本篇帶大家詳細瞭解一下GRE數學中的代數與幾何問題。
知識點解讀，例題較多，耐心讀完思考思考，會有很新收穫哦！
01
代數
1、指數運算法則 Rules of Exponents
首先我們要熟練代數的運算法則：
例題一：
Which of the following are equal to （1/560）-4 ?Indicate all correct answers.
通過指數的運算規則可知：
(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 Function
y=f（x）稱為一個函數
Domain定義域為函數有定義的所有x值
Range值域為函數所有可能的取值
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
先關注AB的區別，先算括號裡，計算順序不同結果不同
u(★3)=u5=26/5=78/15
★(u3)=★(10/3)=16/3=80/15
u(★3)
3、應用 Applications
3.1、工作問題 work problem
工作量=工作效率ⅹ工作時間
A單獨需要a小時完成, B單獨需要b小時完成， A和B一起需要c小時完成：
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
那所需要的時間為72分鐘
3.2利息問題 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（計息期數） =P×(1+i×n)
2、複利
If interest is compounded（複利）, 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：
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
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：2πr
半圓的周長：πr+2r
圓環的面積：(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、座標幾何 Coordinate Geometry
1、兩點之間距離
設兩個點A、B以及座標分別為
，則A和B兩點之間的距離為：
2、直線方程
一般式:Ax+By+C=0(A、B不同時為0)【適用於所有直線】
，
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
閱讀更多 雷哥GRE 的文章
