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2011年11月12日SAT官方每日一题---数学选择

   下面是是2011年11月12日的SAT官方每日一题的内容,是关于数学方面的,题型是选择。SAT官方每日一题是collegeboard每天都会发布的题目,关于SAT考试的三个部分的各个题型。下面我们就一起来看一下这个SAT官方每日一题吧。

  SAT官方每日一题之数学---选择:

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  Mathematics > Standard Multiple Choice

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

  If (x + y)^2 =x^2 + y^2, which of the following statements must also be true? 

  Roman numeral 1. x = 0 

  Roman numeral 2.(x minus y)^2 = x^2 + y^2 

  Roman numeral 3. x times y = 0 

  Answer Choices

  (A) None

  (B) Roman numeral 1only 

  (C) Roman numeral 2only 

  (D) Roman numeral 3only 

  (E) Roman numeral 2and Roman numeral 3

   The correct answer is E

  Explanation

  The quantity (x + y)^2can be expressed as x^2 + 2 times x times y + y^2. If (x + y)^2 = x^2 + y^2, then 2 times x times y = 0and x times y = 0. Since x times y = 0, either x = 0or y = 0or both. Therefore, statement Roman numeral 3must be true, but statement Roman numeral 1, x = 0, is not always true. For statement Roman numeral 2, you can write (x minus y)^2 = x^2 minus 2 times x times y + y^2, and since x times y = 0, it follows that (x minus y)^2 = x^2 + y^2. Therefore, both statements Roman numeral 2and Roman numeral 3must be true.

  下面是一道和SAT官方每日一题相似的题目,供大家练习:  

Table

   The table above shows the temperatures, in degrees Fahrenheit, in a city in Hawaii over a one-week period. If mrepresents the median temperature, frepresents the temperature that occurs most often, and arepresents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f, and a

  Answer Choices

  (A) a less than m less than f 

  (B) a less than f less than m 

  (C) m less than a less than f 

  (D) m less than f less than a 

  (E) a = m less than f 

  The correct answer is A

  Explanation

  Difficulty: Medium

  To determine the correct order of m, f, and a, it is helpful to first place the seven temperatures in ascending order as shown below.  

66697075777878

   The median temperature is the middle temperature in the ordered list, which is 75, so m = 75. The temperature that occurs most often, or the mode, is 78, so f = 78. To determine the average, you can add the seven numbers together and divide by 7. However, you can determine the relationship between the average and the median by inspection. The three numbers greater than 75are closer to 75than are the three numbers smaller than 75. Therefore, the average of the seven numbers will be less than 75. The correct order of m, f, and ais a less than m less than f.

  以上就是关于2011年11月12日SAT官方每日一题中数学选择的详细内容,包括了题目和选项以及答案,后面附有一道相关的练习题。大家可以在备考SAT的过程中关注SAT每日一题的内容,这样就可以更好有不间断的练习,也就能在日积月累的过程中得到提高。

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