在这里想和大家一起探讨一下SAT数学解题方法,SAT数学是中国学生的强项,我们在运用SAT数学解题方法时也会觉得得心应手。因为NEW SAT数学考察范围包括算术及应用题、代数及函数、几何及度量衡、数据分析、统计学及基础概率论。当然这些内容中的绝大部分在中国大陆的数学教学中高二之前就已经全部学习完毕了。
在一次完整的New SAT考试里,数学部分一共包括3个Section ,其中2个Section各需在25分钟内完成,1个Section需要在20分钟内完成。题型则分为两种:选择题和填写空格题。
给大家介绍几种常见的数学解题方法:
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=35140=35354=2。
2. 特殊值法
例题:xy=x+y. If y2, what are all possible values of x that satisfy the equation above?
A. x0, B. 0
解答:y2,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。
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