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TOEFL Directory > TOEFL writing > TOEFL Reading Class Unit 2_Passage 2_Question 12-22
TOEFL Reading Class Unit 2_Passage 2_Question 12-22
You have about 15 minutes to finish this passage.
First,use about 3-4 minutes to read the passage, try to understand the main idea of this passage.
Don't read it so slowly or try to remember all details.You need to do "fast reading",and "scan" the passage.
Second, read questions 1-11, and with questions you go back the passage again and look for correct answers.
Questions 12-22
Passage 2
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 statements 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. The fact is that the mathematician 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 finds 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 occurrences 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.
12. What is the main idea of the passage?
a) Inductive reasoning should be included in the study of math.
b) Mathematics can be studied only in a logical manner.
c) Proving theorems should be the central focus of mathematics.
d) Mathematics courses should concentrate on deductive reasoning.
13. By stating Often mathematics is reduced to a series of definitions, the author implies that
a)mathematics includes more than definitions
b) definitions are rarely studied in mathematics
c) mathematics is best studied by focusing on definitions
d) mathematics is too difficult for most people to understand
14. The word power in the passage is closest in meaning to
a) origin
b) strength
c) quality
d) appropriateness
15. The author believes that many mathematics textbooks underestimate the importance of
b) imagination
c) logic
d) multiplication
e) formulas
16. The word cases in the passage is closest in meaning to
a) situations
b) methods
c) arguments
d) properties
17. According to the author, using inductive reasoning can make learning mathematics more
a) technical
b) enjoyable
c) uniform
d) abstract
18. The word exhibit in the passage is closest in meaning to
a) record
b) show
c) determine
d) limit
19. The word unusual in the passage is closest in meaning to
a) indirect
b) unnecessary
c) uncommon
d) inexact
20. Which of the following is the first step in an inductive reasoning process?
a) Generalization
b) Prediction
c) Definition
d) Observation
21. Why does the author mention sunrise and sunset in paragraph 3 ?
a) To describe how difficult it is to make generalizations
b) To demonstrate that probability is unrelated to mathematics
c) To give an example of a prediction based on a pattern
d) To explain that scientific generalizations may be stated in mathematical language
22. The word Thus in the passage is closest in meaning to
a) however
b) prior to
c) although
d) consequently
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