algebra and trigonometry with analytic geometry_2009_0495559717

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1、ALGEBRAQUADRATICFORMULASPECIALPRODUCTFORMULASSPECIALFACTORINGFORMULASIfa
0,therootsof
xy
xy
x2y2x2y2

xy
xyax2bxc
0are
xy2
x22xyy2x22xyy2

xy2b2b24acx

xy2
x22xyy2x22xyy2

xy22a
xy3
x33x2y3xy2y3x3y3

xy
x2xyy2
xy3
x33x2y3xy2y3x3

2、y3

xy
x2xyy2EXPONENTSANDRADICALSBINOMIALTHEOREMINEQUALITIESaman
amna1/n
2nannIfandthenabbc,ac
xyn
xnn1yn2y2xx
amn
amnam/n
2nam12Ifthenab,acbc
abn
anbnam/n

2namnnkknIfandthenabc0,acbcxyy,kanannnnIfandthenabc0,acbc
n2ab
2a2bnn!

3、bbwhere
kk!
nk!mnana2a
amn
anbn2b1mnmnan
a2a
2anABSOLUTEVALUE
d0SEQUENCESEXPONENTIALSANDLOGARITHMSxdifandonlyifnthtermofanarithmeticsequencewithfirsty
logxmeansay
xadxdterma1andcommondifferencedlogxy
logxlogyaaaxdifandonlyifeitheran
a1
n1dxloga
logaxl

4、ogayxdorxdSumSnofthefirstntermsofanarithmeticysequencelogxr
rlogxnaaMEANSSn

a1analogax
x2ArithmeticmeanAofnnumbersnlogax
xaorSn
2a1
n1da1a2an2A
loga1
0nnthtermofageometricsequencewithfirstlogaa
1terma1andcommonratiorGeometricmeanGofnnumbersa
arn1logx
log10xn

5、1G

aaa1/n,a012nklnx
logxeSumSnofthefirstntermsofageometricsequencelogaulogbu
a1
1rnlogabSn
1rFORMULASFROMGEOMETRYareaAperimeterPcircumferenceCvolumeVcurvedsurfaceareaSaltitudehradiusrRIGHTTRIANGLETRIANGLEEQUILATERALTRIANGLEsscacahhbbsPythagoreanTheorem:c2
a2b2A
1bh

6、P
abc232322h
sA
s24RECTANGLEPARALLELOGRAMTRAPEZOIDawhhlbbA
lwP
2l2w1A
bhA

abh2CIRCLECIRCULARSECTORCIRCULARRINGrusrrRA
r2C
2rA
1r2s
rA

R2r22RECTANGULARBOXSPHERERIGHTCIRCULARCYLINDERhhrwlrV
lwhS
2
hllwhwV
4r3S
4r2V
r2hS
2rh3RIGHTCIRCULARCONEFRUSTUMOFACONEPRI

7、SMrhhhrRV
1r2hS
r2r2h2V
1h
r2rRR2V
BhwithBtheareaofthebase33ANALYTICGEOMETRYDISTANCEFORMULAEQUATIONOFACIRCLEd
P,P
2
xx2
yy2
xh2
yk2
r2122121yyr(h,k)P1(x1,y1)P2(x2,y2)xxSLOPEmOFALINEGRAPHOFAQUADRATICFUNCTIONy
ax2,a0y
ax2bxc,a0yy2y1m
lx2x1yy(x1,y1)(x2,y

8、2)cxxbx2aPOINT-SLOPEFORMOFALINECONSTANTS3.14159yyy1
m
xx1le2.71828(x1,