年10月第一期录屏数学2国庆课程

1、ArithmeticKevin 2015.10.02GRE-quantitative GRE-quantitative reasoning ARITHMETICby KevinGRE Test PatternTimeIssue30minsArgumentQuantitative30mins35minsVerbal 30minsMode1Mode2Verbal QuantitativeAW(I+A)AW(I+A)20/sectionVQV170170VQQVVQQ20/section GRE-quantitative reasoning ARITHMETICby KevinGRE Quantit

2、ative-practiceSources: OG + 150 + MagooshHow to reach utilityization?GRE数学的套路感非常强，需要的是总结重要的是总结的错题！容易在哪里犯错！为什么错？ GRE-quantitative reasoning ARITHMETICby KevinGRE QuantitativeTake it as a game! Know the rules, and attack!AssumptionsEquilateral?Isoceles?=？可能的最小值Least possible valueWordsReference：Math R

3、eviews-OGMath Conventions GRE-quantitative reasoning ARITHMETICby KevinGRE Quantitative Test1. 数值比较选项一定是四个，而且内容、顺序是不变的 GRE-quantitative reasoning ARITHMETICby KevinGRE Quantitative Test2. Multiple choice 单选选项是5个，只需要选一个 GRE-quantitative reasoning ARITHMETICby KevinGRE Quantitative Test3. Multiple cho

4、ice 多选注意选项框是方框时是多选选项有n项，可以选n项，千万不要猜有几个 GRE-quantitative reasoning ARITHMETICby KevinGRE Quantitative Test4. 填空6,000这个“，”是会自动出现的，不要打分数、分母约分或者不约分都是对的！ GRE-quantitative reasoning ARITHMETICby Kevin界面GREGRE Calculator GRE-quantitative reasoning ARITHMETICby KevinArithmetic GRE-quantitative reasoning ARI

5、THMETICby KevinEssentialWords/Concepts1. integer 整数odd/even number prime/composite number multiple 倍数factor/divisor 因数奇数/偶数（可正可负）质数/合数（均为正数）least common multiple 最小公倍数greatest common factor/divisor 最小公倍数remainder 余数prime factorization 质因数分解quotient 商product 乘积prime factor 质因数商和余数都必须为整数25÷4=61 商

6、(quotient)是6，不是6.25 GRE-quantitative reasoning ARITHMETICby Kevin1. factor/divisor可以是正数，也可以是负数2. 质数是只含两个正因数的整数，都是大于1的，没有负的质数（合数也要大于1）3. prime factorization 质因数分解72=23×32120=23×3×5求正因数（positive factor)个数的方法：质因数分解+质因子加一相乘120=23×3×5=23×31×51(3+1)×(1+1)×(1+1)

7、=16120的positive factor有：1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120求因数（positive factor)个数的方法：正因数个数×2120的 factor有：1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120-1 -2 -3 -4 -5 -6 -8 -10 -12 -15 -20 -24 -30 -40 -60 -120 GRE-quantitative reasoning ARITHMETICby KevinEssentialWords/Concepts2. fraction 分数num

8、eratordenominator 分母mixed number 带分数root 根reciprocal倒数3. exponent 指数base 底exponent 指数52 中 base为5，exponent为2也可写作： five to the second powerradicals 根式一个正数平方根有两个（正负各一个）“”下的一定是非负实数（多选题的陷阱）square root 平方根cube root fourth root立方根四次方根（偶次方根都需要根号下的值非负） GRE-quantitative reasoning ARITHMETICby KevinEssentialWo

9、rds/Concepts4. decimal 小数two-digit number 两位数digit 数码decimal point 小数点(digital monster 数码宝贝）thousands hundreds tens ones/units5 2 0.1 2 0 6无限循环小数digit 千位数digit 百位数digit 十位数digit 个位数thousandth hundredth tenthdigit 千分位digit 百分位digit 十分位上面带有bar(横杠）的是重复 GRE-quantitative reasoning ARITHMETICby KevinEssen

10、tialWords/Concepts5. percent 百分数X percent increase增加X%X percent decrease 减少X%Supplement Partsabsolute value 绝对值|x|(表示数轴上数值为x的点到0的距离）重要的不等式|x| + |y| |x+y| ; |x-y| | |x| - |y| | GRE-quantitative reasoning ARITHMETICby KevinImportant Expressionsmillion 106billion 109dozen 12A drop to B= Bbe rounded to

11、四舍五入至加法的表达：A increased by B= A+B A added to B= A+Bthe sum of A and B= A+B减法的表达： A drop by BB less than A= A-B= A-BA diminished/subtracted by B= A-B乘法的表达：the product of A and B= AxBA multiplied by B= AxB除法的表达：A divided by B= A÷B GRE-quantitative reasoning ARITHMETICby KevinKey Points1. 无限循环小数化成分

12、数X=2.310X=23.39X=21X=21/9=7/3Practice: 将0.045化成分数形式2. 四舍五入的规则be rounded to nearest 1/0.1/0.05想象一根数轴负数的四舍五入可以先取绝对值！对绝对值做完四舍五入之后，再加上负号 GRE-quantitative reasoning ARITHMETICby KevinKey Points3. 整除的性质能被3整除的数各个数位(digit)上的数字和是3的倍数 能被9整除的数各个数位(digit)上的数字和是9的倍数abcd=1000a+100b+10c+d=(999+1)a+(99+1)b+(9+1)c+d

13、=999a+99b+9c+(a+b+c+d)4. 倍数的表达与比较A is twice as much as B A is twice BA is more than twice as much as BCPI in 2008 is more than 21% greater than that of 2010 GRE-quantitative reasoning ARITHMETICby KevinKey Points5. 余数的性质余数remainder一定要保证大于零的，是正数27÷4= 6.3-27÷4=-7.16. 最小公倍数和最大公约数求法（别用什么辗转相除法）

14、Step1. 质因数分解Step2. 最小公倍数-找公共质因数，去最低次幂相乘最大公约数-所有质因数，去最高次幂相乘 GRE-quantitative reasoning ARITHMETICby Kevin72和105的最大公约数和最小公倍数72=23x32105=3x5x7公共质因数为3(最低次幂为1)所有质因数为2,3,5,7(最高次幂分别为3,2,1,1)最大公约数=31 =3最小公倍数=23x 32 x5 x7= 2520 GRE-quantitative reasoning ARITHMETICby Kevin一些需要熟记的内容2的1-10幂21=226=6422=427=1282

15、3=828=25624=1629=51225=32210=10243的1-4幂31=332=933=2734=813的次幂的位数是循环的3 9 7 1 3 9 7 15的次幂的位数一定是5完全平方数的末位只能是0 1 4 5 6 9𝟐 =1.414𝟑 =1.71=3.14当题目只问和末位有关的问题是，在计算是可以制考虑末位相乘 GRE-quantitative reasoning ARITHMETICby KevinPractice GRE-quantitative reasoning ARITHMETICby Kevin可以强算，但是没有意义！可通过简单的比较

16、得到！GRE很多题都可以不用动笔得到！ GRE-quantitative reasoning ARITHMETICby Kevin一定要用对技巧，而不是似是而非！ GRE-quantitative reasoning ARITHMETICby Kevin一定要用对技巧，而不是似是而非！ GRE-quantitative reasoning ARITHMETICby KevinIf x is any pricannot be priA. x-4B. x-3C. x-1D. x+2E. x+5mber greater than 2, which of the followingmbers?奇偶性是

17、重要的解题思路质数中只有2是偶数(even number)，其他都是奇数(odd number) GRE-quantitative reasoning ARITHMETICby Kevin GRE-quantitative reasoning ARITHMETICby Kevin GRE-quantitative reasoning ARITHMETICby KevinIf p and r are prinumbers ?A. prB. p+rC. pr+1D. p2+r2mbers, which of the following must be primeE. None of the abo

18、ve answers is correct质数中只有2是偶数(even number)，其他都是奇数(odd number)质数是没有推导公式的 GRE-quantitative reasoning ARITHMETICby Kevin强算一定是GRE quantitative reasoning 里面的下下策计算器位数有限，一定只能用来计算很少很少的部分，尽量少用𝟐𝟕x1𝟎-𝟑 𝟏𝟎=(𝟑 𝟐𝟕 𝟏) ×𝟑&

19、#120785;𝟑𝟑𝟐𝟕𝟎 𝟏𝟎 =𝟏𝟎=2𝟑 𝟏𝟎=𝟑 𝟐𝟑 × 𝟏𝟎=𝟑 𝟖𝟎计算器位数有限，一定只能用来计算很少很少的部分，尽量少用 GRE-quantitative reasoning ARITHMETICby Kevinn/45=k18n=45k+18=(5k

20、+2)x9 GRE-quantitative reasoning ARITHMETICby Kevin很多人跪倒长长的题干上面orzHowever, 这道题读懂你就“赢注”了 GRE-quantitative reasoning ALGEBRAby KevinAlgebraKevin2015.10 GRE-quantitative reasoning ALGEBRAby KevinEssentialWords/Conceptslike terms 同类项coefficient 系数domain 定义域quadratic equations 二次方程simple interest单利compou

21、nd interest 复利variable变量linear equationsolution set 解集slope 斜率线性方程constant 常数intercept 截距intersect 相交quadrant 象限coordinate 坐标parallel 平行parabola 抛物线perpendicular 垂直vertex 顶点 GRE-quantitative reasoning ALGEBRAby KevinKey Points1. 指数式的运算很多人运算的时候喜欢YY杨辉三角形(𝟔𝟑)𝟒=?𝟏=?ҷ

22、83;/𝟑( )𝟑展开式：(x+y)3 =x3+3x2y+3xy2+y3(x-y)3 =x3-3x2y+3xy2-y3(x-y)2 =x2-2xy+y2x2-y2 =(x+y)(x-y) GRE-quantitative reasoning ALGEBRAby Kevin2. 一元二次方程求解 quadratic equationsax2+bx+c=0判别式：=b2-4ac𝒃𝟐𝒃𝟐𝟒𝒂𝒄𝒃𝟐𝒃ү

23、39;ax2+bx+c=a(x2+ x+𝟐)+c-=a(x+)2+=0𝒂𝟒𝒂𝟒𝒂𝟐𝒂𝟒𝒂𝒃𝟐𝟒𝒂𝒄𝒃(x+)2=𝟐𝟐𝒂𝟒𝒂𝒃𝟐𝟒𝒂𝒄𝒃x+=±（）1/2

24、20784;𝟐𝒂𝟒𝒂𝒃𝟐𝟒𝒂𝒄𝒃𝟐𝟒𝒂𝒄x =𝒃+x =𝒃12𝟐𝒂𝟐𝒂 GRE-quantitative reasoning ALGEBRAby Kevin3. 函数function奇函数odd functionf(x)=-f(-x)偶函数even functionf(x)=f(

25、-x) GRE-quantitative reasoning ALGEBRAby Kevin4. 函数与图像知道两点坐标，直线函数表达式的求法？y= kx+by= ax2+bx+c直线二次曲线两直线平行的条件：k1=k2两直线垂直的条件：k1k2= -1（证明）两函数y1=y2比较大小：y= y1-y2，考虑y在定义域上的取值（<0 ，=0， >0）（domain）(x-a)2+(y-b)2 =c2圆 GRE-quantitative reasoning ALGEBRAby Kevin5. 坐标运算中点坐标公式X (a, b)Y (c, d)中点Z坐标 (𝒂+

26、19940;,𝒃+𝒅)𝟐𝟐两点距离公式 𝐥 =(𝒂 𝒄)𝟐+(𝒃 𝒅)𝟐 GRE-quantitative reasoning ALGEBRAby Kevin6. 函数图像变换映象reflection+平移shift+拉伸stretch+压缩shrunkreflection对称对称轴x=0 ; y=0 ; y=x反函数inverse functionc>0f(x) f(x+c)f(x) f(x-c)shiftto

27、the left/rightupward/downwardf(x) f(x)+cf(x) f(x)-cstretch/shrunkhorizontallyverticallyf(x) f(cx)f(x) cf(x) GRE-quantitative reasoning ALGEBRAby Kevin7. 单利与复利运算单利：simple interest 本金永远不变利滚利复利：compound interest本金变动，每年或每月利息加入下年/月计算的本金(本金为P，一年率为r，则认为下一年的本金是P(1+r)本金P，年利率r%， t年利息simpleinterestP(1+tr%)P(1+

28、r%)tcompound interest如果一年内compound n次，计算方法 P（1+𝒓%)ntn GRE-quantitative reasoning ALGEBRAby KevinPractice GRE-quantitative reasoning ARITHMETICby Kevin GRE-quantitative reasoning ALGEBRAby Kevin GRE-quantitative reasoning ALGEBRAby Kevin GRE-quantitative reasoning ALGEBRAby Kevin GRE-quantita

29、tive reasoning ALGEBRAby Kevin GRE-quantitative reasoning ALGEBRAby Kevin GRE-quantitative reasoning ALGEBRAby Kevin GRE-quantitative reasoning ALGEBRAby Kevin GRE-quantitative reasoning ALGEBRAby Kevin GRE-quantitative reasoning ALGEBRAby Kevin GRE-quantitative reasoning ALGEBRAby Kevin GRE-quantit

30、ative reasoning Geometryby KevinGeometryKevin2015.10 GRE-quantitative reasoning Geometryby KevinEssentialWords/Conceptsvertical/opposite angle 对顶角congruent angle 等角right angle 直角the measure ofan angle 角的大小acute/obtuse angle 锐/钝角triangle 三角形pentagon 五边形heptagon 七边形quadrilateral 四边形hexagon 六边形octagon

31、八边形polygon 多边形vertice 多边形顶点diameter 直径regular pentagon 正五边形area 面积perimeter 周长equilateral/isoceles triangle 等边/等腰三角形right triangle 直角三角形 GRE-quantitative reasoning Geometryby KevinEssential直角三角形全等三角形Words/Conceptshypotenuse 斜边leg 直角边Pythagorean Theorem 勾股定理congruent triangle相似三角形similar trianglequad

32、rilateralrectangular/square 长方形/正方形Parallelogram 平行四边形trapezoid 梯形circleradius/diameter/circumference 半径/直径/周长chord/arc/sector 弦/弧/扇形 central angle 圆心角the measure of an arc 弧大小tangent 相切的concentric 同心的inscribed 内接的circumscribed 外接的Differentiate:a polygon is circumscribed about/inscribed in a circle

33、GRE-quantitative reasoning Geometryby KevinEssentialWords/Conceptsrectangular solid 长方体cube 立方体face/edge/vertex 面/棱/顶点(right)circular cylinder (正)圆柱体lateral surface 侧表面volume 体积area 面积surface area 表面积 GRE-quantitative reasoning Geometryby KevinKey Points1. 多边形的内角和(不考虑凹多边形！角度制！)n边形内角和 (n-2)*180o记的方法：

34、划分成三角形，三角形内角和为180 GRE-quantitative reasoning Geometryby KevinKey Points2. 角之间的性质余角 supplementaryangle直角一定要给出“直角符号”才能确定补角 complementary angle对顶角相等，同位角相等，内错角相等角之间的计算 GRE-quantitative reasoning Geometryby KevinKey Points3.三角形和性质A. 等边三角形=等腰三角形+一个内角为60o性质组合判定B. 等腰三角形的顶角的角平分线和中线重合（推等边三角形性质）C. 三角形三边：任意两边之和

35、大于第三边；任意两边之差小于第三边D. 重要的三角形E. 全等、相似三角形判定与性质（删繁就简！考太复杂的判定！) GRE-quantitative reasoning Geometryby KevinKey Points2. 周长，面积，表面积及体积的求算perimeterareasector parallelogram trapezoidsectorL=(圆心角/360)*2r+2r S=底*高S=(上底+下底）*高/2S=(圆心角/360)*r2surface areavolumeright circular cylinderS=2*r2+2rlrectangular solidsphe

36、reV=abcV=4/3 r3 GRE-quantitative reasoning Geometryby KevinKey Points图形并不是drawn to scale，不能完全用题目给出的图形做题3. 一些重要的位置关系A. 圆的内接三角形中有一条边为直径（过圆心）时，对角为直角B. 圆心到切线的半径与切线垂直C. 立体图中的关系 GRE-quantitative reasoning GEOMETRYby KevinPractice GRE-quantitative reasoning Geometryby Kevin GRE-quantitative reasoning Geome

37、tryby Kevin GRE-quantitative reasoning Geometryby Kevin GRE-quantitative reasoning Geometryby Kevin GRE-quantitative reasoning Geometryby Kevin GRE-quantitative reasoning Geometryby Kevin GRE-quantitative reasoning Geometryby Kevin GRE-quantitative reasoning Geometryby Kevin GRE-quantitative reasoni

38、ng Data Analysisby KevinData AnalysisKevin2015.10 GRE-quantitative reasoning Data Analysisby KevinEssentialWords/Concepts1. Graphic Methods for Describing Datafrequency distribution频数分布count计数relative frequency distribution相对频数分布bar graph柱状图segmented bar graph柱状图circle graph饼状图histogram 直方图univariat

39、e/bivariate 单/双变量scatterplot散点图scatter point 散点time plot时间折线图 GRE-quantitative reasoning Data Analysisby Kevin GRE-quantitative reasoning Data Analysisby KevinEssentialWords/Concepts2. Numerical Methods for Describing Dataarithmetic mean/mean/average 算术平均median 中位数mode 众数weighted mean平均3. Measures o

40、f Position/Dispersionquartile 四分位数percentile 百分位数first quartile 第一四分位数third quartile 第三四分位数range 极差、范围second quartile 第二四分位数interquartile range GRE-quantitative reasoning Data Analysisby KevinEssentialWords/Conceptsbox/box-and-whisker plot 箱图2. Counting Methodset 数集finite/infinite set 有限/无限集empty se

41、t 空集 subset 子集intersection 交集universal set 全集union 并集Venn diagram 韦恩图 GRE-quantitative reasoning Data Analysisby KevinEssentialWords/Conceptsstandard variation 标准差sample standard variation 样品标准差population standard variation 总体标准差3. Permutation with Factorial and Combination 排列(与阶乘)和组合n factorial n的阶

42、乘4. Probability 概率random selection 随机选取mutually exclusive 互斥equal likely 等可能Independentdistribution/density curve 分布/密度曲线normal distribution 正态分布 GRE-quantitative reasoning Data Analysisby KevinKey Points1. mode可以有多个，千万不要取平均2. 四分位数的计算方法*关于各个四分位数所在的位置： 第一四分位数：n1 =(n+1)x0.25 第二四分位数：n2 =(n+1)x0.50 第三四分位数：n3 =(n+1)x0.75 interquartile range : Q3-Q1