GRE - T-19
Verbal:
Article one : (From GRE offical guide )
According to most scientists, the universe began approximately 10 to 15 billion years ago and has been expanding ever since. This theory, known as the Big Bang theory, is the fairly direct result of Hubble`s law, which states that objects farther away from Earth are receding faster than those closer. This expansion implies a singular point which all matter is expanding from.
Complicating the scientific explanation is that the Big Bang cannot be thought of as an explosion from some identifiable source-rather, space and time were created in the Big Bang. Furthermore, the relationship between distance and speed is not precisely linear. So, if one were to think of galaxies as particles created in a big bang, these galaxies have both a local component of motion, as well as playing a role in the overall expansion of the universe.
A further complication is that galactic distances are so great that galactic motion, even if the galaxies are moving at incredible speeds, is difficult to observe. Scientists must therefore rely on a "standard candle," an object of known brightness within the galaxy they wish to observe. Using the inverse square law, scientists can then measure the how far that galaxy is away from our own. For instance, suppose a supernova in galaxy A appears one hundred times as bright as one in galaxy B. By the inverse square law, galaxy B is ten times farther away than galaxy A, assuming, of course, that distance is the only factor affecting brightness.
It can be inferred from the sentence highlighted in the passage that a standard candle is useful to scientists for which of the following reasons?
(A) Standard candles do not have their own locus of motion.
(B) Standard candles more reliably adhere to the law of inverse squares than do other supernovas.
(C) Only standard candles provide a known measure of brightness.
(D) Knowledge of an object`s brightness of an object allows scientists to measure the speed at which the object is moving toward Earth.
(E) Knowledge of an object`s brightness allows scientists to accurately measure its distance from Earth.
Key)
A further complication is that galactic distances are so great that galactic motion，so the answer is (E).
we can not chose (D) becasue "even if the galaxies are moving at incredible speeds" this sentence is a emphasis, not a main idea.
According to the passage, if two astronomical objects of differing distances from Earth were observed, which of the following would be true of the object closer to Earth?
(A) It would not be as bright as the object farther from Earth.
(B) It would be younger than the object farther from Earth.
(C) It would be traveling away from the Earth more slowly than the farther object.
Key)
This theory, known as the Big Bang theory, is the fairly direct result of Hubble`s law, which states that objects farther away from Earth are receding faster than those closer.
(C)
According to the passage, a standard candle may not provide an accurate measure of distance if
(A) the galaxy being measured is moving too quickly
(B) interstellar dust makes the object measured appear dimmer than it really is
(C) if the galaxy being measured has a local component of measurement
(D) the particles being measured do not completely accord with a linear motion
(E) the galaxies being measured move at different speeds
Key)
Scientists must therefore rely on a "standard candle," an object of known brightness within the galaxy they wish to observe.
(B)
According to the passage, if two supernovas are observed and one of those supernovas is brighter than the other, scientists can conclude that
(A) the brighter supernova is moving closer to our galaxy at a higher speed
(B) the precise location of the supernova is measurable
(C) the brighter supernova may be closer to our own galaxy
(D) the brighter supernova is farther away from Earth by a distance that is roughly inversely proportional to the dim supernova
(E) the distance between the supernovas and our own galaxy is inversely proportional
Key)
By the inverse square law, galaxy B is ten times farther away than galaxy A, assuming, of course, that distance is the only factor affecting brightness.
(C)
Quantitative
有理數，即可化為分數，再細分除得盡（有限小數），除不盡（循環小數）
有限小數的特徵就是分母是2, 5 的倍數，都可以被二跟五整除
EX: 21X6947 / 132，這個數可以化為有限小數。
從分母132先下手，他的因數有2, 3, 11，剛剛以探討過二和五是不會導致循環小數的，所以先不理會，那3, 11必須要跟分子約分掉（必須整除）才能確保是有限小數。
那這樣說，三和十一就必須是21X6947的因數，
3的倍數判定，『數字和』為三的倍數
21X6947，所以2+1+X+6+9+4+7= 29+X，那Ｘ＝1, 4, 7
11 的倍數判定，以個位數為基準『奇位數和-偶位數和』
21X6947，所以 (7+9+X+2) - (4+6+1) = 7+X，那X= 4
，所以Ｘ＝4
三角函數化銳角，
sin (90k + @) ，＠就是俗稱的『戲踏』，當Ｋ是偶數則函數不變，Ｋ是奇數則函數改cos(90k +@)，正弦變餘弦。
（奇變偶不變，正負看象限）看『原』函數的象限
| sin | cos | tan | |
| 90-@ | +cos | +sin | +cot |
| 90+@ | +cos | -sin | -cot |
| 180-@ | +sin | -cos | -tan |
| 180+@ | -sin | -cos | +tan |
| 270-@ | -cos | -sin | +cot |
| 270+@ | -cos | +sin | -cot |
| 360-@ | -sin | +cos | -tan |
| -@ | -sin | +cos | -tan |
資料來源：李翔數學，堪稱一絕
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