Act Sci Eng Math

8/10/2019 Act Sci Eng Math

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A. As I grew older, I found I had a talent for numbers, and studiedaccountancy.B. Twenty years later, I had gone into engineering, and soon went towork for NASA.C. Throughout high school, I studied acting and drama, and beganworking with dinner theatre after graduation.D. It took me several years, but by the time I was 20, I hadgraduated from clown college and begun working with a smallfamily-run operation.Note: The next set of questions is based on a passagefrom How to Tell a Story and Other Essays by Mark Twain.

6. The humorous story depends for its effect upon the manner of thetelling; the comic story and the witty story upon the matter.A. NO CHANGEB. the telling the comic story

C. the telling-the comic storyD. the telling: the comic story

7. The humorous story may be spun out too grate length, and maywander around as much as it pleases, and arrive nowhere inparticular; but the comic and witty stories must be brief and end witha point.A. NO CHANGEB. to grateC. too greatD. to great

8. The humorous story bubbles gently along, the others burst. Thehumorous story is only a work of art--high and delicate art--and onlyan artist can tell it; but no art is necessary in telling the comic andthe witty story; anybody can do it.A. NO CHANGEB. strictlyC. mainlyD. potentially

9. The art of telling a humorous story--understand, I mean by word ofmouth, not print-was created in America, and has remained at home.The humorous story is told gravely; the teller does his best toconceal the fact that he even dimly suspects that there is anythingfunny about it; but the teller of the comic story tells you beforehandthat it is one of the funniest things he has ever heard, then tells itwith eager delight , and is the first person to laugh when he getsthrough.A. NO CHANGEB. great hurry


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C. eager laughterD. some reluctance

10. And sometimes, if he has had good success, he is so glad andhappy that he will repeat the "nub" of it and glance around fromface to face, collecting applause, and then repeat it again. It is apathetic thing to see.A. NO CHANGEB. pointC. summaryD. punchlineNote: The next set of questions is based on a passagefrom Common Sense by Thomas Paine.

11. Perhaps the sentiments contained in the following pages, arenot YET intensely fashionable to procure them general favour; along habit of not thinking a thing WRONG, gives it a superficial

appearance of being RIGHT, and raises at first a formidable outcryin defense of custom.A. NO CHANGEB. prohibitivelyC. sufficientlyD. OMIT

12. But the tumult soon subsides. Time makesmore converts than reason.A. NO CHANGEB. opponents

C. argumentsD. OMIT13. As a long and violent abuse of power, is generally the Means

of calling the right of it in question (and in Matters too which mightnever have been thought of, had not the Sufferers been aggravatedinto the inquiry) and as the King of England hath undertaken in hisOWN RIGHT, to support the Parliament in what he calls THEIRS,and as the good people of this country are grievously repressedby the combination , they have an undoubted privilege to inquireinto the pretensions of both, and equally to reject the usurpation ofeither.A. grievously oppressed, and by the combinationB. grievously oppressed by the combinationC. grievously repressed in the combinationD. grievously repressed, and in the combination

14. In the following sheets, the author hath studiously avoidedevery thing which is personal among ourselves. Compliments as wellas censure to individuals make no part thereof. The wise, and the


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EngQ1-Answer: The best answer is D. This option precisely defines thelocation wherein the subject of the sentence-the man in the silver suit-canbe found. The sentence as is contains the correct information, but thephrasing interrupts the flow of the sentence, and unnecessarily includes

the specifier "one" in the phrase. Option B is inconclusive, as the center ofthe rings may not necessarily include the inside of a ring, depending onhow the rings are arranged. Option C is incorrectly phrased, as the "one"incorrectly modifies the phrase "center ring." Thus, the best answer isoption D, as it contains the necessary information in a phrasing that is bothfactually and structurally correct.EngQ2-Answer: The best answer is B. The use of "pacing" implies arepetitive motion over a limited space, and as the rest of the phraseidentifies the lion as being inside a cage, no further information is needed.Option A is not appropriate in this case, as it is stylistically incorrect and

contains redundant information. Option C is also redundant, and contains astylistic error; "between the sides" in this context is not a common usage,and is confusingly phrased for most readers. Back and forth is a commonadjectival phrase, but back and forth motion is implied in the word "pacing,"so option D would also be redundant. Thus, the best option is B, as itshortens the sentence to a succinct phrasing and eliminates unnecessaryinformation.EngQ3-Answer: The best answer is C. Since the previous sentence wasspecifically about the lion in his cage, a peripheral mention of the lion'scage that illustrates the subject of this sentence and its relationship to thecage is a solid transition. While the previous sentence mentioned clownsas well, they were not the subject of the sentence, and so the relationshipbetween sentences would not be firmly and logically established by atransition using them. Aerialists were not mentioned at all in the previoussentence, and neither were customers; as a result, there is not a factualbasis on which a transition can be anchored. Thus, the best option is C,which connects the subjects of the sentences and allows for a smooth andlogical transition between them.EngQ4-Answer: The best answer is A. This sentence is written from afirst-person perspective, as illustrated by the use of "I" and "my" forpronouns, so descriptive information that reinforces the "I" point of viewwould be the best choice for adjectives. Option B has redundant phrasing,as arched implies a certain degree of height; overhead can also beinterpreted as redundant in this context, but it is common usage to includeit. Option C is grammatically correct, but is more suited to an impersonalsentence in this context. Option D also contains redundant phrasing and isidiomatically incorrect when combined with the final clause of thesentence. Option A fits smoothly into the first-person perspective, is


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idiomatically correct and completes the metaphor logically; thus, option Ais the best choice.EngQ5-Answer: The best answer is D. The mini-passage expresses thelove the narrator has for circuses, and is written using the past tense,which implies a looking back from the present time and also implies astrong connection with circuses. Option A expresses a change in time, butdoes not link the subject of the sentence thematically with the passage anddoes not follow logically. Option B contains a correct time transition, butalso has no thematic connection to the passage. Option C has both a timetransition and a weak thematic connection, but does not develop it in aconsistent fashion with the passage. Only option D has both the thematicconnection and a time transition, which makes option D the correctanswer.EngQ6-Answer: The best answer is A. The bolded section highlights abreak between clauses in the sentence, and the second clause is a

dependant clause, meaning it cannot stand alone as a sentence. Since thedependant clause requires punctuation to conjoin it to the previous clause,option B would not be an appropriate choice. Hyphens are used to formcompound words, so option C would not be acceptable either. Option Dwould not be the best choice because colons are used primarily to formlists or join clauses (usually parallel or independent clauses). Since theclause beginning with "the comic story" is a dependant clause, the semi-colon would be the most accurate selection from the available options. Asa result, option A is the best choice.EngQ7-Answer: The best answer is D. In the context of the sentence, the

bolded phrase is being used to describe the quality of length, so thephrase as is would not be appropriate to the sentence, which wouldeliminate option A. The word "grate," which is most commonly used as averb for rubbing something against a serrated surface or a noun for ametal hatch cover, would have no bearing on the prepositional phrase, sooption B would not be an acceptable choice. From the context of thesentence, the word "too" as a quantity descriptor is not the proper use, sooption C would not be acceptable. The prepositional phrase "to great" is incontext the only proper choice, so option D would be the correct answer.EngQ8-Answer: The best answer is B. The author is making the point thata humorous story is already a work of art, so adjectives like "potentially"are not correct, eliminating option D. Along these lines, adjectives like"mainly" imply there is some sense in which the term being modified doesnot fully meet the qualification. Since the passage clearly states that thehumorous story is a work of art, such adjectives are not appropriate, andthus option C is not correct. Although the definition of "only" might seem tomake a good fit, the connotation of the word implies a limitation that doesnot match the author's intent, so option A is not correct. The use of the


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word "strictly" does not have the same connotation, and rules out any judgment that the humorous story is not art, which aligns closest with theauthor's intent. Thus, option B is correct.EngQ9-Answer: The best answer is A. The author is drawing acomparison between storytelling styles, and in regard to the comic story,the author demonstrates that the comic story teller makes clear his or herdelight or high opinion of the story. Thus, option D would not be suitable,as the story teller is interested in sharing the tale. A story is generally notrushed in its telling in order to impart maximum information and impact, sooption B would not work in this example. The clause immediately followingthe bolded section says the story teller laughs at the story; in context, thatis the proper placement of the mention of laughter, and other mentionswould be redundant, so option C is not relevant. The term "eager delight"most clearly identifies the story teller's frame of mind in relating a comicstory, so option A would be the correct choice.

EngQ10-Answer: The best answer is D. The author refers to the narrativeclimax of the comic story as being the aspect of the story that generateslaughter. Modern common parlance has different meanings for the word"nub," so in this context, option A would not be suitable. Although the pointof the story may indeed be the central theme meant to be communicated,the expression of the humor is usually more important than the content, sooption B would also not be suitable in this context. A summary of a storythat had just been told would be unnecessarily redundant in virtually allsettings, so option C would not be correct. However, the punchline, orhumorous conclusion, would be the part of the story most likely to elicit

laughs even if repeated, and thus, option D is the correct answer.EngQ11-Answer: The best answer is C. From the context of the sentence,the reader can see that the adverb must modify "fashionable" such that thenext action becomes more likely, and as written, the bolded adverb fails todo that. Thus, option A is not correct. Using "prohibitively" as the adverbwould modify the term such that the end result is exactly opposite of whatthe context implies, so option B is not correct. Given the sentence'sconstruction, an adverb must be used at that location, as "yet" and"fashionable" would not be used correctly without one, so option D is notcorrect. Only option C, with its adverb modifying the term in a positivefashion to agree with the rest of the clause, correctly completes thesentence; thus, option C is correct.EngQ12-Answer: The best answer is A. The author intends to reinforcethe first sentence with the reason expressed in the second sentence, sothe sentences must logically agree. If option B is used, then the sentenceslogically contradict each other and the point is negated. Therefore, optionB is not correct. By the same token, option C is not correct, as using it inthe second sentence also creates a logical negation of the first sentence.


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The sentence structure would be incorrect if option D is selected, as therewould be no term for "more" to modify, so option D is not correct. Onlyoption A offers a logical completion of the second sentence and allows it tocomplement the first sentence; therefore, option A is the correct answer.EngQ13-Answer: The best answer is B. The author is describing anaction taken against a population by a political entity-in this case, KingGeorge III is taking action against the population of the American colonies-so the word "oppress" is the more correct term to use in this situation.Thus, options C and D are automatically excluded, since they use"repress" in their construction. Furthermore, the agent of the tyrannicalaction being taken is a compound of the English king's actions andParliament's, so the term "combination" has a direct relationship to theaction. Given the relationship and the context of the sentence, using acomma to separate the terms would be incorrect, so option A is notsuitable. Only option B uses the correct terminology and punctuation, so

option B is the correct answer.EngQ14-Answer: The best answer is C. In the context of the sentence,the author is using compare and contrast to list what is not included in hiswork. Since the first term is "compliments," the second or contrasting termmust be a word opposite in meaning. Option A is not suitable, as aconundrum is a puzzle or riddle and thus does not fit the author's intention.Option B is also not suitable, as catharsis is an emotional purging and thushas no relation to the sentence. Likewise, option D would not be correct,as a conference also has no relation to the sentence. Only option C, whichholds an opposite definition to compliment, suits the author's contextual

intention, and so option C is the correct answer.EngQ15-Answer: The best answer is B. Reducing the number ofadjectives to one in the sentence would have little effect on the meaning ofthe sentence, as it would have only changed the structure without alteringthe primary adjective. Thus, option A would not be correct. Generally,reducing adjectives makes a sentence more direct but detracts from itsdescriptive nature, so option C would not be correct either. Since formaldiction depends more on tone and syntax than specific numbers of words,option D would not be suitable here either. Only option B, which directlyrefers to the emotional impact of the sentence (and is achieved by gettingdirectly to the point), would be a suitable choice for the suggested change;thus, option B is correct.EngQ16-Answer: The best answer is D. At the time of writing, allgovernments in the Western world (defined in this case as Europe west ofRussia) were as the author identified, so option A would not be suitable.However, there are more than two types of government-for example,democracy as practiced by the Greeks is not mentioned-so option B is notcorrect, as it identifies a condition that the passage has not met. Although


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the author is known as a political philosopher, the opening of the passageexplicitly defines the state as one of the types of government he goes on todiscuss, so option C is not relevant, as the author is discussinggovernments. Only option D strictly defines the purpose of the passageand how it relates to the stated goal of the question; thus, option D iscorrect.EngQ17-Answer: The best answer is B. While commas have multipleuses, their primary usage, and the one the author intends here, is toseparate items in a list. If the comma is placed after the first coordinatingconjunction, as in option A, the emphasis changes from a list to a specificsub-clause; as the rest of the sentence is clearly numerating a list, option Ais therefore not correct. Option C illustrates a comma where neithergrammar nor rhythm would indicate a comma belongs; thus, option C isnot correct. Option D shows a run-on phrase, which in the context of thesentence is incorrect, as it does not correctly demonstrate the list structure

the author intends, and so option D is incorrect. Only option B, whichcorrectly places the comma to illustrate items in a list, fits the context andstructure of the sentence; thus, option B is correct.EngQ18-Answer: The best answer is D. Value judgments such as"interesting," while commonly used in teaching situations, are subjectivemeasurements, and do not reflect the inherent structure or meaning asmuch as the reader's bias. As a result, this option is not valid for thisexample, so option A is not correct. In order for "precise" to apply, thereplacement clause would have to strictly and carefully define a conditionrather than restating it in fewer words. Since this is not the case, option B

is not correct. The change in terms does not carry an emotional weight or asense of urgency, so option C is not suitable. Only option D, whichaccurately describes the condition of expressing more ideas in fewerwords, properly describes the effect of the substituted phrase, so option Dis correct.EngQ19-Answer: The best answer is A. In order for the bolded words tofunction as nouns, they would have to describe a person, place or thing; inother words, something concrete, which neither word does. Therefore,option B is incorrect. Since neither word describes an action that thesubject of a sentence could take or perform, neither word can function as averb. As a result, option C is also incorrect. While the bolded words domodify a word in the sentence in degree, the term being modified-force-isnot a verb, adjective or adverb in itself; in this case, force is a noun.Therefore, the bolded words fail to meet the condition of adverbs, so optionD is incorrect. Since the bolded words modify a noun, they act asadjectives, and so option A is the correct choice.EngQ20-Answer: The best answer is D. The sentence's construction andcontext indicate the author is drawing a conclusion about the nature of


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Note: Unless otherwise stated, all of the following should beassumed. Illustrative figures are NOT necessarily drawn to scale.Geometric figures lie in a plane.The word line indicates a straight line.The word average indicates arithmetic mean.

1. If x2 - mx - 27 = 0 when x = 6, what is the value of m?A. 1.5B. 2C. 3.5D. 5

2. For all x, what is the simplest equivalent of (2x)(x)(2x)(x)(x)?A. 2x6 B. 4x6 C. 4x5

D. 6x3

3. Given that the above triangle is isosceles, if angle WXY is 44, what

measurement must angle XWY have?A. 64B. 68C. 72D. 76

4. If segment WY is 16 units long and segment XZ is 15 units long,how long is segment WX?


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A. 17B. 18C. 19D. 20

5. Given the equations 2x + 2y = 16 and 4x - 3y = -3, what are thevalues of x and y?A. x = 4, y = 6B. x = 2, y = 4C. x = 3, y = 5D. x = 5, y = 3

6. Two friends take a drive around the city. When they get home, theylook at the odometer and their watches, and determine they traveled54 miles in 72 minutes. What was their average speed in miles perhour?

A. 40 miles/hrB. 45 miles/hrC. 50 miles/hrD. 55 miles/hr

7. Provide the simplest equivalent expression to ! 72.A. 8! 3B. 4! 18C. 8! 12D. 6! 2


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8. Given the curve as sketched out on this graph, what is the domain of

the function seen here?A. -5 < x < 6B. -6 " x " 2C. -5 " x " 6D. -6 < x < 2

9. Given the curve as sketched on this graph, what is the range of thefunction seen here?A. -5 < y < 6B. -6 " y " 2C. -5 " y " 6D. -6 < y < 2

10. A student cuts out a cardboard circle that has a radius of 8inches. What is the total circumference of the circle?A. 8# inches

B. 12# inchesC. 16# inchesD. 20# inches

11. As part of a wood shop project, two students build a cabinetthat is 6 feet tall, 2 feet wide and 3 feet deep. Half of the cabinet'sinterior volume will be used for storing tools, leaving the other half


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free for personal items. How much volume will be available forstudents to use?A. 18 cubic feetB. 24 cubic feetC. 36 cubic feetD. 48 cubic feet

12. Given two variables x and y that are directly proportional suchthat x = 3 when y = 8, what value will y have when x = 6?A. 12B. 16C. 20D. 24

13. A student enrolls in a course where the final grade is anaverage of four exams. Before the final exam, the student reviewsthe previous three exam scores, which were 89, 97 and 88. What

score would the student have to receive on the last exam to achieveat least a 90 average for the course?A. 78B. 82C. 86D. 90

14. A teacher goes to the local big box store to purchase suppliesfor a class activity. The teacher buys two bags of apples for a classsnack, and four bottles of glue. The total comes to $5.00 for theapples and $6.50 for the glue. Sales tax for food items is 6%, and for

non-food items is 4%. How much total tax does the teacher pay forthe purchases?A. $0.36B. $0.42C. $0.49D. $0.56


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15. Given the points on the line with the labeled coordinates, what

is the slope?A. 1/3

B. 1/4C. 1/5D. 1/6

16. Having determined the slope of the line, what is the slope-intercept equation of the line shown passing through (6,5)?A. y = 2/3 x + 2B. y = 1/3 x + 1C. y = 2/3 x + 4D. y = 1/3 x + 3

17. A rectangle is three times as long as it is wide. If the total areaof the rectangle is 48 square inches, what is the length of therectangle?A. 3 inchesB. 9 inchesC. 12 inchesD. 18 inches

18. As a prize for winning a game at school, a student gets to picka colored egg from a box. Each egg has a slip of paper inside it


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describing the prize. Red eggs are for candy, blue eggs are for toys,and green eggs are for books. There were 12 red eggs in the box, 8blue eggs and 15 green eggs. Students must draw blind, and theprevious student to draw pulled out an egg for a book. What are thechances that the next student to draw will get an egg for a toy?A. 15/34B. 8/34C. 12/35D. 20/35

19. A physicist is studying a radioactive element in a lab that hasa half-life of 21 days, meaning after 21 days, half of the samplewould be inert. If the initial sample of the element was 500 grams,and the study was scheduled to continue for a total of 12 weeks,how much of the element would still be radioactive at the end of thestudy?

A. 125 gramsB. 93.75 gramsC. 62.5 gramsD. 31.25 grams

20. A student has to finish up work on a project for metal shop.The last piece that needs to be finished is the painting of a metalsphere for the top of a large diorama. The sphere has a radius of 8inches, and must be painted with two coats of paint in order to bepresentable. A quart of the paint the student has in shop class willcover 450 square inches of metal. How many quarts will be sufficient

to paint the sphere with two coats?A. 3B. 4C. 5D. 6


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MaQ1-Answer: The answer is A. If the expression x 2 - mx - 27 = 0 when x= 6, then substituting 6 for x yields (6) 2 -m(6) -27 = 0, which simplifies to 36- 6m - 27 = 0. Adding 27 to both sides of the equation yields 36 - 6m = 27,and adding 6m to both sides yields 36 = 27 + 6m. Subtracting 27 from bothsides shows 9 = 6m; dividing both sides of the equation thus yields m =1.5. To check, substituting 1.5 for the value of m when x = 6 gives 36 -(1.5)(6) - 27 = 0; since (1.5)(6) = 9, the equation simplifies to 36 - 9 - 27 =0, which is correct. Thus, option A is correct.MaQ2-Answer: The answer is C. For any expression of x, multiplying aquantity of x by another quantity causes the exponent of the result to bethe sum of the previous exponents. Thus, (2x)(2x) = (2 * 2)(x * x) = 4 (x *x); since x is understood to have an exponent of 1, this is equivalent to 4(x1 * x1), which yields 4x 2. Now, the original expression can be simplified to4x2(x)(x)(x). By the same token that the first part was reduced to 4x 2,(x)(x)(x) can be simplified to x 3, which leaves the original expression

reduced to (4x2)( x

3). Finally, the compound expression (4x

2)( x

3) can besimplified to 4x 5, which demonstrates that option C is the correct answer.

MaQ3-Answer: The answer is B. Due to the properties of a triangle,angles that abut sides of an isosceles triangle must be the same size, soautomatically angles XWY and XYW must have the same measurement.Since the sum of internal angles of a triangle must add up to 180 in planegeometry, the first step to determining the measurement of XWY is tosubtract 44 from 180, which yields an answer of 136. This is the sum of thetwo base angles of the triangle; thus, by dividing the sum by two, we getthe measure of each of the angles. Dividing 136 by 2 yields the answer of

68, which is the measurement of angle XWY; thus, option B is the correctanswer.MaQ4-Answer: The answer is A. Since segment XZ makes a right anglewith WY, the properties of a triangle indicate that segment WY is bisectedby XZ, meaning segment WZ is 8 units long. Thus, since triangle WZX is aright triangle with segments that are 8 units and 15 units long, thePythagorean theorem can be used to determine the length of triangleWZX's hypotenuse, which in this case is segment WX. So, by plugging inthe known values into the equation form of the theorem a 2 + b 2 = c 2, theresult is (8) 2 + (15) 2 = c 2, c in this case being segment WX. Thus, theequation gives the result 64 + 225 = c 2, which simplifies to c 2 = 289. Thesquare root of 289 is 17, so c = 17, which demonstrates that option A is theanswer.MaQ5-Answer: The answer is C. One method of solving these equationswould be to multiply both equations by numbers that create equivalent yterms, then add the equations and cancel out the y term to solve for x. So,if the first equation is multiplied by 3 and the second equation is multipliedby 2, the new equations are 6x + 6y = 48 and 8x - 6y = -6. Adding these


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equations together cancels the y terms, and leaves 14x = 42. Divide bothsides by 14 to get x by itself, and the result is x = 3. Solving for y in the firstequation yields 6 + 2y = 16; subtract 6 from both sides to get 2y = 10, andthus y = 5. Placing the values for x and y in the second equation yields 12 -15 = -3, which is correct. Thus, option C is correct.MaQ6-Answer: The answer is B. In order to determine the average speedin miles per hour, determine the average speed per minute by dividing thedistance traveled by the time it took to travel the distance, then multiplythat result by 60 (since there are 60 minutes in an hour) to get the averagespeed in miles/hr. Thus, if they traveled 54 miles in 72 minutes, theiraverage speed in miles per minute was 54/72, which equals 0.75miles/minute. Since there are 60 minutes in an hour, multiply 0.75miles/minute by 60 minutes/hour, which yields (0.75)(60) miles/hour, whichequals 45 miles/hour. Thus, their average speed was 45 miles/hr, whichdemonstrates that option B is the correct answer.

MaQ7-Answer: The answer is D. In order to determine the simplestexpression of a square root, it is generally best to factor out the squareroot to its smallest numbers and simplify those. For example, since 72 = 8* 9, ! 72 can be written as the product of ! 8 and ! 9. Thus, ! 72 = ! 8 * ! 9.Since ! 9 = 3, ! 72 = 3 ! 8. However, by the same token as the previoussimplification, ! 8 can be written as ! 4 * ! 2. Since ! 4 = 2, the expressioncan now be written as ! 72 = 3 * 2 * ! 2, which is equal to 6 ! 2. Thus, it isdemonstrated that ! 72 is equal to 6 ! 2, and therefore option D is correct.MaQ8-Answer: The answer is C. In this example, the domain would bethe set of all values of x available on the curve plotted on the graph. The

outer limits of the function are defined by the endpoints; thus, all thepossible points in the domain must lie between the x-values of theendpoints. Since the endpoints are filled-in circles, this indicates that the x-values of the endpoints are included in the domain. Thus, since the leftside of the curve terminates in a closed circle at x = -5, that means that xcan be equal to or more than -5. Similarly, since the right side of thefunction terminates in a closed circle at x = 6, x can be equal to or lessthan 6. Therefore, the relationship of x in this domain is -5 " x " 6, thusdemonstrating that C is the correct answer.MaQ9-Answer: The answer is B. Similarly to the answer to the previousquestion, the range of the function is, in this case, the set of y-valuesavailable on the curve plotted on the graph. Unlike the domain, however,the range is not defined by the endpoints, but the extremes of the curvethat are reached along the y-axis. For example, the smallest value for y isreached at x = -3, instead of x = -5 as would be expected if the endpointswere the defining part of the curve for the y-values. As seen on the graph,the smallest value of y on the curve is -6, so -6 is the lower bound for therange. By the same token, the highest y-value the function reaches is 2.


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Therefore, the range is best written as -6 " y " 2, demonstrating that optionB is correct.MaQ10-Answer: The answer is C. In order to determine thecircumference, or the distance around the outer edge of a geometric figure(which can also be thought of as the perimeter) of a circle, it is necessaryto use the formula C (circumference) = 2 # r, where r is the radius, ordistance from the center of the circle to its edge. In this case, the problemgives the radius as being 8 inches, so in order to compute thecircumference, plug in the value of 8 inches for the radius, which yields C =2# (8 inches). Multiplying through yields an answer of C = 16 # inches,which demonstrates that option C is the correct choice.MaQ11-Answer: The answer is A. In order to figure out the volume of arectangular solid, the formula used is V = hwd, where h is height, w iswidth and d is depth. In this case, the variable h is 6 feet, the variable w is2 feet and the variable d is 3 feet. Plug the values into the formula, and the

result is V = 6 * 2 * 3, or 36 cubic feet. However, the preconditions listed inthe problem state that only half of the total interior volume will be availablefor use, so that figure will have to be divided by 2. Thus, we get 36/2, or18, which yields the answer of 18 cubic feet. Thus, option A is the correctchoice.MaQ12-Answer: The answer is B. Since the information given states thatx and y are in direct proportion such that their ratio is the same as 3 to 8,the best way to visualize the problem is to set up two ratios side by side,presented as x/y = 3/8. Since the problem asks the reader to solve for ywhen x = 6, the ratio can be further modified to read 6/y = 3/8. In order to

set up the relationship for y, perform cross-multiplication of terms to get theequation 3y = 6 * 8, or 3y = 48. Dividing both sides of the equation by 3yields y = 16, thus demonstrating that option B is the correct answer.MaQ13-Answer: The answer is C. In order to achieve a 90 average overthe course of four exams, the scores of the exams must add up to 360,which when divided by the number of exams comes out to 90. According tothe information given in the problem, the student received 89, 97 and 88for the first three tests. When summed, 89 + 97 + 88 = 274. So, in order toget a 90 average, the student must make up the difference between thepresent score total and 360 in order to average out to 90. Thus, 360 - 274= 86, which is the minimum score the student must get to achieve a 90average, demonstrating that option C is the answer.MaQ14-Answer: The answer is D. Since the sales tax differs for differentkinds of items, the separate tax bills must be calculated and then addedtogether to determine the total. If the teacher paid $5 for food and the salestax is 6%, then the sales tax is calculated by multiplying $5 by 0.06, whichequals $0.30 or 30 cents. Next, the sales tax for non-food items iscalculated by multiplying $6.50 by 0.04, which equals $0.26 or 26 cents.


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Thus, the total tax bill is determined by adding the two separate tax totalstogether; $0.30 + $0.26 = $0.56, or 56 cents, which demonstrates thatoption D is the correct answer.MaQ15-Answer: The answer is A. The slope of a line is defined by thetotal of the rise on the y-axis divided by the total of the run on the x-axis,using the formula m (slope) = y2-y1/x2-x1 . In this case, if (6, 5) is used asthe second pair and (-3, 2) is used as the first pair, the value for m with thegiven values becomes (5-2)/6-(-3). Since subtracting a negative number isthe same operation as adding a positive number, the formula yields m =3/9, which simplifies to m = 1/3. Thus, the slope of the line is 1/3,demonstrating that option A is the correct answer.MaQ16-Answer: The answer is D. The slope-intercept equation of a line isgiven as y=mx+b, where m is the slope and b is the constant where theline crosses the y-axis. There are different approaches to figuring out theequation, but given the slope and the set of coordinates the line passes

through, solving for b to obtain the intercept equation is the simplest.Substituting the slope and the coordinates into the formula yields5=1/3(6)+b, which simplifies quickly to 5=2+b, and by subtracting 2 fromboth sides, 3=b. Thus, with the value for b in hand (which is corroboratedby the graph in the previous question), the slope-intercept equation can bewritten as y=1/3 x+3, demonstrating that option D is correct.MaQ17-Answer: The answer is C. The area of a rectangle is determinedby multiplying length by width. In this case, if width is assigned the value x,then the length must be 3x as given in the problem. Thus, the area is(3x)(x), or 3x2. Since the value of the area is given as 48 square inches, it

is clear that 3x2=48, Dividing both sides by 3 yields x2=48/3, or x2=16. Bytaking the square root of both sides of the equation, it demonstrates that x,or the width of the rectangle, is 4 inches. Since the length was given asthree times the width, the next step is to multiple the width of the rectangleby 3, which yields 3*4=12. Thus, the length of the rectangle is 12 inches,demonstrating that option C is correct.MaQ18-Answer: The answer is B. The odds are figured by comparing thetotal number of a chosen option versus the total number of options that canbe selected. To begin with, there were a total of 35 eggs in the box(12+8+15=35), 8 of which were blue, which means there were 8 that wouldyield a toy if chosen. The previous student to draw pulled a green egg,which does not yield a toy; thus, the total number of options decreased byone to 34, but the total number of blue eggs remained at 8. Thus, for thenext draw, the chances of pulling a blue egg and getting a toy were 8 outof a total of 34 eggs in total. Therefore, the chances of getting a toy were8/34, demonstrating that option B is correct.MaQ19-Answer: The answer is D. If half of the sample decays into aninert state every 21 days, or three weeks, then determining the amount of


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sample left is a matter of plotting the decay against the time frame. Sincethe initial sample was 500 grams, the remaining radioactive part of thesample would be half that at 21 days, or 250 grams. After another threeweeks, at the 6-week point, the sample would have halved again, to 125grams still radioactive. At the 9-week point, the sample would have halvedagain, this time to 62.5 grams. Finally, at the 12-week point and the end ofthe study, the sample would have halved again, this time to 31.25 grams.Thus, option D is the correct answer.MaQ20-Answer: The answer is B. The surface area of a sphere is definedby the formula S = 4pr2, where r is the radius of the sphere. Since theradius is given as 8 inches, S can be determined by plugging in the values,which yields S = 4p(8)2, which yields S = 256p square inches, which isroughly equal to 804 square inches. However, since the sphere must begiven two coats, the amount of paint must be sufficient to cover roughly1608 square inches, or two coats of 804 square inches. Since the paint

must cover 1608 square inches, and each quart covers 450 square inches,the number of quarts needed is determined by dividing 1608 by 450, whichyields 1608/450, roughly equal to 3.57 quarts. Through rounding, thenumber of quarts needed is determined to be 4, thus demonstrating thatoption B is correct.


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1 Given the diagram showing identical levels of gas molecules in different

containers, a reasonable inference could be made that there is arelationship between:A. temperature and pressureB. volume and pressureC. temperature and densityD. volume and temperature 2 The relationship between the variables in this diagram is best describedas what type of relationship? A. directB. proportional

C. inverseD. exponential 3 The expression of the relationship between the demonstrated variablesis most commonly known as: A. Coulomb's lawB. Newton's second lawC. Ohm's lawD. Boyle's law 4 Given the information displayed in the diagram, which equation usingthe terms p (pressure), V (volume) and k (constant value) best describes

the relationship between the variables?

A. V=p/kB. pV=kC. pk=V$ D. k=p/V


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9. Given the information in the chart, if a student were to apply heat toequal volumes of all four liquids along with a volume of water, whichliquids would boil before the water?A. Q and SB. R and TC. Q and RD. S and T

10. If a student were to pour samples of the fluids (all insoluble inwater) listed in the table into flasks filled with water, which has adensity of 0.998 g/mL, which liquid would form a layer at the top ofthe flask?I. QII. SIII. TA. I only

B. II onlyC. I and IIID. II and III

11. In working with these fluids in a lab environment, which liquidwould require the greatest caution when working with Bunsenburners?A. QB. RC. SD. T

12. If a student is performing an experiment that requires a liquidthat has a density less than water, has a higher boiling point thanwater, and has a distinctive odor, which of the liquids on the chartwould be best to use?A. QB. RC. SD. T


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13. Based on this chart, which population had the least variation

throughout the time period measured?A. turtlesB. dinosaursC. snakesD. crocodilians

14. Which period listed on the chart likely had the largest numbersof each species mentioned co-existing?A. TriassicB. CretaceousC. QuaternaryD. Permian


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19. What is the total time variance experienced for leaf-sheddingperiods as demonstrated in the experiments listed on this chart?A. 8B. 10C. 16D. 23

20. Based on the information listed on the chart, what naturalprocess would the atmospheric additives tested in this experimentbe most affected and likely cause the variance in leaf-sheddingtimes?A. mitosisB. respirationC. photosynthesisD. replication


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ScQ1-Answer: The best answer is B. The information in the diagramshows identical levels of gas molecules at identical temperatures; in thiscase, 20C. Between the two containers, there is an obvious differential insize, but the given information also shows a difference in atmosphericpressure inside the containers. With other factors remaining equal, theinference is that amounts of gas in a smaller volume (as shown on the left)will experience a greater gas pressure than identical amounts placed in alarger container. Since the temperature is the same in both containers,options A, C, and D are automatically eliminated, leaving only option B.Thus, B is the correct answer.ScQ2-Answer: The best answer is C. As demonstrated by the containersin the diagram, when temperature and mass are kept constant, thepressure of a gas contained within a closed area will rise as the volumedecreases, and by the same token, the pressure will fall as the volumeincreases. Since the relationship is not dependant on both qualities

exhibiting the same trend-i.e. as one rises, so does the other-therelationship is not direct, which eliminates option A. Because there is noprecise measurement of the volume of the containers or their differences,there is insufficient data to determine if the relationship follows amathematical progression, which eliminates options B and D. However, theobservation that as one rises the other falls fits the standard definition ofinverse, making option C the correct choice.ScQ3-Answer: The best answer is D. Coulomb's law refers to therelationship between the magnitudes of point electric charges and theirdistance from each other; since the variables under discussion in this

example are volume and pressure, option A can be eliminated. Newton'ssecond law defines the relationship between rate of change in momentumand the force applied to a body, which eliminates option B. Ohm's lawdefines the relationship between current, potential and resistance in acircuit, which eliminates option C. Only Boyle's law, which defines therelationship between volume and pressure of a gas in an environmentwhere temperature and mass are held constant, address the diagram, andthus D is the correct answer.ScQ4-Answer: The best answer is B. In order to reach a constant valuederived from a relationship between the pressure and volume variables,the expression must be made in terms of the constant value; in otherwords, the relationship that creates the constant value must be expressedin those terms, expressing k as the result of the variables and an operator.Therefore, options A and C can be dismissed, as they do not express theequation in terms of k. Given that the relationship between p and V is aninverse relationship (i.e. as one shrinks, the other expands), option Dwould be less likely to adequately express that, as the ratio between theconstant and the variables would vary too greatly for different values of p


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and V. Only option B, which keeps the ratio between the variablesconstant, adequately expresses the relationship, making B the correctchoice.ScQ5-Answer: The best answer is D. The diagram shows an object influid, which is not creating low-pressure areas around it, which eliminatesoption A. Similarly, a whirlpool effect is not being displayed either, whicheliminates option B. While compression is a part of what is being displayedin the diagram (it can be considered to be what is happening at the leadingedge of the object in the fluid), it is secondary to the primary forces here,and is not of enough merit to be listed separately; thus, option C iseliminated. The upward force on the object is countermanding gravity, andthat force in fluid is buoyancy, making option D the correct answer.ScQ6-Answer: The best answer is D. In order to calculate the forceexerted on the object by the fluid, the amount of fluid displaced by theobject needs to be determined. This is done by determining the volume of

the object, and then multiplying it by the density of the fluid, which yieldsthe total displacement. However, the buoyant force must overcome theacceleration of gravity in order to keep the object afloat, so in addition tothe force of the fluid acting upon the object, the acceleration of gravitymust also be considered. Therefore, the fluid displacement must becombined with the acceleration of gravity in order to completely calculatethe buoyant force; since only option D lists all three factors, D is the correctanswer.ScQ7-Answer: The best answer is C. In order to calculate the forceexerted on the object by the fluid, the amount of fluid displaced by the

object needs to be determined. This is done by determining the volume ofthe object, and then multiplying it by the density of the fluid, which yieldsthe total displacement. As in the previous question, the force of gravitymust be considered; however, since gravity acts in a downward direction,the buoyant force acts in an upward direction, and therefore must beassigned a negative number to reflect its opposite orientation. Thus, whilethe absolute value would be derived by using option D (options A and Bare patently incorrect, as explained in the first part), the correct valuereflecting the buoyant force's opposite orientation to gravity is given usingoption C.ScQ8-Answer: The best answer is B. Remember that the formula forbuoyant force if F = -pVg, where p is the fluid density, V is the volume ofthe object and g is the force of gravity (given a negative number becausebuoyant force acts upwards). The boxes are identical in mass, and the fluidhas the same density, so neither of those measurements will change.However, the first box has twice the volume of the second, which means itdisplaces twice the fluid and therefore has twice the buoyant force actingupon the same mass as the second box does. Thus, the second box only


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ScQ13-Answer: The best answer is A. As displayed on the graph, most ofthe species populations had periods of greater numbers, usually followedby die-offs until a stable level was reached or, in some cases, extinction.Option B is unsuitable for this exact reason; the dinosaurs populationreached its greatest numbers in the Jurassic period, then gradually fell untilextinction, showing too much variance to be the answer. Snakesexperienced a greater level of variation, which makes option C incorrect,and crocodilians, despite having a stable population for most of theirmeasured length, experienced a population jump in the Tertiary andCretaceous periods that disqualifies option D. Only turtles, whosepopulation levels remain almost perfectly flat into the Permian period, showthe least amount of variation, making option A the correct answer.ScQ14-Answer: The best answer is B. While all species listed had somepresence in the Triassic period, three of the five species on the chartended there, and the population spread for all but dinosaurs was minimal,

so option A is not suitable. Dinosaurs were not present in the Quaternaryperiod, so option C is not correct. Since only turtles and dinosaurs hadpresence in the Permian period, option D is not correct either. Only in theCretaceous period, where all five listed species had presence and three ofthem were at or near their greatest numbers, does the graph meet thestated goal; thus, option B is the correct answer.ScQ15-Answer: The best answer is D. A quick glance at the chart showsthat of the species listed, turtles and crocodilians were fairly flat at lowernumbers throughout the time periods measured on the graph, anddinosaurs had smaller growth curves overall than snakes and lizards,

which had the most significant numbers of any species listed, regardless ofwhich time period is being examined. Therefore, options A and C can beautomatically eliminated from further consideration. Upon examination ofthe graph, lizards clearly have greater numbers than snakes, as shown bythe graphic distribution through the Quaternary and Tertiary periods, whichautomatically eliminates option B from consideration. Thus, option D is thecorrect answer.ScQ16-Answer: The best answer is B. While all the listed species existedin the Jurassic, a look at the chart shows that all of them continued on intoat least one more period, thereby eliminating option A from consideration.By the Permian period, only two species had continued on-turtles anddinosaurs-which eliminated option C from further consideration. By thePennsylvanian period, which followed the Permian period, only dinosaurswere left according to the graph, so option D is not suitable. Despite theminiscule extent of three of the five listed species, all five did havedurations in the Triassic period according to the graph, so therefore onlyoption B is the correct answer.


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ScQ17-Answer: The best answer is A. Based on the information in thechart, a tree grown in a normal atmospheric mixture took 18 days to shedall its leaves, while a tree grown in a CO2 enriched atmosphere took a totalof 26 days to shed all its leaves. Simple subtraction shows that this is an 8-day difference between the two, and in order to find the percentage, thedifference must be divided by the original time period. Thus, 8 18, whichcan be expressed as 8/18 or, after simplifying, 4/9, or 0.4444, which givesa value of 44%. Therefore, the increase in time to shed all leaves resultingfrom a CO2 enriched atmosphere is 44%, which means option A is thecorrect answer.ScQ18-Answer: The best answer is C. A quick glance at the chart showsthat the control atmosphere led to a total time of 18 days, which was lessthan at least one term but longer than others, so option A can beeliminated. As demonstrated in the previous question, CO2 actuallyincreased the length of time to shed leaves to 26 days, so option B can be

eliminated. The CO2 + O3 mixture did substantially decrease the totalshed time to 10 days, but as the chart shows, using the O3 mix cut it tothree days, the lowest value on the list. Thus, option D can be eliminated,leaving option C as the correct answer.ScQ19-Answer: The best answer is D. As shown on the chart, theshortest period of time for shedding leaves was three days using O3 as anatmospheric additive. The longest period of time was 26 days, using CO2as an atmospheric additive. Since the only measures needed to determinethe total variance are the high and low values, the other twomeasurements can be ignored for this determination. Thus, the total time

variance would be the difference between the longest period for sheddingleaves measured on the chart and the shortest period measured on thechart. Simple subtraction yields the result, which is 26 days minus 3 days,or 23 days total. Thus, option D would be the correct answer.ScQ20-Answer: The best answer is C. Mitosis, or the process of celldivision, is related to virtually all processes performed by trees, but is toogeneral to fit within the scope of this experiment, thus eliminating option A.Likewise, option D can be eliminated, as replication is another process thatis too general to fit within the scope of the experiment. Respiration issuperficially a good fit for this experiment, but with respect to trees, it is asubcomponent of a larger process of photosynthesis, which directly affectsthe life cycle of leaves; it controls the coloration, functionality and point atwhich the leaf falls, making it a far better choice in terms of the experiment.Thus, option B is discarded, leaving option C as the correct answer.


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Writing Essay SampleIndependent Prompt ExampleYour college administration is considering whether or not thereshould be a physical education requirement for undergraduates.The administration has asked students for their views on the issueand has announced that its final decision will be based on how sucha requirement would affect the overall educational mission of thecollege. Write a letter to the administration arguing whether or notthere should be a physical education requirement forundergraduates at your college.(Do not concern yourself with letter formatting; simply begin yourletter, "Dear Administration.")

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