SAT官方数学习题

　　SAT官方数学习题

　　Read the following SAT test question, then click on a button to select your answer.

　　If = x2, the value of x can be which of the following?

　　–

　　0

　　A. I only

　　B. II only

　　C. III only

　　D. II and III only

　　E. I, II, and III

　　Correct Answer: D

　　Here‘s Why:

　　Roman Numeral Answer Format

　　Roman Numeral I: Can the value of x be –?

　　You could test this answer by substituting – for x in the equation and seeing whether the result is true. But you can also reason this question out without substituting numbers:

　　If x = – , then is a positive number, because any nonzero number squared is positive.

　　If x = –, then is negative.

　　So is negative and x2 is positive.

　　Therefore, x cannot be –.Mark Roman numeral I with an “F” for false.

　　Roman Numeral II: Can the value of x be 0?

　　This is a very easy substitution to make:

　　= x2

　　= 02 = 0

　　Roman numeral II is true, so mark it with a “T” for true.

　　Roman Numeral III: Can the value of x be ?

　　Substitute for x:

　　If x = , then = .

　　Also, x2 = = .

　　Roman numeral III is true, so mark it with a “T” for true.

　　Check the Answers:

　　You now know whether each of the Roman numeral statements is true or false:

　　I is false.

　　II is true.

　　III is true.

　　Find the choice that says only II and III are true.

　　Difficulty: Hard