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数学机经1

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注: 原题目为黑色字体, 版本二为深紫色字体, 版本三为深黄绿色字体, 若新寂静贡献者关于题目描述与原有题目完全相同,LZ会在题目下方用蓝色字体标出本题已经在本月寂静内出现几次, 不会另作新版本标出. 希望大家不要忽视变体题, 或者补充条件, 以免JJ出现反作用, 另外请注意LZ每天的标识, 有的题多次出现, 可能为本月的高频考题, 值得大家注意. 粉色字体为LZ添加内容, 大家加油~~~

1.28 1-25 12 ,17 1.29 26-37 12 , 15, 25 1.30 38-72 4, 6, 21, 23, 25, 37 1.31 73-127 4(补充), 5, 7(补充)*2, 10, 12*2, 13*2, 14, 16*2, 18, 19, 21, 22(补充), 29 , 32, 34 , 37, 41, 51&51, 60, 60 , 60, 61, 61,67(补充)*2,70, 78, 79, 80,87, 102(补充) 2.1 128-141 16,18, 33,40,60,61, 67, 75,79, 80(补充), 82,95(补充),109, 24新观点 2.2 1.81!-80!/79!

2.12本书选5本有几种选择 512C=792 =12*11*10*9*8除以5! 本题在本月寂静中已出现2次

3.10个人里面也四个人懂法文,其他六个人不是懂西班牙文就是懂忘了什么语言(不重样) 从这10人里面选三个,至少一个人懂法文有几种可能 选项好像是 20, 40, 60, 80, 100

1002012036310CC

4.a^m 大於 C^n 补充:101. DSA^n是否大于 B^m (n和m的位置可能被我记反，大家讨论看看) （1）A=B^3 （2）3m我选了C DS n^m>m^n? 1) n>m 2)n<=2m

5.員工重新分配~有50個人沒有被重分, 80%人...结论好像是求有多少人被重分? 5.工厂迁址，原工厂员工有50人没有迁走，迁走去新工厂的员工占原工厂员工的80%，问原工厂多少员工 （题很简单，不过说的很绕，考试时候看清点，很可能有变体） 6.長方體8"寬",12"不確定",10"高",有一邊開了一個門,问说要多少gallon 漆 本题已在本月寂静内出现两次

7.問m^n 完全平方數嗎 补充:m的n次方是不是一个完全平方数？ 1.m是完全平方数 2.n是完全平方数好像是B吧 本题已在本月寂静中出现两次

8.给了个神马数，说是Man，Woman和Child的总和，然后M/W=5/4,W/C=1/2，问女人多少？

9. (27,145)* (10^11-10^10)/10^13的小数点后第一位是几，我选的似乎1，27145这个数字可能不一定准确，我记得中间是有个逗号的，差点看成小数点... 答案是3

10. (a - b + c)/(x - y + z) + R = 0，问R是多少？（加减号不是很确定，不过应该算出来没问题，注意结果有两种可能的表示方法） Hsien0803补充:注意答案選項把-放到分母就行了 本题已在本月寂静中出现3次

11.DS: f(x) = px^5 + qx^3 + rx，问f(1)? (1) f(-1) = 4 (2) pqr > 0 狗爸选的A

12. 一个镇子上2400人，在11月和12月两个月的时候人数不变，11月的失业率nearest to 6%，11月的就业的人在12月份都继续工作，然后说12月份失业率是nearest to 3%，问12月份就业的人在11月份没工作的有多少？答案：50， 98，其他的不是比50小就是比98大，题目有点长，可能我没特别看懂。。。

补充:答案都不是正确的只要最接近的,选项好像是10, 50, 100, xxxxx忘了 就是他给的值乘上不知道是(6.4-2.5)%, 还是(5.5-3.4)%,大约是这个意思,希望大家看得懂

补充:还有就是11 12月employment和unemploymen那题，JJ得答案好像是72，但选项里没有72，只有 50 98 132等，做得时候时间不太多了，就蒙了一个。

本题在本月寂静中已出现5次(注意题中注明了百分比是采用四舍五入得出的!) 13. DS: 说一条number line上有从左到右五个点，R,S,T,X,W（考试时有图），R的坐标是-5，W的坐标是11，X在T和W之间，问T的坐标？ （1）RS = 1/3RT (2) RS = 1/5RW 这个题目我相当没把握，number line必须是整数么？犹豫了很久，选了E... mz0123补充:数轴不是必须整数，我觉得选C (1)单独肯定不充分 (2)RW=16, RS=16/5. S坐标为-9/5，还是不能求出T的坐标 合并条件，可求得T坐标为23/5 (LZ表示赞同)

本题已在本月寂静内出现3次 14. 说什么pumpers的，X pumpers用Y时间能够神马Z liters水来着，然后说Y pumpers用X时间能够神马Z liters水（字母的顺序不是很确定），问1个pumper需要多少时间搞xyz liter水？选项忘了。题目有点长，有点不太确定，不过意思差不多，应该不难

DS X个pumpers用Z分钟能够抽Y liters水来着，Y个pumpers用X分钟能够抽 Z liters水，问1个pumper需要多少时间抽xyz liter水？字母顺序可能错了… (1)x^2+y^2=… (2)xy=… 虽然题目不确定，但我蛮确定这题选A…

15. DS：n odd？ （1）n^4个位数字不是1 (2) n^8和n^9有相同的个位数字 举了5和6两个例子，选的E

举对例子也很快. 如果计算个位数的话(1)=>9,3,1n

(2)=>8,7,4,2n 所以n个位数可能值为0,5,6选E . 这题算是变体么? DS d得n次方是odd？ 1）（d+3）/6 divisible 2) n/3 divisible(记不清了)

16. 还有一个和足球有点关系的排列组合题，说是一个队伍一个门将，三个后卫，四个中场，三个前锋（传说中的343阵型）在练习技战术，说门将传给一个后卫，后 卫传给一个中场，中场传给另外一个中场，然后这个再传给前锋，前锋完成射门（这战术够简单。。。），做题有个图，不过不影响解题，说一共有多少种不同的战 术演练方法，还提示说中场的顺序不同，组合不同，似乎是3x4x3x3=108。

本题已在本月寂静内出现4次 17. 有一个长方体是24x20x10 inch，用厚度为1inch的东西包起来，问包的东西体积是多少? 本题在本月寂静内出现了2次.

补充:已经有的JJ ：有一个长方体是24x20x10 inch，用厚度为1inch的东西包起来，问包的东西体积是多少? 选项只有近似值 2000 4000 什么的 V体积=24x20x1x2+12x26x1x2+12x20x2x1=2064 我选的2000

18.一个群组有60个人,deposit 有48人, share stock有 35人, 还有好像是bonus 27人, 有deposit的也有bonus有19人,有share stock的都有deposit, 三个都有的12人,问三个都没有的有几人 选项有0,1,2,3,4 答案是4,（韦恩图） 本题在本月寂静中出现5次

19. B 5 C

A 9 D 一个梯形ABCD如上图, 已知BC//AD, 有一点E在D的右边使四边形ABCD面积等于三角形ABE面积相等,求DE为多少? 本题在本月寂静中出现2次

20. 十字坐标上三角形ABC, A(-3,-10), B(15,-10), 求三角形面积 (a) C点在y=-1 在线 (b) C点在x=1 在线(这个不确定) 答案应该是A

21. 一个人存了100在银行两年,年利率r percent求两年后利息,用r表示 选项好像有1/2r, r, 2r , 100r, 200r

问利息 amount x, annual rate 4%, 然后y年 很简单 x(1.04)^y 本题在本月寂静中出现3次 22. xy>0, xz>0 下列哪一个一定正确 x>0 y>0 z>0 yz>0 上面条件好像只有三个选项就是 only I, only II, only III, I and II……类似这种选项 结论是yz>0 补充: xy>0, xz>0 下列哪一一定正确 (1)x>0 (2)y>0 (3)z>0 (4)yz>0 (5)xyz>0(新增选项) 23. 一条直线与y=x 相交于(2,2)判断该线斜率为正或负 (a) 该直线与x轴交点为+ (b) 该直线与y轴交点>2 答案是B

变体题.DS一直线与y＝－x交于（－2，2） 1）与y轴截距大于0 2）与x轴截距大于0

24. H是不是质数 (a)任一个H的因子>H1/2 (就是根号下H) (b)任一个H的因子都>H/2 此处引用sdcar的答案： a) sufficient. Because factors show up in pairs except for its square root. In this case, the only factor is the number H itself.

b) sufficient. Similar to the above rationale. When H > 4, H/2 > the square root of H DDDDDDDDDDDDDDDDD 此处引用gedn01的观点: 找到一条公理 [如果大于1的整数a不能被所有不超过根号a的素数整除，那么a一定是素数] ETS很明显是在考查这个定理 a)成立，可以确定H是否为质数 b)不成立，不确定H是否为质数

25. 右图是一个半球体容器(抱歉word只能或出这样) 半径为r,一个人装水好像是要给青蛙喝的(青蛙喝水吗?) r/2 水面面积为1800,隔天水下降到了离底部r/2的地方 问这时候水表面积为多少? r/2 本题作辅助线可求出下降后的水面半径,与原半径关系, 即可得出答案S=1350

本题已在本月寂静内出现了3次. 26.一等腰三角形三边分别是t-4，2t-20 和t-6，问边长可能是？（三个等式很确定） 1. 26

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数学课后教学反思简短(13篇)

数学课后教学反思简短(13篇)

数学课后教学反思简短（13篇）数学课后教学反思简短篇1学生现在年龄还小根本不知该怎样学习，更不知怎样进展反思，那就需要我们教师进展指导。

那么在当前课改试验中，如何真实培育学生的反思习惯和力量，是教师教学反思的核心，也是我应当重点反思的地方。

以我自己这阶段的教学经受和以前的学习经受，有以下的感受：1、要求做好课堂简要摘记。

当前，教师讲学生听已成了教学中最普遍的方法。

而要学生对教学的内容进展反思，听是远远不够的。

要反思，就要有内容。

所以学生就要先进展课堂简要摘记。

课堂简要摘记给学生供应了反思的依据。

学生也能从课堂简要摘记中更好的体验课堂所学习的内容，学生的学习活动也成了有目标，有策略的主体行为，可促使教师和学生进展探究性，讨论性的活动。

有利于学生在学习活动中获得个人体验，提高个人的制造力，所以课堂简要摘记是学生进展反思的重要环节。

这一点我就尝试过，刚开头我没有让学生做课堂简要摘记。

当过几天之后，有些同学把学过的学问遗忘了，让他们翻课堂简要摘记时他们却什么也没有。

而另外一些做了笔记的学生却把握的较好，我才感觉到要求学生做笔记的重要性。

学生现在年龄太小还没有学习的主动性，需要教师来引导。

所以就要求他们开头做课堂简要摘记，刚开头并且每天检查。

一星期过后，效果就出来。

2、指导学生把握反思的方法。

课堂教学是开展反思性学习的主渠道。

在课堂教学中有意识的引导学生从多方位、多角度进展反思性的学习。

学生的实践反思，可以是对自身的熟悉进展反思，如，对日常生活中的事物及课堂中的内容，都可引导学生多问一些为什么？；也可以是联系他人的实践，引发对自己的行为的比拟反省，我们可以多引导学生进展同类比拟，到达“会当凌绝顶，一览众山小”的境地；也可以是对生活中的一种现象，或是四周的一种思潮的分析评价，此外学生的反思还何以是阶段性的，如：一节课尾声时，让学生进展一下反思，想想自己这节课都有什么收获？还有哪些疑问？当天睡前，反思一下今日自己的感受；或是一周反思一下自己的进步和缺乏等等。

考前必看的新GRE有代表性的数学题

考前必看的新GRE有代表性的数学题

大蚂蚱美国留学社区-我们战斗在美国！1.y=2x2+7x – 3 x y2. The figure above shows the graph of a function f, defined by f(x)=|2x|+4 for all numbers x. For which of the following functions g defined for all numbers x does the graph of g intersect the graph of f ? A g(x)x–2 B g(x)x3 C g(x)2x – 2 D g(x)2x3 E g(x)3x – 2 3.Each employee of a certain company is in either Department X or Department Y, and there are more than twice as many employees in Department X as in Department Y. The average (arithmetic mean) salary is $25,000 for the employees in Department X and is $35,000 for the employees in Department Y. Which of the following amounts could be the average salary for all of the employees in the company? Indicate all such amounts. A $26,000 B $28,000 C $29,000 D $30,000 E $31,000 F $32,000 G $34,000 4.Working alone at its constant rate, machine A produces k car parts in 10 minutes. Working alone at its constant rate, machine B produces k car parts 大蚂蚱美国留学社区-我们战斗在美国！in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce k car parts? ____________minutes5. 1)If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008 ? A $727,200 B $792,000 C $800,000 D $880,000 E $968,000 2)At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008 ? Give your answer to the nearest 0.1 percent. ___________% 3)Which of the following statements must be true? Indicate all such statements. A For 2008 the dollar amount of sales at Store R was greater than that at each of the other four stores. B The dollar amount of sales at Store S for 2008 was 22 percent less than that for 2006. C The dollar amount of sales at Store R for 2008 was more than 17 percent greater than that for 2006. 6.A certain store sells two types of pens: one type for $2 per pen and the other type for $3 per pen. If a customer can spend up to $25 to buy pens at the store and there is no sales tax, what is the greatest number of pens the customer can buy? A9 B 10 C 11 D 12 E 20 7.A list of numbers has a mean of 8 and a standard deviation of 2.5. If x is a number in the list that is 2 standard deviations above the mean, what is the value of x ? x=______ 大蚂蚱美国留学社区-我们战斗在美国！8.Frequency Distribution for List X Number 1 2 3 5 Frequency 10 20 18 12 Frequency Distribution for List Y Number 6 7 8 9 Frequency 24 17 10 9 List X and list Y each contain 60 numbers. Frequency distributions for each list are given above. The average (arithmetic mean) of the numbers in list X is 2.7, and the average of the numbers in list Y is 7.1. List Z contains 120 numbers: the 60 numbers in list X and the 60 numbers in list Y. Quantity A Quantity B The average of the 120numbers in list Z The median of the 120 numbers in list Z 9.The figure above shows the graph of the function f in the xy-plane. What is the value of f ( f (–1)) ? A –2 B –1 C0 D1 E2 10.By weight, liquid A makes up 8 percent of solution R and 18 percent of solution S. If 3 grams of solution R are mixed with 7 grams of solution S, then liquid A accounts for what percent of the weight of the resulting solution? A 10% B 13% C 15% D 19% E 26% 11.Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer? A 0.5 B 0.6 C 0.7 D 0.8 E 0.9 12.Line k lies in the xy-plane. The x-intercept of line k is –4, and line k passes through the midpoint of the line segment whose endpoints are (2, 9) and (2, 0). What is the slope of line k ? Give your answer as a fraction._______ 大蚂蚱美国留学社区-我们战斗在美国！13. In the course of an experiment, 95 measurements were recorded, and all of the measurements were integers. The 95 measurements were then grouped into 7 measurement intervals. The graph above shows the frequency distribution of the 95 measurements by measurement interval. Quantity A Quantity B The average (arithmetic The median of the 95 mean) of the 95 measurements Measurements 14.The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively. Quantity A Quantity B th 750 The value at the 75 percentile of the distribution of X 15.If 1+x+x2+x3=60, then the average (arithmetic mean) of x, x2, x3, and x4 is equal to which of the following? A 12x B 15x C 20x D 30x E 60x 大蚂蚱美国留学社区-我们战斗在美国！16. Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are (2, 4) and the coordinates of point Q are (8, 6). What are the coordinates of point R ? A (3, 2) B (3, 3) C (4, 4) D (5, 2) E (6, 2) 17.Let S be the set of all positive integers n such that n2 is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S ? Indicate all such integers. A 12 B 24 C 36 D 72 18.The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4inches. Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the students in the class? Indicate all such statements. A The tallest male student in the class is 5.8 inches taller than the tallest female student in the class. B The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class. C The average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class. 19.A random variable Y is normally distributed with a mean of 200 and a standard 大蚂蚱美国留学社区-我们战斗在美国！deviation of 10. Quantity A Quantity B The probability of the event 1/6 that the value of Y is greater than 220 20.In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry?__________students 21.The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a $10 bill and received the correct change, which was less than $3.00. Which of the following statements must be true? Indicate all such statements. A The price of the book was less than $9.50. B The price of the book was greater than $6.90. C The sales tax was less than $0.45.22.Which of the following statements individually provide(s) sufficient additional information to determine the area of triangle ABC above? Indicate all such statements. A DBC is an equilateral triangle. B ABD is an isosceles triangle. C The length of BC is equal to the length of AD. D The length of BC is 10. E The length of AD is 10 23.The fabric needed to make 3 curtains sells for $8.00 per yard and can be purchased only by the full yard. If the length of fabric required for each curtain is 1.6 yards and all of the fabric is purchased as a single length, what is the total cost of the fabric that needs to be purchased for the 3 curtains? A $40.00 B $38.40 C $24.00 D $16.00 E $12.80 24.The fabric needed to make 3 curtains sells for $8.00 per yard and can be 大蚂蚱美国留学社区-我们战斗在美国！purchased only by the full yard. If the length of fabric required for each curtain is 1.6 yards and all of the fabric is purchased as a single length, what is the total cost of the fabric that needs to be purchased for the 3 curtains? A $40.00 B $38.40 C $24.00 D $16.00 E $12.80 25.In the xy-plane, the point with coordinates (–6, –7) is the center of circle C. The point with coordinates (–6, 5) lies inside C, and the point with coordinates (8, –7) lies outside C. If m is the radius of C and m is an integer, what is the value of m ? m =_____ 26.What is the least positive integer that is not a factor of 25! and is not a prime number? A 26 B 28 C 36 D 56 E 58 27If 1 is expressed as a terminating decimal, how many nonzero digits 1/[(211)(517)] will the decimal have? A One B Two C Four D Six E Eleven 28.Eight hundred insects were weighed, and the resulting measurements, in milligrams, are summarized in the boxplot below. (a) What are the range, the three quartiles, and the interquartile range of the measurements? (b) If the 80th percentile of the measurements is 130 milligrams, about how many measurements are between 126 milligrams and 130 milligrams? 大蚂蚱美国留学社区-我们战斗在美国！29.The figure shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown. Suppose the heights of a population of 3,000 adult penguins are approximately normally distributed with a mean of 65 centimeters and a standard deviation of 5 centimeters. (a) Approximately how many of the adult penguins are between 65 centimeters and 75 centimeters tall? (b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin’s height will be less than 60 centimeters? Give your answer to the nearest 0.05 机经题： 8月 5选1 1. 3 个数的平均数是 30，把这 3 个数翻倍之后也加在这个 list 中。

【小站教育】GMAT数学笔记

【小站教育】GMAT数学笔记

GMAT数学笔记GMAT 数学备考关键词一、知识点：准确掌握二、词汇、表达法：读懂题目三、熟练：平均两分钟一道题考试相关问题一、时间与题量二、题型三、机经与换题库四、其它If a and b are positive integers such that a –b and a/b are both even integers, which of the following must be an odd integer?（A）a/2 （B）b/2 （C）(a+b)/2（D）(a+2)/2 （E）(b+2)/2If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M?(A) 600 (B)700 (C) 900 (D) 2,100 (E) 4,900复习注意事项*战略上重视*初等数学的思维*解法力求稳妥清晰*把握好DS 题型*熟练重于技巧推荐复习步骤*知识点查缺补漏*背熟词汇*复习课上所学*OG，及其它相关资料*机经：第一章算术1. integer (whole number): 整数* positive integer：正整数，从1 开始，不包括0。

2. odd & even number 奇数与偶数* 凡整数均具有奇偶性，如－1 是奇数，0 是偶数。

* 奇+奇=偶，奇+偶=奇…若干个整数相乘，除非都是奇数，其乘积才会是奇数…例：If a and b are positive integers such that a –b and which aare both even integers, bof the following must be an odd integer?(A）a (B）b (C)a +b(D)a + 2(E)b + 22 2 2 2 23. prime number & composite number 质数与合数* A prime number is a positive integer that has exactly two different positive divisors,1 and itself.* A composite number is a positive integer greater than 1 that has more than two divisors.* The numbers 1 is neither prime nor composite, 2 is the only even prime number.4. factor(divisor) & prime factor 因子和质因子* 一个数能被哪些数整除，这些数就叫它的因子（因数、约数）。

机械数学考试题及答案高一

机械数学考试题及答案高一

机械数学考试题及答案高一一、选择题（每题3分，共30分）1. 以下哪个选项是三角函数的基本恒等式？A. sin²x + cos²x = 1B. sinx + cosx = 1C. sinx - cosx = 1D. sinx * cosx = 1答案：A2. 已知直线方程为y = 2x + 3，求该直线与x轴交点的横坐标。

A. -1.5B. 1.5C. -3D. 3答案：A3. 计算定积分∫₀¹ (x² - 2x + 1) dx的结果。

A. 0B. 1/3C. 1D. 2答案：C4. 以下哪个函数是奇函数？A. f(x) = x²B. f(x) = x³C. f(x) = xD. f(x) = |x|答案：B5. 已知向量a = (3, -2)和向量b = (-1, 4)，求向量a与向量b的点积。

A. 2B. -2C. 10D. -10答案：D6. 以下哪个选项是二项式定理的展开式？A. (a + b)ⁿ = ∑(Cₙᵐ * a^(n-m) * b^m)B. (a + b)ⁿ = ∑(Cₙᵐ * a^m * b^(n-m))C. (a + b)ⁿ = ∑(Cₙᵐ * a^(n-m) * b^m)D. (a + b)ⁿ = ∑(Cₙᵐ * a^m * b^(n-m))答案：B7. 计算极限limₓ→∞ (x² - 4x + 3) / (x² + 2x + 1)的结果。

A. 1B. 0C. ∞D. -∞答案：A8. 已知函数f(x) = 2x - 3，求该函数的反函数。

A. f⁻¹(x) = (x + 3) / 2B. f⁻¹(x) = (x - 3) / 2C. f⁻¹(x) = (x + 3) / 4D. f⁻¹(x) = (x - 3) / 4答案：A9. 以下哪个选项是复数的代数形式？A. a + biB. a - biC. a + bD. a - b答案：A10. 计算圆的面积，其中半径为3。