SAT数学长难题干审题解析技巧

大部分中国的SAT考生面临SAT数学考试时，的问题不是解决“数学问题”，而是解决“阅读问题”，这里的阅读问题指的就是对于长难题干的理解，或者数学关系的英文表达的理解。今天我们拿2道2019年4月北美school day真题进行举例分析。    

1. A city with 120,000 residents is voting on a proposal that would eliminate overnight parking of vehicles on the city's streets. An independent company randomly surveys 1,200 residents to see whether or not residents would support this proposal. The outcome of the survey shows that 60% of the residents surveyed approve of the proposal with a margin of error of 2%. Which of the following statements is a plausible conclusion from the outcome of the survey?

A) Exactly 60% of city residents approve eliminating overnight parking.

B) There are 72,000 city residents who approve eliminating overnight parking.

C) About 2% of the city residents do not approve eliminating overnight parking.

D) Between 58% and 62% of the city residents approve eliminating overnight parking.

解析：

1. 辨析考点：快速扫描题干信息，提取关键词“margin of error”, 确认为“边际误差”考点。

2. 提取数据：population-120,000 residents ; ‚sample- 1,200 residents ; ƒpercentage-60% ; „margin of error- 2%.

3. 结论得出：根据margin of error考点，即“margin of error为从样本数据推到整体数据所产生的边际误差”，1200人的样本同意该法案的比率为百分之六十，则整体120000居民同意该法案的比率为（样本比率加减margin of error），也就是58%~62%之间的居民同意该法案。所以答案选D。

2.An initial investment of $1,000 is made at a constant annual interest rate. The graphs above show the corresponding future value, v, in dollars, of the investment for different annual interest rates, r, after 20 years. One graph shows the value when the interest is compounded daily, and the other graph shows the value when the interest is compounded annually. Which of the following statements is true?

A) As r increases at a constant rate, v increases more rapidly if interest is compounded annually rather than daily.

B) As r increases at a constant rate, v increases more rapidly if interest is compounded daily rather than annually.

C) As r increases at a constant rate, the difference in interest compounded daily and interest compounded annually increases at a constant rate.

D) If r= 15% and interest is compounded annually, a $1,000 investment will be worth $20,000 after 20 years.

解析：

1. 辨析考点：函数图像类题型。

2. 提取信息：

图表上方注明图表信息为 future value of an investment after 20 years for different interest rates, 即不同利率下某项投资二十年后的价值对比。

横坐标对应annual interest rate，即年利率，对应字母为r。

纵坐标对应future value，即未来价值，对应字母为v。

圆点图标对应的线为compounded daily, 即每日复利。

方块图标对应的线为compounded annually, 即每年复利。

3. 辨析选项：问题为选择正确的答案，则快速扫描选项，发现A,B,C选项表述接近，都是在比较随着r增长，v在两条线上增长的快慢。观察图像得出，随着r的增长，v在圆点图标线上增长的速度更快，故B选项正确。D选项描述错误，r为15%时，compounded daily对应的值为20000，而compounded annually 对应的值为15000。