Science and Nature Critical Reading
Questions 1–7 are based on the following passage.
This passage details the life and illustrious career of Sir Isaac Newton, preeminent scientist and mathematician.
Tradition has it that Newton was sitting under an apple tree when an apple fell on his head, and this made him understand that earthly and celestial gravitation are the same. A contemporary writer, William Stukeley, recorded in his Memoirs of Sir Isaac Newton's Life a conversation with Newton in Kensington on April 15, 1726, in which Newton recalled "when formerly, the notion of gravitation came into his mind. It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the round, thought he to himself. Why should it not go sideways or upwards, but constantly to the earth's centre."
Sir Isaac Newton, English mathematician, philosopher, and physicist, was born in 1642 in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire. His father had died three months before Newton's birth, and two years later his mother went to live with her new husband, leaving her son in the care of his grandmother. Newton was educated at Grantham Grammar School. In 1661 he joined Trinity College, Cambridge, and continued there as Lucasian professor of mathematics from 1669 to 1701. At that time the college's teachings were based on those of Aristotle, but Newton preferred to read the more advanced ideas of modern philosophers such as Descartes, Galileo, Copernicus, and Kepler. In 1665, he discovered the binomial 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 Universal Gravitation and discovered that white light is composed of all the colors of the spectrum. These findings enabled him to make fundamental 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 Philosophiae naturalis principia mathematica (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 discoveries 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 considered 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 warden, then master, of the mint. He represented Cambridge University in Parliament, and was president of the Royal Society from 1703 until in Parliament, and was president of the Royal Society from 1703 until 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 illustration of the Earth's gravitational pull.
- Newton invented a theory of geometry for the trajectory of apples falling perpendicularly, sideways, and up and down.
- In what capacity was Newton employed?
- Physics Professor, Trinity College
- Trinity Professor of Optics
- Professor of Calculus at Trinity College
- Professor of Astronomy at Lucasian College
- Professor of Mathematics at Cambridge
- In line 36, what does the term clockwork universe most nearly mean?
- eighteenth-century government
- the international dateline
- Newton's system of latitude
- Newton's system of longitude
- Newton's Laws of Motion
- According to the passage, how did Newton affect Kepler's work?
- He discredited his theory at Cambridge, choosing to read Descartes instead.
- He provides an explanation of Kepler's laws of planetary motion.
- He convinced the Dean to teach Kepler, Descartes, Galileo, and Copernicus instead of Aristotle.
- He showed how Copernicus was a superior astronomer to Kepler.
- He did not understand Kepler's laws, so he rewrote them in English.
- Which of the following is NOT an accolade received by Newton?
- Which of the following is NOT an accolade received by Newton?
- Order of Knighthood
- Master of the Royal Mint
- Prime Minister, Parliament
- Lucasian Professor of Mathematics
- Of the following, which is last in chronology?
- Philosophiae naturalis principia mathematica
- Memoirs of Sir Isaac Newton's Life
- Newton's Laws of Motion
- Optiks
- invention of a reflecting telescope
- Which statement best summarizes the life of Sir Isaac Newton?
- distinguished inventor, mathematician, physicist, and great thinker of the seventeenth century
- eminent mathematician, physicist, and scholar of the Renaissance
- noteworthy physicist, astronomer, mathematician, and British Lord
- from master of the mint to master mathematician: Lord Isaac Newton
- Isaac Newton: founder of calculus and father of gravity
Questions 8–15 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.
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 insulation. 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 harmful 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 condition known as asbestosis. Asbestosis, a thickening and scarring of the lung tissue, usually occurs when a person is exposed to high asbestos levels over an extensive period of time. Unfortunately, the symptoms do not usually appear until about twenty years after initial exposure, making it difficult to reverse or prevent. In addition, smoking while exposed to asbestos fibers could further increase the risk of developing lung cancer. When it comes to asbestos exposure in the home, school, and workplace, there is no safe level; any exposure is considered harmful and dangerous. Prior to the 1970s asbestos use was ubiquitous—many commercial 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 material in their homes if they suspect it may contain asbestos. If the material 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 appropriate officials to find out proper handling and disposal procedures, if warranted. 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 asbestos-containing building materials. The Environmental Protection Agency (EPA) has published 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 management 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 actions taken or planned in the school; designating a contact person to ensure the responsibilities of the local education agency are properly implemented; performing periodic surveillance of known or suspected asbestos-containing building material; and providing custodial staff with asbestos awareness training.
- In line 12 the word friable most nearly means
- ability to freeze.
- warm or liquid.
- easily broken down.
- poisonous.
- crunchy.
- Which title would best describe this passage?
- The EPA Guide to Asbestos Protection
- Asbestos Protection in Public Buildings and Homes
- Asbestos in American Schools
- The AHERA—Helping Consumers Fight Asbestos-Related Disease
- How to Prevent Lung Cancer and Asbestosis
- According to this passage, which statement is true?
- Insulation material contains asbestos fibers.
- Asbestos in the home should always be removed.
- The AHERA protects private homes against asbestos.
- Asbestosis usually occurs in a person exposed to high levels of asbestos.
- Asbestosis is a man-made substance invented in the 1970s.
- In line 23, the word ubiquitous most nearly means
- sparse.
- distinctive.
- restricted.
- perilous.
- universal.
- Lung cancer and asbestosis are
- dangerous fibers.
- forms of serious lung disease.
- always fatal.
- only caused by asbestos inhalation.
- the most common illnesses in the United States.
- The main purpose of this passage is to
- teach asbestos awareness in the home and schools.
- explain the specifics of the AHERA.
- highlight the dangers of asbestos to your health.
- provide a list of materials that may include asbestos.
- use scare tactics to make homeowners move to newer houses.
- The tone of this passage is best described as
- cautionary.
- apathetic.
- informative.
- admonitory.
- idiosyncratic.
- For whom is the author writing this passage?
- professional contractors
- lay persons
- students
- school principals
- health officials
Questions 16–23 are based on the following two passages.
The following two passages tell of geometry's Divine Proportion, 1.618.
Passage 1
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 0 and 1, then create each subsequent 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 numbers, they will equal the last Fibonacci number used in the series times the next Fibonacci number. This property results in the Fibonacci spiral seen in everything from seashells to galaxies, and is written mathematically as: 1^{2} + 1^{2} + 2^{2} + 3^{2} + 5^{2} = 5 × 8.
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 as the number of clockwise spirals is 55 and the number of counterclockwise spirals is 89; 89 divided by 55 = 1.618, the Divine Proportion. 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 vertexes 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 pentagon 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 five-point 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 pentagram, 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.
Passage 2
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 number PHI." He pronounced it fee.
"Nice job, Stettner," Langdon said. "Everyone, meet PHI." [ . . . ] "This number PHI," Langdon continued, "one-point-six-one-eight, 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 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 fundamental building block in nature. Plants, animals, even human beings all possessed dimensional properties that adhered with eerie exactitude to the ratio of PHI to 1.
"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 segmentation— all displaying astonishing obedience to the Divine Proportion.
"This is amazing!" someone cried out.
"Yeah," someone else said, "but what does it have to do with art?" [ . . . ] "Nobody understood better than da Vinci the divine structure 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 divisions. 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."
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."
- The tone of Passage 2 may be described as
- fascinated discovery.
- blandly informative.
- passionate unfolding.
- droll and jaded.
- dry and scientific.
- According to both passages, which of the following are synonyms?
- pentagon and pentacle
- pinecones and sunflower seed spirals
- Divine Proportion and PHI
- Fibonacci sequence and Divine Proportion
- Fibonacci sequence and PHI
- In Passage 2, line 20, ubiquity of PHI most nearly means its
- rareness in nature.
- accuracy in nature.
- commonality in nature.
- artificiality against nature.
- 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.
- 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
- 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?
- According to both passages, the terms ancient Mystery Schools (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.
- Which of the following is NOT true of the pentagon?
- It is considered both divine and magical by many cultures.
- It is a geometric figure with five equal sides meeting at five equal angles.
- It is a geometric figure with five equal sides meeting at five equal angles.
- If you draw an inverted inner pentagon inside a pentagon, it is in PHI ratio to the initial outer pentagon.
- A polygon having five sides and five interior angles is called a pentagon.