Sat - MC Grawhill part 84 docx

This means that it demonstrates clear and con-sistent competence in that it • develops an insightful point of view on the topic • demonstrates exemplary critical thinking • uses effectiv

Detailed Answer Key

Section 1

One particularly interesting exception to a rule is the

orbit of Mercury For hundreds of years, Sir Isaac

Newton’s laws of motion and gravity stood as a

testa-ment to the power of mathematics to describe the

universe Newton’s equations showed that the moon

did not revolve around the earth because the gods

willed it to, or because of the abstract perfection of a

circular orbit Rather, it circled the earth because

doing so obeyed a simple mathematical formula:

Newton’s Universal Law of Gravitation It was a

sin-gular achievement in the history of science

The equation was not only elegant, but

enor-mously powerful It was used to predict the existence

of two new planets before they were even seen:

Nep-tune and Pluto Astronomers actually began to doubt

the power of the Universal Law of Gravitation when

they noticed that Uranus was not behaving the way

the equation said it should Its orbit was wobblier

than Newton’s law predicted Could the law be

incor-rect? A few careful scientists noticed that the law

could still be correct if another planet, further from

the sun, were tugging at Uranus Indeed, astronomers

looked carefully and found a planet they called

Nep-tune As even further confirmation of Newton’s law,

irregularities in Neptune’s orbit led astronomers to

find Pluto exerting yet another tiny gravitational tug

at the edge of the solar system It seemed that

New-ton’s equation could do no wrong

But it was wrong When astronomers began to no-tice irregularities in Mercury’s orbit, they surmised, naturally, that another planet must be near the sun tug-ging at Mercury They even went so far as to call the undiscovered planet Vulcan But even the most careful observations revealed no such planet How could this equation, so powerful and elegant, be wrong? It turned out that Newton’s equation broke down a bit as gravi-tational force became great, as it did near the sun It wasn’t until the 20th century that Einstein’s theory of General Relativity tweaked Newton’s equation to make

it explain the precession of Mercury’s orbit

The value of Mercury’s orbit, in fact, lies not so much in its ability to “prove” Einstein’s theory as in its ability to disprove Newton’s It was the exception

to a very powerful rule It seems to suggest that, in sci-ence, nothing is truly sacred; everything must be ex-amined If one of the most powerful and elegant equations in all of science—one that had been “proven” time and again by rigorous experiment—could turn out to be wrong (albeit only by a tiny bit, in most or-dinary circumstances), how much can we trust our own beloved “truths” about our universe? So many of

us believe we know at least a few things that are “ab-solutely true.” But can we say that we are more in-sightful, intelligent, or rigorous than Isaac Newton? Perhaps we should be more like the scientists, and look for the holes in our theories

The following essay received 6 points out of a possible 6 This means that it demonstrates clear and con-sistent competence in that it

• develops an insightful point of view on the topic

• demonstrates exemplary critical thinking

• uses effective examples, reasons, and other evidence to support its thesis

• is consistently focused, coherent, and well organized

• demonstrates skillful and effective use of language and sentence structure

• is largely (but not necessarily completely) free of grammatical and usage errors

Consider carefully the issue discussed in the following passage, then write an essay that answers the ques-tion posed in the assignment

We like to believe that physical phenomena, animals, people, and societies obey

pre-dictable rules, but such rules, even when carefully ascertained, have their limits Every

rule has its exceptions

Assignment: What is one particularly interesting “exception” to a rule? Write an essay in which you

answer this question and discuss your point of view on this issue Support your position logically with examples from literature, the arts, history, politics, science and technology, current events, or your experience or observation

When we are children, everyone—parents, teachers

and friends—tells us that we should never lie It’s even

one of the ten commandments in the Bible This is a

rule that many believe should have no exceptions It

is just something you should not do Lying is bad, and

being truthful is good End of story

But I believe that this rule has its exceptions, as

many rules do Sometimes lying can even be

consid-ered the right thing to do It’s obviously not good to

lie just because you don’t feel like telling the truth or

just because you might look better if you lie There

has to be a good reason to deceive someone in order

for it to be a valid action

For instance, sometimes telling the truth can really

hurt a situation more than it helps For example, my

friend is in a dance company, and I went to see her

in the Nutcracker dance performance this past

week-end Even though she was pretty good, the whole

thing was long, boring, and a lot of the dancers were

not very good I know that she would not want to

hear that So instead of telling her the truth, I lied

and told her how great it was This is what is called

a ‘white lie.’ Yes, I was deceiving her, but there was

really very little to come from telling her the truth

that the show was a disaster What is the point of

telling the truth there if it is only going to hurt

every-one involved?

Recently, I watched a documentary about the Vietnam War The documentary focused on a troop of

25 soldiers and their experience in the war and how they grew closer together as a group as the time went

by One of the soldiers, a 16 year old boy who had lied about his age so that he could fight, died because he made a bad decision and chased after a Vietnamese soldier into the woods without anyone else to back him up Part of the reasoning behind this action, they explained, was because he spent his entire life trying

to prove to his parents that he was not a failure at everything and that he could be a hero A fellow troop-mate knew what he had done, knew the struggle for respect he was going through at home, and wrote the formal letter home to the family telling them how their son had died in an honorable fashion saving sev-eral members of the troop with his heroism Some might argue that it was bad to lie about his death, but

I would argue that this was a valiant thing done by the soldier who wrote the letter because it allowed the family to feel better about the death of their young son in a war so many miles away

To summarize, in general, it is best not to lie But there are in fact situations where it is better to tell par-tial truths than the whole truth It is important to avoid lying whenever possible, but it is also important to know when it is OK to tell a slight variation to the truth

The following essay received 4 points out of a possible 6, meaning that it demonstrates adequate

compe-tence in that it

• develops a point of view on the topic

• demonstrates some critical thinking, but perhaps not consistently

• uses some examples, reasons, and other evidence to support its thesis, but perhaps not adequately

• shows a general organization and focus but shows occasional lapses in this regard

• demonstrates adequate but occasionally inconsistent facility with language

• contains occasional errors in grammar, usage, and mechanics

A lot of rules have exceptions because there are

dif-ferent circumstances for everybody and also people

grow up and the old rules don’t apply anymore One

afternoon back in elementary school, I got in trouble

when I took my friend’s Capri-Sun drink out of his

lunchbox and took a sip without asking his

permis-sion My teacher caught me in the act and yelled at me

reciting the “Golden Rule.” She said: How would you

feel if he took your drink and had some without

ask-ing you? I guess I would have been pretty annoyed I

hate it when people drink from the same glass as me

It seemed like a pretty fair rule that I should only do

things to other people that I would be OK with them

doing to me

This interaction with my 3rd grade teacher stuck

with me throughout my education experience and I

heard her voice in my head many times as I was

about to perform questionable acts upon others

around me It kept me from doing a lot of pranks like

I used to do like tie Eric’s shoelaces together and

putting hot pepper flakes in Steve’s sandwich one

afternoon while he went off to get himself another cup of water

But this rule seemed to get a bit more difficult to follow as I got older and found myself in more com-plex relationships Sometimes I wanted to be treated

in ways that my friends did not want to be treated I wanted my friends to call me each night so that we could talk and catch up on the day’s events so I would call each of them every night to chat This annoyed

my friends though who did not like talking on the phone Or, I would always point out to my friends when something they were wearing did not look good because I wanted to be told such things so that I did not embarrass myself This made a LOT of my friends very angry at me and cost me a few good friendships

“Do unto others” is a rule that requires a bit of thought and a lot of good judgment Doing unto others things that I was hoping they would do to me some-times cost myself friendships I think it is better to re-serve that rule for things that I might consider negative rather than positive

The following essay received 2 points out of a possible 6, meaning that it demonstrates some

incompe-tence in that it

• has a seriously limited point of view

• demonstrates weak critical thinking

• uses inappropriate or insufficient examples, reasons, and other evidence to support its thesis

• is poorly focused and organized and has serious problems with coherence

• demonstrates frequent problems with language and sentence structure

• contains errors in grammar and usage that seriously obscure the author’s meaning

Linear pair: z + x = 180

Substitute: 55 + x = 180

Subtract 55: x= 125

Since lines l and m are parallel:

x = c = 125

Alternate interior: z = a = 55

x = c = 125

a + b + c = 55 + 125 + 125 = 305

(Chapter 10, Lesson 1: Lines and Angles)

7 E

Subtract 16:

Divide by 7:

Square both sides: x= 81 (Chapter 8, Lesson 4: Working with Roots)

8 D Work backwards with this problem Each term, starting with the second, is 2 less than the square root of the previous term So to work back-wards and find the previous term, add 2 and then square the sum: 2nd term = (1 + 2)2= 32= 9

1st term = (9 + 2)2= 112= 121 (Chapter 11, Lesson 1: Sequences)

9 C Before trying to solve this with geometrical formulas, analyze the figure The rectangle is divided into 15 squares Each of the 15 squares is split into 2 identical triangles, which means there are 30 trian-gles total Of those 30 triantrian-gles, 15 of them are shaded

in, or half of the figure This means that half of the

area, or 45, is shaded

(Chapter 10, Lesson 5: Areas and Perimeters) (Chapter 6, Lesson 2: Analyzing Problems) (Chapter 6, Lesson 4: Simplifying Problems)

10 C The long way:

★16 = 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 +

4 + 3 + 2 + 1 = 120

★13 = 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 78

★16 −★13 = 120 − 78 = 42 More simply, this can be solved without actually calcu-lating the sums Just focus on the terms in the sum of

★16 that are not “cancelled” by the terms in ★13 :

★16 −★13 = 15 + 14 + 13 = 42 (Chapter 9, Lesson 1: New Symbol or Term Problems)

7 x=63

7 x+16=79

Section 2

1 C It does not matter how big each station is All

that matters is the total area and how many stations

there are

(Chapter 10, Lesson 5: Areas and Perimeters)

(Chapter 9, Lesson 2: Mean/Median/Mode Problems)

2 D Solve for a and b: 3a= 15

4b= 10

Plug in a and b:

(Chapter 8, Lesson 1: Solving Equations)

3 A Pick the employee whose line has the largest

positive slope This is Employee 1 Her line has the

largest “rise over run.” Her salary increases

approxi-mately $20,000 in 8 years, or roughly $2,500 per year

(Chapter 11, Lesson 5: Data Analysis)

4 D Use unit analysis and solve:

Total number of buckets = 20 + 20 = 40

(Chapter 7, Lesson 4: Ratios and Proportions)

Combine like terms: (2x + 4)(9x − 2)

Combine like terms: 18x2+ 32x − 8

(Chapter 8, Lesson 5: Factoring)

6 D

60

children bucket

children buckets

a

adults bucket

adults buckets

a

2 5 2

average total

pieces

ft

6 stations

2

= = 3 600, =600fft2

55° 125° 55° 125°

125° 55° 125° 55°

m l

Detailed Answer Key

11 D Look at the right (units) column first.

Y + X = X

Look at the 10s column: 3 + Y = 3

Because Y= 0, we know there is no carried

digit

Look at the left (1,000s) column:

X+ 5 = 13 Subtract 5: X= 8

(Chapter 9, Lesson 3: Numerical Reasoning Problems)

12 B Write out an equation given the average:

Multiply by 3: x + y + 3y = 9x

Combine like terms: x + 4y = 9x

(Chapter 9, Lesson 2: Mean/Median/Mode Problems)

13 C

x

+ +3 =

15 E

z°

(z− 1)°

(180− x°) (180− w)°

y° x° w° (y+ 1)°

The simplest method is to use the Triangle External

Angle theorem, which says that the measure of an

“exterior angle” of a triangle equals the sum of the

measures of the two “remote interior angles,” so x = y

+ z and w = (z − 1) + ( y + 1) = y + z Therefore, w = x.

Another, more involved method is to write an

equa-tion for each triangle:

Triangle on left: y + z + (180 − x) = 180

Triangle on right: (y + 1) + (z − 1) + (180 − w) = 180

Subtract 180 and simplify: y + z − w = 0

(Chapter 10, Lesson 2: Triangles)

14 B Pick a value for r, like 19, that makes this

statement true (r must be 9 more than some multiple

of 10.) If r is 19, then r+ 2 is 21 When 21 is divided by

5, it leaves a remainder of 1

(Chapter 7, Lesson 7: Divisibility)

The best way to solve this problem is to draw the lines With each line you draw, attempt to create as many intersection points as possible The maximum number of intersection points possible with 5 lines is

10, as shown above

(Chapter 6, Lesson 2: Analyzing Problems)

16 B The probability of selecting a king is 1/4, and the probability of selecting a queen is 2/7 To find the probability of randomly choosing a jack, add up the probabilities of choosing a king and a queen and sub-tract that sum from 1 1⁄4+2⁄7

Find a common denominator: 7⁄28+8⁄28=15⁄28

Subtract from 1: 1 −15⁄28=13⁄28

(Chapter 9, Lesson 6: Probability Problems)

17 E

V

U

T

Y

X

W

50°

60°

60°

60°

2x°

x°

65°

65°

Since ΔVXT is equilateral, its angles all measure 60°.

Mark the diagram as shown

If WU = WY, then ∠WUY = ∠WYU = 65°.

∠VWU (2x°) is twice as large as ∠VUW (x°).

There are 180 degrees in a triangle: x + 2x + 60° = 180°

Combine like terms: 3x+ 60° = 180°

The angles on one side of a line add up to 180°:

40° + 65° + ∠TUY = 180°

Combine like terms: 105° + ∠TUY = 180°

(Chapter 10, Lesson 2: Triangles)

18 A The question asks: what percent of m− 4 is

n+ 2?

Translate the question:

Multiply by 100: x(m − 4) = 100(n + 2)

Divide by (m− 4):

(Chapter 7, Lesson 5: Percents)

19 C Like so many SAT math questions, this has an

elegant solution and a few not-so-elegant solutions

Most students will take the “brute force” path and

start by evaluating the height function when t= 10:

h(10) = −5(10)2+ 120(10) + m = 700 + m Then they will

try to find the other solution to the equation:

700 + m = −5t2+ 120t + m

Subtract 700 + m: 0 = −5t2+ 120t − 700

Factor the quadratic

(the tricky step): 0 = −5(t − 10)(t − 14)

Apply the 0 product property: t= 10 or 14

Obviously, factoring a quadratic can be a pain, but in

this problem you can make it easier by remembering

that the equation must be true for t= 10, which means

that you already know one of the factors: t− 10

The truly elegant solution, though, comes from

rec-ognizing that the function is quadratic and using the

symmetry of parabolas Clearly, the height of the

rocket is m when t= 0 When is the height next equal

to m? The next time that −5t2+ 120t is equal to 0 This

is a much easier quadratic to solve:

−5t2+ 120t = 0

Apply the 0 product property: t= 0 or 24

Since these two values of t give the same height, they

must be reflections of each other over the parabola’s

axis of symmetry The axis of symmetry is therefore

halfway between t = 0 and t = 24, at t = 12 (This is

when the rocket is at its maximum height.) So when is

the rocket at the same height as it is at t = 10? At t = 14,

since 10 and 14 are both the same distance from 12

y

t

0

m

12

10 14

24

m

= ( + )

−

4

x

100×( −4)= +2

20 C Work month by month with the price: Start of Jan: d

After Jan: d − 2d = 8d

After Feb: .8d + (.4)(.8d) = 1.12d

After Mar: 1.12d − (.25)(1.12d) = 84d

After Apr: .84d + (.25)(.84d) = 1.05d

(Chapter 8, Lesson 7: Word Problems) (Chapter 7, Lesson 5: Percents)

Or, more simply, remember that each percent change

is a simple multiplication: d(.8)(1.4)(.75)(1.25) = 1.05d.

(Chapter 6, Lesson 6: Finding Alternatives)

Section 3

1 A The bistro is world-renowned, so it is famous

and successful Both words should be positive

delec-table = pleasing to the taste; scrumptious = delicious;

unpalatable = bad tasting; tantalizing = exciting be-cause kept out of reach; debilitating= sapping energy;

savory= pleasing to the taste

2 D The first word represents something that

could put a country on the brink of war The second

word represents something that could cause it to

explode into destructive conflict dissension=

disagree-ment; harmony = concord; instigation = provocation;

strife = violent disagreement; provocation = rousing of anger; unanimity = complete agreement; agitation =

disturbance

3 B For over 500 years, art historians have argued

about the emotion behind the Mona Lisa’s enigmatic

(mysterious) smile This would make the painting the

source of much debate or discussion assent=

agree-ment; deliberation= discussion of all sides of an issue;

for goods or services; reconciliation = the act of re-solving an issue

4 C Every year, crowds of people travel to Elvis’s

hometown to pay tribute (respect) Therefore, he was

a very well-respected or admired musician satirized=

made fun of, mocked; unexalted = not praised; revered

= respected, worshipped; despised = hated; shunned =

avoided

5 C The poker player uses tactics (strategies) to

out-think his opponents, so his tactics must be intellectual.

This is why he is called “the professor.” obscure= not

well understood; cerebral = using intellect; transparent = easily understood; outlandish= bizarre, unusual

6 E Detractors are critics who would likely say

something negative about the aesthetics of the

build-ing, whereas its developers would likely claim that the

project would be a great success adversary=

oppo-nent; enhancement= something that improves the

ap-pearance or function of something else; gratuity= tip;

embellishment = decoration or exaggeration; windfall

= unexpected benefit; defacement = act of vandalism;

calamity = disaster; atrocity = horrific crime; boon =

benefit

7 B Poe wrote tales of cruelty and torture, so they

must have been horrific His tales mesmerized his

readers, so they must have been hypnotizing tenuous

= flimsy; spellbinding = mesmerizing; grotesque =

distorted, horrifying, outlandish; enthralling=

capti-vating; interminable = never-ending; sacrilegious =

grossly disrespectful; eclectic= deriving from a

vari-ety of sources; sadistic= taking pleasure in others’

pain; chimerical = unrealistically fanciful, illusory;

8 D The DNA evidence was vital to proving the

de-fendant’s innocence The missing word should mean

to prove innocent or free from blame perambulate=

walk through; expedite = speed up; incriminate =

ac-cuse of a crime; exculpate = free from blame;

equivo-cate= avoid telling the whole truth

9 B Debussy is said to have started the breakdown

of the old system (line 3) and then to have been the first

who dared to make his ear the sole judge of what

was good harmonically (lines 6–7) Therefore, the old

system did not allow this and was a rigid method for

writing harmonies

10 D The passage as a whole describes Debussy’s

inventiveness as a composer of musical harmony

11 B The hot-air balloon trip is an analogy for the

difficulties involved in exploring the ocean

12 A These are examples of the limited and

rela-tively ineffective methods (lines 15–16) that make

ocean exploration a difficult and expensive task (lines

18–19)

13 D This primal concept is revealed by the fact that

the paintings of Stone Age artists are charged with

magical strength and fulfilled other functions

be-yond the mere representation of the visible (lines 8–10).

14 E To be charged with magical strength is to be

filled with magical strength.

15 A The stylistic change was from the naturalism

based on observation and experience to a geometrically stylized world of forms discoverable through thought and speculation (lines 45–48) In other words,

artists were depicting ideas rather than just objects and animals

16 B The sculptures are said to be ample witnesses

(line 63) to the fact that art of this period contained

elements of nạveté side by side with formalized compositions (lines 59–62).

17 A The passage states that Renaissance art is

characterized by the discovery of linear and aerial

per-spective (lines 80–81), that is, the ability to imply

depth in painting, while the earlier art of the period of

the catacombs (line 71) was averse to any spatial illu-sions (line 74) and contained action pressed onto the holy, two-dimensional surface (lines 75–76).

18 C Transitional forms (line 9) are described as

fossils that gradualists would cite as evidence for their

position (line 8), which is that evolution proceeds

gradually

19 E This case is mentioned as an illustration of the

theory of punctuated equilibrium (lines 11–12).

20 B The passage says that one explanation for the

extinction of the dinosaurs is that a meteorite created

a cloud of gas and dust that destroyed most plants and

the chain of animals that fed on them (lines 42–48).

21 D This sentence is discussing fossil evidence The supportive structures are those bones that sup-port the weight of the body

22 E The passage states in lines 35–38 that the biggest mass extinction in history happened between the Paleozoic era and the Mesozoic era, thereby im-plying that there were far fewer species in the early Mesozoic era than there were in the late Paleozoic era

23 B In lines 66–71, the passage states that the

probable key to the rapid emergence of Homo erectus was a dramatic change in adaptive strategy: greater reliance on hunting through improved tools and other cultural means of adaptation.

24 C The author presents several examples of mass extinctions and environmental changes that would likely lead to punctuated evolution but also describes

species like Homo erectus, which remained fairly

sta-ble for about 1 million years (lines 72–73).

15 B This phrase lacks parallel structure A good

revision is a charismatic leader.

(Chapter 15, Lesson 3: Parallelism)

16 B The sentence indicates two reasons, not one (Chapter 15, Lesson 4: Comparison Problems)

17 D This phrase is redundant Circuitous means

roundabout.

(Chapter 15, Lesson 12: Other Modifier Problems)

18 D Eluded means evaded, so this is a diction error.

The correct word here is alluded, meaning hinted at.

(Chapter 15, Lesson 11: Diction Errors)

19 B As it is written, the sentence is a fragment

Change clutching to clutched to complete the thought.

(Chapter 15, Lesson 15: Coordinating Ideas)

20 E The sentence is correct

21 C This is a comparison error A grade point

av-erage cannot be higher than her classmates, but rather

higher than those of the rest of her classmates.

(Chapter 15, Lesson 4: Comparison Problems)

22 B Both the emissary and the committee are sin-gular, so the pronoun their should be changed to its (if it refers to the committee) or his or her (if it refers

to the emissary)

(Chapter 15, Lesson 5: Pronoun-Antecedent Disagreement)

23 D The verb receive does not agree with the singu-lar subject each and so should be changed to receives.

(Chapter 15, Lesson 1: Subject-Verb Disagreement)

24 E The sentence is correct

25 B The subject of this sentence is genre, so the correct conjugation of the verb is encompasses.

(Chapter 15, Lesson 1: Subject-Verb Disagreement)

26 C The proper idiom is method of channeling or

method for channeling.

(Chapter 15, Lesson 10: Idiom Errors)

27 C The sentence does not make a comparison,

but rather indicates a result, so the word as should be replaced with that.

(Chapter 15, Lesson 10: Idiom Errors)

28 A The word perspective is a noun meaning point

of view In this context, the proper word is prospective, which is an adjective meaning having the potential to be.

(Chapter 15, Lesson 11: Diction Errors)

Section 4

1 B The original phrasing is a fragment Choice

(B) completes the thought clearly and concisely

(Chapter 12, Lesson 8: Write Clearly)

2 A The original phrasing is best

3 E This phrasing is concise, complete, and in the

active voice

(Chapter 12, Lesson 9: Write Concisely)

4 D The participle pretending modifies Chandra

and not Chandra’s attempt, so the participle dangles.

Choice (D) corrects the problem most concisely

(Chapter 15, Lesson 7: Dangling and Misplaced

Participles)

5 D The original phrasing contains a comparison

error, comparing his speech to the candidates Choice

(D) best corrects the mistake

(Chapter 15, Lesson 4: Comparison Problems)

6 A The original phrasing is best

7 C The original phrasing is not parallel Choice

(C) maintains parallelism by listing three

consecu-tive adjecconsecu-tives

(Chapter 15, Lesson 3: Parallelism)

8 D The pronoun their does not agree with its

an-tecedent, student Choice (C) is close, but including

the word also implies that the tests do indicate

acad-emic skill

(Chapter 15, Lesson 5: Pronoun-Antecedent

Disagreement)

9 B The original phrasing is a sentence fragment

Choices (C) and (D) are incorrect because semicolons

must separate independent clauses

(Chapter 15, Lesson 15: Coordinating Ideas)

10 E The phrase requested that indicates that the

idea to follow is subjunctive The correct subjunctive

form here is be.

(Chapter 15, Lesson 14: The Subjunctive Mood)

11 A The original phrasing is best

12 B The past participle form of to write is written.

(Chapter 15, Lesson 13: Irregular Verbs)

13 D This phrase is redundant and should be omitted

(Chapter 15, Lesson 12: Other Modifier Problems)

14 E The sentence is correct

Since 7,000 out of the total of 14,000 items sold were CDs, 14,000 − 7,000 = 7,000 were DVDs Since 4,500 of these DVDs were new, 7,000 − 4,500 = 2,500 were used (Chapter 11, Lesson 5: Data Analysis)

3 D Set up a ratio:

Set up a proportion:

(Chapter 7, Lesson 4: Ratios and Proportions)

4 E Divide this complex-looking shape into a square and two right triangles

Areasquare= (5)(5) = 25 Areatriangle=1⁄2(2)(5) = 5 Total shaded area = Areasquare+ Areatriangle+ Areatriangle=

25 + 5 + 5 = 35 (Chapter 10, Lesson 5: Areas and Perimeters)

1

bag

0 ounces

bags

00 ounces

pounds 6 ounces

5

4 00 20 00

pounds pounds

$ = x$

29 D The list of camp activities should be parallel

The verbs should consistently be in the present tense,

so will write should be changed to write.

(Chapter 15, Lesson 3: Parallelism)

30 B This phrasing is concise and parallel and

makes a logical comparison

(Chapter 15, Lesson 3: Parallelism)

31 C Chaplin’s mother’s mental illness is not

perti-nent to the main ideas of paragraph 1

(Chapter 12, Lesson 7: Write Logically)

32 D In the original phrasing, the opening

modi-fiers are left dangling Choice (D) corrects this

prob-lem most concisely

(Chapter 15, Lesson 8: Other Misplaced Modifiers)

33 E This choice is most parallel

(Chapter 15, Lesson 3: Parallelism)

34 A Sentence 11 introduces the idea that some

were interested in more than Chaplin’s art Sentence

9 expands on this fact with the specific example of

Senator McCarthy’s interest in Chaplin’s political

be-liefs Sentence 10 extends the ideas in sentence 9

(Chapter 15, Lesson 15: Coordinating Ideas)

35 D This sentence provides the best transition

from the idea that Chaplin’s films contained political

messages to a discussion of their specific messages

about domestic and international issues

(Chapter 12, Lesson 7: Write Logically)

Section 5

1 B Eric earns a 5% commission on each $200

stereo, so he makes ($200)(.05) = $10 per stereo So if

he makes $100 on x stereos, 10x= 100

(Chapter 8, Lesson 1: Solving Equations)

(Chapter 7, Lesson 5: Percents)

2 A Fill in the table:

Jane’s Discount Music Superstore

Holiday Sales

New

Used

Total

4,500

3,000 7,500

2,500

7,000

4,000 6,500

y

x

7

(5,5)

7

O

5 5 2

2

5 D If each of the small cubes has a volume of

8 cubic inches, then each side of the smaller cubes

must be 2 inches long So the dimensions of the box are

6, 4, and 4 To find the surface area, use the formula:

SA = 2lw + 2lh + 2wh

You are told that the volume of the prism is 300π Since this is 1⁄4of a cylinder, the entire cylinder would have a volume of 4(300π) = 1,200π

A

C

B

D

50 10

24 26

50

Plug in values: SA= 2(6)(4) + 2(6)(4) + 2(4)(4)

Simplify: SA= 48 + 48 + 32 = 128

(Chapter 10, Lesson 7: Volumes and 3-D Geometry)

6 C Don't waste time doing the calculation: −15 +

−14 + −13 + −12 + −11 + −10 + −9 + −8 + −7 + −6 + −5 +

−4 + −3 + −2 + −1 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9

+ 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19

In-stead, think logically The sum of the numbers from

−15 to +15 is 0 They cancel out completely: −15 + 15

= 0, −14 + 14 = 0, −13 + 13 = 0, etc Therefore, y must

be greater than 15 With a little checking, it's easy to

see that 16 + 17 + 18 + 19 = 70, so y = 19 The total

number of integers from −15 to 19, inclusive, is

19 − (−15) + 1 = 35

(Chapter 9, Lesson 3: Numerical Reasoning Problems)

7 C The general strategy is to find out how many

matches there are if each plays every other player

once and multiply that by 2

Opponents:

Player 1: 2, 3, 4, 5, 6, 7 6

Player 2: 3, 4, 5, 6, 7 5

Player 3: 4, 5, 6, 7 4

Player 4: 5, 6, 7 3

Total head to-head-matchups: 21

Since they play each opponent twice, there is a total

of 21 × 2 = 42 matches

(Chapter 9, Lesson 5: Counting Problems)

8 B The area of the base of the prism is 12.5π

Since this is one-quarter of a circle, the entire circle

has an area of 4(12.5π) = 50π

πr2= area Substitute: πr2= 50π

Divide by π: r2= 50

Take square root: r= 50

πr2h= volume of a cylinder Substitute: πr2h= 1,200π

Divide by π: r2h= 1,200 Substitute :

Finally, to find the distance from point A to point B, no-tice that AB is the hypotenuse of a right triangle with legs AD and DB First you must find the value of AD:

Simplify: 50 + 50 = 100 = (AD)2

Solve for AB: (AD)2+ (DB)2= (AB)2 Substitute: (10)2+ (24)2= (AB)2

Combine like terms: 676 = (AB)2

(Chapter 10, Lesson 3: The Pythagorean Theorem) (Chapter 10, Lesson 7: Volumes and 3-D Geometry)

9 135 Set up an equation: x + (3y + 3) = 180°

Substitute y + 1 for x: y + 1 + 3y + 3 = 180°

Combine like terms: 4y+ 4 = 180°

Solve for 3y+ 3: 3(44) + 3 = 135° (Chapter 10, Lesson 1: Lines and Angles)

( ) +( ) =( )AD

502 1 200 ( ) h= ,