PrepAccelerator’s

ACT CRASH COURSE

Dr. Sampath

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PrepAccelerator’s ACT Crash Course:English

Dr. SampathPrepAccelerator.com

Usage/Mechanics

1: Verb Tense 2: Subject-Verb Agreement

3: Commas for Phrases 4: General Punctuation

5: General Punctuation

Rhetorical Skills

6: Meaning 7: Improvement

8: Transitional Expressions 9: Wordiness and Redundancy

Notes Notes

Notes Notes

Passage II

SOCIAL SCIENCE: This passage is adapted from the article“Green Music in the Rain Forest” by Suzanne Charlé, whichappeared in the Fall 2002 Ford Foundation Report.

OELA is an acronym based on Portuguese words rather thanthe English words used in this article. A luthier is a maker ofstringed musical instruments.

The Amazonian Workshop School for Fabricationof Stringed Instruments (OELA) is a small part of alarger effort to create a sustainable harvest of the greatAmazon forest and to give employment to the region’sburgeoning population.

“Few people know that the Amazon is one of themost rapidly urbanizing regions of the world,” observesJosé Gabriel López, a Ford Foundation program officerin Brazil. The city of Manaus, for example, has grownin the past decade from 850,000 to 1.5 million. “Thisrural-urban migration and the resultant urban shanty-towns stand as living symbols of failed or nonexistentrural development policies,” López says. “In manyplaces, small-scale rural producers have been aban-doned—devoid of health and education services, credit,technical assistance and opportunity. What RubensGomes, founder of the workshop school, and his col-leagues have created in Manaus is hope.”

Gomes knows how to build hope. The school, henotes proudly, is the first to make stringed instrumentsin the Amazon. And it is the first in all of the Americasto construct instruments exclusively of lumber har-vested in an environmentally and socially sustainablemanner certified by the Forest Stewardship Council.

“Officially, there are 30 million cubic meters ofwood cut in the Amazon annually,” Gomes says.“Twenty million of this is wasted—sawdust, scraps,unwanted wood left to rot. And those are the officialnumbers. The motive of this school is to transform whatis lost into things of value. Many people could dothis—but there are no schools teaching carpentry in theAmazon.”

OELA is meant to help fill the void. To graduate,each student must make a stringed instrument. All theguitars are made from certified wood. Gomes explainsthat traditionally, Brazilian rosewood and ebony wereused in the construction of guitars. But because ofintense harvesting, these trees are close to extinction.“I’ve been working for years, trying to find Amazonwoods that are unknown on the market, that are in plen-tiful supply and that can be used in instrumentmaking,” Gomes says. He experimented with dozensbefore he found types that have the right strength andsound. (Like other master luthiers, he can tell by touch-ing the wood whether it will reverberate well.) Once heidentified the woods as possible substitutes, he sentthem to a laboratory to be tested for the right grain anddensity. Today, Brosimum rubescens is substituted forrosewood, Aniba canellila for ebony, and Protiumspecies for Brazilian mahogany and cedar. These and

some 25 other undervalued tropical hardwoods havefound their way into the luthiers’ workshop, taking thepressure off the better-known woods.

For the past year, master luthier Raúl Lage fromthe Fernando Ortiz Instrument-Making School of theCuban Music Institute has been working with the stu-dents. There are hurdles, he cautions, a number of themtechnical. The high humidity in Manaus means that thewood will crack in drier climates unless properlytreated. Glue frequently doesn’t hold. These problemsare slowly being resolved.

There is also a major obstacle outside the work-shop: The resistance of buyers to new woods. Thus far,most of the instruments have been sold to environmen-talists, some of whom “adopt” a student by paying hisor her tuition; the student’s “project guitar” is thengiven to the donor as a gift.

There is also the possibility of contract work fromoutside the Amazon. Gomes’s hopes were raisedrecently when the president of a well-known guitarcompany based in Nashville, Tennessee, ordered 15 guitars to be auctioned off for the RainforestAlliance.

Lage cautions that it will be a long time before anyof the students can command a master luthier’s fee.“There is a saying,” Lage says. “Anyone can make onegood guitar; it takes a master to make one every time.”

José Lucio do Nascimento Rabelo, director of thetechnical school, says, “By learning this skill, studentscome to look at the forest in a new way; there are waysother than logging for plywood and firewood to earn aliving, to better the life of the people.” One of thewoods being used as a replacement for the preciousrosewood, he notes, is typically used to make charcoal.

Such an appreciation for the forest, says Rabelo,could have a huge effect on the survival of the rainforest; some 80 percent of the students come from otherparts of the state of Amazonas, and virtually all of themreturn to their home towns. “Some,” he adds, “go on tobecome politicians who will have a direct influence onthe future of the forest.”

11. Which of the following assumptions would be mostcritical for a reader to accept in order to agree fullywith the author’s claims in the passage?

A. Shantytowns in the Amazon need to be relocated ifthe forest is to be saved.

B. Learning to make consistently good guitarsrequires access to the best materials available.

C. Small-scale rural producers in the Amazon canhelp preserve the forest by being innovative.

D. Consumers outside of the Amazon can do little tohelp prevent deforestation.

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34

35

12. In the context of the passage, the statement “All theguitars are made from certified wood” (lines 34–35)most nearly suggests that Gomes’s workshop:

F. uses environmentally sustainable woods in itsguitars.

G. isn’t doing enough to stop unnecessary deforesta-tion in the Amazon.

H. has little chance of pleasing both musicians andenvironmentalists.

J. uses only traditional woods in making its guitars.

13. It can most reasonably be inferred from the passagethat regarding OELA, the author feels:

A. skeptical of the workshop’s aims.B. dismayed by the workshop’s low productivity.C. supportive of the workshop’s goals.D. confident that the workshop could be duplicated in

other places.

14. The main purpose of the second paragraph (lines 6–18)is to:

F. draw attention to the Amazon’s tremendous popu-lation growth.

G. explain the necessity for ventures such asGomes’s.

H. explain the presence of the Ford Foundation in theAmazon.

J. justify raising taxes to increase social services inthe Amazon.

15. The main function of the fifth paragraph (lines 33–53)is to:

A. demonstrate the woodworking skills required to bea master luthier.

B. explore the limitations of science as compared tointuition.

C. outline the scientific reasons why one type ofwood cannot be replaced by another.

D. show that experiments led to the discovery of goodsubstitutes for rare woods.

16. The passage notes all of the following as problems thatthe fledgling Amazon guitar industry has experiencedEXCEPT that:

F. glue on the guitars sometimes doesn’t hold.G. the wood used may crack in drier climates.H. woods usable for guitars have become extinct.J. buyers resist guitars made with nontraditional

woods.

17. The passage indicates that, as a group, the OELA stu-dents may impact the survival of the rain forestsbecause most of them:

A. care deeply enough about music to spend theirlives making musical instruments.

B. will return to their homes and spread their envi-ronmental knowledge.

C. are willing to endure personal hardships in orderto use their new skills.

D. will have political careers after they return home.

18. In the passage, Gomes indicates that of the wood cut inthe Amazon rain forest each year, approximately howmuch wood is wasted?

F. One-fourthG. One-thirdH. One-halfJ. Two-thirds

19. The passage states that all of the following are woodstraditionally used for making stringed instrumentsEXCEPT:

A. Aniba canellila.B. rosewood.C. Brazilian mahogany.D. ebony.

20. According to the passage, when an OELA student is“adopted,” he or she receives:

F. tuition.G. room and board.H. food and clothing.J. a musical instrument.

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3 3

PrepAccelerator’s ACT Crash Course:Math

Dr. SampathPrepAccelerator.com

1: Ratio and Proportion (60 sec)

A container is 18 full of water. After 10 cups of water are

added, the container is 34 full. What is the volume of the

container, in cups?

F. 1313 G. 131

2 H. 15 J. 16 K. 40

2: Counting (45 sec)

Which of the following expressions gives the number ofdistinct permutations of the letters in DETERGENT?

A. 9! B.9!2! C.

9!3! D.

9!(3!)(2!) E.

9!5!

3: Mean/Median/Mode (45 sec)

Dina has 5 biology tests this semester and has scored 91,87, 82, and 94 on the first 4 tests. How much should shescore on the 5th test so that her semester average scorewill be 90?A. 88.5

B. 90

C. 91.5

D. 93

E. 96

4: Exponents (45 sec)

For all positive values of p and q, which of the followingexpressions is equivalent to

p√p7 · q3 4

√q−5 ?

A. p52q

94 B. p

92q

54 C. p

72q

94 D. p

72q

74 E. p

92q

74

5: Polynomials (60 sec)

When asked how old a building was, the architect said,“Square the age of the building, and subtract 8 times itsage, and the result is 48.” What is the age of the building?

A. 12B. 14C. 16D. 18E. 20

6: Inequalities (45 sec) 7: Complex Numbers (30 sec)

8: Logarithms (60 sec) 9: Matrices (45 sec)

What must be the value of y for the matrix[y yy −16

]to

have a determinant of 64?

A. −16B. −8C. −4D. −1

4E. 16

10: Points (60 sec)The points E (6, 4) andF (14, 12) lie in the standard(x , y) coordinate plane. PointD lies on EF between E andF such that the length of EFis 4 times the length of DE .What are the coordinates ofD?

F. (7, 5) G. (8, 6) H. (8, 8)J. (10, 8) K. (12, 10)

11: Slope (30 sec)

What is the slope of a line in the standard (x , y)coordinate plane that goes through the point (2, 3) andhas a y -intercept of 4?

A. -4 B. -2 C. -12 D. -14 E. 1

12: Angles (60 sec)

In the figure, line ` is parallel toline m. Transversals t and u

intersect at point A on ` andintersect m at points C and B,respectively. Point X is on m,the measure of ∠ACX is 130◦,and the measure of ∠BAC is80◦. How many of the anglesformed by rays of `, m, t, and u

have measure 50◦?

A. 4 B. 6 C. 8 D. 10E. 12

13: Cylinders (75 sec)

A can of soda pop has the shape of a right circularcylinder with an inside height of 8 inches and an insidediameter of 3 inches. When you pour the soda pop fromthe full can into a cylindrical glass with an inside diameterof 4 inches, about how many inches high is the soda popin the glass?

(Note: The volume of a right circular cylinder is πr 2h.)

A. 223

B. 412

C. 6 D. 4√3 E. 24

14: Triangles (60 sec)

In right triangle ∆ADE below, DE is parallel to BC , and ED isperpendicular to AB at D. The length of AB is 5 feet, the lengthof BC is 12 feet, and the length of AD is 2 feet. What is thelength of AE in feet?

A. 2.6

B. 3.9

C. 5.2

D. 7.8

E. 10.4

15: Trigonometry (75 sec)A baby at A spots her toy at Dand crawls in a straight line toit. Then she crawls in a straightline to her crib at E. Spottingher father at C, she next crawlsin a straight line to him. Hadthe baby crawled in a straightline directly from A to C, whatdistance in feet would she havecovered?

A. 24 B. 25 C. 26D. 27 E. 28

Passage III

Cloud cover is the percent of Earth’s surface coveredby clouds. Cloud cover may increase because of anincrease in the cosmic ray flux (number of high-energy par-ticles from space reaching Earth per m2 per hour). Table 1shows how Earth’s cover of low clouds (0 km to 3.2 kmaltitude) varies with the cosmic ray flux. Figures 1−3 showthe relative cosmic ray flux, RCRF (the percent below theflux measured on October 1, 1965), and the monthly aver-age cover of high clouds (6.0 km to 16.0 km altitude),middle clouds (3.2 km to 6.0 km altitude), and low clouds,respectively, from January 1980 to January 1995.

Table 1 adapted from E. Palle Bagó and C. J. Butler, “The Influenceof Cosmic Rays on Terrestrial Clouds and Global Warming.” ©2000by Institute of Physics Publications, Ltd.

Figure 1

Figure 2

Figure 3

Figures adapted from Nigel Marsh and Henrik Svensmark, “LowCloud Properties Influenced by Cosmic Rays.” ©2000 by TheAmerican Physical Society.

Jan.1980

Jan.1985

Jan.1990

Jan.1995

RC

RF

(%)

27.5

28.0

28.5

29.0

29.5

year

mon

thly

ave

rage

cove

r of

low

clo

uds

(%)

monthly average cover of cloudsRCRF

Key

0

2

4

6

8

Jan.1980

Jan.1985

Jan.1990

Jan.1995

RC

RF

(%)

19.0

19.5

20.0

20.5

21.0

year

mon

thly

ave

rage

cove

r of

mid

dle

clou

ds (%

)

monthly average cover of cloudsRCRF

Key

0

2

4

6

8

Jan.1980

Jan.1985

Jan.1990

Jan.1995

RC

RF

(%)

mon

thly

ave

rage

cove

r of

high

clo

uds

(%)

12.5

13.0

13.5

14.0

14.5

year

monthly average cover of cloudsRCRF

Key

0

2

4

6

8

Table 1

Cosmic ray flux(particles/m2/hr)

Cover of low clouds(%)

340,000 27.8360,000 28.1380,000 28.4400,000 28.7420,000 29.0

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13. The percent of Earth’s surface covered by high cloudsin January 1987 was closest to which of the following?

A. 13.0%B. 13.5%C. 14.0%D. 14.5%

14. Based on Table 1, a cosmic ray flux of 440,000 parti-cles/m2/hr would correspond to a cover of low cloudsthat is closest to which of the following?

F. 28.7%G. 29.0%H. 29.3%J. 29.6%

15. Is the statement “The monthly average cover of lowclouds is more directly correlated with cosmic ray fluxthan is the monthly average cover of high clouds” con-sistent with Figures 1 and 3 ?

A. Yes, because the plot for the monthly averagecover of low clouds more closely parallels the plotfor RCRF.

B. Yes, because the plot for the monthly averagecover of high clouds more closely parallels theplot for RCRF.

C. No, because the plot for the monthly average coverof low clouds more closely parallels the plot forRCRF.

D. No, because the plot for the monthly average coverof high clouds more closely parallels the plot forRCRF.

16. Which of the following figures best represents themonthly average cover of high, middle, and low cloudsin January 1992 ?

17. High clouds are composed primarily of ice crystals,whereas low clouds are composed primarily of waterdroplets. This difference is most likely because theaverage air temperature at altitudes from:

A. 0 km to 3.2 km is at or below 0°C, whereas theaverage air temperature at altitudes from 3.2 km to6.0 km is above 0°C.

B. 0 km to 3.2 km is at or below 0°C, whereas theaverage air temperature at altitudes from 6.0 km to16.0 km is above 0°C.

C. 0 km to 3.2 km is above 0°C, whereas the averageair temperature at altitudes from 3.2 km to 6.0 kmis at or below 0°C.

D. 0 km to 3.2 km is above 0°C, whereas the averageair temperature at altitudes from 6.0 km to 16.0 kmis at or below 0°C.

middle

cloud

s

clou

d co

ver

high c

louds

low cl

ouds

middle

cloud

s

clou

d co

ver

high c

louds

low cl

ouds

middle

cloud

s

clou

d co

ver

high c

louds

low cl

ouds

middle

cloud

s

clou

d co

ver

high c

louds

low cl

ouds

F.

G.

H.

J.

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Passage V

An astronomy class is given the following facts aboutstellar evolution.

1. A star’s evolution can be divided into 3 stages: pre-main sequence (pre-MS), main sequence (MS), andpost-main sequence (post-MS).

2. Gravity causes part of a cloud of gas and dust tocollapse and heat up, creating a pre-MS star. Thestar’s hot dust and gas emit its energy.

3. A pre-MS star becomes an MS star when the starproduces the majority of its energy by fusinghydrogen nuclei (protons) at its center to makehelium nuclei.

4. An MS star becomes a post-MS star when the starexpands in volume and produces the majority of itsenergy by fusing hydrogen to make helium in ashell surrounding its center.

5. The more massive a star, the more rapidly the starpasses through each of the 3 stages of its evolution.

Two students discuss the evolution of the Algolsystem—Algol A, a 3.6-solar-mass MS star; Algol B, a 0.8-solar-mass post-MS star; and Algol C, a 1.7-solar-massMS star. (One solar mass = the Sun’s mass.) The 3 starsorbit a mutual center of mass, with Algol A and Algol Bmuch closer to each other and to the center of mass than toAlgol C.

Student 1

The 3 stars of the Algol system formed at the sametime from the same cloud of gas and dust. Algol B, origi-nally the most massive of the 3 stars, became a post-MSstar and expanded in volume while Algol A remained anMS star. Because the matter in the outer parts of Algol Bwas more strongly attracted to Algol A than to the matterin the inner parts of Algol B, this matter flowed from Algol B to Algol A, and, over time, Algol A became moremassive than Algol B.

Student 2

Algol B was not part of the original Algol system(Algol A and Algol C). Algol B and the original Algolsystem formed in different clouds of gas and dust at differ-ent times and moved in 2 different but intersecting orbitsaround the center of the galaxy. During a particular orbit,Algol B encountered the original Algol system at the inter-section of the 2 orbits and became part of the Algol system.

Algol B became a post-MS star while Algol A andAlgol C remained MS stars. Algol B never lost mass toAlgol A. Algol B was always less massive than Algol A.

24. Based on Student 2’s discussion, Algol B is part of thepresent Algol system because of which of the follow-ing forces exerted on Algol B by the original Algolsystem?

F. Electric forceG. Magnetic forceH. Gravitational forceJ. Nuclear force

25. Based on Student 1’s discussion and Fact 4, whilematter flowed between Algol A and Algol B, Algol Bproduced the majority of its energy by fusing:

A. hydrogen nuclei to make helium nuclei at itscenter.

B. hydrogen nuclei to make helium nuclei in a shellsurrounding its center.

C. helium nuclei to make hydrogen nuclei at itscenter.

D. helium nuclei to make hydrogen nuclei in a shellsurrounding its center.

26. Suppose that chemical composition is uniform amongstars formed from the same cloud of gas and dust, butthat chemical composition varies among stars formedfrom different clouds of gas and dust. Student 2 wouldmost likely agree with which of the following state-ments comparing the chemical compositions of thestars in the present-day Algol system at the time theyformed?

F. Algol A and Algol B had the most similarcompositions.

G. Algol A and Algol C had the most similar compositions.

H. Algol B and Algol C had the most similar compositions.

J. Algol A, Algol B, and Algol C had the same composition.

27. If the mass of the Sun is 2.0 × 1030 kg, what is the massof Algol C ?

A. 1.6 × 1030 kgB. 2.0 × 1030 kgC. 3.4 × 1030 kgD. 7.2 × 1030 kg

28. Which of the following statements best explains whythe reaction described in Fact 3 requires a high temper-ature and pressure?

F. All protons are positively charged, and likecharges attract each other.

G. All protons are positively charged, and likecharges repel each other.

H. All electrons are negatively charged, and likecharges attract each other.

J. All electrons are negatively charged, and likecharges repel each other.

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29. Based on Fact 5 and Student 1’s discussion, which ofthe 3 stars in the Algol system, if any, was most likelythe first to become an MS star?

A. Algol AB. Algol BC. Algol CD. The 3 stars became MS stars at the same time.

30. Based on Fact 5, would Student 2 agree that by thetime Algol A stops being an MS star, Algol A willhave spent as much time being an MS star as Algol Bspent being an MS star?

F. Yes, because according to Student 2, Algol A hasalways been more massive than Algol B.

G. Yes, because according to Student 2, Algol A hasalways been less massive than Algol B.

H. No, because according to Student 2, Algol A hasalways been more massive than Algol B.

J. No, because according to Student 2, Algol A hasalways been less massive than Algol B.

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PrepAccelerator’s ACT MATH Cheat Sheet

Algebra

xa xb = xa+b ; xp

xq = xp−q ; (xm )n = xmn

x0 = 1; x1 = x; x−m = 1xm ; x

mn = npxm

FOIL (First, Outer, Inner, Last): (a +b)(c +d) = ac +ad +bc +bd

Quadratic formula: ax2 +bx + c = 0 has roots

x = −b ±√

b2 −4ac

2a

Logarithm: x = au ⇒ loga x = u (a base, u exponent)

loga 1 = 0 and loga a = 1

loga x y = loga x + loga y (product)

loga

( x

y

)= loga x − loga y (quotient)

loga xp = p loga x (power)

Plane Geometry

Perimeter = a +b + cArea = 1

2 base×height = 12 ch

Area = 12 ab sinC

A B

CD

sp

2s

s

45◦

45◦90◦

Perimeter = 4s; Area = s2; Diagonal = sp

2

A B

CD

p`2 +w 2

w

`90◦

Perimeter = 2(`+w); Area = `w ; Diagonal =√`2 +w2

Area = h( b1+b2

2)= height×base average

r

d

Circumference = 2πr =πd ; Area = πr 2

`

h w

Surface Area = 2(`w +`h +wh); Volume = `wh

Surface Area = 2πr h +2πr 2; Lateral Area = 2πr h;Volume = πr 2h

Coordinate GeometryLine:

1. Slope = m = y2−y1

x2−x1= rise

run

2. Distance =√

(y2 − y1)2 + (x2 −x1)2

3. Equation: y = mx +b

Circle with center (h,k) and radius r : (x −h)2 + (y −k)2 = r 2

Trigonometry

A B

C

c

ab

θ◦

soh-cah-toa

sin θ = opphyp = a

b = 1cscθ

cos θ = adjhyp = c

b = 1secθ

tan θ = oppadj = a

c = 1cotθ

A B

C

c

ab

Cosine Law: c2 = a2 +b2 −2ab cosC

Sine Law:a

sin A = bsinB = c

sinC