forever 21 Posted November 9, 2003 Share Posted November 9, 2003 Please try to answer....I know that your answers would be a great help for my review. Thanks... ----> Some people believe that Mathematics is a difficult, dull subject that is to be pursued only in a clear cut, logical fashion. This belief is perpetuated because of the way Mathematics is presented in many textbooks. Often Mathematics is reduced to a series of definitions, methods to solve various types of problems, and theorems. Theorems are statement whose truth can be established by means of deductive reasoning and proofs. This is not to minimize the importance of proof in mathematics, for it is the very thing that gives Mathematics its strength. But the power of the imagination is every bit as important as the power of deductive reasoning. ----> The long history in the development of a concept or any of the unproductive approaches that were taken by early mathematicians is not always addressed in mathematics courses. That fact is that the mathematicians seeks out relationships in simple cases, looks for patterns, and only then tries to generalize. It is often much later that the generalization is proved and find its way into an actual textbook. ----> One way we can learn much about Mathematics and in the meantime find enjoyment in the process is by studying numerical relationships that exhibit unusual patterns. For example, children may find it easier to learn their multiplication tables by exploring the patterns that the numbers display. Even complicated arithmetic problems can sometimes be solved by using patterns. Given a difficult problem, a mathematician will often try to solve a simpler, but similar problem. This type of reasoning - first observing patterns and then predicting answers in complicated problems - is an example of INDUCTIVE REASONING. It involves reasoning from particular facts or individual cases to a general statement that may be true. The more individual occurences that are observed, the better able we are to make a correct generalization. For instance, we can predict the exact time of sunrise and sunset each day. This is an example of inductive reasoning since the prediction is based on a large number of observed cases. Thus, there is a very high probability that the prediction will be successful. 1.What is the main idea of the passage? a.inductive reasoning should be included in the study of mathematics b. mathematics can be studied only in a logical manner c. proving theorems should be the central focus of math. d. Mathematics courses should concentrate on deductive reasoning. 2. By stating often mathematics is reduced to a series of definition, the author implies that a. math include more than definition b.definition are rarely studied in math c. math is best studied by focusing definition d. math is too difficult for most people to understand. 3. The word power is close in meaning to a. origin b. strength c. quality d. appropriateness 4. The author believes that many math textbooks underestimate the importance of a. imagination b. logic c. multiplication d. formulas 5 The word cases in the passaage is close in meaning to a. situations b. methods c. arguments d. properties 6. According to the author, using inductive reasoning can make learning math more a. technical b. enjoyable c. uniform d. abstract 7. The word exhibit in the passage is close in meaning to a. record b. show c. determine d. limit 8. The word unusual in the passage is closest in meaning to a. indirect b. unnecessary c. uncommon d. inexact 9. Which of the ff is first step in an inductive reasoning process? a. generalization b. prediction c. definition d. observation 10. Why does the author mention sunrise and sunset in paragraph 3? a. to describe how difficult it is to make generalization b. to demonstrate that probability is unrelated to math. c. to give an example of a prediction based on pattern d. to explain that scientific generalizations may be stated in mathematical language 11.The word thus in the passage is close in meaning to a. however b. prior to c. although d. consequently Quote Link to comment Share on other sites More sharing options...
vbket Posted November 11, 2003 Share Posted November 11, 2003 Originally posted by forever 21 Please try to answer....I know that your answers would be a great help for my review. Thanks... ----> Some people believe that Mathematics is a difficult, dull subject that is to be pursued only in a clear cut, logical fashion. This belief is perpetuated because of the way Mathematics is presented in many textbooks. Often Mathematics is reduced to a series of definitions, methods to solve various types of problems, and theorems. Theorems are statement whose truth can be established by means of deductive reasoning and proofs. This is not to minimize the importance of proof in mathematics, for it is the very thing that gives Mathematics its strength. But the power of the imagination is every bit as important as the power of deductive reasoning. ----> The long history in the development of a concept or any of the unproductive approaches that were taken by early mathematicians is not always addressed in mathematics courses. That fact is that the mathematicians seeks out relationships in simple cases, looks for patterns, and only then tries to generalize. It is often much later that the generalization is proved and find its way into an actual textbook. ----> One way we can learn much about Mathematics and in the meantime find enjoyment in the process is by studying numerical relationships that exhibit unusual patterns. For example, children may find it easier to learn their multiplication tables by exploring the patterns that the numbers display. Even complicated arithmetic problems can sometimes be solved by using patterns. Given a difficult problem, a mathematician will often try to solve a simpler, but similar problem. This type of reasoning - first observing patterns and then predicting answers in complicated problems - is an example of INDUCTIVE REASONING. It involves reasoning from particular facts or individual cases to a general statement that may be true. The more individual occurences that are observed, the better able we are to make a correct generalization. For instance, we can predict the exact time of sunrise and sunset each day. This is an example of inductive reasoning since the prediction is based on a large number of observed cases. Thus, there is a very high probability that the prediction will be successful. Here is my answer: 1.What is the main idea of the passage? c. proving theorems should be the central focus of math.2. By stating often mathematics is reduced to a series of definition, the author implies that c. math is best studied by focusing definition 3. The word power is close in meaning to b. strength 4. The author believes that many math textbooks underestimate the importance of b. logic 5 The word cases in the passaage is close in meaning to a. situations 6. According to the author, using inductive reasoning can make learning math more b. enjoyable 7. The word exhibit in the passage is close in meaning to b. show 8. The word unusual in the passage is closest in meaning to c. uncommon 9. Which of the ff is first step in an inductive reasoning process? d. observation 10. Why does the author mention sunrise and sunset in paragraph 3? c. to give an example of a prediction based on pattern 11.The word thus in the passage is close in meaning to d. consequently Can you tell me how many right ans? Quote Link to comment Share on other sites More sharing options...
forever 21 Posted November 14, 2003 Author Share Posted November 14, 2003 To everybody! Could you please help me with the reading comprehension section. My exam will be next week. Thanks in advance. Quote Link to comment Share on other sites More sharing options...
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