Sat - MC Grawhill part 25 ppsx

You may have used different words, but be sure that the first word is positive in tone and corresponds roughly to articulate and that the second word is negative and corresponds roughly t

Answer Key 5: Using Context Intelligently

Concept Review 5

1 Parallelism is the grammatical and logical

consis-tency in phrases that list or compare things in a

sentence

2 A modifier is a word or phrase that describes

an-other word A word that modifies a noun is called

an adjective, and a word that modifies a verb, an

adjective, or another adverb is an adverb.

3 Try to infer its meaning from its usage in the

sen-tence, then look it up in the dictionary to see if

you are correct, then make a flashcard for the

word using the College Hill system described in

Chapter 3

4 Britain can hardly be considered an island, despite

the fact that it is separated from the European

continent both physically and linguistically

5 Even while it maintains a deep respect, even

rev-erence, for its history, Britain can hardly be

con-sidered archaic.

6 Britain can hardly be considered an empire,

hav-ing been reduced to a mere shadow of the vast do-minion it once was

7 The speakers ran the gamut from the eloquent to

the bumbling; some were articulate while others spoke with profound ineptitude (You may have

used different words, but be sure that the first

word is positive in tone and corresponds roughly to

articulate and that the second word is negative and

corresponds roughly to ineptitude in meaning.)

8 I did not want to sit through another lecture that was rambling and mind-numbing; rather, I was

hoping for one that was focused and engaging.

(You may have used different words, but be sure

that both words are positive in tone and that the first corresponds roughly to focused and that the second word corresponds roughly to engaging in

meaning.)

SAT Practice 5

1 E Something pedestrian and conventional is

ordi-nary and uses methods that have been used many

times before Therefore it is not new.

lucidity = clarity; analysis = examination of parts;

articulation = expression; mediocrity =

average-ness; innovation= novelty, creativity

2 B To raze something is to destroy it completely.

If a historical building is not razed, it is preserved

or, even better, made new again

renovated= made new again

3 C Brevity of expression is conciseness.

vivid = full of lively forms or colors; concise = to

the point; accessible = easily understood; concrete

= perceived through the senses

4 D A melée is a fight If the groups were fighting,

they probably have disagreed with each other.

Therefore the melée was not unexpected.

5 B A highway that has been devastated by the

earthquake would be hard to travel through.

impassable= unable to be travelled through

6 E Those who think they can write a novel if they

simply sit down and type are probably unaware of

how challenging such a task is They are naive.

amateur = nonprofessional; candid = frank and

honest; renowned = reputable, well-known;

skepti-cal = inclined to doubting; superb = exceptional;

timid = shy; naive = lacking a sophisticated

understanding

7 D If something cannot be tested with scientific

rigor and is not a reliable method, it must be

with-out a reasonable, scientific basis

intuitive= based on hunches rather than reason;

ornamental= decorative

8 A Despite indicates contrast Paranoia and extreme competitiveness are certainly bad things.

Of course, cutthroat executives would claim that they help, but they can’t really be helpful to success

in the business world.

by-products = results of a process; conducive = helpful; detrimental = harmful; inequities = unfair

situations

9 D If something is transformed into a menacing

poison, then it must not have been so bad before.

Perhaps it was only a little bit troublesome.

epidemic = a broad outbreak; derivative = repetitive

of previous works; rudiment = basic element;

virulent = dangerous; nuisance = annoyance

Lesson 6: The Toughest Sentences

There are two ways to complete this sentence Modern

film directors might like or dislike the natural

half-sentences and interrupted thoughts that characterize genuine human speech If they like them, they would use

them; choice (A) supports this reading If they don’t

like them, they would prefer more formal dialogue Choice (B) gives formal and (D) gives stilted, which convey that idea But if the directors use formal lan-guage, they wouldn’t assume imperfect dialogue, so (B) is out Likewise, if they used stilted (formal) dia-logue, they wouldn’t adopt imperfect dialogue So (A)

is the correct response

Abstract vs Concrete

Tough Sentences

Some sentences are tough not because they

have tough vocabulary, but because they have

a complicated or ambiguous logical structure

Negatives can easily complicate a sentence

and are easily overlooked Watch carefully for

negative words like not, hardly, rarely, lacking,

etc., because they are as important as the key

words! When you encounter a sentence with

negatives, it may help to paraphrase the

sen-tence more “positively.”

Some sentences are tough to work with because

they are ambiguous; that is, they have more

than one possible interpretation, usually one

positive and one negative Since there are

usu-ally only two possibilities, just try them both

Concrete nouns, which usually represent

peo-ple and objects, are typically easier to

under-stand than abstract nouns, which typically

represent quantities, qualities, or ideas When

we focus on the concrete nouns in a sentence more than the abstract ones, we can misread the sentence Pay special attention to abstract nouns in sentences

Negatives

Example:

Their approach was not unlike that of the

Neo-Darwinians, whose lack of respect for

quasi-scientific methods was far from unknown in the

University community.

This sentence is easier to work with if it is first

para-phrased without so many negatives:

Their approach was like that of the Neo-Darwinians,

whose support for the scientific method was well

known in the University community.

Ambiguous Sentences

Example:

The recent trend of using - dialogue in films

can be traced to directors who have - the

natural half-sentences and interrupted thoughts

that characterize genuine human speech

(A) halting embraced

(B) formal assumed

(C) imperfect eschewed

(D) stilted adopted

(E) passionate endured

Example:

The dissent regarding the new restrictions on student parking was - those who wanted to

be able to drive freely to school

(A) spearheaded by (B) surprising to (C) troublesome to (D) disputed by (E) disregarded by

This sentence is not about the parking restrictions, but rather about the dissent It’s easy to misread if you don’t focus on the word dissent (We overlook it

be-cause it’s so abstract.) If you wanted to drive freely to

school, how would you feel about the dissent

regard-ing parkregard-ing restrictions? You’d probably be one of the

people dissenting! You may even initiate the dissent,

which is why (A) is the best choice

Concept Review 6: The Toughest Sentences

1 What, other than tough vocabulary, can make a sentence hard to understand?

2 What are abstract nouns, and why should you pay close attention to them in sentences?

3 Circle the abstract nouns and draw boxes around the concrete nouns in the sentence below

The lack of interest among the voters ensured that the referendum about the new playground could sneak through, even though it contained some objectionable clauses.

Paraphrase the following sentences to minimize negatives

4 It is not uncommon to find people who refuse to deny that ghosts exist.

5 The council did not fail to block a single motion.

Complete the following ambiguous sentences in two ways, with different tones

6 Despite the of the climb, the explorers were beginning to believe that the trek would soon become

Despite the of the climb, the explorers were beginning to believe that the trek would soon become

7 Far from being on the issue of gun control, Will has on the issue for many years

Far from being on the issue of gun control, Will has on the issue for many years

SAT Practice 6: The Toughest Sentences

1 The country’s confidence, formerly sustained by

an - sense of power, was replaced by an

equally exaggerated sense of - following the

hasty evacuation of its troops from three foreign

capitals

(A) inflated weakness

(B) overwhelming inviolability

(C) erratic hysteria

(D) unquestioned omnipotence

(E) arbitrary resolution

2 According to their detractors, the leaders of the

Union for Progressive Politics do not truly

-change, but simply rehash old and discredited

theories of political philosophy

(A) admonish

(B) censor

(C) advocate

(D) caricature

(E) hinder

3 Dr Cuthbert often - his former associates for

not continuing to support him; apparently he

harbored great animosity because of their - of

him

(A) disparaged endorsement

(B) excoriated abandonment

(C) exonerated denunciation

(D) extolled betrayal

(E) venerated dismissal

4 Despite her gregariousness, Andrea seems to

have been a woman who cherished her

-highly

(A) colleagues

(B) friendships

(C) privacy

(D) integrity

(E) humility

5 It is extremely rare to see a politician - any

opinion that is widely unpopular; it seems that,

for them, public censure is more - even than

death

(A) conform to desirable

(B) tolerate exciting

(C) reject feared

(D) espouse painful

(E) manipulate natural

6 The cogency and animation he showed in private belied his reputation for a notably - style of lecturing

(A) tepid (B) incisive (C) versatile (D) infrequent (E) fluent

7 The haiku, with its -, its reduction of natural and everyday events to their mere essence, seems

to economically depict the - of even the sim-plest human experience

(A) casualness destructiveness (B) optimism barrenness (C) capriciousness rigidity (D) digressiveness precariousness (E) conciseness poignancy

8 Sadly, most people who say they want change in public schools will struggle to resist it, or at least - its effects on them

(A) initiate (B) distort (C) palliate (D) defend (E) enhance

9 Despite the - literature debunking the theory of ESP, a critical and rational awareness of the sub-ject continues to - most of the public

(A) vivid pervade (B) voluminous elude (C) provocative captivate (D) ambiguous perplex (E) incomprehensible escape

Answer Key 6: The Toughest Sentences

Concept Review 6

1 Complicated or ambiguous logical structure

2 Abstract nouns are nouns that represent ideas,

quantities, or qualities; that is, they represent

things that cannot be directly perceived

3 The lack (abstract noun) of interest (abstract noun)

among the voters (concrete noun) ensured that the

referendum (abstract noun) about the new

play-ground (concrete noun) could sneak through, even

though it contained some objectionable clauses

(ab-stract noun).

4 It is common to find people who believe in ghosts.

5 The council blocked every motion.

6 Despite the ease of the climb, the explorers were

beginning to believe that the trek would soon

be-come treacherous (or some similar words) Despite the arduousness of the climb, the

explor-ers were beginning to believe that the trek would

soon become easier (or some similar words)

7 Far from being passive on the issue of gun control, Will has pontificated on the issue for many years.

(or some similar words)

Far from being consistent on the issue of gun con-trol, Will has equivocated on the issue for many

years (or some similar words)

SAT Practice 6

1 A What would follow a hasty evacuation of a

country’s troops? A feeling of being overwhelmed

and defeated, most likely This feeling of

weak-ness, we are told, is just as exaggerated as the sense

of power just prior to the withdrawal

inviolability = invincibility; erratic = irregular;

hyste-ria = irrational and exaggerated emotion;

omnipo-tence = supreme power; arbitrary = based on whim

and random power; resolution= determination

2 C If their detractors (critics) believe that they

only rehash old and discredited theories, then they

are suggesting that they do not really speak out for

change

admonish = reprimand; censor = eliminate

objec-tionable material; advocate = speak in favor of;

caricature = exaggerate comically; hinder = get in

the way of

3 B If his associates did not continue to support

him, they must have abandoned him If he

har-bored animosity for them, he must have criticized

them

disparaged = criticized harshly; endorsement =

show of support; excoriated= criticized harshly;

exonerated = proved innocent; denunciation =

con-demnation; extolled = praised highly; venerated =

honored

4 C Despite indicates contrast Gregariousness is

sociability Its opposite is solitude, reclusiveness,

or privacy.

5 D If public censure is like death, politicians must

not like it They must never openly adopt a widely

unpopular opinion

conform = do what is expected; espouse = adopt publicly; manipulate= take control of

6 A Cogency is persuasiveness and animation is liveliness To belie is to misrepresent, so he must

not have a reputation for being lively and

persua-sive, so people must think he’s dull

tepid = dull, lukewarm; incisive = keen and thoughtful; versatile = well-rounded; fluent =

smooth, flowing

7 E The first word must mean something like

re-duction to its essence, and the second word must

mean something like essence.

barrenness = starkness; capriciousness = whimsy, randomness; digressiveness= tendency to go off

topic; precariousness = danger; conciseness = brevity; poignancy= sharpness of feeling

8 C If they resist it, then they want to prevent its effects on him, or at least minimize its effects on

them

initiate = begin; distort = twist; palliate = make less severe; enhance= make better

9 B Despite indicates irony If there is literature de-bunking the theory of ESP, it would be ironic if the

public failed to develop a critical and rational

awareness of the subject What would make it

even more ironic is if the literature were plentiful.

vivid = full of vibrant imagery; pervade = fill com-pletely; voluminous = plentiful; elude = escape cap-ture or understanding; provocative = tending to

elicit strong reactions; captivate = capture;

am-biguous = unclear; perplex = confuse;

incompre-hensible= beyond understanding

WHAT THE SAT MATH IS

REALLY TESTING

CHAPTER 6

✓

1 Mapping Problems

2 Analyzing Problems

3 Finding Patterns

4 Simplifying Problems

5 Connecting to Knowledge

6 Finding Alternatives

7 Thinking Logically

8 Checking Your Work

Copyright © 2008 by The McGraw-Hill Companies, Inc Click here for terms of use

What Is Mapping?

Mapping a problem means orienting yourself to the

problem and representing its information It’s like

pulling out a map before you start a trip The map

shows you where you’re going but not how to get

there On some tough SAT math problems, half the

battle is “mapping”—orienting yourself to the problem

and figuring out what it’s asking

Tips for mapping tough SAT math problems:

• Write out any diagrams, equations, or tables

that represent the key information in the

problem You don’t get neatness points on

the SAT—good test-takers scribble all over

the test booklet Writing things down helps

you to keep track of the information as well

as your thought process

• Notice any restrictions on the unknowns

For instance, do they have to be integers or

positive numbers or multiples of some

number? Are they measures of angles or

segments or areas in a figure? Underline key

restrictions

• Know the definitions of special terms such

as primes, integers, factors, multiples,

perimeter, and so on, and underline these

terms when you see them

• Notice whether any unknowns can take any

values that you choose or have only one

par-ticular value that you have to find You can

solve many complicated-looking problems

by just choosing values for the unknowns!

• Read carefully and notice exactly what the

problem is asking for Does it ask you to

solve an equation? Find the value of an

ex-pression? Find an area? Underline what

the problem is asking you to find so that

you don’t lose track of it

• Notice whether the question is

multiple-choice, and if so, notice the range of the

an-swer choices If the anan-swers are far apart,

you might be able to just estimate an answer

to zero in on the right choice Also, notice

how the choices are expressed Are they

frac-tions, decimals, radicals, algebraic

expres-sions? Noticing this often helps you to see

what you have to do to get the answer

Watch for the Common Mix-Ups

Even the best students sometimes miss questions be-cause they misinterpret key terms in the problem You can avoid this by underlining these key terms and thinking about the terms they are commonly confused with

• A perimeter is the distance around a figure Don’t confuse it with area, which is the

num-ber of square units that fit inside a figure

• The circumference formula for a circle

is c = 2 πr Don’t confuse it with the area

formula of a circle, which is a = πr2 To avoid confusing them, remember that

area is always measured in square units, so

its formula contains the “square.”

• An odd number is any integer not divisible

by 2 Don’t confuse it with a negative

num-ber, which is any number less than 0 These

two are commonly confused because both

of these words have a “bad” tone

• An even number is any integer divisible by 2 Don’t confuse it with an integer in general,

which is any positive or negative whole number These two are commonly confused because when we talk of a number dividing another “evenly,” we really mean that it goes

in an integer number of times, not necessar-ily an even number of times.

• A product is the result of a multiplication Don’t confuse it with a sum, which is the

result of addition

Don’t Rush—Avoid Quick Gimmicks

Always read the whole problem carefully before deciding how to solve it SAT math questions—especially medium and hard-level ones—are designed to trap students who don't read carefully or who pigeon-hole questions too quickly Getting an answer quickly doesn’t help if it’s the wrong answer

It’s important to be prepared for what you’ll see in the Math sections on test day Visit our Online Practice Plus at www MHPracticePlus/SATmath for more tools and resources to help.

Concept Review I: Mapping Problems

1 Describe what it means to “map” a problem

2 Why is it important to consider the choices (in a multiple-choice question) as part of the problem?

Define the following terms, and indicate what terms they are sometimes confused with

Equations or inequalities are powerful “mapping” tools Translate the following statements into equations or inequalities Be sure to specify the meanings of any unknowns you may use

7 The sum of two consecutive odd numbers is 28

8 Ellen is twice as old as Maria

9 Last year, Jennifer was twice as old as Brian is now

SAT Practice 1: Mapping Problems

Map each of the following problems before solving it Use the space for scratchwork, and underline any key words in the problem Then solve each problem

1. The product of five consecutive even integers is 0

What is the greatest possible value of any one of

these integers?

2. The perimeter of a rectangle is 28 inches, and its

area is x square inches If x is an even integer,

what is the greatest possible value of x?

3. Carlos begins with twice as much money as

David After Carlos gives $12 to David, Carlos still

has $10 more than David How much money did

they have combined at the start?

(A) $32

(B) $66

(C) $68

(D) $92

(E) $102

4. Corinne travels from home to work at an average

speed of 50 miles per hour, and returns home by

the same route at 60 miles per hour It takes her

10 more minutes to get to work than it takes her

to get home How many miles is it from Corinne’s

home to work?

(A) 25

(B) 35

(C) 50

(D) 75

(E) 90

Do Your Scratchwork Here

Concept Review I

1 To map means to represent the general problem

situation and goal, either mentally or on paper

2 Because the choices tell you the range of values to

consider, as well as the form of the numbers

(in-tegers, fractions, etc.) and format (factored,

deci-mal, etc.)

3 Odd means an integer not divisible by 2 and is

sometimes confused with negative because of the

“negative” tone of both words

4 Even means an integer divisible by 2 and is

some-times confused with positive because of the

“posi-tive” tone of both words

5 Perimeter means distance around a figure and is

sometimes confused with area, which is the

num-ber of square units that fit inside a figure.

6 Integers are whole numbers and negative whole

numbers and are sometimes confused with

count-ing numbers, which are the positive integers: 1, 2,

3, 4,

7 Let n be the smaller of the two numbers Then the next odd number is n+ 2, so an equation that says that the sum of two consecutive odd numbers is

28 is n + n + 2 = 28.

8 Let e stand for Ellen’s current age and m stand for

Maria’s current age An equation that says that

Ellen is twice as old as Maria is e = 2m.

9 Let j stand for Jennifer’s age now and b stand for Brian’s age now Last year, Jennifer was j− 1 years old, so an equation that says that last year Jennifer

was twice as old as Brian is now is j − 1 = 2b.

SAT Practice 1

1 8 If the product of a set of integers is 0, then one of

the numbers must be 0 To maximize the value of any

one of them, let 0 be the smallest of the integers

If they are consecutive even integers, they must

be 0, 2, 4, 6, and 8 If your answer was 4, then you

overlooked the fact that the numbers are even.

2 48 Your first tool in mapping a geometry

prob-lem is a good diagram This one has no diagram,

so you must draw your own Draw a rectangle,

labeling its width w and its length l:

3 E Let c be the number of dollars Carlos had to start and d be the number of dollars David had to start The question asks for the value of c + d If Carlos

begins with twice as much money as David, then

c = 2d After Carlos gives $12 to David, he has c − 12 dollars, and David has d+ 12 dollars If Carlos still

has $10 more than David, then c − 12 = (d + 12) + 10.

Simplify: c − 12 = d + 22

Add 12: c = d + 34 Substitute c = 2d: 2d = d + 34 Subtract d: d= 34 Plug back in: c= 2(34) = 68

So c + d = 34 + 68 = 102.

4 C To “map” this problem, you must know that

distance = speed × time You must find the num-ber of miles from Corinne’s home to work, so call

that d If she travels from home to work at an

average speed of 50 miles per hour, then it must

take her d/50 hours, or 60 × d/50 = 6d/5 minutes If

she returns home at 60 miles per hour, it must

take her d/60 hours, or 60 × d/60 = d minutes If it

takes her 10 more minutes to get to work than it takes her to get home, then:

Simplify:

Multiply by 5: d= 50

d

5= 10

6d d

5 − =10

Since the perimeter of the rectangle is 28 inches,

you can set up an equation: 2w + 2l = 28 Divide

both sides of the equation by 2 to get w + l = 14.

Since the area is x, you can set up the equation lw = x.

If x is even, then l and w can’t both be odd (Can

you see how we know that?) You should be able

to see that the possible values for w and l are 2

and 12, 4 and 10, and 6 and 8 (Check them

and see.) This means that x can have values of

2 × 12 = 24, 4 × 10 = 40, or 6 × 8 = 48 The greatest

of these, of course, is 48

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