GRE数学考试代数与几何常见题型解析

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GRE数学考试 GRE数学

代数与几何是数学课程学习中最重要的两大部分，在GRE数学考试中也有着比较多的涉及。今天易伯华小编就带大家一起来解析一下GRE数学考试中几何与代数部分的常见题型以及解题思路，一起来了解一下吧！01、代数1、指数运算法则 Rules of Exponents首先我们要熟练代数的运算法则：例题一：Which of the following are equal to （1/560）-4 ?Indicate all correct answers.通过指数的运算规则可知：(1/560)^-4=560^4A:560^4*(560-1)/559=560^4B:560^-10C:70^4*8^4=560^4D:560^8所以答案为AD2、函数 Functiony=f（x）称为一个函数Domain定义域为函数有定义的所有x值Range值域为函数所有可能的取值例题二：★b=b+2 and ub=（b^2+1）/bQuantityA Quantity Bu(★3) ★(u3)A.QuantityAis greater.B.Quantity B is greater.C.The two quantities are equal.D.The relationship cannot be determined from the information given.答案：B先关注AB的区别，先算括号里，计算顺序不同结果不同u(★3)=u5=26/5=78/15★(u3)=★(10/3)=16/3=80/15u(★3)★(u3)3、应用 Applications3.1、工作问题 work problem工作量=工作效率ⅹ工作时间A单独需要a小时完成, B单独需要b小时完成， A和B一起需要c小时完成：1/a+1/b=1/c例题三：Working alone, pump A can empty a pool in 3 hours. Working alone, pump B canempty the same pool in 2 hours. Working together, how many minutes will it takepumpAand pump B to empty the pool?A.72B.75C.84D.96E.108答案：A效率：PA=1/3;PB=1/2A和B一起工作：1/3+1/2=1/t那所需要的时间为72分钟3.2利息问题 interest problem1、单利Interest can be computed in two basic ways. With simple annual interest(单利), the interest is computed on the principal only and is equal to (principal)*(interest rate)*time.F(本金与利息之和)=P（本金）+P×i（利率）×n（计息期数） =P×(1+i×n)2、复利If interest is compounded（复利）, then interest is computed on the principal as well as on any interest already earned.F=P*(1+i)^n例题四：A certain money market account that had a balance of $48,000 during all of lastmonth earned $360 in interest for the month.At what simple annual interest rate didthe account earn interest last month?答案E月利率：i=360/48000*100%年利率：I=12i=9%02、几何1、三角形性质：等边三角形 equilateral triangle直角三角形 right triangle例题一：QuantityA Quantity BX yA.QuantityAis greater.B.Quantity B is greater.C.The two quantities are equal.D.The relationship cannot be determined from the information given.答案B13+x^2=2511+y^2=252、四边形性质平行四边形 parallelogram正方形 Square3、圆 Circles半径r、圆周率π、直径d、R大半径、h高圆的面积：πr^2圆的周长：2πr半圆的周长：πr+2r圆环的面积：(R^-r^)π圆柱的体积：πr^2h圆柱的表面积：πr^2*2+πdh圆环的体积：（R^2-r^2）πh例题二：Quantity A Quantity BArea of semicircular region Area of triangular region ABCA.QuantityAis greater.B.Quantity B is greater.C.The two quantities are equal.D.The relationship cannot be determined from the information given.答案：AA,B,C都在圆周上，三角形ABC的面积比半圆面积小4、坐标几何 Coordinate Geometry1、两点之间距离设两个点A、B以及坐标分别为、 ，则A和B两点之间的距离为：2、直线方程一般式:Ax+By+C=0(A、B不同时为0)【适用于所有直线】，A1/A2=B1/B2≠C1/C2←→两直线平行A1/A2=B1/B2=C1/C2←→两直线重合横截距a=-C/A纵截距b=-C/B例题三：In the xy-coordinate system, the distance between points (2√3,−√2)and(5√3,3√2)is approximatelyA.4.1B.5.9C.6.4D.7.7E.8.1答案D用公式：√[(5√3-2√3)^2+(3√2+√2)^2]=√59≈7.7