新SAT数学题目中常考语法句型,历年真题为例


来源:   时间:2017-04-18 10:03:52

  新SAT考试中的数学题目,除了考查学生对于数学知识点的掌握水平,还会检验考生对于题干的快速理解能力。因此,掌握题目中常常出现的重要语法句型,对于我们的准确解题至关重要。今天,我们就以2016年5月亚太卷的SAT数学真题,以及可汗学院的模拟题为例,解析数学题目中两种常见的语法知识点。
 
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  1、Twice as many A as B

  twice as many A as B这个句型的含义是 A = 2B,也就是 A 是B的两倍。我们一起来看下面这道来自可汗学院的题目:
 
  1. Abby is buying a widescreen TV that she will hang on the wall between two windows. The windows are 36 inches apart, and wide screen TVs are approximately twice as wide as they are tall. Of the following, which is the longest that the diagonal of a widescreen TV can measure and still fit between the windows?
  A. 32 inches     B. 42 inches
  C. 55 inches     D. 60 inches
 
  题干部分画下划线的“twice as wide as they are tall”表示“宽是高的两倍”,这是TV的最常见的长相。
 
  当然,要正确解出本题,还要看清楚“Of the following, which is the longest that……”这句话。也就是说,本题求的是“相对最大值”,我们需要从四个选项中找到一个符合题目要求的最大值。
  本题答案是:A
 
  twice as many A as B这个句型,也会在不等式类题型中出现。现在,我们一起来看2016年5月份亚太区Section 3的这道真题。
 
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  大家注意红色框中的“The service wants to buy at least twice as many containers of detergent as containers of fabric softener”。很明显,它符合twice as many A as B这个句型,也就是“containers of detergent”的数量至少是“containers of fabric softener”数量的两倍:d≥2s.
 
  综合第一个不等式的内容,本题的正确答案是:A
 
  twice as many A as B句型有很多变体,比如 half as many A as B,表示 B = 2A;而 three times as many A as B表示A = 3B
 

  2. What fraction of A are B ?

  fraction 表示“分数”,但在 SAT 以及ACT考试中,fraction 通常用在what fraction of A are B 句型中,表示“比例”,可以被 proportion 和 probability 等词汇代替。
 
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  现在,我们一起来看一下2016年5月份亚太区Section 3的20题
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  在可汗学院的模拟题中,fraction 会被proportion,probability,frequency,percentage等词汇代替:
  What fraction / proportion / probability / frequency / percentage of A are B
 
  我们来看下面这道题:
 
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  本题的问题属于What percentage of A are B句型,与我们刚刚讲解的真题的唯一不同,是答案用百分比来表示:What percentage of those books with 500 or more pages are from the 19th century?
 
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  有时,what fraction of A are B 句型会稍加变形,变成“Of A,what fraction are B”的形式。我们一起来看2016年5月份亚太卷Section 4 的第8题:
 
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  本题属于“Of A,what fraction are B”句型的衍生形式:“Of the people who chose vanilla ice cream, what fraction chose hot fudge as a topping?
 
  因此,A(people who chose vanilla ice cream)做分母,而A中的B(people who chose hot fudge as a topping)做分子,因此答案应该选择 D 。
 
  综上所述,SAT 数学中的很多题目,其实在同时考查数学水平和英语快速阅读能力,只要同时夯实数学和英语基础,才能在最短的备考时间内,取得最快的成绩提升。(文:新东方 张志峰)
 


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