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  1.outlier(异常值)

  此考点在official guide(Page257)中只是一带而过,且OG四套中并未有相关题目,但在12月亚洲真题考试中却考到了一题。OG中对outlier的定义:A data set may have a few values that are much larger or smaller than the rest of the values in the set. These values are called outliers.

  考察方向:

  outliers that are larger than the rest of the points in the data set tend to make the mean greater than the median. 即异常值大于一组数据中的剩余数值,则平均数大于中位数。

  outliers that are smaller than the rest of the points in the data set tend to make the mean less than the median. 即异常值小于一组数据中的剩余数值,则平均数小于中位数。

  例题(选自可汗学院)

  A.The mean is greater than the median.

  B.The median is greater than the mean.

  C.The mean and the median are about the same.

  D.There is not enough information to determine the mean

  首先确定考点,选项比较的是mean和median的大小;然后看图,很明显,右边有一个数值远远高于左边的数据,确定为outlier 比其它数据要大,因此mean大于median, 对应A选项。

  2.symmetry(对称性)

  此考点在OG中也是一带而过,且在OG四套中未有例题,但在6月份亚洲考试中有考察,题目为:y=1/2x-3, 这个方程关于y轴对称,然后函数会变什么(题目为回忆版,暂不列出选项)

  OG对symmetry的描述如下:

  If the graph of f is symmetric about the y-axis, then f is an even function, that is f(-x)=f(x) for all x in the domain of f.

  If the graph of f is symmetric about the origin, then f is an odd function, that is f(-x)=-f(-x) for all x in the domain of f.

  考察方向:

  f(-x)=f(x) 关于y轴对称,为even function(偶函数)

  f(-x)=-f(-x) 关于原点对称,为odd function(奇函数)

  f(-x)=-f(x)关于x轴对称,既不是奇函数也不是偶函数

  例题(选自可汗学院练习)

  The graph of h is shown above. If f(x)=h(?x), which of the following represents the graph of f?

  首先确定考点为函数的对称性问题;题干中f(x)=h(?x), 那么h(-x)和h(x)之间的关系是关于y轴对称,可以快速锁定答案为A选项。

  3.asymptote(渐近线)

  此考点在official guide(P273)有提到过,但在OG四套,以及2016年的考题中均未有相关考题出现,但既然OG有提到,就不排除有考的可能性。

  OG中对asymptote的描述如下:

  If the values of f approach a fixed value, say, K, as x gets very large and positive or very large and negative, the graph of f has a horizontal asymptote at y=K. If f is a rational function whose denominator is zero and numerator is nonzero at x=a, then the graph of f has a vertical asymptote at x=a.

  考察方向:

  指数函数的渐近线:如y=2x 的渐近线为y=0, y=2x +2 的渐近线为y=2.

  有理函数的渐近线:y=1/x的渐近线为x=0(vertical asymptote), y=0(horizontal asymp-tote); y=1/(x+1)的渐近线为x=-1(vertical asymptote), y=0(horizontal asymptote).

  例题(选自可汗学院)

  此题题干说vertical asymptote为x=3, 可以得出x=3的时候分母应该为0,很快就可以得出选项为B。

  以上内容由智课小编为大家整理的关于“SAT数学容易忽视的考点解析”,希望可以帮助到大家,小编在此预祝大家在考试中取得好成绩!

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