SAT数学练习题 含详细答案解析(1).

　　下面是5道SAT数学练习题，每道题目后面都有答案和详细的解析，希望同学们在练习的时候先不看答案，看看自己的能做对几道题，然后再与答案对照，找出错题原因，针对自己的SAT数学复习进行查漏补缺。

　　1. If f(x) = x² – 3, where x is an integer, which of the following could be a value of f(x)?

　　I 6

　　II 0

　　III -6

　　A. I only

　　B. I and II only

　　C. II and III only

　　D. I and III only

　　E. I, II and III

　　Correct Answer: A

　　解析:

　　Choice I is correct because f(x) = 6 when x=3. Choice II is incorrect because to make f(x) = 0, x² would have to be 3. But 3 is not the square of an integer. Choice III is incorrect because to make f(x) = 0, x² would have to be –3 but squares cannot be negative. (The minimum value for x2 is zero; hence, the minimum value for f(x) = -3)

　　2. For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?

　　A. 48

　　B. 49

　　C. 50

　　D. 51

　　E. 52

　　Correct Answer: C

　　解析:

　　1 < 4n + 7 < 200. n can be 0, or -1. n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1. The largest value for n will be an integer < (200 - 7) /4. 193/4 = 48.25, hence 48. The number of integers between -1 and 48 inclusive is 50