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GRE数学考试代数与几何常见题型解析

本文出处:IB培训 发布时间:2020-04-03 10:00:17 字体大小: A+ A-

  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A加未来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!


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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:


image.png


例题一:


Which of the following are equal to (1/560)-4 ?Indicate all correct answers.

image.png


通过指数的运算规则可知:


(1/560)^-4=560^4


A:560^4*(560-1)/559=560^4


B:560^-10


C:70^4*8^4=560^4


D:560^8

所以答案为AD


2、函数 Function


y=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)/b


QuantityA               Quantity B


u(★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=80/15


u(★3)<★(u3)


3、应用 Applications


3.1、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 can


empty the same pool in 2 hours. Working together, how many minutes will it take


pumpAand pump B to empty the pool?


A.72


B.75


C.84


D.96


E.108


答案:A


效率:PA=1/3;PB=1/2


A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 problem


1、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 last


month earned $360 in interest for the month.At what simple annual interest rate did


the 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:


image.png



QuantityA       Quantity B


X                     y


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


13+x^2=25


11+y^2=25




2、四边形性质


平行四边形 parallelogram


正方形 Square




3、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:


image.png


Quantity A                                Quantity    B


Area of semicircular region     Area of triangular region ABC




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:A


A,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 Geometry


1、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 approximately


A.4.1


B.5.9


C.6.4


D.7.7


E.8.1




答案D


用公式:√[(5√3-2√3)^2+(3√2+√2)^2]=√59≈7.7


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