新SAT数学全解:中国学生能否延续以往优势?

<- 分享“美国留学那些事儿”微信公众号到您的社交圈,让更多的人知道!

收藏文章 赞一个 已赞 2016-04-13 美国留学那些事儿


今年新SAT考试登场,中国学生是否还能继续延续以往在数学科目上的优势呢?

新旧SAT对比:






新SAT考查知识点:






题目分析


新SAT数学不仅在知识点考查方面更加贴近实际生活应用,包括题目和题型也变得更加接地气。最明显的表现是题目长度大大增加,单词难度加大,长句出现频率增加,这对学生的阅读能力和速度提出了更高的要求。


阅读量增加

与美国学生相比,以往中国学生赢在数学知识和计算能力,但中国学生在专业英语词汇量、与实际生活联系、逻辑思维、批判性思维阅读上与美国学生存在很大差距。


应对策略


所以,在单词方面,学生首先要对数学专业词汇以及常见表达熟练掌握,同时在平常也需要更多积累其他STEM相关领域词汇和背景知识。针对题目中的长句,则需要快速理解题意辨识出考查的知识点,然后分析句子结构,迅速剥离出与解题相关的数据信息。包括题目最后的问题也会经常出现在长句中,如果句子没有读懂,那么很有可能会减缓做题速度甚至会影响解题切入点。
例题:
An online store receives customer satisfaction ratings between 0 – 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings.
题目主要意思为:一家在线商店会收到评分为0-100分之间的顾客满意度评价,收到的前10个评价得分平均为75,如果要保证前20个评价的平均得分为85,商店收到的第11个评价的最少为多少分?
大家可以发现题目非常贴近我们的生活,在网购如此发达的中国,相信大家作为买家都给过店家评价吧。
在这道题中,商店需要计算好评率。这类题我们都可以看做“应用题”,解答应用题首先需要将题目给出的情境抽象化:
在0-100中先按顺序选择10个数,他们的平均数为75,如果再依次选择10个数,为了保证这20个数的平均数为85,第11个数最少应该是几?

然后再根据我们已经掌握的相关知识点解题即可。


题目的内容和形式更加多样化:与实际生活、工作相结合

要求:积累与留心更多社会常识与经验


例题:
A bank has opend a new branch and ,as part of a promotion, the bank branch is offering $1,000 certificates of deposit at an interst rate of 4% per year, compounded semiannually. The bank is selling certificates with terms of 1,2,3 or 4 years. Which of the following fuctions gives the total amount, A, in dollars, a customer will receive when a certificate with a term of k years is finnally paid.
A) A= 1,000(1+0.04K)
B) A=1,000(1+0.08K)
C) A=1,000(1.04)k
D) A=1,000(1.04)2k

解读:银行几乎与每个人的生活都息息相关,存款利率与收益具体如何计算则是这道题考查的重点。


例题:
The cost of using a telephone in a hotel meeting room is $0.20 per minute. Which of the following equations represents the total cost c, in dollars, for h hours of phone use?
A) c = 0.20(60h)
B) c = 0.20h+60
C) c = 60h/0.20
D) c = 0.20h/60

解读:在实际生活中,在酒店除了房间费用,其他费用包括电话,mini-bar里的食品,甚至网络都是要收取相应费用的。这道题则是需要我们根据题目提供的信息建立酒店会议室电话费的计算公式。


图表题增加

要求:提高解读和整合数据能力


例题:
Michael swam 2,000 yards on each of eighteen days. The scatterplot above shows his swim time for and corresponding heart rate after each swim. The line of best fit for the data is also shown. For the swim that took 34 minutes, Michael’s actual heart rate was about how many beats per minutes less than the rate predicted by the line of best fit?
A) 1
B) 2
C) 3
D) 4

解读:想要看懂图表,就需要理解图表中横纵轴以及点、线对应题目中的哪些文字信息。 这道题中则需要重点理解根据已知数据做出的预测与实际数据之间是会存在偏差,然后根据题目要求计算出实际差值。


与STEM,美国社会科学知识等领域紧密相关
要求:具备相应的科学背景知识、信息处理能力以及逻辑推理能力
例题:
a = 1,052 + 1.08t
The speed of a sound wave in air depends on the air temperature. The formula above shows the relationship between a, the speed of a sound wave, in feet per second, and t, the air temperature, in degrees Fahrenheit (°F). Which of the following expresses the air temperature in terms of the speed of a sound wave?
A) t = (a-1052)/1.08
B) t = (a+1052)/1.08
C) t = (1052-a)/1.08
D) t = 1.08/(a+1052)

解读:这答题涉及物理学科相关知识,题目中已经给出公式以及相应解释。只要理解变量的意义以及相应单位,就可以按照题目要求解题。


例题:
The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states joined the United States between 1776 and 1849 and x states joined between 1850 and 1900, which of the following equations is true?
A) 30x=2
B) 2x=30
C) x2=30
D) x+30=2

解读:美国是联邦制国家,各个州加入联邦的时间不同,这道题以此背景,实际上考查学生找到变量和常量,建立简单方程式的能力。


例题:
In order to determine if treatment X is successful in improving eyesight, a research study was conducted. From a large population of people with poor eyesight, 300 participants were selected at random. Half of the participants were randomly assigned to receive treatment X, and the other half did not receive treatment X. The resulting data showed that participants who received treatment X had significantly improved eyesight as compared to those who did not receive treatment X. Based on the design and results of the study, which of the following is an appropriate conclusion?
A) Treatment X is likely to improve the eyesight of people who have poor eyesight.
B) Treatment X improves eyesight better than all other available treatments.
C) Treatment X will improve the eyesight of anyone who takes it.
D) Treatment X will cause a substantial improvement in eyesight.
解读:这道题给我们简述了一个改善视力科学实验,从实验对象的选择,分组到进行实验,最后要求学生根据以上信息得出科学结论。


“点击”‘阅读原文’


点击展开全文