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501 Critical Reading Questions (25) (30) (35) (40) (45) (50) (55) (60) theorem and began to develop a mathematical theory that would later become calculus However, his most important discoveries were made during the two-year period from 1664 to 1666, when the university was closed due to the Great Plague Newton retreated to his hometown and set to work on developing calculus, as well as advanced studies on optics and gravitation It was at this time that he discovered the Law of Uni- versal Gravitation and discovered that white light is composed of all the colors of the spectrum These findings enabled him to make fun- damental contributions to mathematics, astronomy, and theoretical and experimental physics Arguably, it is for Newton’s Laws of Motion that he is most revered These are the three basic laws that govern the motion of material objects Together, they gave rise to a general view of nature known as the clockwork universe The laws are: (1) Every object moves in a straight line unless acted upon by a force (2) The acceleration of an object is directly proportional to the net force exerted and inversely proportional to the object’s mass (3) For every action, there is an equal and opposite reaction In 1687, Newton summarized his discoveries in terrestrial and celestial mechanics in his Pftilosopftiae naturalis principia matftematica (Mathematical Principles of Natural Philosophy), one of the greatest milestones in the history of science In this work he showed how his principle of universal gravitation provided an explanation both of falling bodies on the earth and of the motions of planets, comets, and other bodies in the heavens The first part of the Principia, devoted to dynamics, includes Newton’s three laws of motion; the second part to fluid motion and other topics; and the third part to the system of the world, in which, among other things, he provides an explanation of Kepler’s laws of planetary motion This is not all of Newton’s groundbreaking work In 1704, his dis- coveries in optics were presented in Opticks, in which he elaborated his theory that light is composed of corpuscles, or particles Among his other accomplishments were his construction (1668) of a reflecting telescope and his anticipation of the calculus of variations, founded by Gottfried Leibniz and the Bernoullis In later years, Newton consid- ered mathematics and physics a recreation and turned much of his energy toward alchemy, theology, and history, particularly problems of chronology Newton achieved many honors over his years of service to the advancement of science and mathematics, as well as for his role as war- den, then master, of the mint He represented Cambridge University 189 501 Critical Reading Questions in Parliament, and was president of the Royal Society from 1703 until (65) his death in 1727 Sir Isaac Newton was knighted in 1705 by Queen Anne Newton never married, nor had any recorded children He died in London and was buried in Westminster Abbey Based on Newton’s quote in lines 6–10 of the passage, what can best be surmised about the famous apple falling from the tree? There was no apple falling from a tree—it was entirely made up Newton never sits beneath apple trees Newton got distracted from his theory on gravity by a fallen apple Newton used the apple anecdote as an easily understood illus- tration of the Earth’s gravitational pull Newton invented a theory of geometry for the trajectory of apples falling perpendicularly, sideways, and up and down 343 a b c d e 344 In what capacity was Newton employed? a Physics Professor, Trinity College b Trinity Professor of Optics c Professor of Calculus at Trinity College d Professor of Astronomy at Lucasian College e Professor of Mathematics at Cambridge 345 In line 36, what does the term clockwork universe most nearly mean? a eighteenth-century government b the international dateline c Newton’s system of latitude d Newton’s system of longitude e Newton’s Laws of Motion 346 According to the passage, how did Newton affect Kepler’s work? a He discredited his theory at Cambridge, choosing to read Descartes instead b He provides an explanation of Kepler’s laws of planetary motion c He convinced the Dean to teach Kepler, Descartes, Galileo, and Copernicus instead of Aristotle d He showed how Copernicus was a superior astronomer to Kepler e He did not understand Kepler’s laws, so he rewrote them in English 190 501 Critical Reading Questions 347 Which of the following is NOT an accolade received by Newton? a Member of the Royal Society b Order of Knighthood c Master of the Royal Mint d Prime Minister, Parliament e Lucasian Professor of Mathematics 348 Of the following, which is last in chronology? a Pftilosopftiae naturalis principia matftematica b Memoirs of Sir Isaac Newton’s Life c Newton’s Laws of Motion d Optiks e invention of a reflecting telescope 349 Which statement best summarizes the life of Sir Isaac Newton? a distinguished inventor, mathematician, physicist, and great thinker of the seventeenth century b eminent mathematician, physicist, and scholar of the Renaissance c noteworthy physicist, astronomer, mathematician, and British Lord d from master of the mint to master mathematician: Lord Isaac Newton e Isaac Newton: founder of calculus and father of gravity Questions 366–373 are based on the following passage This passage outlines the past and present use of asbestos, the potential health hazard associated with this material, and how to prevent exposure (1) (5) (10) Few words in a contractor’s vocabulary carry more negative connotations than asbestos According to the Asbestos Network, “touted as a miracle substance,” asbestos is the generic term for several naturally occurring mineral fibers mined primarily for use as fireproof insula- tion Known for strength, flexibility, low electrical conductivity, and resistance to heat, asbestos is comprised of silicon, oxygen, hydrogen, and assorted metals Before the public knew asbestos could be harm- ful to one’s health, it was found in a variety of products to strengthen them and to provide insulation and fire resistance Asbestos is generally made up of fiber bundles that can be broken up into long, thin fibers We now know from various studies that when this friable substance is released into the air and inhaled into the lungs over a period of time, it can lead to a higher risk of lung cancer and a 191 501 Critical Reading Questions (15) (20) (25) (30) (35) (40) (45) (50) (55) condition known as asbestosis Asbestosis, a thickening and scarring of the lung tissue, usually occurs when a person is exposed to high asbestos lev- els over an extensive period of time Unfortunately, the symptoms not usually appear until about twenty years after initial exposure, mak- ing it difficult to reverse or prevent In addition, smoking while exposed to asbestos fibers could further increase the risk of developing lung can- cer When it comes to asbestos exposure in the home, school, and work- place, there is no safe level; any exposure is considered harmful and dangerous Prior to the 1970s asbestos use was ubiquitous—many com- mercial building and home insulation products contained asbestos In the home in particular, there are many places where asbestos hazards might be present Building materials that may contain asbestos include fireproofing material (sprayed on beams), insulation material (on pipes and oil and coal furnaces), acoustical or soundproofing material (sprayed onto ceilings and walls), and in miscellaneous materials, such as asphalt, vinyl, and cement to make products like roofing felts, shingles, siding, wallboard, and floor tiles We advise homeowners and concerned consumers to examine mate- rial in their homes if they suspect it may contain asbestos If the mate- rial is in good condition, fibers will not break down, releasing the chemical debris that may be a danger to members of the household Asbestos is a powerful substance and should be handled by an expert Do not touch or disturb the material—it may then become damaged and release fibers Contact local health, environmental, or other appropri- ate officials to find out proper handling and disposal procedures, if war- ranted If asbestos removal or repair is needed you should contact a professional Asbestos contained in high-traffic public buildings, such as schools presents the opportunity for disturbance and potential exposure to students and employees To protect individuals, the Asbestos Hazard Emergency Response Act (AHERA) was signed in 1986 This law requires public and private non-profit primary and secondary schools to inspect their buildings for asbestoscontaining building materials The Environmental Protection Agency (EPA) has pub- lished regulations for schools to follow in order to protect against asbestos contamination and provide assistance to meet the AHERA requirements These include performing an original inspection and periodic re-inspections every three years for asbestos containing material; developing, maintaining, and updating an asbestos man- agement plan at the school; providing yearly notification to parent, teacher, and employee organizations regarding the availability of the school’s asbestos management plan and any asbestos abatement 192 501 Critical Reading Questions actions taken or planned in the school; designating a contact person to ensure the responsibilities of the local education agency are prop- erly implemented; performing periodic surveillance of known or sus- pected asbestos-containing building material; and providing custodial (60) staff with asbestos awareness training 350 In line 12 the word friable most nearly means a ability to freeze b warm or liquid c easily broken down d poisonous e crunchy 351 Which title would best describe this passage? a The EPA Guide to Asbestos Protection b Asbestos Protection in Public Buildings and Homes c Asbestos in American Schools d The AHERA—Helping Consumers Fight Asbestos-Related Disease e How to Prevent Lung Cancer and Asbestosis 352 According to this passage, which statement is true? a Insulation material contains asbestos fibers b Asbestos in the home should always be removed c The AHERA protects private homes against asbestos d Asbestosis usually occurs in a person exposed to high levels of asbestos e Asbestosis is a man-made substance invented in the 1970s 353 In line 23, the word ubiquitous most nearly means a sparse b distinctive c restricted d perilous e universal 354 Lung cancer and asbestosis are a dangerous fibers b forms of serious lung disease c always fatal d only caused by asbestos inhalation e the most common illnesses in the United States 193 501 Critical Reading Questions 355 The main purpose of this passage is to a teach asbestos awareness in the home and schools b explain the specifics of the AHERA c highlight the dangers of asbestos to your health d provide a list of materials that may include asbestos e use scare tactics to make homeowners move to newer houses 356 The tone of this passage is best described as a cautionary b apathetic c informative d admonitory e idiosyncratic 357 For whom is the author writing this passage? a professional contractors b lay persons c students d school principals e health officials Questions 374–381 are based on the following two passages The following two passages tell of geometry’s Divine Proportion, 1.618 PASSAf tE (1) (5) (10) PHI, the Divine Proportion of 1.618, was described by the astronomer Johannes Kepler as one of the “two great treasures of geometry.” (The other is the Pythagorean theorem.) PHI is the ratio of any two sequential numbers in the Fibonacci sequence If you take the numbers and 1, then create each subse- quent number in the sequence by adding the previous two numbers, you get the Fibonacci sequence For example, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 If you sum the squares of any series of Fibonacci num- bers, they will equal the last Fibonacci number used in the series times the next Fibonacci number This property results in the Fibonacci spi- ral seen in everything from seashells (15) 2 2 to galaxies, and is written math- ematically as: + + + + = × Plants illustrate the Fibonacci series in the numbers of leaves, the arrangement of leaves around the stem, and in the positioning of leaves, sections, and seeds A sunflower seed illustrates this principal 194 501 Critical Reading Questions (20) (25) (30) (35) (40) as the number of clockwise spirals is 55 and the number of counter- clockwise spirals is 89; 89 divided by 55 = 1.618, the Divine Propor- tion Pinecones and pineapples illustrate similar spirals of successive Fibonacci numbers PHI is also the ratio of five-sided symmetry It can be proven by using a basic geometrical figure, the pentagon This five-sided figure embodies PHI because PHI is the ratio of any diagonal to any side of the pentagon—1.618 Say you have a regular pentagon ABCDE with equal sides and equal angles You may draw a diagonal as line AC connecting any two ver- texes of the pentagon You can then install a total of five such lines, and they are all of equal length Divide the length of a diagonal AC by the length of a side AB, and you will have an accurate numerical value for PHI—1.618 You can draw a second diagonal line, BC inside the pen- tagon so that this new line crosses the first diagonal at point O What occurs is this: Each diagonal is divided into two parts, and each part is in PHI ratio (1.618) to the other, and to the whole diagonal—the PHI ratio recurs every time any diagonal is divided by another diagonal When you draw all five pentagon diagonals, they form a fivepoint star: a pentacle Inside this star is a smaller, inverted pentagon Each diagonal is crossed by two other diagonals, and each segment is in PHI ratio to the larger segments and to the whole Also, the inverted inner pentagon is in PHI ratio to the initial outer pentagon Thus, PHI is the ratio of five-sided symmetry Inscribe the pentacle star inside a pentagon and you have the pen- tagram, symbol of the ancient Greek School of Mathematics founded by Pythagoras—solid evidence that the ancient Mystery Schools knew about PHI and appreciated the Divine Proportion’s multitude of uses to form our physical and biological worlds PASSAf tE (1) (5) (10) Langdon turned to face his sea of eager students “Who can tell me what this number is?” A long-legged math major in back raised his hand “That’s the num- ber PHI.” He pronounced it fee “Nice job, Stettner,” Langdon said “Everyone, meet PHI.” [ ] “This number PHI,” Langdon continued, “one-point-six-oneeight, is a very important number in art Who can tell me why?” [ ] “Actually,” Langdon said, [ ] “PHI is generally considered the most beautiful number in the universe.” [ ] As Langdon loaded his slide projector, he explained that the number PHI was derived from the 195 501 Critical Reading Questions (15) (20) (25) (30) (35) (40) (45) (50) Fibonacci sequence—a progression famous not only because the sum of adjacent terms equaled the next term, but because the quotients of adjacent terms possessed the astonishing property of approaching the number 1.618—PHI! Despite PHI’s seemingly mystical mathematical origins, Langdon explained, the truly mind-boggling aspect of PHI was its role as a fun- damental building block in nature Plants, animals, even human beings all possessed dimensional properties that adhered with eerie exactitude to the ratio of PHI to “PHI’s ubiquity in nature clearly exceeds coincidence, and so the ancients assumed the number PHI must have been preordained by the creator of the universe Early scientists heralded 1.618 as the Divine Proportion.” [ ] Langdon advanced to the next slide—a close-up of a sun- flower’s seed head “Sunflower seeds grow in opposing spirals Can you guess the ratio of each rotation’s diameter to the next? “1.618.” “Bingo.” Langdon began racing through slides now—spiraled pinecone petals, leaf arrangement on plant stalks, insect segmenta- tion—all displaying astonishing obedience to the Divine Proportion “This is amazing!” someone cried out “Yeah,” someone else said, “but what does it have to with art?” [ ] “Nobody understood better than da Vinci the divine struc- ture of the human body He was the first to show that the human body is literally made of building blocks whose proportional ratios always equal PHI.” Everyone in class gave him a dubious look “Don’t believe me?” Try it Measure the distance from your shoulder to your fingertips, and then divide it by the distance from your elbow to your fingertips PHI again Another? Hip to floor divided by knee to floor PHI again Finger joints Toes Spinal divi- sions PHI, PHI, PHI My friends, each of you is a walking tribute to the Divine Proportion.” [ ]”In closing,” Langdon said, “we return to symbols.” He drew five intersecting lines that formed a five-pointed star “This symbol is one of the most powerful images you will see this term Formally known as a pentagram—or pentacle, as the ancients called it—the symbol is considered both divine and magical by many cultures Can anyone tell me why that may be?” Stettner, the math major, raised his hand “Because if you draw a pentagram, the lines automatically divide themselves into segments according to the Divine Proportion.” 196 501 Critical Reading Questions Landgon gave the kid a proud nod “Nice job Yes, the ratios of line segments in a pentacle all equal PHI, making the symbol the ultimate expression of the Divine Proportion.” 358 The tone of Passage may be described as a fascinated discovery b blandly informative c passionate unfolding d droll and jaded e dry and scientific 359 According to both passages, which of the following are synonyms? a pentagon and pentacle b pinecones and sunflower seed spirals c Divine Proportion and PHI d Fibonacci sequence and Divine Proportion e Fibonacci sequence and PHI 360 In Passage 2, line 20, ubiquity of PHI most nearly means its a rareness in nature b accuracy in nature c commonality in nature d artificiality against nature e purity in an unnatural state Both passages refer to the “mystical mathematical” side of PHI Based on the two passages, which statement is NOT another aspect of PHI? PHI is a ratio found in nature PHI is the area of a regular pentagon PHI is one of nature’s building blocks PHI is derived from the Fibonacci sequence PHI is a math formula 361 a b c d e Which of the following techniques is used in Passage 1, lines 13–18 and Passage 2, lines 24–26? explanation of terms comparison of different arguments contrast of opposing views generalized statement illustration by example 362 a b c d e 197 501 Critical Reading Questions All of the following questions can be explicitly answered on the basis of the passage EXCEPT What is the ratio of the length of one’s hip to floor divided by knee to floor? What is the precise mathematical ratio of PHI? What is the ratio of the length of one’s shoulder to fingertips divided by elbow to fingertips? What is the ratio of the length of one’s head to the floor divided by shoulder’s to the floor? What is the ratio of each sunflower seed spiral rotation’s diameter to the next? 363 a b c d e According to both passages, the terms ancient Mystery Scftools (Passage 1, line 43), early scientists (Passage 2, line 22), and ancients (Passage 2, line 46) signify what about the divine proportion? Early scholars felt that the Divine Proportion was a magical number Early scholars found no scientific basis for the Divine Proportion Early mystery writers used the Divine Proportion Early followers of Pythagoras favored the Pythagorean theorem over the divine proportion Early followers of Kepler used the Divine Proportion in astronomy 364 a b c d e 365 Which of the following is NOT true of the pentagon? a It is considered both divine and magical by many cultures b It is a geometric figure with five equal sides meeting at five equal angles c It is a geometric figure whereby PHI is the ratio of any diagonal to any side d If you draw an inverted inner pentagon inside a pentagon, it is in PHI ratio to the initial outer pentagon e A polygon having five sides and five interior angles is called a pentagon Questions 382–390 are based on the following passage The following passage describes the composition and nature of ivory (1) Ivory skin, ivory teeth, Ivory Soap, Ivory Snow—we hear “ivory” used all the time to describe something fair, white, and pure But where does ivory come from, and what exactly is it? Is it natural or man- [...]... and Passage 2, lines 24–26? explanation of terms comparison of different arguments contrast of opposing views generalized statement illustration by example 362 a b c d e 197 501 Critical Reading Questions All of the following questions can be explicitly answered on the basis of the passage EXCEPT What is the ratio of the length of one’s hip to floor divided by knee to floor? What is the precise mathematical... the Fibonacci series in the numbers of leaves, the arrangement of leaves around the stem, and in the positioning of leaves, sections, and seeds A sunflower seed illustrates this principal 194 501 Critical Reading Questions (20) (25) (30) (35) (40) as the number of clockwise spirals is 55 and the number of counter- clockwise spirals is 89; 89 divided by 55 = 1.618, the Divine Propor- tion Pinecones and... said, [ ] “PHI is generally considered the most beautiful number in the universe.” [ ] As Langdon loaded his slide projector, he explained that the number PHI was derived from the 195 501 Critical Reading Questions (15) (20) (25) (30) (35) (40) (45) (50) Fibonacci sequence—a progression famous not only because the sum of adjacent terms equaled the next term, but because the quotients of adjacent... why that may be?” Stettner, the math major, raised his hand “Because if you draw a pentagram, the lines automatically divide themselves into segments according to the Divine Proportion.” 196 501 Critical Reading Questions Landgon gave the kid a proud nod “Nice job Yes, the ratios of line segments in a pentacle all equal PHI, making the symbol the ultimate expression of the Divine Proportion.” 358 The.. .501 Critical Reading Questions 355 The main purpose of this passage is to a teach asbestos awareness in the home and schools b explain the specifics of the AHERA c highlight the dangers of asbestos to your health... cautionary b apathetic c informative d admonitory e idiosyncratic 357 For whom is the author writing this passage? a professional contractors b lay persons c students d school principals e health officials Questions 374–381 are based on the following two passages The following two passages tell of geometry’s Divine Proportion, 1.618 PASSAf tE 1 (1) (5) (10) PHI, the Divine Proportion of 1.618, was described... diagonal to any side d If you draw an inverted inner pentagon inside a pentagon, it is in PHI ratio to the initial outer pentagon e A polygon having five sides and five interior angles is called a pentagon Questions 382–390 are based on the following passage The following passage describes the composition and nature of ivory (1) Ivory skin, ivory teeth, Ivory Soap, Ivory Snow—we hear “ivory” used all the