新SAT数学深度解析

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SAT数学深度解析

一、新旧SAT对比



SAT

            SAT

计分标准

非填空题答错扣分

             错题不扣分

sub score

新增对科学、历史、社会科学

领域学习能力分析

考试时间

70min

80min

考试形式

3部分均可用计算器

2部分,部分不可使用计算器

25min+25min+20min

25min+55min

题目数量

44单选+10填空

45单选+13填空

题目长度

平均35字,最长200

平均45字,最长300

考察知识

1、数字和运算

1、代数核心内容

2、代数和函数

2、解决问题和分析数据

3、几何和测量

3、通往高等数学

4、数据分析,统计和概率

4、附加内容

 

二、新SAT数学知识点变化

删除:奇偶数、质数、因子、整除、数列、排列组合

新增:分布、方差、复数、高次方程(组)、指数函数、三角函数、解析几何

 

三、新SAT数学考察知识分布比例

1、代数核心内容:33%

2、解决问题和分析数据29%

3、通往高等数学28%

4、附加内容10%

 

四、新SAT数学知识点分布概览

方程25%、直角坐标轴11%、比例/百分比8%、常量/变量6%、函数6%、几何6%、线性不等式(组)5%、多项式5%、指示4%、平均值/中位数4%、概率4%、三角函数和弧度3%、单位3%、图表3%、分布和方差2%、解析几何1%、分数小数1%、复数1%、绝对值1%

 

五、新SAT全面分析

1、题目的变化 

SAT数学不仅在知识点考查方面更加贴近实际生活应用,包括题目和题型也变得更加接地气。最明显的表现是题目长度大大增加,单词难度加大,长句出现频率增加,这对学生的阅读能力和速度提出了更高的要求。所以学生必须提高自身英语阅读能力。


2、题目的内容和形式趋于多样化

题目与实际生活和工作相结合,要求学生累积与留心更多社会经验与常识,学了知识就要用知识解决实际问题,而不是为了考试而学知识。

例题:

  A bank has opend a new branch and ,as part of a promotion, the bank branch is offering $1,000 certificates of deposit at an interst rate of 4% per year, compounded semiannually. The bank is selling certificates with terms of 1,2,3 or 4 years. Which of the following fuctions gives the total amount, A, in dollars, a customer will receive when a certificate with a term of k years is finnally paid.

 

  A) A= 1,000(1+0.04K)

 

  B) A=1,000(1+0.08K)

 

  C) A=1,000(1.04)k

 

  D) A=1,000(1.04)2k

 

解读:银行几乎与每个人的生活都息息相关,存款利率与收益具体如何计算则是这道题考查的重点。而对于中国学生来说,这无疑增加了难度,大家平时要多了解这方面的常识才行。


 3、图表题的增加

要求学生提高对数据的解读和整合能力。

 

例题:


Michael swam 2,000 yards on each of eighteen days. The scatterplot above shows his swim time for and corresponding heart rate after each swim. The line of best fit for the data is also shown. For the swim that took 34 minutes, Michael’s actual heart rate was about how many beats per minutes less than the rate predicted by the line of best fit?

  A) 1

  B) 2

  C) 3

  D) 4

解读:想要看懂图表,就需要理解图表中横纵轴以及点、线对应题目中的哪些文字信息。 这道题中则需要重点理解根据已知数据做出的预测与实际数据之间是会存在偏差,然后根据题目要求计算出实际差值。

4、与STEM,美国社会科学知识等领域紧密相关

要求:具备相应的科学背景知识、信息处理能力,以及逻辑推理能力 


  例题:

  a = 1,052 + 1.08t

 

  The speed of a sound wave in air depends on the air temperature. The formula above shows the relationship between a, the speed of a sound wave, in feet per second, and t, the air temperature, in degrees Fahrenheit (°F). Which of the following expresses the air temperature in terms of the speed of a sound wave?

 

  A) t = (a-1052)/1.08

 

  B) t = (a+1052)/1.08

 

  C) t = (1052-a)/1.08

 

  D) t = 1.08/(a+1052)

 

  解读:这答题涉及物理学科相关知识,题目中已经给出公式以及相应解释。只要理解变量的意义以及相应单位,就可以按照题目要求解题。

 

  例题:

 

  The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states joined the United States between 1776 and 1849 and x states joined between 1850 and 1900, which of the following equations is true?

 

  A) 30x=2

 

  B) 2x=30

 

  C) x2=30

 

  D) x+30=2

 

  解读:美国是联邦制国家,各个州加入联邦的时间不同,这道题以此背景,实际上考查学生找到变量和常量,建立简单方程式的能力。

 

  例题:

 

  In order to determine if treatment X is successful in improving eyesight, a research study was conducted. From a large population of people with poor eyesight, 300 participants were selected at random. Half of the participants were randomly assigned to receive treatment X, and the other half did not receive treatment X. The resulting data showed that participants who received treatment X had significantly improved eyesight as compared to those who did not receive treatment X. Based on the design and results of the study, which of the following is an appropriate conclusion?

 

  A) Treatment X is likely to improve the eyesight of people who have poor eyesight.

 

  B) Treatment X improves eyesight better than all other available treatments.

 

  C) Treatment X will improve the eyesight of anyone who takes it.

 

  D) Treatment X will cause a substantial improvement in eyesight.

 

解读:这道题给我们简述了一个改善视力科学实验,从实验对象的选择,分组到进行实验,最后要求学生根据以上信息得出科学结论。

 

总体看来,新SAT相对于中国学生来说要求更高了,但是扎实的基础知识依然是中国学生的优势,只是要对美国社会科学知识等领域要有所了解,同时要增加自身的数据分析和整合能力、增加与咱们日常生活息息相关的实物的了解,切忌做一个只会读书考试的人。

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