Essential

Words/Conceptslike

terms

同類項 coefficient

系數GRE-tative

reasoning

ALGEBRA——by

Kevinquadratic

equations二次方程定義域compound

interest復利

linear

equation線性方程

solution

set解集simple

interest 單利variable 變量quadrant

象限coordinate

坐標parallel

平行parabola

拋物線intercept截距intersect相交slope斜率

perpendicular垂直vertex頂點constant常數GRE-tative

reasoning

ALGEBRA——by

KevinKey

Points1.指數式的運算(??)???/??=?很多人運算的時候喜歡YY(????)???=???展開式：(x+y)3

=x3+3x2y+3xy2+y3(x-y)3

=x3-3x2y+3xy2-y3(x-y)2

=x2-2xy+y2

x2-y2

=(x+y)(x-y)三角形GRE-tative

reasoning

ALGEBRA——by

Kevin2.一元二次方程求解quadratic

equationsax2+bx+c=0

判別式：Δ=b2-4ac??ax2+bx+c=a(x2+

x+??

????????

??????)+c-

=a(x+????????)2+?????????????????=0(x+

)2=???????????????????????????1

2?????????????????x+??

=±（??

???????）1/2????

??????x

=???+

???????????

x

=????GRE-tative

reasoning

ALGEBRA——by

Kevin3.函數function奇函數odd

functionf(x)=-f(-x)偶函數even

functionf(x)=f(-x)GRE-tative

reasoning

ALGEBRA——by

Kevin4.函數與圖像知道兩點坐標，直線函數表達式的求法？y=kx+b

直線y=ax2+bx+c

二次曲線兩直線平行的條件：k1=k2兩直線垂直的條件：k1k2=

-1 （證明）兩函數y1=y2比較大小：y=y1-y2，考慮y在定義域上的取值（<0，=0，>0）（

）(x-a)2+(y-b)2

=c2

圓GRE-tative

reasoning

ALGEBRA——by

Kevin5.坐標運算中點坐標公式X

(a,

b)Y

(c,

d)中點Z坐標(??+??,??+??)??

??兩點距離公式

??

= (???

??)??+(??

?

??)??GRE-tative

reasoning

ALGEBRA——by

Kevin6.函數圖像變換—映象reflection+平移shift+拉伸stretch+壓縮shrunkreflection

對稱

對稱軸x=0

;

y=0

;

y=x

反函數inverse

functionshiftto

theleft/rightupward/downwardstretch/shrunkhorizontallyverticallyc>0f(x)

→

f(x+c)f(x)→

f(x-c)f(x)

→

f(x)+cf(x)

→

f(x)-cf(x)

→f(cx)f(x)

→

cf(x)GRE-tative

reasoning

ALGEBRA——by

Kevin7.單利與復利運算單利：simple

interest本金

不變復利：compound

interest本金變動，每年或每月利息加入下年/月計算的本金(本金為P，一年率為r，則認為下一年的本金是P(1+r))本金P，年利率r%，

t年利息

simple

interestcompound

interestP(1+tr%)P(1+r%)t利滾利n如果一年內compound

n次，計算方法

P（1+??%)ntGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinGRE-tative

reasoning

ALGEBRA——by

KevinEnd

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