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！
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=560^4
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：
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：
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