4道SAT数学难题.

　　下面为大家搜集了4道SAT数学难题，供大家在备考的时候进行适当的准备。解答SAT数学难题可以比常规的题目更加容易了解SAT数学考试的出题思路和方法。下面我们来看看详细内容吧。

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　　1.Which of the following CANNOT be the lengths of the sides of a triangle?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　2.for all integersIfis a function dined for all positive integers, andsatisfies the two conditions above, which of the following could be the dinition of?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　3.If, what is the value of?

　　(A) 6

　　(B) 10

　　(C) 12

　　(D) 30

　　(E) 60

　　4.In a community ofpeople, each person owns a dog or a cat or both. If there aredog owners andcat owners, how many of the dog owners own no cat?

　　(A)

　　(B)

　　(C)

　　(D)

　　(E)

　　Explanation

　　1.The correct answer is B

　　The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Four of the answer choices can be eliminated because each set of three numbers can be the lengths of three sides of a triangle. For example, in the third choice, the sum of any two numbers is greater than the third number. However, the second choicecannot be the lengths of the sides of a triangle, sinceis not greater than. This choice is the correct answer, since the question asked which set of numbers could NOT be lengths of the sides of a triangle.　　

　　2.The correct answer is B

　　If, then, so the second condition fails. If,then, so the second condition fails for this function also. The other three options satisfy, so it remains to check whether they satisfy the first condition.

　　If, and, thenand, so it is not true thatfor all integers. This means that the functiondoes not satisfy the first condition. If, and, thenand, so it is not true thatfor all integers. This means that the functiondoes not satisfy the first condition.

　　However, if, then, for all integers. Also,.Therore, the functionis the only option that satisfies both conditions.

　　3.The correct answer is B

　　Multiplying both sides of the equationbygives, which simplifies to. Dividing both sides of the equationbygives, and so.

　　While programming the answer key for the Official SAT Question of the Day application on collegeboard.org, the answer to the November 23rd question was incorrectly entered into the application "A (6)" instead of "B (10)." While the question, hint, and answer explanation were displayed correctly, anyone who entered the correct answer "B (10)" received a message indicating that response was incorrect. We have resolved the issue and apologize for any confusion this may have caused.

　　4.The correct answer is C

　　To solve this problem, you must realize that some of thedog owners also own cats and some of thecat owners also own dogs. This has to be true becauseis more than! The question asks how many of the dog owners donot own cats. To solve the problem, first find the number of people who own both a dog and a cat. To do this, letequal the number who own both a dog and a cat. Then. (Note: Addingandcountstwice, somust be subtracted from the sum to get.) Next, the equationcan be solved for, yielding. Finally, the number of dog owners who own no cat is.

　　以上就是这4道SAT数学难题的全部内容，后面附有详细的答案解析。大家可以在备考自己的SAT数学考试的时候，进行适当的参考和借鉴之用。