GRE数学大纲及要点!.doc

一、数学考察的范围1. Arithmetic算术部分包括整数的性质和种类，比如整除性、因子分解、质数、余数、奇数偶数；算术运算、指数、根；估算、百分比、比、比率、绝对值、数轴、小数表达、数列。2. Algebra代数包括指数运算；因式分解、简化代数式；函数、等式、不等式；解一次方程和二次方程、解不等式；解联立方程、方程组；用方程解决文字题；解析几何、函数图像、函数图像解方程和不等式、截距、斜率。3. Geometry几何包括平行、垂直、圆、三角形、等腰三角形、等边三角形、306090三角形、四边形、其他多边形、全等和相似图形、三维图形、面积、周长、体积、毕达哥拉斯定理、角度计算。不考察证明的能力。4. Data analysis包括描述统计学比如平均数、中位数、众数、极差、均方差、四分位差、四分位、百分位；分析图和表，包括折线图、柱状图、饼图、箱型图、散点图、频数分布；概率初步、合成事件、独立事件、随机变量、概率分布、正态分布；计数方法、排列、组合、维恩图。不考推论统计。二、数学考察的题型四种题型：1. 数值比较quantitative comparison questions2. 单选题 multiple-choice questions-select one answer choice3. 多选题 multiple-choice questions-select one or more answer choices4. 数值输入题 numeric entry questions三、答题的注意事项1. become familiar with the answer choices.2. avoid unnecessary computations.3. remember that geometric figures are not necessarily drawn to scale.4. plug in numbers5. simplify the comparison6. use the fact that the answer is there.7. examine the answer choices8. for questions that require approximations, scan the answer choices to see how close an approximation is needed.9. note whether you are asked to indicate a specific number of answer choice or all choices that apply.10. in some questions that involve conditions that limit the possible values of numerical answer choices, it may be efficient to determine the least and/or the greatest possible value.11. avoid lengthy calculations by recognizing and continuing numerical patterns.12. make sure you answer the question that is asked.13. if you are asked to round your answer, make sure you round to the required degree of accuracy.14. examine your answer to see if it is reasonable with respect to the information given.15. 填空题几个注意：1要先点选输入框 2删除要用backspace 3负号就用那个连词符号 4如果要改成正的，再次输入连词符号就变成正数了 5计算器上的transfer display可以直接把计算器里得出的结果转到输入框里面 6 2.5和2.50是一样的 7 除非要求四舍五入，否则不要输入近似值 8如果是分数，一般分子numerator和分母denominator是两个独立的框 9分数不必须约分16. scan the data presentation briefly to see what it is about, but do not spend time studying all of the information in detail17. bar graphs and circle graphs, as well as other graphical displays of data, are drawn to scale, so you can read or estimate data visually from such graphs.18. the questions are to be answered only on the basis of the data presented, everyday facts (such as the number of days in a year), and your knowledge of mathematics.19. MR表示 memory recall, M+ 表示memory sum, MC 表示 memory clear.20. 当第一次按M，屏幕上显示的数字被纪录在计算器的内存里面，屏幕右边出现M字母，表示内存记忆被使用。以后每一次按M按键，都会把当前的屏幕上显示的数字加到内存的数字上，并以得到的和来取代原来内存的记忆值。当按MR按键的时候，内存里面记忆的值被调出，就是最后的结果。如果要清空内存，按MC按键，这个时候右边的M标志就消失了四、需要知道的数学常识1. 都是实数，没有虚数2. 10进制，除非另外说明。3. billion是10的9次方，dozen是12个，是3.14近似4. 23.5近似到各位是24, 123.985近似到百分位是123.99, 36.5近似到各位是375. 循环小数的循环节上画一个横线。(how？)6. 因子factor，可正可负，因子一般都是整数，倍数不一定(2是6的因子；6是2的倍数Multiple，-6也是2的倍数)7. 最小公倍数Lowest Common Multiple和最大公约数Greatest Common Divisor（整数a除以整数b(b0) 除得的商正好是整数而没有余数，我们就说a能被b整除，或b能整除a。a称为b的倍数，b称为a的约数。）8. 余数、被除数、除数、商的定义被除数除数=商除数=(被除数-余数)商9. 质数的定义10. 奇数偶数不一定是正数11. 0既不是正的，也不是负的12. 小于等于、大于等于、约等于、不等于、绝对值、平方根、阶乘、平行、垂直等的符号需要知道13. 没有定义的情况：分母为0,根号下面为负数，0的0次方14. 有时候，字母摆在一起不表示乘法，比如consider a three-digit integer denoted by XYZ, where X, Y, and Z are digits.15. 如果一个函数的定义域没有明说，那么就默认是整个实数范围，复合函数会考。16. 只考欧几里德平面，三角形内角和18017. 直线没有端点18. 多边形是凸的，闭合的19. 解析几何一般都是按照比例画的20. nonempty sets非空集, empty set空集, intersection交集, union并集, disjoint sets(没关系的两个集) or mutually exclusive sets（互相排斥集？）21. the integers from 0 to 9, inclusive。 包括了10个元素，而during the years from 1985 to 2005 不管说不说inclusive 都包括了21年22. measures of central tendency, measures of position, measures of dispersion23. 如果有偶数个数，那么median表示按照升序排列的这串数字的中间两个数的算术平均24. mode可以不只一个25. quartile可以指那个点，也可以指一个区，比如the cows weight is in the third quartile of the weights of the herd 这个时候quartile 就是指一个区域group26. 25th percentile = the first quartile; the 50th percentile equals the second quartile, or median; the 75th percentile equals the third quartile.27. standard deviation of the data refers to the nonnegative square root of the mean of the squared differences between m and each of the data. also known as the population standard deviation and is not to be confused with the sample standard deviation. Sample standard deviation is divided by n-1 for technical reasons.28. frequency distribution29. relative frequency distributions30. the mean of the random variable X is the sum of the products XP(X) for all values of X.31. the mean of a random variable X is also called the expected value of X or the mean of the probability distribution of X32. In any group of data, most of the data are within about 3 standard deviations above or below the mean.33. The process of subtracting the mean from each value and then dividing the result by the standard deviation is called standardization. Its a useful tool because for each data value, it provides a measure of position relative to the rest of the data independently of the variable for which the data was collected and the units of the variable.34. universal set35. median 把曲线下面的面积平均分成两块面积相等的部分，mean要算上这块面积的重量，所以og上那个图的mean要在median的右边，因为越往右，越重36. 所以m