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新SAT数学如何取得高分

编辑:麦格教育

摘要

数学词汇
 
词汇是一切的基础,数学也不例外,备考过SAT的同学都知道,大部分错题的原因都是读不懂题。比如isoceles, trapezoid这些单词,同学们都认识么?所以为了拿到数学满分,同学们一定要背单词!


 基础能力
 
根据CB官网的信息,新SAT数学主要考查考生三项能力:
o   
核心代数(Heart of Algebra)
o   
数据分析(Problem Solving and Data Analysis)
o   
高级数学(Passport to Advanced Math)
 
核心代数和高级数学主要考查同学们的基础数学能力,主要包括:
o   
算数(Arithmetic)
o   
函数(Function)
o   
几何(Geometry)
o   
概率(Probability)
 
这些知识都是同学们高中学过的,而且普通高中的数学难度要高于SAT数学考试。
 
从教学的经验来看,同学们容易出错的地方是函数和概率部分。这两方面,同学们要加深理解并且加大练习。我们来看一道新SAT的例题:
 
For a polynomial p(x), the value of p(3) is
2.Which of the following must be true about p(x) ?

A) x − 5 is a factor of p(x).

B) x − 2 is a factor of p(x).

C) x + 2 is a factor of p(x).

D) The remainder when p(x) is divided by x − 3 is 2.
 
解析:
 
这道题目需要同学们深层次理解函数的赋值, p(3)=-2, 我们可以看做p(x) = (x-3) Q(x) -2, 那么p(x) / (x-3) = Q(x) - 2/(x-3), 因此p(x)除以x-3 余数是-2。答案选D.
 
如果同学们觉得正面解题思路太复杂,在考试的时候记得灵活使用试数法。根据题干p(3) = -2, 我们可以假设 p(x) = x² - 11. 这样A,B,C都可以排除,答案选D



读图表能力
 
SAT数学对于考试图表分析能力的要求有了明显的提高,这类题目不仅会出现在数学部分,也会出现在阅读和语法部分。我们来看一道例题:



The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown.


1. How many of the nine people have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?

A. 2  B  4   C 6    D 9


2. Which of the following is the best interpretation of the slope of the line of best fit in the context of this problem?

A. The predicted height increase in centimeters for one centimeter increase in the first metacarpal bone

B. The predicted first metacarpal bone increase in centimeters for every centimeter increase in height

C. The predicted height in centimeters of a person with a first metacarpal bone length of 0 centimeters

D. The predicted first metacarpal bone length in centimeters for a person with a height of 0 centimeters


3. Based on the line of best fit, what is the predicted height for someone with a first metacarpal bone that has a length of 4.45 centimeters?

A. 168 centimeters    B. 169 centimeters    C. 170 centimeters   D. 171 centimeters
 

 


解析:
 
这是一道需要考生读懂图表的大题:
 
第一题考查理近似线比较远的离散的点有几个,通过数图中里近似线较远的点,可以得出答案4个(注意在x=4的地方也有一个点), 答案选B.
 
第二题考查了线性(一次)函数的意义,线性函数代表因变量(y) 随着自变量(x)变化而线性变化,所以答案选A.
 
第三题考查函数的取值,当x取值4.45,通过读图标得出y取值170 cm. 答案选C.
 


实验能力
 
改革后的SAT数学将加强应用题的考查,我们来看下面的例题:
 
1. A researcher wanted to know if there is an association between exercise and sleep for the population of 16-year-olds in the United States. She obtained survey responses from a random sample of 2000 United States 16-year-olds and found convincing evidence of a positive association between exercise and sleep. Which of the following conclusions is well supported by the data?
 
A. There is a positive association between exercise and sleep for 16-year-olds in the United States.
B. There is a positive association between exercise and sleep for 16-year-olds in the world.C. Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for 16-year-olds in the United States.D. Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for 16-year-olds in the world.
 
解析:
 
题目叙述说科学家在United States采样了200016-year-old的样本,并且发现有found convincing evidence of a positive association found convincing evidence of a positive association. 那么根据实验,我们也仅能得出结论是在United States, 而不是the world, 并且只能说有positive association, 不能说is caused by, 这道题目考查的就是实验的严谨性。答案选A.
 

 


让我们来看另一道题目:
2. A research assistant randomly selected 75 undergraduate students from the list of all students enrolled in the psychology-degree program at a large university. She asked each of the 75 students,
How many minutes per day do you typically spend reading? The mean reading time in the sample was 89 minutes, and the margin of error for this estimate was 4.28 minutes. Another research assistant intends to replicate the survey and will attempt to get a smaller margin of error. Which of the following samples will most likely result in a smaller margin of error for the estimated mean time students in the psychology-degree program read per day?
 
A. 40 randomly selected undergraduate psychology-degree program students

B. 40 randomly selected undergraduate students from all degree programs at the college

C. 300 randomly selected undergraduate psychology-degree program students

D. 300 randomly selected undergraduate students from all degree programs at the college
 
这又是一道需要大量阅读的题目,仔细阅读完,其实考查了一个概念 “margin of error, 就是误差; 为了减小误差,可以增大样本量,当然一定要在实验对象的范围内增大样本量。因此本题选 C.
 

建议
 
同学们在具备了上述四个能力之后,还需要最后一个,就是细心做题。因为马虎失分是非常可惜的,然而很多同学都不能保证把自己会的题目都做对。下面给大家3点建议,大家在做题的时候一定要谨记:
 
要点1:一定要审好题,即搞清楚明给的条件,暗示的条件以及所求的内容。
 
要点2:一定要一步一步地演算,不要跳过每一步骤。你可能认为这样会耽误时间,这样一步一个脚印地走下去不仅不会耽误时间,反而因为不用回头检查会节省时间;况且往往检查的思路和作题思路相同,常常有错也不易查出。
 
要点3: 确认直接求得的未知数是否是试题的最后所问。SAT试题中常有类似X+1等于几的问题,考生常常解出了X就完事了,忘了题目问的是X+1而不是X
 

结语
 
改革后的SAT更偏重考生的阅读图表能力,和实验应用能力。考查的方法与ACT科学的Data类型题目非常相似,同学们可以拿来做练习。总体来说,新SAT数学拿满分不是梦,勤加练习加上细心答题,满分将离你不远!



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