives, thus c is negative (5) Only answer choice C has negative values for both a and c

Quick Tips: If a is negative, then the parabola looks like a frown If a is positive, then the parabola looks like a smile

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37.

B

Tools: probability Steps: (1) Find the total number of socks in the bag ( )

(2) John, Connor, and Tom each remove 2 socks of each color type (170 socks left) (3) The bag now contains 38 individual green socks and the probability for Mike

to select a pair of green socks is

Quick Tips: Pay attention to the language in the word problem, since pair refers to two socks at a time

38. √ A Tools: roots and powers Steps: (1) If a number is positive and less than one, then the number is a positive decimal

(2) We can solve this equation by inputting a positive decimal that is easy to work with for powers and roots, such as 0.25

(3) √ (4) Thus,

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

The root of a decimal will always result in a decimal that is larger than the original value

39. 2 A

Tools: standard deviation Steps: (1) Find the average of the values:

(2) Subtract the average from each value and square it (3) (4) Find the average of these new values

(5)

(6) Take the square root of the average of the new values to find the standard

deviation: √ Quick Tips: Standard deviation questions take multiple steps and should be saved until the

end of the exam

40. C

Tools: solving quadratics through factoring Steps: (1) Set the equation equal to zero and factor out the quadratic to solve for x

(2) (3) Set each of the factors equal to zero and solve to find the values for x (4) (5)

Quick Tips: If all of the signs in the quadratic are negative, then the number with the largest absolute value is paired with the parenthesis with the negative sign and the number with the smallest absolute is paired with the positive sign

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41. 20 C Tools: systems of linear equations Steps: (1) For the number of tables in the restaurant:

(2) For the number of people able to be sat: (3) Solve for y to find the number of tables that seat 4 people by replacing x with

(substitution) in the second equation (4) (5)

Quick Tips: It doesn’t matter which variable you select to represent the tables that seat 4 people, the answer will be the same

42. 121 D

Tools: averages Steps: (1) Find the average of the scores, but count the unknown value of the sixth test

twice, or , and our divisor must include this fact (7 instead of 6)

(2)

(3) (4)

Quick Tips: You can eliminate answer choices A and B because they are too low to get Adrian’s overall average up to a 100

If a value is counted twice, then the value is technically two numbers that count towards the mean

43. 800 liters A

Tools: indirect variation Steps: (1) “inversely” signals that we need to use inverse variation (

)

(2) Input the temperature for x since it affects the amount of water in the pool

(3)

(4) Now that we know our constant, we can input the new temperature

(5)

Quick Tips: Indirect variation is different from direct variation in that you cannot solve this problem using a proportion

44. B

Tools: solving quadratic equations Steps: (1) Since is a single value, we can treat it as such

(2)

(3) (4) Solve by factoring the quadratic out (5) (6)

Quick Tips: Input these values into the original equation to test your answers

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45. √ C Tools: tangent to a circle Steps: (1) If an object is tangent to a circle, the angle formed is ; thus, the triangle is a

triangle and its ratio applies (2) Since the base, or side length opposite the , is equal to 4, then the height of

the triangle, or side length opposite the , is √ (3) Find the area of the triangle

(4)

√

√

√

Quick Tips: Be sure to keep your ratios for the side lengths of straight opposite side length will always be the smallest value

46. [

] D

Tools: scalar multiplication Steps: (1) The value in front of the A is the scalar that we must multiply to each value in

the matrix (2) row 1, column 1: (3) row 1, column 2: (4) row 1, column 3: (5) row 2, column 1: (6) row 2, column 2: (7) row 2, column 3: (8) row 3, column 1: (9) row 3, column 2: (10) row 3, column 3:

Quick Tips: Each product remains in the same place as its multiplier The product for row 1, column 1 is only found in answer choice D, so you can

stop multiplying after the first number

47. 125 B

Tools: multiplying polynomials Steps: (1) Look to the first and last terms in the larger polynomial and determine the

factors for both (2) and (3) If you setup three empty parentheses with the c’s and d’s in each parenthesis,

you will see it is the same as the original binomial of (4) Since , replace each parenthesis with the value of 5 and multiply (5)

Quick Tips: If the first and last terms in a polynomial are taken to the power of 3, create three parentheses and look to the factors of the first and last terms

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Essay

What is something you have accomplished that has made a great impact on you? Brainstorming The prompt is asking you about something that you have done that has had an effect on your life in some way. After completing this task, you could be a completely different person, or you are more firmly set on the path towards your goals. This accomplishment could be big or small, charitable or self-serving, or serious or hilarious. It doesn’t matter. As long as the thing you accomplishment affected you in some meaningful way, it works. For example:

Victory or defeat in a sport Award won or lost in a competition Book or book series that you’ve read Vacation you’ve taken Community service you’ve completed Family event you’ve attended Church activity in which you’ve participated Individual (human or animal) that you’ve formed a relationship with Goals that you’ve met in and/or out of school Movie that you’ve seen Outline

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Section 5 – Essay (EXAMPLE) 30 Minutes

Please write your essay prompt here.

What is something you have accomplished that has made a great impact on you?

Something that I have accomplished that has made a great impact on me is the

vacation I took to England last year. I had never been outside of the U.S., and I was

very excited when my parents told me we would be flying to London right after my

midterms. My classmates and I had just learned about Shakespeare in English and

read abridged versions of several of his plays, so my parents thought it would be a

great idea to visit his home. Plus, we had been learning about Stonehenge and various

other ruins in History, and my parents said I should see some of them in person.

Upon visiting Stratford-upon-Avon, Stonehenge, and the museums in London, my

interest in the world outside of my home and school grew immensely.

Although we spent the first day of the trip walking around London, I like to say our

trip really started on the second day when we drove to Shakespeare’s hometown,

Stratford-upon-Avon. The village was beautiful, but I really wanted to see the home of

“The Father of English Literature,” as my teacher would say. A woman greeted us with

the introduction to his “Romeo and Juliet,” and I was impressed with how easily she spoke

Shakespeare’s words. Then, I felt so strange as we entered his home, and a wave of goose-

bumps swept over me. I could imagine Shakespeare playing about the house and

growing up to be the man who would forever change the English language. By just

standing in the middle of his home, I felt a respect for Shakespeare that was greater than

anything I had felt in the classroom.

On the third day of our trip, we ventured out to see Stonehenge. I had seen pictures

and information on Stonehenge, but I honestly had no idea what to expect. When we

arrived, I looked out at the ruin and felt the same strange feeling as I did in

Shakespeare’s home. Stonehenge was amazing. We arrived early, so the sun hit the

stones in a way that made them seem mystical. I didn’t even bother to listen to the

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audio tour as I slowly circled the ruin. We learned about so many ruins in History, but

here I was standing near one of the most well-known. Someone placed these enormous

stones here centuries ago for a purpose we still haven’t quite figured out, and I walked

on the same ground they did all those years ago. I eventually walked back to our rented

car in a daze, and I spent the rest of the day thinking about the people who built

Stonehenge and what it would be like to meet them in person.

Even with Stratford-upon-Avon and Stonehenge nearby, London is not empty of its

own wonders. For the rest of our trip, we visited many museums and saw equally

amazing things as Shakespeare’s home and Stonehenge. In particular, I was most

interested in the Rosetta Stone, the large stone tablet that allowed us to decipher several

ancient languages. The Rosetta Stone was at the forefront of the British Museum’s

collection, and tons of tourists surrounded its glass case. The stone was much larger

than I anticipated, and I could clearly see the various markings covering it. Just as with

Shakespeare’s home and Stonehenge, I suddenly imagined scientists discovering the

Rosetta Stone and marveling at the opportunities it presented to understanding ancient

languages. It was amazing to me that a rock could open so many doors to solving

history’s secrets. I wanted to know what other seemingly mundane object was the key

to more of history, and we scoured the British Museum searching for them.

All in all, my family’s trip to England was an eye-opening experience. I saw with

my own eyes the makers of all that I was learning in school and not just from what I

was reading in class. My family and I even discussed everything we had seen over

afternoon tea in the British Museum, which is something I had never done with what I

learned in school over dinner at home. I was truly excited about learning, and my trip

to England still fuels that excitement to this day. In the end, visiting Stratford-upon-

Avon, Stonehenge, and London’s museums opened me up not only to information but to

the desire for that information. I can’t wait for our trip to South America next year to see

the all of the ruins there!