代數(shù)與幾何是數(shù)學(xué)課程學(xué)習(xí)中最重要的兩大部分，在GRE數(shù)學(xué)考試中也有著比較多的涉及。今天A加未來(lái)小編就帶大家一起來(lái)解析一下GRE數(shù)學(xué)考試中幾何與代數(shù)部分的常見(jiàn)題型以及解題思路，一起來(lái)了解一下吧！

01、代數(shù)

1、指數(shù)運(yùn)算法則 Rules of Exponents

首先我們要熟練代數(shù)的運(yùn)算法則：

例題一：

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

通過(guò)指數(shù)的運(yùn)算規(guī)則可知：

(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

所以答案為AD

2、函數(shù) Function

y=f（x）稱為一個(gè)函數(shù)

Domain定義域?yàn)楹瘮?shù)有定義的所有x值

Range值域?yàn)楹瘮?shù)所有可能的取值

例題二：

★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

先關(guān)注AB的區(qū)別，先算括號(hào)里，計(jì)算順序不同結(jié)果不同

u(★3)=u5=26/5=78/15

★(u3)=★(10/3)=16/3=80/15

u(★3)<★(u3)

3、應(yīng)用 Applications

3.1、工作問(wèn)題 work problem

工作量=工作效率ⅹ工作時(shí)間

A單獨(dú)需要a小時(shí)完成, B單獨(dú)需要b小時(shí)完成， A和B一起需要c小時(shí)完成：

1/a+1/b=1/c

例題三：

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

那所需要的時(shí)間為72分鐘

3.2利息問(wèn)題 interest problem

1、單利

Interest can be computed in two basic ways. With simple annual interest(單利), the interest is computed on the principal only and is equal to (principal)*(interest rate)*time.

 F(本金與利息之和)=P（本金）+P×i（利率）×n（計(jì)息期數(shù)） =P×(1+i×n)

2、復(fù)利

If interest is compounded（復(fù)利）, then interest is computed on the principal as well as on any interest already earned.

 F=P*(1+i)^n

例題四：

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、幾何

1、三角形性質(zhì)：

等邊三角形 equilateral triangle

直角三角形 right triangle

例題一：

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、四邊形性質(zhì)

平行四邊形 parallelogram

正方形 Square

3、圓 Circles

半徑r、圓周率π、直徑d、R大半徑、h高

圓的面積：πr^2

圓的周長(zhǎng)：2πr

半圓的周長(zhǎng)：πr+2r

圓環(huán)的面積：(R^-r^)π

圓柱的體積：πr^2h

圓柱的表面積：πr^2*2+πdh

圓環(huán)的體積：（R^2-r^2）πh

例題二：

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都在圓周上，三角形ABC的面積比半圓面積小

4、坐標(biāo)幾何 Coordinate Geometry

1、兩點(diǎn)之間距離

設(shè)兩個(gè)點(diǎn)A、B以及坐標(biāo)分別為

、 ，則A和B兩點(diǎn)之間的距離為：

 

2、直線方程

一般式:Ax+By+C=0(A、B不同時(shí)為0)【適用于所有直線】

 

，

 

A1/A2=B1/B2≠C1/C2←→兩直線平行

A1/A2=B1/B2=C1/C2←→兩直線重合

橫截距a=-C/A

縱截距b=-C/B

例題三：

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