SAT数学实用解题技巧

2022-05-23 18:29:24

  

  就纯知识难度上,SAT难度要远远小于国内高中知识水平,SAT数学考试内容多是“广而不精”类型的,即所涉及的范围比较广,而考察的深度比较浅,考生只需要把考题(多是应用类型)转化为初中所学的知识即可。

  众所周知,就SAT的各科来说,数学部分是最简单的,也是提分最容易的,即时间的边际效用是最高的,所以应该在SAT复习的初期把数学掌握到一个娴熟的程度,然后维持一定的热度即可。但是还有很多考生的数学不能考到780分或者800分,究其原因可能是把做错的原因归结为粗心大意或者知识欠缺,或者是不熟悉SAT的考试形式。注意,任何考试,粗心大意也是一种错误,不要因为这个而迁就了自己,要试着去规避。因为就纯知识难度上,SAT难度要远远小于国内高中知识水平,SAT数学考试内容 多是“广而不精”类型的,即所涉及的范围比较广,而考察的深度比较浅,考生只需要把考题(多是应用类型)转化为初中所学的知识即可。

  例如:

  Figure I Figure II Figure III

  Figures I and II above show two stacks of identical pails and their heights. If n is the number of pails in a stack and n>1, the height of the stack , in inches, is given by h(n)=2n+8. The number 2 in the equation represents what quantity shown in Figure III?

  (A) a, the height of one pain

  (B) b, the height of the overlap of two pails

  (C) c, the distance between the top of one pail and the top of the next pail in the stack.

  (D) d, the diameter of the bottom of each pail

  (E) e, the volume of the bottom pail that remains after the second pail is stack on top of it.

  在英文环境下,很多国内考生大脑就忙不过来了——需要经过对考题翻译,然后转化为数学知识,因为翻译是隐性的,许多考生脑子就卡壳了。其实如果翻译成中文,这道题顶多会放在国内高二学生数列部分的基础练习部分。但是因为SAT不考等差等 比数列,这道题的情景也是比较简单的,因为很容易观察到四个桶比三个桶多一个c,五个桶比四个桶多一个c,而从h(n)=2n+8 里我们知道,h(4)比h(3)多的就是系数2,h(5)比h(4)多的也是系数2,所以这道题用观察法就可以得到了。

  就纯知识难度上,SAT难度要远远小于国内高中知识水平,SAT数学考试内容多是“广而不精”类型的,即所涉及的范围比较广,而考察的深度比较浅,考生只需要把考题(多是应用类型)转化为初中所学的知识即可。

  其实从SAT的出题逻辑来说,SAT I的数学就需要基本的四则运算和简单的数理逻辑以及观察、空间想象能力,因为专业一点的知识只会在SAT II中考察,所以SAT I的数学只考察最基本的数学知识。既然只考察最基本的数学知识,考生在平常的复习中也大可不必再像国内高中一样要经过大量的训练,其实只要经过一些题目的训练,熟悉题型,然后加速把SAT数学转化为中文题目的速度(最好是直接用英文思维来读题,不必转化),而且最关键的一点就是,国内学校教的一些方法在SAT数学中还是非常有用的,因为SAT是一门对时间要求非常高的考试,一般来说,你做题的时间越短,方法越简单,做对的概率越大,不然很可能得不偿失。

  下面笔者举了一些在SAT数学中常用的简单方法,其实这些方法在国内数学考试中是常用的,考生也要试着去用,可以节省时间,同时提高准确率:

  1. 列举法

  2. 代入法

  3. 特殊值法

  列举法解题:

  (1)The units digit of 23333 is how much less than the hundredths digit of

  (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

  (2)what is the units digit of 1597365?

  代入法解题:

  (1)Bob has a pile of poker chips that he wants to arrange in even stacks. If he stacks them in piles of 10, he has 4 chips left over. If he stacks them in piles of 8, he has 2 chips left over. If Bob finally decides to stack the chips in only 2 stacks, how many chips could be in each stack?

  A. 14 B. 17 C. 18 D. 24 E. 34

  (2)If x and y are two different integers and the product 35xy is the square of an integer, which of the following could be equal to xy?

  A. 5 B.70 C. 105 D. 140 E. 350

  (3) If x2=y3 and (x-y)2=2x, then y could equal

  (A) 64 (B) 16 (C) 8 (D) 4 (E) 2

  (4)For positive integers p, t, x and y, if px=ty and x-y=3, which of the following CANNOT equal t?

  A. 1 B. 2 C. 4 D. 9 E. 25

  (5)If 3t-3>6s+9 and t-5s<12, and s is a positive integer less than 4, then t could be any of the following EXCEPT

  A. 6 B. 8 C. 10 D.12 E. 23

  (6)If n and p are integers greater than 1 and if p is a factor of both n+3 and n+10, what is the value of p?

  A. 3 B. 7 C. 10 D. 13 E. 30

  特殊值法:

  (1) If x is a positive integer greater than 1, and x3-4x is odd, then x must be

  (A) even (B) odd (C) prime (D) a factor of 8 (E) divisible by 8

  (2) If the graph above is that of f(x), which of the following could be f(x)

  A. f(x)=

  B. f(x)=

  C. f(x)=|x|+3

  D. f(x)=|x+3|

  E. f(x)=|3x|

  (3) xy=x+y. If y>2, what are all possible values of x that satisfy the equation above?

  A. x<0, B. 02

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