数学备课材料基础课件5session

SAT核心数学

SAT

Math1800-2000

第

4

课Session4Session4:ComprehensiveMath4算数Arithmetic代数Algebra几何Geometry统计StatisticsContentsSession4:ComprehensiveMath4Arithmetic–OverviewArithmetic–FiveAreasPropertiesofNumbersAdvancedComputationPercent/Ratio/ProportionAverageExponent/RootSession4:ComprehensiveMath4Arithmetic–Average:Table1AverageMeanMedianMode•arithmeticmean•Themiddlenumber•ThemostcommonE.g.:Wearrangethe

followingninenumbersin

order:

2,3,3,3,7,12,14,15,19Arithmeticmean=(2+3+3+3+7+12+14+15+19)/9(numbers)Median=7;(Forexample,ifa<b<c,thenthemedianofthe

list{a,b,c}isb,and,ifa<b<c<d,thenthemedianofthelist{a,b,c,d}isthemeanofbandc;i.e.,itis(b+c)/2.)Mode=3Session4:ComprehensiveMath4Arithmetic–Average:TwoTestAreas1Arithmeticmean算数平均值2Median中位数Session4:ComprehensiveMath4Arithmetic–Average:ArithmeticmeanSession4:ComprehensiveMath4Arithmetic–Average:ArithmeticmeanSession4:ComprehensiveMath4Arithmetic–Average:ArithmeticmeanSession4:ComprehensiveMath4Arithmetic–Average:ArithmeticmeanTestTips•设一组数据为X1，X2，...，Xn，

简单的算术平均数的计算公式

为：M=（X1+X2+X3…+Xn)/n；•根据上述公式求数据中某一

数值，进行灵活的公式变化；•考题一般比较简单，数据较少。ExerciseOG:5-2-06,6-2-05,6-4-036-8-11,7-7-06,7-3-088-3-18,9-2-16,9-5-0710-5-07Session4:ComprehensiveMath4Arithmetic–Average:MedianSession4:ComprehensiveMath4Arithmetic–Average:MedianSession4:ComprehensiveMath4Arithmetic–Average:MedianTestTips•中位数：也就是选取中间的数,

一种衡量集中趋势的方法；•当变量值的项数N为奇数时，处于

中间位置的变量值即为中位数.当N为偶数时，中位数则为处于中间

位置的2个变量值的平均数(先将数

据按大小顺序排列）;•熟悉中位数定义，会根据中位数

求数列中某一个数据。ExerciseOG:8-7-19,9-2-06Session4:ComprehensiveMath4Algebra–OverviewAlgebra–FiveAreasVariablesFunctionsInequalityLinearFunctionQuadraticFunctionSession4:ComprehensiveMath4Algebra–LinearFunction:Chart1LinearFunction•Alineisincreasingifitgoesupfromlefttoright.Theslopeispositive.•Alineisdecreasingifitgoesdownfromlefttoright.Theslopeisnegative.•Ifalineishorizontaltheslopeiszero.Thisisaconstantfunction.E.g.y=4.•Ifalineisverticaltheslopeisundefined.E.g.x=5.•Twolinesareperpendiculariftheproductoftheirslopesis−1oronehasaslopeof0andtheotherhasanundefinedslope.Session4:ComprehensiveMath4Algebra–LinearFunction:FourTestAreas1-2Point求取线上点Constant求取常值(一般表示为b)3-4Slope求取斜率Function-expression函数表达式Session4:ComprehensiveMath4Algebra–LinearFunction:PointSession4:ComprehensiveMath4Algebra–LinearFunction:Point

ExerciseOG:10-5-19Session4:ComprehensiveMath4Algebra–LinearFunction:ConstantTestTips•一次函数：y=kx+b(b为常数)，

其中x是自变量，y是因变量；•

一般求b都是通过带入线上点

到表达式来求取b;•左边题11属于特殊情况求常

值，亦可算作求斜率。Session4:ComprehensiveMath4Algebra–LinearFunction:SlopeSession4:ComprehensiveMath4Algebra–LinearFunction:Slope

ExerciseOG:7-9-11,8-9-09Session4:ComprehensiveMath4Algebra–LinearFunction:Function-expressionSession4:ComprehensiveMath4Algebra–LinearFunction:Function-expressionSession4:ComprehensiveMath4Algebra–LinearFunction:Function-expressionTestTips•一次函数：y=kx+b(b为常数)，

其中x是自变量，y是因变量；•关于求表达式，一般分为求

表达式形式和表达式在坐标

轴的形状；•根据函数性质求解，如斜率

的正负，直线间斜率关系，

和坐标轴交点。ExerciseOG:8-7-14Session4:ComprehensiveMath4Geometry–OverviewGeometryCircles&LinesandAnglesTriangleArea&ThirdSideRule&SimilarTrianglesRectangleArea&CoordinateGeometryGraphingFunctions/EquationsPolygons&SolidsSession4:ComprehensiveMath4Geometry–GraphingFunctions/Equations:TwoTestAreas1Lineequation折线方程2Curvilinearequation曲线方程Session4:ComprehensiveMath4Geometry–GraphingFunctions/Equations:LineequationSession4:ComprehensiveMath4Geometry–GraphingFunctions/Equations:LineequationSession4:ComprehensiveMath4Geometry–GraphingFunctions/Equations:LineequationSession4:ComprehensiveMath4Geometry–GraphingFunctions/Equations:LineequationSession4:ComprehensiveMath4Geometry–GraphingFunctions/Equations:LineequationTestTips•折性方程问题求解；•考点多为求斜率，求方程式，

求折线图；•需要根据线性方程本身性质

结合题目本身信息来求解，

重点关注x轴y轴间的对应关

系。ExerciseOG:2-2-03,2-2-04,6-2-1710-5-18Session4:ComprehensiveMath4Geometry–GraphingFunctions/Equations:CurvilinearequationSession4:ComprehensiveMath4Geometry–GraphingFunctions/Equations:CurvilinearequationSession4:ComprehensiveMath4Geometry–GraphingFunctions/Equations:CurvilinearequationSession4:ComprehensiveMath4Geometry–GraphingFunctions/Equations:CurvilinearequationTestTips•曲线方程问题求解；•考点多为求常值,最值,曲线

形状,映射,沿x轴y轴平移,倍

数等；•需要根据曲性方程性质来求

解,分析曲线形状,曲线平移

形状不变,位置变化；表达式

加倍,曲线形状发生变化。

ExerciseOG:4-9-08,7-7-20,10-8-09Session4:ComprehensiveMath4Statistic:OverviewStatisticLogicRounding/ChartsStats/ProbablityPatterns/SequenceCounting/VisualSession4:ComprehensiveMath4Statistic:Patterns/Sequence:Table1SequenceArithmeticsequenceGeometricsequenceOthersequence•Itisasequenceofnumberssuchthatthedifferencebetweentheconsecutivetermsisconstant.•E.g.5,7,9,11,13,15…•

Itisasequenceofnumberswhereeachtermafterthefirstisfoundbymultiplyingthepreviousonebyafixed,non-zeronumbercalledthecommonratio.•E.g.3,6,12,24,48,56…•Itisasequencewhichisneitheraarithmeticsequencenorgeometricsequence.•E.g.2,5,11,23,47,95…;E.g.1,3,5,7,11,13,17…Session4:ComprehensiveMath4Statistic:Patterns/Sequence:Table2ArithmeticsequenceGeometricsequence等差数列等比数列Session4:ComprehensiveMath4Statistic:Patterns/Sequence:ThreeTestAreas1Arithmeticsequence等差数列2Geometricsequence等比数列3Othersequence其他数列Session4:ComprehensiveMath4Statistic:Patterns/Sequence:ArithmeticsequenceSession4:ComprehensiveMath4Statistic:Patterns/Sequence:ArithmeticsequenceTestTips•等差数列问题求解；•熟练运用等差数列性质求解，

如某两项之间等式，求和公

式；ExerciseOG:9-2-01Session4:ComprehensiveMath4Statistic:Patterns/Sequence:GeometricsequenceSession4:ComprehensiveMath4Statistic:Patterns/Sequen