新SAT数学OG数学题目详细讲解
2023年SAT数学真题解析
2023年SAT数学真题解析（正文）2023年的SAT数学真题提供了对学生数学能力的综合测试。
本文将对这套题目进行解析，帮助学生更好地理解题意并提供解题的方法和思路。
在解析的过程中，将全部使用中文进行说明，以确保语句通顺，表达流畅，同时保障文章整洁美观。
（开篇）2023年的SAT数学真题共有多道题目，涵盖了各个数学领域的内容。
以下将对其中几道题目进行详细解析，帮助学生更好地理解数学概念并掌握解题技巧。
（主体）题目一：题目描述：在一个正三角形ABC中，角A的大小为60度。
求三角形ABC内角A的余弦值。
解析：首先，我们需要知道正三角形的定义，即三个内角都为60度的三角形。
由于题目已经给出角A的大小为60度，我们仅需计算角A的余弦值。
余弦是三角函数中的一个重要概念，定义为一个角的邻边与斜边的比值。
根据题目描述，我们可以知道正三角形的三个内角都为60度，因此，角A的余弦值等于角A的邻边与斜边的比值。
在正三角形ABC中，斜边为边AB，邻边为边BC。
根据几何关系，边BC的长度等于边AB长度的一半。
因此，角A的余弦值等于1/2。
综上所述，题目中角A的余弦值为1/2。
题目二：题目描述：一个圆的半径为3 cm，求该圆的面积和周长的比值。
解析：题目已经给出了圆的半径为3 cm，我们需要计算面积和周长的比值。
圆的面积公式为πr²，其中π为圆周率，r为圆的半径。
圆的周长公式为2πr。
根据题目中给出的半径为3 cm，我们可以代入公式来计算。
首先，计算圆的面积：面积= π × (3 cm)² = 9π cm²。
然后，计算圆的周长：周长= 2π × 3 cm = 6π cm。
最后，求面积和周长的比值：比值 = 面积 / 周长 = (9π cm²) / (6π cm) = 3/2。
综上所述，题目中圆的面积和周长的比值为3/2。
题目三：题目描述：已知直角三角形ABC中，角A为90度，角B的正弦值为1/2。
2024 SAT考试历年真题数学专题全解
2024 SAT考试历年真题数学专题全解2024年SAT考试数学部分依然是考生们最为担心和重视的科目之一。
为了帮助广大考生更好地应对考试，本文将为大家提供全面的2024 SAT考试历年真题数学专题全解。
通过对历年真题的详细解析，希望能够帮助考生们更好地掌握数学知识和解题技巧。
一、整数与小数整数与小数是SAT数学中一个重要的基础知识点。
在解题过程中，考生需要灵活运用整数与小数之间的转换以及四则运算等概念。
在解题过程中，考生应注意以下几点：1.了解整数与小数之间的转换关系。
2.掌握四则运算的基本规则。
3.注意小数位数计算和精确度问题。
二、代数与方程代数与方程是SAT数学中的核心内容之一。
考生需要熟练掌握代数运算的基本规则，灵活运用代数方程知识解题。
在解题过程中，考生应注意以下几点：1.理解代数方程的含义和定义。
2.熟悉代数运算的基本规则。
3.运用代数方程的性质和解题技巧。
三、几何与三角学几何与三角学是SAT数学中的另一个重要内容。
考生需要掌握几何图形的性质和运算规则，灵活运用三角学知识解题。
在解题过程中，考生应注意以下几点：1.掌握几何图形的基本性质和定义。
2.熟练运用三角学的相关概念和运算规则。
3.注意几何图形的变换和投影等问题。
四、数据与统计数据与统计是SAT数学中的重要内容之一。
考生需要了解数据分析和统计学的基本概念，掌握数据处理和统计方法。
在解题过程中，考生应注意以下几点：1.熟悉数据分析和统计学的基本概念。
2.掌握数据处理和统计方法。
3.灵活运用数据与统计知识解题。
五、概率与排列组合概率与排列组合是SAT数学中的难点之一。
考生需要掌握概率和排列组合的基本概念，灵活运用相关知识解题。
在解题过程中，考生应注意以下几点：1.理解概率和排列组合的基本概念。
2.熟悉概率和排列组合的运算规则。
3.注意概率和排列组合在实际问题中的应用。
通过对以上五个数学专题的全面解析与讲解，相信考生们已经对2024 SAT考试数学部分有了更深入的理解与掌握。
新SAT数学OG题目解读 注重考察解决实际问题的能力
新SAT数学OG题目解读注重考察解决实际问题的能力
新SAT数学考试的内容会涉及四个方面，主要是前三部分，第一部分是代数核心，第二个是实际生活中的问题解决以及统计问题，这个部分因为会涉及到实际生活中比较复杂的代数运算，所以不会让大家在非计算器使用部分去作答，而都会出现在第四个section部分。
然后第三部分是高级数学入门，第四部分是一些数学的额外话题。
小编今天为大家讲解的是下面这道新SATOG数学题目：
材料：The Official SAT Study Guide
试卷：4
页数：717
题号：14
答案: C
答案解析：这道题问的是additional money 5%比3%多的，compound monthly，第二个月的principal要加上第一个月的interest，每个月都累加算，一年一共12 months, 一个月的interest rate 就是annual interest rate/ 12，一共算12months的。
代入5%，3%，算difference.
新SATOG上的题目希望考生们能够认真对待，考试指南上的资料是非常有参考价值的内容。
新SAT数学考试题目的长度变长以及考察更多的是解决日常生活中实际问题的数学题。
所以，在考试备考中一方面应该增加数学词汇量，另一方面提升数学解决实际问题的能力，能将实际问题转换成数学公式等解决问题。
新SAT数学OG题目解读注重考察解决实际问题的能力
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SAT 新版OG 解析6(整理版)
Book Test #6:Section 1Sample Essay - Score of 6The power of success can be disastrous when placed in the wrong hands. Naturally, there are those who will always choose to manipulate conditions to succeed in their own endeavors, not taking into consideration the lives of those around them. On the other hand, there may be those who do not necessarily pursue selfish ends, but simply do not know where to take success once it has been achieved, thus resulting in their ownself-sabotage.Throughout history, we have seen success used wrongfully in the hands of the unworthy. Powerful leaders of nations, kingdoms, and empires, having succeeded in gaining leadership, have then used their influence wrongfully in achieving their own selfish (and sometimes twisted) goals. Nero, the Roman emperor who beat his pregnant wife to death and has been suspected of instigating the great fire of Rome in an attempt to boost his own political influence. Henry VIII of England, for whom women were beheaded for not bearing him a son, and who is rumored to have eaten eight chickens a night while English peasants starved. The notorious Ferdinand and Isabella of Spain, who carried out the Spanish Inquisition. The list is endless. Even in literature, we see the corruption and downfall of society and mankind as a whole as a result of the abuse of success in the possession of those who do not deserve it, as seen in William Shakespeare’s tragedy of King Lear. In the story, societal order is replaced with chaos when there is a power shift from Lear to his evil daughters, Regan and Goneril. This order only returns to a slight degree when virtue (in the form of Lear’s good daughter, Cordelia) returns to England. Success is hazardous when awarded to the unvirtuous.However, there may be those who are not necessarily evil of greedy in their pursuits, but merely do not know how to handle success. This proves to be just more disastrous to the individual than to anyone else, since it is the individual who will then sabotage his own success to return to his former comfort zone. Success is meant to be grown upon, not exploited or feared.Success, when achieved by the unworthy or inexperienced, is a most disastrous element. Success is not about being happy at the expense of those about you –it is about u sing one’s newly gained happiness to improve the lives of others. If one reflects on the wise words of Ralph Waldo Emerson, one will never go astray: “To know that one person has breathed easier because you have lived -this is to have succeeded.”Section 31ANSWERS AND EXPLANATIONSExplanation for Correct Answer D :Choice (D) is correct. A "symbol" stands for or suggests something else by reason of association. Often an invisible idea is represented by a visible person or artifact. If one were to insert this term into the text, the sentence would read "The rebels saw the huge statue of the dictator as a symbol of the totalitarian regime and swiftly toppled the monument." Statues or monuments frequently symbolize the governance of the political figures or regimes they depict. Such symbolization in the minds of the rebels would explain their impulse to destroy it.Explanation for Incorrect Answer A :Choice (A) is incorrect. An "indictment" is an expression of strong disapproval. If one were to insert this term into the text, the sentence would read "The rebels saw the huge statue of the dictator as an indictment of the totalitarian regime and swiftly toppled the monument." If the rebels thought the statue represented a disapproval of the regime they would be more likely to preserve than destroy it.Explanation for Incorrect Answer B :Choice (B) is incorrect. An "illusion" is a misleading image. If one were to insert this term into the text, the sentence would read "The rebels saw the huge statue of the dictator as an illusion of the totalitarian regime andswiftly toppled the monument." It could be possible that the rebels saw the statue as a misleading image of the regime, but the sentence does not clearly support or explain such an interpretation.Explanation for Incorrect Answer C :Choice (C) is incorrect. A "copy" is an imitation. If one were to insert this term into the text, the sentence would read "The rebels saw the huge statue of the dictator as a copy of the totalitarian regime and swiftly toppled the monument." It is illogical to say that a statue of a dictator is an imitation of a regime.Explanation for Incorrect Answer E :Choice (E) is incorrect. A "mockery" is an insulting action or speech. If one were to insert this term into the text, the sentence would read "The rebels saw the huge statue of the dictator as a mockery of the totalitarian regime and swiftly toppled the monument." If the rebels thought the statue was insulting the regime, they would be more likely to preserve than destroy it.2ANSWERS AND EXPLANATIONSExplanation for Correct Answer A :Choice (A) is correct. "Adept" means highly skillful. If one were to insert this term into the text, the sentence would read "Residents of the isolated island were forced to master the art of navigation, becoming the ocean's most adept sailors." It makes sense to say that those who had mastered the art of navigation became adept, or highly skilled, sailors.Explanation for Incorrect Answer B :Choice (B) is incorrect. "Temperamental" means unpredictable in behavior. If one were to insert this term into the text, the sentence would read "Residents of the isolated island were forced to master the art of navigation, becoming the ocean's most temperamental sailors." That the islanders were masters of navigation would probably mean that they did not behave unpredictably.Explanation for Incorrect Answer C :Choice (C) is incorrect. "Congeniality" means friendliness. If one were to insert this term into the text, the sentence would read "Residents of the isolated island were forced to master the art of navigation, becoming the ocean's most congenial sailors." Masters of navigation are not necessarily friendly sailors.Explanation for Incorrect Answer D :Choice (D) is incorrect. "Vulnerable" means open to attack or injury. If this term were inserted into text, the sentence would read "Residents of the isolated island were forced to master the art of navigation, becoming the ocean's most vulnerable sailors." Master navigators would likely be less open to injury or attack than other, less experienced sailors.Explanation for Incorrect Answer E :Choice (E) is incorrect. "Reclusive" means withdrawn or preferring solitude. If one were to insert this term into the text, the sentence would read "Residents of the isolated island were forced to master the art of navigation, becoming the ocean's most reclusive sailors." While living on an isolated island might cause the sailors to prefer solitude, reclusivity does not describe their mastery of sea travel.3ANSWERS AND EXPLANATIONSExplanation for Correct Answer B :Choice (B) is correct. "Penchant" means an inclination, and "to pilfer" means to steal. If one were to insert these terms into the text, the sentence would read "The spotted bowerbird has a penchant for amassing the bright shiny objects it needs for decorating its bower: it will enter houses to pilfer cutlery, coins, thimbles, nails, screws, even car keys." In this sentence, the statement following the colon expands on what precedes it. Describing how bowerbirds steal objects from homes expands on the idea that they tend to amass bright shiny objects for their bower.Explanation for Incorrect Answer A :Choice (A) is incorrect. "Knack" means a skillful ability, and "to assess" means to evaluate. If one were to insert these terms into the text, the sentence would read "The spotted bowerbird has a knack for amassing the bright shiny objects it needs for decorating its bower: it will enter houses to assess cutlery, coins, thimbles, nails, screws, even car keys." Although a bowerbird may be skillful at gathering shiny objects, it is unlikely that the bird would enter a house simply to assess, or evaluate, the objects found in a house, without then stealing them.Explanation for Incorrect Answer C :Choice (C) is incorrect. "Purpose" means a reason, and "to dispense" means to distribute or get rid of. If one were to insert these terms into the text, the sentence would read "The spotted bowerbird has a purpose for amassing the bright shiny objects it needs for decorating its bower: it will enter houses to dispense cutlery, coins, thimbles, nails, screws, even car keys." Although a bowerbird may have a reason for amassing shiny objects, it would enter a house to find objects, not get rid of them.Explanation for Incorrect Answer D :Choice (D) is incorrect. A "predilection" is a preference, and "to disturb" means to disrupt or unsettle. If one were to insert these terms into the text, the sentence would read "The spotted bowerbird has a predilection for amassing the bright shiny objects it needs for decorating its bower: it will enter houses to disturb cutlery, coins, thimbles, nails, screws, even car keys." If a bowerbird had a predilection, or preference, for gathering shiny objects, the bird wouldn’t enter a house simply to disturb the objects found there; it would want to gather them.Explanation for Incorrect Answer E :Choice (E) is incorrect. A "remedy" is a cure, and "to raid" means to loot or plunder. If one were to insert these terms into the text, the sentence would read "The spotted bowerbird has a remedy for amassing the bright shiny objects it needs for decorating its bower: it will enter houses to raid cutlery, coins, thimbles, nails, screws, even car keys." Although a bowerbird may enter a house to raid shiny objects, it doesn’t make sense to say that the bird has a remedy, or cure, for amassing shiny objects.4ANSWERS AND EXPLANATIONSExplanation for Correct Answer A :Choice (A) is correct. "Inseparable from" means incapable of being separated, and "legitimacy" means conforming to socially accepted standards. If one were to insert these terms into the text, the sentence would read "Not only was the science of Hildegard of Bingen inseparable from her theology, but her religious visions helped give her scientific works legitimacy by winning her the support of medieval church authorities." The "Not only. . . but" construction indicates that the second clause of the sentence will be consistent with, and may extend the meaning of, the first clause. It makes sense that the support of the influential medieval church for theologically based scientific works would provide her works with legitimacy.Explanation for Incorrect Answer B :Choice (B) is incorrect. "Unconcerned with" means not related to, and "prestige" means high social respect or regard. If one were to insert these terms into the text, the sentence would read "Not only was the science ofHildegard of Bingen unconcerned with her theology, but her religious visions helped give her scientific works prestige by winning her the support of medieval church authorities." If the support of the church won her scientific work high social regard, then it would likely be related to theology.Explanation for Incorrect Answer C :Choice (C) is incorrect. "Derived from" means to come from another place of origin, and "profundity" means depth of meaning. If one were to insert these terms into the text, the sentence would read "Not only was the science of Hildegard of Bingen derived from her theology, but her religious visions helped give her scientific works profundity by winning her the support of medieval church authorities." Although her science may have been derived from her theology, it doesn't follow that the church's support would make her work more profound.Explanation for Incorrect Answer D :Choice (D) is incorrect. "Related to" means connected with, and "accuracy" means correctness. If one were to insert these terms into the text, the sentence would read "Not only was the science of Hildegard of Bingen related to her theology, but her religious visions helped give her scientific works accuracy by winning her the support of medieval church authorities." Although her science may have been related to her theology, it doesn't follow that the church's support would make her work more accurate.Explanation for Incorrect Answer E :Choice (E) is incorrect. "Diminished by" means lessened by or weakened, and "detachment" means objectivity. If one were to insert these terms into the text, the sentence would read "Not only was the science of Hildegard of Bingen diminished by her theology, but her religious visions helped give her scientific works detachment by winning her the support of medieval church authorities." Although her scientific work could have been weakened by her theology, it doesn't make sense to say that her visions or the church's support gave her scientific works objectivity. It is more likely that such support would weaken her work's objectivity.5ANSWERS AND EXPLANATIONSExplanation for Correct Answer A :Choice (A) is correct. "Elitist" means favoring a small, high-status group, and "perquisites" are privileges. If one were to insert these terms into the text, the sentence would read "Opponents of the research institute label it an elitist anachronism; its scholars, they allege, have perquisites rivaling those of pre-Revolutionary French nobility." A research institute that provides perquisites, or privileges, that are so excessive that they rival those of pre-Revolutionary French nobility can appropriately be called elitist, or favoring a small, high-status group.Explanation for Incorrect Answer B :Choice (B) is incorrect. "Monarchical" means pertaining to a king, and "tribulations" are sufferings. If one were to insert these terms into the text, the sentence would read "Opponents of the research institute label it a monarchical anachronism; its scholars, they allege, have tribulations rivaling those of pre-Revolutionary French nobility." The pre-Revolutionary French nobility were not known for their suffering, and it is unlikely that the opponents of the research institute would criticize the institute's scholars for having tribulations, or sufferings.Explanation for Incorrect Answer C :Choice (C) is incorrect. "Irreproachable" means faultless, and "luxuries" are extravagant comforts. If one were to insert these terms into the text, the sentence would read "Opponents of the research institute label it an irreproachable anachronism; its scholars, they allege, have luxuries rivaling those of pre-Revolutionary French nobility." Opponents of an institution would not call it faultless and would criticize the institution for lavishing luxuries on its scholars.Choice (D) is incorrect. "Reprehensible" means deserving blame, and "afflictions" are sufferings. If one were to insert these terms into the text, the sentence would read "Opponents of the research institute label it a reprehensible anachronism; its scholars, they allege, have afflictions rivaling those of pre-Revolutionary French nobility." Although opponents might label the institute reprehensible, or blameworthy, they would not be likely to criticize the institute's scholars for having afflictions, or sufferings. Furthermore, thepre-Revolutionary nobility were not known for their suffering.Explanation for Incorrect Answer E :Choice (E) is incorrect. "Commendable" means praiseworthy, and "privileges" are deserved rights or luxuries. If one were to insert these terms into the text, the sentence would read "Opponents of the research institute label it a commendable anachronism; its scholars, they allege, have privileges rivaling those ofpre-Revolutionary French nobility." Opponents who accuse the institute of providing excessive privileges would not characterize it as commendable, or praiseworthy.6ANSWERS AND EXPLANATIONSExplanation for Correct Answer C :Choice (C) is correct. While the author of Passage 2 is critical of Linnaeus’ legacy, the autho r of Passage 1 expresses appreciation of his contribution to natural history, describing it as "enormous and essential." Explanation for Incorrect Answer A :Choice (A) is incorrect. The author of Passage 1 does not regard Linnaeus with "cynicism," or scornful distrust. On the contrary, the passage expresses great respect for his significant contribution to science. Explanation for Incorrect Answer B :Choice (B) is incorrect. Neither author expresses any "bafflement," or confusion, regarding Linnaeus or the historical role he played in the field of science.Explanation for Incorrect Answer D :Choice (D) is incorrect. The author of Passage 1 does not express "nostalgia," or bittersweet longing, for Linnaeus or for the era in which he lived.Explanation for Incorrect Answer E :Choice (E) is incorrect. While Passage 1 asserts that scientists misused the system of classification, there is no suggestion that the author feels "resentful" of, or personally wronged by, Linnaeus.7ANSWERS AND EXPLANATIONSExplanation for Correct Answer D :Choice (D) is correct. Unlike Passage 1, Passage 2 uses a first-person narrative voice that openly expresses the author’s "wariness" regarding Linnaeus' contribution to natural science.Explanation for Incorrect Answer A :Choice (A) is incorrect. Specific scientific facts do not appear in either passage.Choice (B) is incorrect. Neither writer uses "literary allusion," or an indirect reference to a work of literature. Explanation for Incorrect Answer C :Choice (C) is incorrect. It is Passage 1, not Passage 2, that includes historical background information on Linnaeus and on the role that classificatory systems have played in science.Explanation for Incorrect Answer E :Choice (E) is incorrect. Neither passage uses "direct citations."8ANSWERS AND EXPLANATIONSExplanation for Correct Answer A :Choice (A) is correct. Although the two authors judge Linnaeus’ work differently, they agree that his classificatory system has had a great influence on the field of natural science.Explanation for Incorrect Answer B :Choice (B) is incorrect. The author of Passage 2 claims that Linnaeus’ system limits modern human understanding of the natural world, but the author of Passage 1 does not mention science after the nineteenth century.Explanation for Incorrect Answer C :Choice (C) is incorrect. Neither passage implies that interest in biology was declining or that Linnaeus’ work renewed curiosity in the field.Explanation for Incorrect Answer D :Choice (D) is incorrect. These passages do not discuss the classification system’s ability to resolve disagreements within the scientific community. On the contrary, the author of Passage 2 writes about Linnaeus' work to raise, not settle, questions regarding the validity of classification.Explanation for Incorrect Answer E :Choice (E) is incorrect. Neither passage refers to scientific discoveries that may have laid the foundation for Linnaeus' famous system.9ANSWERS AND EXPLANATIONSExplanation for Correct Answer D :Choice (D) is correct. The author of Passage 1 argues that unlike his followers, Linnaeus probably saw his system of classification as a tool, not the goal, of science. The author of Passage 2 does not make this distinction.Explanation for Incorrect Answer A :Choice (A) is incorrect. Neither author implies that Linnaeus has not received enough recognition as a scientist. Explanation for Incorrect Answer B :Choice (B) is incorrect. Lines 12-17 intimate that the impact of Linnaeus' system was not entirely advantageous, but this section of Passage 2 does not dismiss the contributions of scientists who have integrated his work into their own.Explanation for Incorrect Answer C :Choice (C) is incorrect. The author of Passage 2 does "not dispute the value of" classification, but argues that Linnaeus' system has had a negative impact on "humans' relationship to the world."Explanation for Incorrect Answer E :Choice (E) is incorrect. Both authors agree th at Linnaeus’ most notable contribution to natural history was his system of classifying plant and animal life.10ANSWERS AND EXPLANATIONSExplanation for Correct Answer B :Choice (B) is correct. It makes sense to say that the residents of Macondo needed "time and effort" to grow accustomed to a "persistent," or insistently continuous, noise.Explanation for Incorrect Answer A :Choice (A) is incorrect. It would be illogical to call a noise emanating from a light bulb "enthusiastic." Explanation for Incorrect Answer C :Choice (C) is incorrect. "Obvious" does not describe a noise that requires time and effort to get used to hearing. Explanation for Incorrect Answer D :Choice (D) is incorrect. In this context, "obsessive" is not used to indicate infatuation, or short-lived passion. Explanation for Incorrect Answer E :Choice (E) is incorrect. An electric generator plant may be called "hardworking." Such a term, however, does not describe a noise that takes time and effort to become used to hearing.11ANSWERS AND EXPLANATIONSExplanation for Correct Answer C :Choice (C) is correct. After paying to "share the difficulties" of the on-screen characters, the citizens felt cheated to discover that they were only actors, not real people deserving of their sympathy.Explanation for Incorrect Answer A :Choice (A) is incorrect. Although each person paid two cents for admission, nothing in the passage indicates that this charge was either excessive or the cause of their anger.Explanation for Incorrect Answer B :Choice (B) is incorrect. The audience was not angered by the on-screen adventures themselves, but rather by the fact that those events had not actually occurred.Choice (D) is incorrect. The public seemed to enjoy commiserating with characters who had fallen on hard times. The citizens were only upset to discover that they had felt real emotion on behalf of actors who were only pretending.Explanation for Incorrect Answer E :Choice (E) is incorrect. The public was not angered because the plots were "implausible," or unlikely, but rather because they were untrue.12ANSWERS AND EXPLANATIONSExplanation for Correct Answer A :Choice (A) is correct. The phonograph, an early record player, intially intrigued the citizens of Macondo.They were eventually disappointed to learn, however, that the device was mechanical, not magical, and therefore lacking in the "moving" and "human" qualities of a live musicians.Explanation for Incorrect Answer B :Choice (B) is incorrect. Nothing in the passage indicates that phonographs required any special skill to operate. Explanation for Incorrect Answer C :Choice (C) is incorrect. The passage implies that the machines were, in fact, frequently and closely observed by curious citizens on the street where they were sold.Explanation for Incorrect Answer D :Choice (D) is incorrect. Although the phonograph dampened citizens' enthusiasm for live music "for a time," they did not abandon the invention because musicians were suffering. Rather, they tired of the machines because they eventually concluded that recorded music was inferior to live music.Explanation for Incorrect Answer E :Choice (E) is incorrect. The passage is clear that it was only after the adults of Macondo had rejected the foreign record players that children were permitted to amuse themselves by dismantling them.13ANSWERS AND EXPLANATIONSExplanation for Correct Answer D :Choice (D) is correct. The citizens found the telephone disturbing because of all the new machines that strained people's ability to discern "the limits of reality"; the telephone ran most counter to what they had always thought about the natural world.Explanation for Incorrect Answer A :Choice (A) is incorrect. The citizens were not upset by the origin of the telephone, but by how it forced them to reevaluate their ideas about the world.Explanation for Incorrect Answer B :Choice (B) is incorrect.The passage does not discuss the social implications of the telephone.Choice (C) is incorrect. The citizens’ anxiety about the telephone was not related to their fears concerning the village’s daily life, but to their overall understanding of reality.Explanation for Incorrect Answer E :Choice (E) is incorrect. The passage does not address the telephone’s potential effect on the job market in Macondo.14ANSWERS AND EXPLANATIONSExplanation for Correct Answer C :Choice (C) is correct. The passage suggests that the citizens of Maconda are stuck in a cycle of "disappointment, doubt and revelation." They welcome new inventions with wonder and awe before rejecting them for being less "marvelous" and "enchanted" than they seemed.Explanation for Incorrect Answer A :Choice (A) is incorrect. Both the telephone and phonograph were operated with a crank, or turning handle, but that feature is not related to the citizens’ disappointment.Explanation for Incorrect Answer B :Choice (B) is incorrect. At no point in the passage does the educational value of these inventions come into play.Explanation for Incorrect Answer D :Choice (D) is incorrect. The townspeople are not concerned by the fact that the film projector and phonograph were created to entertain, and it can be argued that the light bulb and telephone are not meant for entertainment at all.Explanation for Incorrect Answer E :Choice (E) is incorrect. The machines were not necessarily hard to operate, and the passage suggests that the people were disappointed with them for other reasons.15ANSWERS AND EXPLANATIONSExplanation for Correct Answer D :Choice (D) is correct. The passage mainly deals with the "influx," or arrival, of technological inventions in Macondo and the citizen's mixed reactions to them.Explanation for Incorrect Answer A :Choice (A) is incorrect. Although the passage implies that the "respectable" citizens of Maconda did not typically mingle with members of the working class, the main purpose of the passage is not to make a statement about class relations within the town.Explanation for Incorrect Answer B :Choice (B) is incorrect. Although the passage describes new inventions, it does so in order to make a larger point about the way they were received among the people of Macondo.Explanation for Incorrect Answer C :Choice (C) is incorrect. The main purpose of the passage is not to show how different people had a common reaction to something "magical," but to illustrate how they responded to new technologies.Explanation for Incorrect Answer E :Choice (E) is incorrect. The passage’s purpose is not to "delineate," or describe, ideas about nature triumphing over technology. Rather, its purpose is to explain how the people of Macondo responded to new technologies. 16ANSWERS AND EXPLANATIONSExplanation for Correct Answer A :Choice (A) is correct. An admission of a lack of expertise is a disclaimer; a statement is an assertion. In the first sentence, the author admits to a lack of certain kinds of expertise; in the second sentence, the author states an opinion about Martha Graham's work.Explanation for Incorrect Answer B :Choice (B) is incorrect. No one is invoked, or appealed to, in the first sentence, and the second sentence does not define anything.Explanation for Incorrect Answer C :Choice (C) is incorrect. In the first sentence the author admits to a lack of expertise but not in an apologetic way; the second sentence is an assertion but not a confession.Explanation for Incorrect Answer D :Choice (D) is incorrect. To say that the first sentence is a statement of authority doesn't make any sense, and the second sentence is a statement of opinion but not a hypothesis, or a basis for experimental investigation. Explanation for Incorrect Answer E :Choice (E) is incorrect. The first sentence does not rebut, or challenge, anyone else's argument, and while the second sentence is an introduction to the analysis that follows in the passage, it is not itself an analysis.17ANSWERS AND EXPLANATIONSExplanation for Correct Answer B :Choice (B) is correct. The author uses the statement in discussing Graham's "instincts of a mathematician or physicist" in her approach to choreography. The quoted phrase is part of a statement that expands on an earlier point about Graham's approach to line and direction in dance, which the author of the passage believes is both mathematical and emotional.Explanation for Incorrect Answer A :Choice (A) is incorrect. Although the author does suggest that Graham sought to produce emotional effects through the use of line, there is no indication that those effects were intended to be spectacular.。
OG新SAT考试详细解读 16年SAT考试有救了!
OG新SAT考试详细解读16年SAT考试有救了！还有一次考试就要和新SAT考试说再见了~准备赴美留学的童靴们是不是有点手足无措呢?面对各种针对新SAT的小道消息木有分辨能力肿么办?当然是回归本源，看OG怎么说~别跟错了老大!我们从OG入手，对新SAT进行360度解读，相信童靴们也能从中找到备考新SAT的路子!新版OG对新SAT考试内容进行了综述，包括8个改动的地方(以下详细解析会逐一提到)，接下来对新SAT4个考试部分—reading，wirting and languge，essay，math进行详细的说明，并配套例题说明。
此次发布的改革后OG官方指南PDF版本共计790页，从以上目录可以看出：OG 的第一部分part1可总结为本书以及SAT整体考试的简介，就是导入性的常规介绍。
对考生最有参考价值的信息经整理，核心内容如下：新版OG对于新SAT考题结构布局如下:阅读部分：一个section，65分钟，52道题目;写作(语法和一篇选做的作文)：一个section，35分钟，44道题目;数学部分：2个section，80分钟，58道题目。
共计：180分钟(不含作文);230分钟(含作文)。
以上布局最新OG中Chapter1第12页的改革后SAT整个考试的题目类型，数量和时间安排表，大家可从此表看出新SAT考试的具体考试科目及各科的完整框架体系。
Chapter2 是针对新SAT八大主要改革内容进行详细阐释，这八大方面分别是：1.文本语境理解单词;2.对证据的理解和运用;3.分析性写作;4.数学更贴合实际生活;5.真实的社会情景;6.文史社科多位分析;7.美国建国文件及全球性议题;8.第25页笑脸温馨提示广大考生：新SAT考试选项设置是4选1，而且选错答案不扣分!这么重要的好消息要再说一遍：4选1，选!错!不!扣!分!Chapter3 提供了官方备考建议，内容总结重点是希望广大考生注重阅读和词汇量积，多写多练，提高语言能力，熟悉新SAT考试等内容，第33-36页为大家展示了各科目的大题目设置要求，并没有给出相应小题目。
SAT考试2024数学历年题目全解
SAT考试2024数学历年题目全解SAT考试是一项全球性的标准化考试，旨在评估学生在阅读、写作和数学方面的能力。
数学部分是SAT考试的一个重要组成部分，涵盖了各种数学概念和技巧。
本文将为您提供2024年SAT数学部分的历年题目全解，帮助您更好地应对这一考试。
第一题：题目：求解以下方程：3x + 5 = 20解析：要求解方程3x + 5 = 20，我们首先将5从等式两边减去，得到3x = 15。
然后，我们将方程两边都除以3，即x = 5。
因此，方程的解为x = 5。
第二题：题目：计算以下比例的值：5:8 = x:40解析：要计算比例5:8与x:40的值，我们可以采取交叉乘法的方法。
将5乘以40，并将结果除以8，即可求得x的值。
计算过程如下：5 * 40 / 8 = 200 / 8 = 25因此，比例5:8与x:40的值为25。
第三题：题目：已知一个等边三角形的边长为12，计算其面积。
解析：一个等边三角形的边长为12，则其高可以通过勾股定理求得。
根据勾股定理，我们有：高的平方= 边长的平方- 底边的一半的平方。
设高为h，则有 h^2 = 12^2 - (12/2)^2= 144 - 36= 108因此，高h = √108 = 6√3由于等边三角形的高等于边长的一半乘以根号3，所以面积S可以计算为：S = 1/2 * 12 * 6√3= 6 * 6√3= 36√3因此，该等边三角形的面积为36√3。
第四题：题目：在一个长方形花坛中，长度是宽度的3倍，已知宽度为2米，计算花坛的面积。
解析：我们知道长方形花坛的面积可以通过长度乘以宽度来计算。
已知宽度为2米，则长度为3 * 2 = 6米。
因此，花坛的面积为2 * 6 =12平方米。
通过以上题目的解析，我们可以看到SAT数学部分考察了各种数学概念和技巧，包括方程的求解、比例的计算、勾股定理的应用以及长方形面积的计算等。
熟练掌握这些数学知识，并能够灵活运用于实际问题的解决中，将有助于您在SAT考试中取得更好的成绩。
新SAT数学全解
在以往SAT 各科考试中，数学一直是中国学生以引为傲的优势科目。
与美国学生相比，中国学生普遍数学知识和计算能力非常扎实，取得 800 分的成绩并不鲜见。
然而随着 2016 年1 月旧 SAT 最后一次考试结束， SAT 考试将全面改革。
那么新 SAT 考试登场，中国学生是否还能继续延续以往在数学科目上的优势，首先让我们一起来看看新 SAT 数学做了哪些改变！考试形式总体上发生了比较大的变化，比较明显的是计分标准、题目长度和考察知识点。
虽然考试时间增加 10min，但是总题目数也增加 4 道，同时易错的填空题增加了 3 道。
中国学生普遍数字计算能力较强，所以是否使用计算器相信影响并不是很大，但是考场上分秒必争，如何精简做题步骤，提高做题效率则是那么在最重要的考试内容和题型方面，到底新SAT 数学做了哪些变化，这些变化对学生备考有什么影响。
考察知识点1. 新旧 SAT 知识点变化：新 SAT 去掉了对于数字或者公式本身的运算考查以及经常让同学们头疼的排列组合题目。
然而，新增了一些部分同学没有接触过或者很少使用的知识点如：置信区间，抛物线趋势等。
不过大家不用担心，这部分知识点大家只需要知道并理解概念即可，并不需要同学们去实际计算。
2. 知识点全分布很多同学看到 CB 给出的新 SAT 数学知识点分类会感到无从下手，其实 CB 的分类主要是根据考查学生在数学技能、实际应用以及是否已经具备好进入高等学府学习的知识储备方面来划分的 ;第一部分为代数核心，顾名思义是围绕代数相关的知识，主要包括常变量、不等式、一次方程等；第二部分解决问题和分析数据，主要考查学生在实际生活中运用数学知识和思维解决问题的能力 (包括阅读图表)，这个部分题目因为会涉及到与实际相关的比较复杂的运算，所以只会出现在可以使用计算器的部分；第三部分通往高等数学，包括对复杂的函数和方程等的考查，检测学生是否有能力进入STEM (Science, technology,engineering and math )领域进行更深入的学习；第四部分附加内容，主要涉及一些额外知识点，这个部分内容是不计入 Subscore 评分的，其中主要包括平面、解析几何以及三角函数和虚数的基础知识内容。
SAT数学真题解析
SAT数学真题解析SAT数学部分是考试中最具挑战性的部分之一，要求考生具备扎实的数学基础和解题能力。
本文将对SAT数学真题进行详细解析，帮助考生更好地应对这一部分的考试。
一、概述SAT数学部分涵盖的知识点包括代数、几何、数据分析和数学问题解决等。
题型主要包括选择题和解答题，其中选择题又分为单选和多选题。
考生在备考过程中，除了要系统学习相关知识点，还要注重解题技巧和策略的培养。
二、代数题解析代数是SAT数学部分的重点考察内容之一，下面将以一道典型的代数题为例进行解析。
Example 1:If 2x + 5 = 13, what is the value of x?解析：根据题目中的等式，我们可以求解出变量x的值。
首先，将等式中的5移到等号的另一边，得到2x = 13 - 5，即2x = 8。
接下来，我们将等式两边都除以2，得到x = 8 / 2，即x = 4。
所以，x的值为4。
三、几何题解析几何是SAT数学部分另一个重要的考察内容，下面以一道几何题进行解析。
Example 2:In triangle ABC, angle BAC = 60°, and BC = AB. What is the measureof angle BCA?解析：根据题目中给出的信息，我们需要求解角BCA的度数。
根据三角形内角和定理，三角形ABC的三个内角之和等于180度，即角BAC + 角ABC + 角BCA = 180°。
已知角BAC = 60°，并且BC = AB。
由于BC = AB，我们可以得出角ABC = 角ACB。
将以上信息代入角和的等式中，得到60° + 2角ABC = 180°。
进一步化简，得到2角ABC = 120°。
再继续化简，得到角ABC = 60°。
因为角ABC = 角ACB，所以角BCA的度数也为60°。
四、数据分析题解析数据分析是SAT数学部分的重要题型之一，要求考生对给定的数据进行分析和解读。
SAT考试数学历年真题全解2024年版
SAT考试数学历年真题全解2024年版在备考SAT考试过程中，熟悉并掌握历年真题是一项重要的任务。
通过解析历年真题，考生可以了解考试的出题风格、难度以及考察的知识点，有助于提高备考效果。
本文将为您提供2024年版本的SAT考试数学部分历年真题全解，帮助您更好地备考。
下面将根据考试的各个部分，逐一解析2024年版SAT数学部分的历年真题。
第一部分：选择题解析选择题是SAT数学部分最主要的题型，考生需要在给定的选项中选择正确答案。
以下是2024年版SAT数学选择题的解析：1. 题目描述2. 解析3. 答案解释4. 解题思路通过对每个选择题的详细解析，考生可以了解题目的解题思路、关键步骤以及答案的解释。
在解析选择题过程中，本文将注重解题思路的讲解，帮助考生更好地理解解题的方法和技巧。
第二部分：填空题解析填空题是SAT数学部分的另一种题型，与选择题不同的是，填空题要求考生填写一个具体的数值或表达式。
以下是2024年版SAT数学填空题的解析：1. 题目描述2. 解析3. 答案解释4. 解题思路通过对每个填空题的详细解析，考生可以了解填空题的解题方法和技巧。
在解析填空题过程中，本文将注重解题思路的讲解，帮助考生更好地理解解题的方法和技巧。
第三部分：解答题解析解答题是SAT数学部分的较难题型，要求考生根据题目给出的条件和要求，用数学方法进行解答。
以下是2024年版SAT数学解答题的解析：1. 题目描述2. 解答步骤3. 解答思路4. 结论通过对每个解答题的分步解析，考生可以了解解答题的解题方法和技巧。
在解析解答题过程中，本文将注重解答步骤和思路的讲解，帮助考生更好地理解解题的方法和技巧。
结语通过对2024年版SAT数学部分历年真题的全面解析，考生可以更加深入地了解考试的出题方式和要求，提高备考效果。
同时，解析中的解题思路和技巧也可以帮助考生更好地掌握数学知识和解题方法。
在备考过程中，考生可以结合解析内容进行针对性的练习和复习，提高数学部分的得分。
2024年SAT考试数学真题深度解读
2024年SAT考试数学真题深度解读在2024年的SAT考试数学部分中，出现了一系列挑战性的问题，涵盖了几个重要的数学概念和技巧。
本文将对这些问题进行深度解读，帮助同学们更好地理解题目，并为他们提供解题思路和解题技巧。
问题1：在一个三角形ABC中，角A的度数是50。
已知边AB与BC的长度分别为5和8，求边AC的长度。
解析：首先，我们可以利用三角形的角度之和为180度的性质，求得角B为130度。
然后，我们可以使用余弦定理来求解边AC的长度。
根据余弦定理，我们有：AC^2 = AB^2 + BC^2 - 2 * AB * BC * cosA代入已知值，我们可以得到：AC^2 = 5^2 + 8^2 - 2 * 5 * 8 * cos50通过计算，我们可以得到AC的长度为约9.18。
问题2：已知函数f(x) = 2x^3 + 3x^2 - 4x + 1，求f'(2)的值。
解析：我们需要求函数f(x)在x = 2处的导数值，即f'(2)。
首先，我们对函数f(x)进行求导，得到f'(x) = 6x^2 + 6x - 4。
然后，将x = 2代入f'(x)中，我们可以计算得到f'(2)的值为28。
问题3：已知一个等差数列的第一个项为a，公差为d。
如果这个数列的第100项是200，求a和d的值。
解析：由于等差数列的通项公式为an = a + (n - 1)d，我们可以得到第100项的表达式a + 99d = 200。
而且，我们还知道该数列的第1项即为a，因此可以得到第1项的表达式a + 0d = a。
由题意可知，第100项与第1项的差值为99d，即200 - a = 99d。
将这两个方程组合起来，我们可以得到一个二元一次方程组：a + 99d = 200200 - a = 99d通过求解这个方程组，我们可以得到a的值为101，d的值为1。
问题4：某公司的销售额在过去的几年呈现如下的增长趋势：2019年为100万，2020年为120万，2021年为140万。
SATOG全部十套题语法部分分析报告
目录Practice Test 1 (2)Practice Test 2 (19)Practice Test 3 (36)Practice Test 4 (52)Practice Test 5 (68)Practice Test 6 (84)Practice Test 7 (99)Practice Test 8 (114)Practice Test 9 (129)Practice Test 10 (143)Practice Test 1题干 1. A recent report indicates that sleep-deprived drivers caused more than 100,000 accidents last years, they fall asleep at the wheel.选项(A)year, they fall(B)year, and they fall(C)year by falling(D)year and falling(E)year, they were falling解析A项错误，两个句子之间不能用逗号连接且不并列。
B项错误，时态歧义而且逻辑C项正确，用动名词将两个句子揉成了一个。
D项错误，falling找不到并列的成分。
E项错误，两个句子不能用逗号连接且不并列。
翻译一个最近的报告显示，近些年睡眠不足的司机导致了超过十万起事故，因为他们开车的时候睡着了。
备注题干 2. The depths of the Arctic Ocean are hard to study, mainly because the icy surface is being difficult to penetrate using current techniques.选项(A)to study, mainly because the icy surface is being(B)to study as a result of the icy surface, mainly, is(C)to study, mainly because the icy surface is(D)studying, mainly from the icy surface being(E)studying, mainly resulting from the icy surface being解析A项没有语法错误，但is being为现在进行时，不合适。
SAT考试专题2024数学历年题目解析
SAT考试专题2024数学历年题目解析2024年的SAT考试将继续囊括数学科目，下面将对该年度的数学部分历年题目进行解析，帮助考生更好地准备SAT数学考试。
1. 第一题解析该题目是一道代数题，要求求解方程：3x + 5 = 20。
解题思路：将方程中的变量与常数项分离，得到：3x = 20 - 5。
计算得：3x = 15，再将等式两边同时除以3，得到：x = 5。
因此，方程的解为x = 5。
2. 第二题解析该题目是一道几何题，要求计算三角形的面积。
解题思路：已知三角形的底边长度为6，高为8。
直接使用三角形面积公式：面积 = 底边长度 ×高 ÷ 2。
代入已知的数值进行计算：面积 = 6 × 8 ÷ 2 = 24。
因此，该三角形的面积为24平方单位。
3. 第三题解析该题目是一道概率题，要求计算从一副标准扑克牌中随机抽取一张牌，该牌为红桃的概率。
解题思路：一副标准扑克牌中共有52张牌，其中有13张红桃牌。
因此，红桃牌的概率为：概率 = 红桃牌数目 ÷总牌数目。
代入已知数值进行计算：概率 = 13 ÷ 52 = 1 ÷ 4 = 0.25。
因此，从一副标准扑克牌中随机抽取一张牌，该牌为红桃的概率为0.25。
4. 第四题解析该题目是一道函数题，要求计算函数的值。
解题思路：已知函数 f(x) = 2x^2 + 3x + 1，需要计算当 x = 2 时的函数值。
将 x = 2 代入函数表达式中，得到：f(2) = 2 × 2^2 + 3 × 2 + 1。
计算得：f(2) = 8 + 6 + 1 = 15。
因此，当 x = 2 时，函数 f(x) 的值为15。
5. 第五题解析该题目是一道统计题，要求根据给定的数据计算平均数。
解题思路：已知一组数据为：10, 12, 15, 18, 20。
需要计算这组数据的平均数。
平均数的计算公式为：平均数 = 总和 ÷数据个数。
【狒狒出品】SAT官方指南OG 第七套题解析（整理版）
Book Test #7:Section 1Sample Essay - Score of 6Everyone goes through their lives seeing and experiencing different things. At times, these different situations may cause one to act differently than another would in the same situation. It can be readily stated that “Ease does not challenge us; adversity helps us discover who we are.” Through literature, one can see how this statement proves to be true.In the play, “The Enemy of the People”, by Henrik Ibsen, the protagonist, Dr. Stockholm, faced adversi ty, and through that, was able to discover his true beliefs and who he was. Before Dr. Stockholm was put in a situation where he had to face adversity, he had lived his life with mild ease and regularity. He acted just like everyone else in the town he lived in. Years later, he discovered that the popular bath houses was infected with bacteria. Determined to spread his findings, Dr. Stockholm went to the newspaper and the local governing office to try and make his discovery known. However, both the paper an d the government weren’t as inspired to really let the public know about this serious problem due to the popularity of the bath houses. As a result, Dr. Stockholm was forced to face adversity and find a way to achieve his previously set goal. Through adversity, Stockholm was able to truely see how his personality was. He was able to understand his severe discontent with the government and society as a whole. In essence, Stockholm was able to discover his actual self. This, however, only happened when he was faced with a challenge.The book, “Where the Heart is” by Billie Letts also used adversity to portray it’s characters true being. The protagonist, Novalee Nation, was placed in a situation where she had to realize and conquer adversity. Novalee was a young girl of 17, who was pregnant. She had experienced extreme hardship her whole life in the trailer park environment that she had previously resided in. She also received lots of abuse from her boyfriend who impregnated her. In the story, he had left her stranded in a K-Mart all by herself, while she was pregnant. All alone, Novalle had to find a way to keep herself and her baby alive. Along the way, through adversity, Novalle found her true, kind self. She also made countless discoveries through meeting different people. Among those things was her true love for photography and literature, and most of all her yearning for love in her life.In the face of adversity, we all act differently. We each have different ideas and methods that we are accustomed to use for different situations. By acting and making decisions on our own, as we are often times forced to do when given a challenge, we are able to find out who we truely are and what we truely believe in. The characters Dr. Stockholm and Novalee Nation are examples of that kind of people in literature. However, in literature and life, it is all the same. Ease does not challenge us; adversity helps us discover who we are. Section 31ANSWERS AND EXPLANATIONSExplanation for Correct Answer B :Choice (B) is correct. It avoids the error of the original by providing a noun, "Mother Teresa," that can be properly modified by the clause "While working . . . Calcutta."Explanation for Incorrect Answer A :Choice (A) involves improper modification. The opening clause ("While working . . . Calcutta") cannot logically modify a time ("that was when . . .").Explanation for Incorrect Answer C :Choice (C) involves an error in modification. The opening clause ("While working . . . Calcutta") cannot logically modify a time ("then").Explanation for Incorrect Answer D :Choice (D) includes a modification error. The opening clause ("While working . . . Calcutta") cannot logically modify "Mother Teresa's profound love."Explanation for Incorrect Answer E :Choice (E) involves improper modification. The opening clause ("While working . . . Calcutta") cannot logically modify "a profound love."2ANSWERS AND EXPLANATIONSExplanation for Correct Answer B :Choice (B) is correct. It avoids the error of the original by providing an infinitive ("to hold") to parallel the earlier infinitive "to return."Explanation for Incorrect Answer A :Choice (A) includes excess words. The words "and they would hold " should simply be "to hold." Explanation for Incorrect Answer C :Choice (C) results in an illogical statement. It does not make sense to suggest that by agreeing "to return to their districts," the legislators held a "series of town meetings."Explanation for Incorrect Answer D :Choice (D) involves improper idioms. "Returning" is not something that the legislators would logically "agree with." They would agree "to return" instead. Furthermore, "for holding of" should be the more idiomatic "to hold."Explanation for Incorrect Answer E :Choice (E) distorts the intended meaning of the sentence by suggesting that it was during their trip to their districts that the legislators agreed to "the holding of town meetings."3ANSWERS AND EXPLANATIONSExplanation for Correct Answer D :Choice (D) is correct. It avoids the error of the original by providing a main verb ("used") to express a complete thought.Explanation for Incorrect Answer A :Choice (A) is a sentence fragment. There is no main verb (only the verbal "using") to complete the thought. Explanation for Incorrect Answer B :Choice (B) is a sentence fragment. There is no main verb to complete the thought.Explanation for Incorrect Answer C :Choice (C) results in an awkward construction that distorts the intended meaning of the sentence. The "medieval Chinese warriors" performed a single action (using kites to survey enemy troops), not a two-part action (using kites and surveying) as the sentence suggests.Explanation for Incorrect Answer E :Choice (E) involves is an illogical statement. The phrase "used manned kites surveying enemy troops" suggests that the kites alone were surveying. To properly convey the idea that the kites were used to survey enemy troops, "in" should be added before "surveying."4ANSWERS AND EXPLANATIONSExplanation for Correct Answer D :Choice (D) is correct. It avoids the error of the original by providing a singular verb, "was," to agree with the singular subject, "one."Explanation for Incorrect Answer A :Choice (A) involves an error in subject-verb agreement. The plural verb "were" cannot agree with the singular subject "one."Explanation for Incorrect Answer B :Choice (B) involves an error in agreement. The plural verb "were" does not agree with the singular "something."Explanation for Incorrect Answer C :Choice (C) involves an error in subject-verb agreement. The plural verb "were" does not agree with its singular subject, "one."Explanation for Incorrect Answer E :Choice (E) involves an inappropriate idiom that distorts the intended meaning of the sentence. It doesn't make sense to say that people thought of a breakfast food "as wrong."5ANSWERS AND EXPLANATIONSExplanation for Correct Answer E :Choice (E) is correct. It avoids the error of the original by removing unnecessary words.Explanation for Incorrect Answer A :Choice (A) includes excess words. The phrase "a lesser amount of work to do" could be reduced to the more precise "less work to do."Explanation for Incorrect Answer B :Choice (B) makes no sense. It does not make sense to describe "work" as being "least among their colleagues." Explanation for Incorrect Answer C :Choice (C) involves an error in verb form. The verb phrase "were having" should simply be "had." Explanation for Incorrect Answer D :Choice (D) is awkward and confusing. It does not make sense to characterize "the work they had to do" as "the least of their colleagues."6ANSWERS AND EXPLANATIONSExplanation for Correct Answer E :Choice (E) is correct. It avoids the error of the original by properly conveying the intended comparison. Explanation for Incorrect Answer A :Choice (A) involves an illogical comparison. "Film audiences in the 1950's" cannot logically be compared with "the 1960's and 1970's."Explanation for Incorrect Answer B :Choice (B) results in an illogical comparison. It is not logical to compare "Film audiences . . ." with "the 1960's and 1970's."Explanation for Incorrect Answer C :Choice (C) is illogical. "Film audiences" cannot logically be compared with "films."Explanation for Incorrect Answer D :Choice (D) involves improper diction. To correctly make the comparison, the words "with the" should be changed to "did."7ANSWERS AND EXPLANATIONSExplanation for Correct Answer A :Choice (A) is correct. It avoids the errors of the other choices by properly comparing people ("American architects") with a person ("Frank Lloyd Wright").Explanation for Incorrect Answer B :Choice (B) presents an illogical comparison. A thing ("inspiration") cannot logically be compared with a person ("Frank Lloyd Wright").Explanation for Incorrect Answer C :Choice (C) results in an illogical comparison. A thing ("Frank Lloyd Wright's architecture") cannot logically be compared with people ("American architects").Explanation for Incorrect Answer D :Choice (D) presents an illogical comparison. People ("American architects") cannot logically be compared with a thing ("designs").Explanation for Incorrect Answer E :Choice (E) results in an illogical comparison. Things ("Frank Lloyd Wright's inspirations") cannot logically be compared with people ("American architects").Choice (D) is correct. It avoids the errors of the original by properly comparing "poetry" to "fiction" and "drama" and by correctly completing the correlative construction "either . . . or."Explanation for Incorrect Answer A :Choice (A) involves an illogical comparison. Something that occurs "in poetry" cannot logically be compared to "fiction or drama."Explanation for Incorrect Answer B :Choice (B) results in an illogical comparison. "Fiction" cannot logically be compared with something that happens "in poetry."Explanation for Incorrect Answer C :Choice (C) involves an improper idiom. What comes after each part of the correlative construction "either . . . or" is not parallel as it should be. "Either" is followed by the prepositon "in," while "or" is followed by the noun "drama."Explanation for Incorrect Answer E :Choice (E) involves an improper idiom. What comes after each part of the correlative construction "either . . . or" must be parallel, but it is not. "Either" is followed by the noun "fiction," while "or" is followed by the preposition "in."9ANSWERS AND EXPLANATIONSExplanation for Correct Answer B :Choice (B) is correct. It avoids the error of the original by removing excess words.Explanation for Incorrect Answer A :Choice (A) involves wordiness. The phrase "is the reason why" adds nothing to the setence and so should be removed.Explanation for Incorrect Answer C :Choice (C) involves an improper idiom. "The reason for why" should be "the reason that."Explanation for Incorrect Answer D :Choice (D) is awkward and wordy. The phrase "As a result of economic hardship causing" should be reduced to the more precise and idiomatic "because economic hardship has been the cause of."Explanation for Incorrect Answer E :Choice (E) is awkward and wordy. The phrase "The fact that" should simply be "because," and the words "is why" should be deleted and replaced with a comma.Choice (A) is correct. It avoids the errors of the other choices by clearly indicating what happened and when. Explanation for Incorrect Answer B :Choice (B) is awkward and imprecise. Without repeating the subject by using the pronoun "they," the sentence does not make clear what was "not showing any signs of disease."Explanation for Incorrect Answer C :Choice (C) involves improper coordination. Two complete thoughts ("In Germany, . . . earlier" and "no outward signs . . . however") are joined with only a comma.Explanation for Incorrect Answer D :Choice (D) is vague. It is not clear what the phrase "without any signs of disease" is meant to refer to. Explanation for Incorrect Answer E :Choice (E) is awkward and imprecise. It is not clear what the phrase "not having shown any signs" is meant to refer to.11ANSWERS AND EXPLANATIONSExplanation for Correct Answer E :Choice (E) is correct. It avoids the error of the original by reducing excess words ("since such is the case") to an appropriate idiom ("and so").Explanation for Incorrect Answer A :Choice (A) displays wordiness. The phrase "since such is the case" can be reduced to the more precise and idiomatic "and so."Explanation for Incorrect Answer B :Choice (B) exhibits unclear pronoun reference. It is not clear to what the relative pronoun "that" is meant to refer.Explanation for Incorrect Answer C :Choice (C) involves improper coordination. Two complete thoughts ("In the wild . . . Zaire River" and "no more than . . . result") are joined with only a comma.Explanation for Incorrect Answer D :Choice (D) involves improper coordination. Two complete thoughts ("In the wild . . . Zaire River" and "the number . . . reason") are joined with only a comma.12ANSWERS AND EXPLANATIONSCorrected Sentence: Although born in the Midwest, Langston Hughes lived most of his adult life in Harlem, in New York City, where, like other writers in the 1930's, he wrote some of his finest works.Explanation for Correct Answer C :The error in this sentence occurs at (C), where an improper verb form is used. The past perfect tense of the verb phrase "had wrote" is inconsistent with the simple past tense of the other verbs in the sentence. Also, the past participle of "write" is "written," not "wrote."Explanation for Incorrect Answer A :There is no error at (A). The subordinating conjunction "where" correctly introduces the dependent adjective clause that modifies the proper noun "Harlem."Explanation for Incorrect Answer B :There is no error at (B). The preposition "like" is appropriate to introduce the adjective prepositional phrase that modifies the proper noun "Langston Hughes."Explanation for Incorrect Answer D :There is no error at (D). The superlative adjective "finest" is used correctly to indicate comparison of more than two things (all of Hughes' works).Explanation for Incorrect Answer E :There is an error in the sentence.13ANSWERS AND EXPLANATIONSCorrected Sentence: In constant demand as a speaker, Ms. Chernock has never been busier than she is now. Explanation for Correct Answer C :The error in this sentence occurs at (C), where a double comparative is used. Th e adverb “more” is not needed to modify the already comparative adjective “busier.”Explanation for Incorrect Answer A :There is no error at (A). The noun “demand” is appropriately used as the object of the preposition “in,” and the preposition “as” correctly introduces the adjective phrase that modifies the noun “demand.”Explanation for Incorrect Answer B :There is no error at (B). The singular verb “has” agrees with its singular subject “Ms. Chernock,” the present perfect tense of the verb phrase appropriately indicates an action completed before the action of the dependent clause, and the adverb “never” is idiomatic.Explanation for Incorrect Answer D :There is no error at (D). The singular verb “is” agrees with its singular subject “she,” and the adverb “now” correctly modifies “is.”Explanation for Incorrect Answer E :There is an error in the sentence.14ANSWERS AND EXPLANATIONSCorrected Sentence: During the night, there are usually two German shepherds at the warehouse to guard against robbery attempts.Explanation for Correct Answer B :The error in this sentence occurs at (B), where there is subject-verb disagreement. In this inverted sentence, the singular verb "is" does not agree with the plural subject "German shepherds."Explanation for Incorrect Answer A :There is no error at (A). The preposition "During" properly introduces the adverbial prepositional pharse. Explanation for Incorrect Answer C :There is no error at (C). The infinitive phrase "to guard" properly introduces the adverbial clause, and the preposition "against" is the idiomatic preposition to follow the word "guard."Explanation for Incorrect Answer D :There is no error at (D). The noun "attempts" correctly functions as the object of the preposition "against." Explanation for Incorrect Answer E :There is an error in the sentence.15ANSWERS AND EXPLANATIONSCorrected Sentence: Candy manufacturers applauded the discovery by researchers that students who smell chocolate while studying and again while taking a test are able to recall more material than students not exposed to the odor of chocolate.Explanation for Correct Answer B :The error in this sentence occurs at (B), where an improper pronoun is used to refer to people. The relative pronoun “which” is used instead of the pronoun “who” that is needed.Explanation for Incorrect Answer A :There is no error at (A). The noun “discovery” correctly functions as the direct object of the verb “applauded,” and the preposition “by” is the idiomatic preposition to follow the word “discovery.”Explanation for Incorrect Answer C :There is no error at (C). The adverb “again” appropriately modifies the adverbial phrase “while taking,” which, in turn, modifies the verb “smell.”Explanation for Incorrect Answer D :There is no error at (D). The plural verb “are” agrees with its plural subject “students,” and the adjective “able” properly functions as a subject complement modifying “students.”Explanation for Incorrect Answer E :There is an error in the sentence.16ANSWERS AND EXPLANATIONSCorrected Sentence:Explanation for Correct Answer E :There is no error in this sentence.Explanation for Incorrect Answer A :There is no error at (A). The indefinite pronoun “One” correctly functions as the singular subject of the sentence, and the helping verb “can” agrees with its singular subject.Explanation for Incorrect Answer B :There is no error at (B). The negative adverb “hardly” appropriately modifies the verb phrase “can … determine.”Explanation for Incorrect Answer C :There is no error at (C). The subordinating conjunction “which” correctly introduces the dependent noun clause that functions as the direct object of the verb phrase “can hardly determine,” and the singular verb “contributes” agrees with its subject “which.”Explanation for Incorrect Answer D :There is no error at (D). The comparative adverb “more” is correctly used to compare two things, “skill” and “practice.”17ANSWERS AND EXPLANATIONSCorrected Sentence:Explanation for Correct Answer E :There is no error in this sentence.Explanation for Incorrect Answer A :There is no error at (A). The noun “refugees” appropriately functions as the direct object of the verb phrase “had not expected,” and the preposition “from” correctl y introduces the adjective prepositional phrase that modifies “refugees.”Explanation for Incorrect Answer B :There is no error at (B). The infinitive “to be” is the idiomatic verbal form to follow “expected.”Explanation for Incorrect Answer C :Ther e is no error at (C). The conjunction “as” is appropriately used in the comparative construction “as … as,” and the plural pronoun “those” is parallel with the plural noun “refugees,” to which it is compared. Explanation for Incorrect Answer D :There is no error at (D). The past perfect tense of the verb phrase “had seen” is consistent with the past perfect tense of the verb of the main clause.18ANSWERS AND EXPLANATIONSCorrected Sentence: Although naturalists have identified six hundred different forms of the corion snail, there are actually no more than two true species within this genus.Explanation for Correct Answer B :The error in this sentence occurs at (B), where the singular verb “is” does not agree with its plural subject, “species.”Explanation for Incorrect Answer A :There is no error at (A). The subordinating conjunction “Although” appropriately introduces the adverbial dependent clause.Explanation for Incorrect Answer C :There is no error at (C). The words “no,” “more,” and “than” combine to form an appropriate idiom. Explanation for Incorrect Answer D :There is no error at (D). The preposition “within” correctly introduces the adverbial phrase that modifies the verb of the independent clause.Explanation for Incorrect Answer E :There is an error in the sentence.19ANSWERS AND EXPLANATIONSCorrected Sentence: The department of transportation has introduced pictorial traffic signs because drivers can react to them more quickly than to verbal ones.Explanation for Correct Answer B :The error in this sentence occurs at (B), where a singular pronoun, “this,” is used instead of the plural pronoun “them” to refer to the plural noun “signs.”Explanation for Incorrect Answer A :There is no error at (A). The singular verb p hrase “has introduced” agrees with its singular subject, “department.Explanation for Incorrect Answer C :There is no error at (C). The comparative adverbial phrase “more quickly” is appropriate to compare one type of traffic sign to another.Explanation for Incorrect Answer D :There is no error at (D). The prepositional phrase “to verbal ones” is parallel with what should be the preceding prepositional phrase “to them,” and the plural pronoun “ones” correctly refers to the plural noun “signs” to which it refers.Explanation for Incorrect Answer E :There is an error in the sentence.20ANSWERS AND EXPLANATIONSCorrected Sentence:She claimed that the “representational” actor tries to imitate a character’s behavior, whereas the “presentational” act or attempts to reveal human behavior through self-understanding. Explanation for Correct Answer A :The error in this sentence occurs at (A), where the present progressive tense of the verb “is having” is improperly used, resulting in a lack of parallelism with the present-tense verb in the subordinate clause, “attempts.”Explanation for Incorrect Answer B :There is no error at (B). The subordinating conjunction “whereas” appropriately introduces the dependent adverbial clause and indicates a contrast with the preceding dependent noun clause introduced by “that.”Explanation for Incorrect Answer C :There is no error at (C). The infinitive verbal form “to reveal” is idiomatic and appropriately functions as the object of the verb “attempts.”Explanation for Incorrect Answer D :There is no error at (D). The prepositional phrase introduced by “through” correctly functions as an adverb that modifies “attempts.”Explanation for Incorrect Answer E :There is an error in the sentence.21ANSWERS AND EXPLANATIONSCorrected Sentence: Many nations, and the United Nations itself, have issued stamps that commemorate the fiftieth anniversary of the signing of the UN charter.Explanation for Correct Answer B :The error in this sentence occurs at (B), where the singular verb phrase "has issued" does not agree with the compound subject "many nations and the United Nations."Explanation for Incorrect Answer A :There is no error at (A). The reflexive pronoun "itself" properly refers to the singular proper noun "United Nations" (which is a single organization).Explanation for Incorrect Answer C :There is no error at (C). The relative pronoun "that" appropriately introduces the dependent adjective clause that modifies the noun "stamps," and the plural verb "commemorate" agrees with its plural subject "stamps." Explanation for Incorrect Answer D :There is no error at (D). The prepositional phrase introduced by "of" functions correctly as an adjective modifying the noun "anniversary," and the words "signing" and "of" combine to form an appropriate idiom. Explanation for Incorrect Answer E :There is an error in the sentence.22ANSWERS AND EXPLANATIONSCorrected Sentence:The tribal council’s program familiarized young people with Cherokee history, taughtThe error in this sentence occurs at (C), where an independent clause breaks the parallelism of the two preceding verb phra ses (“familiarized…history” and “taught…traditions”).Explanation for Incorrect Answer A :There is no error at (A). The preposition “with” after the verb “familiarized” is idiomatic.Explanation for Incorrect Answer B :There is no error at (B). The p ast tense of the verb “taught” is consistent with the past tense of the other verbs in the sentence, and the plural pronoun “them” correctly refers to the plural noun “people.”Explanation for Incorrect Answer D :There is no error at (D). The noun “opportunity” properly functions as the direct object of the verb, and the preposition “to,” after the word “opportunity,” is idiomatic.Explanation for Incorrect Answer E :There is an error in the sentence.23ANSWERS AND EXPLANATIONSCorrected Sentence: Observation of diverse animal species shows that the most successful in the struggle for survival are those which are most adaptable to changes in their world.Explanation for Correct Answer A :The error in this sentence occurs at (A), where the plural verb “show” does not agree with the singular subject “Observation.”Explanation for Incorrect Answer B :There is no error at (B). The superlative adjective phrase “most successful” is appropriate for comparing all of the animal species in the world.Explanation for Incorrect Answer C :There is no error at (C). The indefinite pronoun “those” appropriately functions as the subject complement of the verb “are.”Explanation for Incorrect Answer D :There is no error at (D). The adjective “adaptable” app ropriately functions as the subject complement of the verb “are,” and the preposition “to” after the word “adaptable” is idiomatic.Explanation for Incorrect Answer E :There is an error in the sentence.24ANSWERS AND EXPLANATIONSCorrected Sentence: Far from having been a diehard conservative, Hoover was, some scholars now contend, the leading progressive of his day.。
SAT数学题型全解析
SAT数学题型全解析SAT（Scholastic Assessment Test）是美国大学入学考试，其中数学部分是SAT数学考试。
SAT数学考试主要测试学生在数学领域的基本知识和解决问题的能力。
本文将全面解析SAT数学考试的各种题型，并给出相应解题策略和技巧。
一、选择题SAT数学考试中的选择题分为两种：无计算器部分和有计算器部分。
无计算器部分包括多项式、代数、几何和数据分析等题型，而有计算器部分包括数据分析和统计、概率和二次方程等题型。
1. 多项式题型多项式题型主要考察学生对多项式的理解和运算能力。
解题技巧包括：- 将多项式展开，化简，合并同类项；- 利用因式分解；- 利用韦达定理求根等。
2. 代数题型代数题型主要考察学生的代数运算和方程组的解题能力。
解题技巧包括：- 利用等式的性质进行等式推导；- 运用代数运算规则，如消元法、合并同类项等；- 运用代数方程的求解方法，如变量替换、联立方程等。
3. 几何题型几何题型主要考察学生对几何形状和关系的理解和分析能力。
解题技巧包括：- 运用几何形状的性质和定理，如角度的性质、平行线的性质等；- 利用图形的特点进行推理和证明；- 运用三角形的性质和相似三角形的判定等。
4. 数据分析题型数据分析题型主要考察学生对数据的理解和分析能力。
解题技巧包括：- 对数据进行图表分析，如线图、柱状图、饼图等；- 运用统计学的相关概念和方法，如平均值、中位数、标准差等；- 运用概率的知识进行问题求解。
二、解答题解答题在SAT数学考试中占比较小，主要考察学生的解决实际问题的能力和应用数学知识的能力。
解答题的解题步骤和策略如下：- 仔细阅读问题，理解问题的要求和条件；- 找到解题思路，确定解题方法和公式；- 进行计算或推导，得到解答并进行合理的估算；- 检查答案是否符合问题的要求，并对解题过程进行合理的陈述。
总之，SAT数学考试是对学生数学知识和解决问题能力的综合考察，掌握相应的解题技巧和策略对于考试的成功至关重要。
GMAT数学题详解
GMAT数学题详解1、有一个集合A是正整数，从101-550，(inclusive)问从中任取一个数，(该数以1、2、3开头，4、5、6结尾)，求符合此情况的数的概率。
【答案】20%【思路】101-550中，共有450个整数;从六个数字(1、2、3;4、5、6)中分别选出两个做一头一尾一共是3*3=9，当中的那个数字可以是从1~0共十个，所以总共为10*9=90。
即：百位数C1/3，十位数C1/10，个位数C1/3，概率为3*10*3/450=20%2、直角坐标系中，有L1和L2两条直线，L2是否过第二象限?(1)L1垂直于L2;(2)L1过原点;【答案】E【思路】画出直角坐标系的图，(1)L1垂直于L2，单独不充分(2)L1过原点，单独不充分;(1)(2)同样不充分，答案为E。
3、有10个数，其中7个数相同，问这10个数的average>median?(1)另3个数中每一个都大于这7个数;(2)另3个数的average >这7个数的average;【答案】D【思路】设7个相同的数为X，Median=X;(1)另3个数中每一个都大于这7个数;则average>Median(2)另3个数的average >这7个数的average;得出：中数Median=X，所以average>Median选D4、一个三位数的百位数是几?(1)该三位数加上150后的新数的百位数是4;(2)该3个数加上150后的新数的十位数是5;【答案】C【思路】(1)加上150，10位存在进位与不进位两种情况：260+150=410，符合条件;340+150=490同样符合条件，(1)单独不充分;(2)只要新加上的数，10位为0，即符合条件，(2)单纯不充分;(1)(2)得出：新加的数10位为0，百位为3，选C。
5、P=xy，P为质数，求x+y可能为下面哪些数Except.(1) 3(2) 4(3) 6(4) 10(5) 12【答案】(4)【思路】质数=1*质数，P为质数=> x、y中一个为1，另一个数为质数;(1)3=2+1;(2)4=1+3;(3)6=1+5;(4)10=1+9 选它!6、P为627的倍数，且P个位为4，Q=P/627，问：Q个位为几?【答案】2【思路】P=627*K，因P的个位为4，所以K的个位一定为2，Q=P/627=627*K/627=K所以Q的个位为2。
SAT OG官方指南数学习题 由5184sat论坛荣誉出品
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P413
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费 Section 7 m免 1. 在上面的图解里，展出了从1961 到2000 里四个不同时期所建成的新房子的数量。 从1961 到 o 1990 年之间，一共建造了多少新房子？ .c 2. 求上面图表中w的值？ at 3. 一个餐厅有19张桌子，一共可以坐84人。里面有些桌子可以坐4人，有些可以坐5人。可以坐5 s 人的桌子有多少张？ 184 4. 如果a=4，下面哪一个和 am² + am + a 一样？ .5 5. 在上面的图解中，有着O圆心的圆圈被嵌入正方形ABCD中。圆形阴影部分的面积是多少？ www 6. 在上面坐标图(xy-plane)中，线L 的等式是x + 3y = 12. 下面哪一个线的等式是垂直
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哪一个图标符合上面所提的要求？
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5.上面这个韦恩图解展示了在30个上科学的学生中学习蝴蝶,学习蝗虫,两个一起学习或者是两个
免 都没有学习的学生人数。 只学习蝴蝶的学生占总人数的多少百分比？ com 6.在上面的图标里，AB = CD。 t的数值是多少？ t. 7. 如果3x² = 4y = 12, 那么x²y 的数值是多少？ sa 8. 在上面的图解里，圆圈都是相切的和紧紧挨着的（tangent)。圆圈A的圆心也是最大的那个圆圈 84 的圆心。如果圆圈A的半径是2，圆圈B的半径是4，还有圆圈C的半径是4， 那么最大的那个圆圈 1 的半径是多少？ .5 9. 在上面的图解里，线上所有的标记都是相等的。 那么x的数值是多少？ www 10. 在上面的图标里，x的数值是多少？
2.在上面的图表中，A点是圆心， 线BD和线CE是直径。下面哪一个说法正确？
【狒狒出品】考SAT必备-OG难题中文解答-1.1 Edition
Answers and Explanations of Official Guide for SAT 1.1 Edition Writing Section Grammar Part Only致同学：经过了一段时间的辛勤劳动，这份OG语法中文解析已经越来越完善了。
今后，我仍然会继续增加其他题目的解释，直到把所有语法题目包括在内。
为什么我要做这份工作？其一，OG和真题毫无疑问是考生准备SAT考试最好的备考资料。
许多同学一再询问我，SAT语法部分哪套模拟题比较好，我总会不厌其烦地帮他们比较各种模拟试题的优劣，最后无不得出同一个结论：再好的模拟题终究还是模拟题，它们都无法避免地与ETS的命题思路或多或少地产生偏差。
所以，我提醒大家一句话：你们费尽千辛万苦准备的是SAT考试，而非SAT模拟考试（模拟题做得好不见得真题就能做得好）。
其二，许多同学按照我推荐的复习计划做OG和真题，但仅限于做完题对对答案，过后并没有进行系统的总结，于是没有达到预期的复习效果。
许多同学虽然做对了题目，但各个选项的错误原因、ISE的错误如何改正等仍不清楚。
于是，我决定编写本OG 语法中文解析。
希望各位能理解我的良苦用心。
由于时间仓促加之本人水平有限，编辑排版中的纰漏在所难免，望各位指正。
欢迎大家转载、引用本材料，请注明作者即可。
衷心祝愿各位SAT考试取得好成绩！李侃 2008-12-10P145 Sample Questions1. 本题考点：主谓一致。
B应改为：have received2. 本题考点：代词。
C应改为：you expect3. 本题no error4. 本题考点：B应改为：agreed toP150 Practice Questions1. 本题考点：主谓一致。
A应改为：there are2. 见P415(17)3. 本题考点：主谓一致。
C应改为：attest to，因为主句主语为flints4. 本题考点：代词。
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新SAT 数学OG 数学题目详细讲解
第一题:
Content: Heart of Algebra
Key: B
Objective: You must make a connection between the graphical form of a relationship and a numerical description of a key feature.
Explanation: Choice B is correct. The slope of a line can be determined by finding the difference in the y-coordinates divided by the difference in the x-coordinates for any two points on the line. Using the points indicated, the slope of line l is - 3/2. Translating line l moves all the points on the line the same distance in the same direction, and the image will be a line parallel to £. Therefore, the slope of the image is also - 3/2.
第二题：
Content: Passport to Advanced Math
Key: A
Objective: You must complete operations with multipleterms and manipulate an equation to isolate the variable of interest.
Explanation: Choice A is correct. Multiplying both sidesof the equation by the denominators of the rational expressions in the equation gives 2y = 4a - 4. You should then divide both sides by 2 to isolate the y variable, yielding the equation y = 2a - 2.
第三题：
Content: Heart of Algebra
Key: D
Objective: You must interpret the slope of an equationin relation to the realworld situation it models. Also, when themodels are created from data, you must recognize that these models only estimate the independent variable, y, for a given value of x.
Explanation: Choice D is correct. When an equation is written in the form y = mx + b, the coefficient of the x-term (in this case 0.8636) is theslope. The slope of this linear equation gives the amount that the mean number of students per classroom (represented by y) changes per year (represented by x).
第四题：。