4种常见的SAT数学解题方法介绍

2022-05-18 10:44:40

  

  本文给大家介绍几种常见的SAT数学题的解题方法:

  1. 代入法

  例题: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解答:将答案依次带入,发现只有D选项35xy=35×140=35×35×4=(35×2)2。

  2. 特殊值法

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

  A. x<0, B. 0

  解答:y>2,不妨假设它为3,3x=x+3,x=3/2,一目了然D即为正确选项。

  3. 巧解法

  例题:At a certain diner, Joe orders 3 doughnuts and a cup of coffee and is charged $2.25. Stella orders 2 doughnuts and a cup of coffee and is charged $1.70. What is the price of 2 doughnuts?

  A. $ 0.55 B. $ 0.60 C. $ 1.10 D. $ 1.30 E. $ 1.80

  解答:按照常规的解题思路,我们可以用字母x和y分别指代“炸面包圈”和“咖啡”的价格,然后建立2个方程式3 x+y= $ 2.25 , 2 x+y= $ 1.70,最后求出方程组的解x=$ 0.55,

  y =$ 0.6。

  但是只要稍作思考,我们不难发现解题的捷径—— 3个炸面包圈加1杯咖啡的价格与2个炸面包圈加1 杯咖啡的价格相减,余额就是1个炸面包圈的价格:$ 2.25 -$ 1.70 =$ 0.55 。此时,我们还要注意的是,千万不能掉入命题者的陷阱而选择A,,因为A选项只是1个炸面包圈的价格。所以,正确答案应该是C选项。

  4. 逻辑推理法

  SAT数学题中有一类题和数学运算毫无关联,采用逻辑推理即可完成。此类题题目较少,但十分新颖。乍一看让人有些迷惑不解,其实只要掌握了恰当的方法,解题十分容易。

  例题:

  Family   Numbers of Consecutive Nights

  Jackson    10

  Callan   5

  Epstein   8

  Liu   6

  Benton    8

  The table above shows the number of consecutive nights that each of five families stayed at a certain hotel during a 14-night period. If the Liu family’s stay did not overlap with the Benton family’s stay, which of the 14 nights could be a night on which only one of the five families stayed at the hotel?

  A. The 3rd B. The 5th C. The 6th D. The 8th E. The 10th

  解答:此题只要借助线段,便一目了然了。既然原文说“the Liu family’s stay did not overlap with the Benton family’s stay”,而且两家刚好加在一起正好是14晚,那么不妨将这14晚设为一段长14cm的线段,从6cm处分割:

  Liu Benton family family︳______ ____︳_________________︳

  0 6cm 14cm

  ________10cm__________︳

  ________10cm__________︳

  由于Jackson family是剩余家庭里呆得时间最长的,所以只要从他家看起即可。该题可以简单转化为一段长10cm的线段在14cm范围内左右移动,要么露出最左面的 0~4cm空间(不包括4),要么留出最右面的10~14cm(不包括10)。所以没有被Jackson family所覆盖的只有这两个区间,也就是说只有一家居住的只能是前三天或后三天,答案为A。

  从上面的最后一道例题我们不难看出,对于中国学生而言,答好数学题的前提是读题能力,即英语能力,试想如果考生consecutive(连续的), overlap(重叠)等词认识有障碍,那么即使最后能猜出词义,也必然会浪费一定时间。所以,考生仍然要通过多做题来熟悉数学中的常用单词,特别是代数和几何方面的专用名词,如divisible(可被整除的),quotient(商),round to(四舍五入),equivalent equation(同解方程/等价方程),infinite decimal(无穷小数), recurring decimal(循环小数),concentric circles(同心圆),adjacent angle(邻角),segment of a circle(弧形),circumference/perimeter (周长),cross section(横截面),coordinate system(坐标系),Pythagorean theorem(勾股定理),等等。

  如果大家能熟练数学掌握方面的词汇,并通过真题不断进行练习,那么最后考出理想的SAT数学成绩甚至800分满分对聪明的中国考生而言绝非难事。#p#分页标题#e#

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