高考数学公式总结 谁能给我 总结一下高考数学基本公式
\u9ad8\u4e2d\u6570\u5b66\u516c\u5f0f\u603b\u7ed3\u6b63\u5f26\u5b9a\u7406 a/sinA=b/sinB=c/sinC=2R \u6ce8\uff1a \u5176\u4e2d R \u8868\u793a\u4e09\u89d2\u5f62\u7684\u5916\u63a5\u5706\u534a\u5f84
\u4f59\u5f26\u5b9a\u7406 b^2=a^2+c^2-2accosB \u6ce8\uff1a\u89d2B\u662f\u8fb9a\u548c\u8fb9c\u7684\u5939\u89d2
\u5706\u7684\u6807\u51c6\u65b9\u7a0b (x-a)^2+(y-b)^2=^r2 \u6ce8\uff1a\uff08a,b\uff09\u662f\u5706\u5fc3\u5750\u6807 \u001f
\u5706\u7684\u4e00\u822c\u65b9\u7a0b x^2+y^2+Dx+Ey+F=0 \u6ce8\uff1aD^2+E^2-4F>0
\u629b\u7269\u7ebf\u6807\u51c6\u65b9\u7a0b y^2=2px y^2=-2px x^2=2py x^2=-2py
\u76f4\u68f1\u67f1\u4fa7\u9762\u79ef S=c*h \u659c\u68f1\u67f1\u4fa7\u9762\u79ef S=c'*h
\u6b63\u68f1\u9525\u4fa7\u9762\u79ef S=1/2c*h' \u6b63\u68f1\u53f0\u4fa7\u9762\u79ef S=1/2(c+c')h'
\u5706\u53f0\u4fa7\u9762\u79ef S=1/2(c+c')l=pi(R+r)l \u7403\u7684\u8868\u9762\u79ef S=4pi*r2
\u5706\u67f1\u4fa7\u9762\u79ef S=c*h=2pi*h \u5706\u9525\u4fa7\u9762\u79ef S=1/2*c*l=pi*r*l
\u5f27\u957f\u516c\u5f0f l=a*r a\u662f\u5706\u5fc3\u89d2\u7684\u5f27\u5ea6\u6570r >0 \u6247\u5f62\u9762\u79ef\u516c\u5f0f s=1/2*l*r
\u9525\u4f53\u4f53\u79ef\u516c\u5f0f V=1/3*S*H \u5706\u9525\u4f53\u4f53\u79ef\u516c\u5f0f V=1/3*pi*r2h
\u659c\u68f1\u67f1\u4f53\u79ef V=S'L \u6ce8\uff1a\u5176\u4e2d,S'\u662f\u76f4\u622a\u9762\u9762\u79ef\uff0c L\u662f\u4fa7\u68f1\u957f
\u67f1\u4f53\u4f53\u79ef\u516c\u5f0f V=s*h \u5706\u67f1\u4f53 V=pi*r2h
\u500d\u89d2\u516c\u5f0f
tan2A=2tanA/[1-(tanA)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2 -1=1-2(sina)^2
\u534a\u89d2\u516c\u5f0f
sin(A/2)=\u221a((1-cosA)/2) sin(A/2)=-\u221a((1-cosA)/2)
cos(A/2)=\u221a((1+cosA)/2) cos(A/2)=-\u221a((1+cosA)/2)
tan(A/2)=\u221a((1-cosA)/((1+cosA)) tan(A/2)=-\u221a((1-cosA)/((1+cosA))
cot(A/2)=\u221a((1+cosA)/((1-cosA)) cot(A/2)=-\u221a((1+cosA)/((1-cosA))
\u548c\u5dee\u5316\u79ef
2sinAcosB=sin(A+B)+sin(A-B)
2cosAsinB=sin(A+B)-sin(A-B) )
2cosAcosB=cos(A+B)-sin(A-B)
-2sinAsinB=cos(A+B)-cos(A-B)
sinA+sinB=2sin((A+B)/2)cos((A-B)/2
cosA+cosB=2cos((A+B)/2)sin((A-B)/2)
tanA+tanB=sin(A+B)/cosAcosB
\u67d0\u4e9b\u6570\u5217\u524dn\u9879\u548c
1+2+3+4+5+6+7+8+9+\u2026+n=n(n+1)/2
1+3+5+7+9+11+13+15+\u2026+(2n-1)=n2 \u001e
2+4+6+8+10+12+14+\u2026+(2n)=n(n+1) 5
1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+\u2026+n^2=n(n+1)(2n+1)/6
1^3+2^3+3^3+4^3+5^3+6^3+\u2026n^3=n2(n+1)2/4
1*2+2*3+3*4+4*5+5*6+6*7+\u2026+n(n+1)=n(n+1)(n+2)/3
\u5e38\u7528\u5bfc\u6570\u516c\u5f0f
1.y=c(c\u4e3a\u5e38\u6570) y'=0
2.y=x^n y'=nx^(n-1)
3.y=a^x y'=a^xlna
y=e^x y'=e^x
4.y=logax y'=logae/x
y=lnx y'=1/x
5.y=sinx y'=cosx
6.y=cosx y'=-sinx
7.y=tanx y'=1/cos^2x
8.y=cotx y'=-1/sin^2x
9.y=arcsinx y'=1/\u221a1-x^2
10.y=arccosx y'=-1/\u221a1-x^2
11.y=arctanx y'=1/1+x^2
12.y=arccotx y'=-1/1+x^2
1\uff0e\u96c6\u5408\u5143\u7d20\u5177\u6709\u2460\u786e\u5b9a\u6027\u2461\u4e92\u5f02\u6027\u2462\u65e0\u5e8f\u6027
2\uff0e\u96c6\u5408\u8868\u793a\u65b9\u6cd5\u2460\u5217\u4e3e\u6cd5 \u2461\u63cf\u8ff0\u6cd5
\u2462\u97e6\u6069\u56fe \u2463\u6570\u8f74\u6cd5
3\uff0e\u96c6\u5408\u7684\u8fd0\u7b97
\u2474 A\u2229(B\u222aC)=(A\u2229B)\u222a(A\u2229C)
\u2475 Cu(A\u2229B)=CuA\u222aCuB
Cu(A\u222aB)=CuA\u2229CuB
4\uff0e\u96c6\u5408\u7684\u6027\u8d28
\u2474n\u5143\u96c6\u5408\u7684\u5b50\u96c6\u6570\uff1a2n
\u771f\u5b50\u96c6\u6570\uff1a2n-1\uff1b\u975e\u7a7a\u771f\u5b50\u96c6\u6570\uff1a2n-2
\u9ad8\u4e2d\u6570\u5b66\u6982\u5ff5\u603b\u7ed3
\u4e00\u3001 \u51fd\u6570
1\u3001 \u82e5\u96c6\u5408A\u4e2d\u6709n \u4e2a\u5143\u7d20\uff0c\u5219\u96c6\u5408A\u7684\u6240\u6709\u4e0d\u540c\u7684\u5b50\u96c6\u4e2a\u6570\u4e3a \uff0c\u6240\u6709\u975e\u7a7a\u771f\u5b50\u96c6\u7684\u4e2a\u6570\u662f \u3002
\u4e8c\u6b21\u51fd\u6570 \u7684\u56fe\u8c61\u7684\u5bf9\u79f0\u8f74\u65b9\u7a0b\u662f \uff0c\u9876\u70b9\u5750\u6807\u662f \u3002\u7528\u5f85\u5b9a\u7cfb\u6570\u6cd5\u6c42\u4e8c\u6b21\u51fd\u6570\u7684\u89e3\u6790\u5f0f\u65f6\uff0c\u89e3\u6790\u5f0f\u7684\u8bbe\u6cd5\u6709\u4e09\u79cd\u5f62\u5f0f\uff0c\u5373 \uff0c \u548c \uff08\u9876\u70b9\u5f0f\uff09\u3002
2\u3001 \u5e42\u51fd\u6570 \uff0c\u5f53n\u4e3a\u6b63\u5947\u6570\uff0cm\u4e3a\u6b63\u5076\u6570\uff0cm<n\u65f6\uff0c\u5176\u5927\u81f4\u56fe\u8c61\u662f
3\u3001 \u51fd\u6570 \u7684\u5927\u81f4\u56fe\u8c61\u662f
\u7531\u56fe\u8c61\u77e5\uff0c\u51fd\u6570\u7684\u503c\u57df\u662f \uff0c\u5355\u8c03\u9012\u589e\u533a\u95f4\u662f \uff0c\u5355\u8c03\u9012\u51cf\u533a\u95f4\u662f \u3002
\u4e8c\u3001 \u4e09\u89d2\u51fd\u6570
1\u3001 \u4ee5\u89d2 \u7684\u9876\u70b9\u4e3a\u5750\u6807\u539f\u70b9\uff0c\u59cb\u8fb9\u4e3ax\u8f74\u6b63\u534a\u8f74\u5efa\u7acb\u76f4\u89d2\u5750\u6807\u7cfb\uff0c\u5728\u89d2 \u7684\u7ec8\u8fb9\u4e0a\u4efb\u53d6\u4e00\u4e2a\u5f02\u4e8e\u539f\u70b9\u7684\u70b9 \uff0c\u70b9P\u5230\u539f\u70b9\u7684\u8ddd\u79bb\u8bb0\u4e3a \uff0c\u5219sin = \uff0ccos = \uff0ctg = \uff0cctg = \uff0csec = \uff0ccsc = \u3002
2\u3001\u540c\u89d2\u4e09\u89d2\u51fd\u6570\u7684\u5173\u7cfb\u4e2d\uff0c\u5e73\u65b9\u5173\u7cfb\u662f\uff1a \uff0c \uff0c \uff1b
\u5012\u6570\u5173\u7cfb\u662f\uff1a \uff0c \uff0c \uff1b
\u76f8\u9664\u5173\u7cfb\u662f\uff1a \uff0c \u3002
3\u3001\u8bf1\u5bfc\u516c\u5f0f\u53ef\u7528\u5341\u4e2a\u5b57\u6982\u62ec\u4e3a\uff1a\u5947\u53d8\u5076\u4e0d\u53d8\uff0c\u7b26\u53f7\u770b\u8c61\u9650\u3002\u5982\uff1a \uff0c = \uff0c \u3002
4\u3001 \u51fd\u6570 \u7684\u6700\u5927\u503c\u662f \uff0c\u6700\u5c0f\u503c\u662f \uff0c\u5468\u671f\u662f \uff0c\u9891\u7387\u662f \uff0c\u76f8\u4f4d\u662f \uff0c\u521d\u76f8\u662f \uff1b\u5176\u56fe\u8c61\u7684\u5bf9\u79f0\u8f74\u662f\u76f4\u7ebf \uff0c\u51e1\u662f\u8be5\u56fe\u8c61\u4e0e\u76f4\u7ebf \u7684\u4ea4\u70b9\u90fd\u662f\u8be5\u56fe\u8c61\u7684\u5bf9\u79f0\u4e2d\u5fc3\u3002
5\u3001 \u4e09\u89d2\u51fd\u6570\u7684\u5355\u8c03\u533a\u95f4\uff1a
\u7684\u9012\u589e\u533a\u95f4\u662f \uff0c\u9012\u51cf\u533a\u95f4\u662f \uff1b \u7684\u9012\u589e\u533a\u95f4\u662f \uff0c\u9012\u51cf\u533a\u95f4\u662f \uff0c \u7684\u9012\u589e\u533a\u95f4\u662f \uff0c \u7684\u9012\u51cf\u533a\u95f4\u662f \u3002
6\u3001
7\u3001\u4e8c\u500d\u89d2\u516c\u5f0f\u662f\uff1asin2 =
cos2 = = =
tg2 = \u3002
8\u3001\u4e09\u500d\u89d2\u516c\u5f0f\u662f\uff1asin3 = cos3 =
9\u3001\u534a\u89d2\u516c\u5f0f\u662f\uff1asin = cos =
tg = = = \u3002
10\u3001\u5347\u5e42\u516c\u5f0f\u662f\uff1a \u3002
11\u3001\u964d\u5e42\u516c\u5f0f\u662f\uff1a \u3002
12\u3001\u4e07\u80fd\u516c\u5f0f\uff1asin = cos = tg =
13\u3001sin( )sin( )= \uff0c
cos( )cos( )= = \u3002
14\u3001 = \uff1b
= \uff1b
= \u3002
15\u3001 = \u3002
16\u3001sin180= \u3002
17\u3001\u7279\u6b8a\u89d2\u7684\u4e09\u89d2\u51fd\u6570\u503c\uff1a
0
sin 0 1 0
cos 1 0 0
tg 0 1 \u4e0d\u5b58\u5728 0 \u4e0d\u5b58\u5728
ctg \u4e0d\u5b58\u5728 1 0 \u4e0d\u5b58\u5728 0
18\u3001\u6b63\u5f26\u5b9a\u7406\u662f\uff08\u5176\u4e2dR\u8868\u793a\u4e09\u89d2\u5f62\u7684\u5916\u63a5\u5706\u534a\u5f84\uff09\uff1a
19\u3001\u7531\u4f59\u5f26\u5b9a\u7406\u7b2c\u4e00\u5f62\u5f0f\uff0c =
\u7531\u4f59\u5f26\u5b9a\u7406\u7b2c\u4e8c\u5f62\u5f0f\uff0ccosB=
20\u3001\u25b3ABC\u7684\u9762\u79ef\u7528S\u8868\u793a\uff0c\u5916\u63a5\u5706\u534a\u5f84\u7528R\u8868\u793a\uff0c\u5185\u5207\u5706\u534a\u5f84\u7528r\u8868\u793a\uff0c\u534a\u5468\u957f\u7528p\u8868\u793a\u5219\uff1a
\u2460 \uff1b\u2461 \uff1b
\u2462 \uff1b\u2463 \uff1b
\u2464 \uff1b\u2465
21\u3001\u4e09\u89d2\u5b66\u4e2d\u7684\u5c04\u5f71\u5b9a\u7406\uff1a\u5728\u25b3ABC \u4e2d\uff0c \uff0c\u2026
22\u3001\u5728\u25b3ABC \u4e2d\uff0c \uff0c\u2026
23\u3001\u5728\u25b3ABC \u4e2d\uff1a
24\u3001\u79ef\u5316\u548c\u5dee\u516c\u5f0f\uff1a
\u2460 \uff0c
\u2461 \uff0c
\u2462 \uff0c
\u2463 \u3002
25\u3001\u548c\u5dee\u5316\u79ef\u516c\u5f0f\uff1a
\u2460 \uff0c
\u2461 \uff0c
\u2462 \uff0c
\u2463 \u3002
\u4e09\u3001 \u53cd\u4e09\u89d2\u51fd\u6570
1\u3001 \u7684\u5b9a\u4e49\u57df\u662f[-1\uff0c1]\uff0c\u503c\u57df\u662f \uff0c\u5947\u51fd\u6570\uff0c\u589e\u51fd\u6570\uff1b
\u7684\u5b9a\u4e49\u57df\u662f[-1\uff0c1]\uff0c\u503c\u57df\u662f \uff0c\u975e\u5947\u975e\u5076\uff0c\u51cf\u51fd\u6570\uff1b
\u7684\u5b9a\u4e49\u57df\u662fR\uff0c\u503c\u57df\u662f \uff0c\u5947\u51fd\u6570\uff0c\u589e\u51fd\u6570\uff1b
\u7684\u5b9a\u4e49\u57df\u662fR\uff0c\u503c\u57df\u662f \uff0c\u975e\u5947\u975e\u5076\uff0c\u51cf\u51fd\u6570\u3002
2\u3001\u5f53 \uff1b
\u5bf9\u4efb\u610f\u7684 \uff0c\u6709\uff1a
\u5f53 \u3002
3\u3001\u6700\u7b80\u4e09\u89d2\u65b9\u7a0b\u7684\u89e3\u96c6\uff1a
\u56db\u3001 \u4e0d\u7b49\u5f0f
1\u3001\u82e5n\u4e3a\u6b63\u5947\u6570\uff0c\u7531 \u53ef\u63a8\u51fa \u5417\uff1f \uff08 \u80fd \uff09
\u82e5n\u4e3a\u6b63\u5076\u6570\u5462\uff1f \uff08 \u5747\u4e3a\u975e\u8d1f\u6570\u65f6\u624d\u80fd\uff09
2\u3001\u540c\u5411\u4e0d\u7b49\u5f0f\u80fd\u76f8\u51cf\uff0c\u76f8\u9664\u5417 \uff08\u4e0d\u80fd\uff09
\u80fd\u76f8\u52a0\u5417\uff1f \uff08 \u80fd \uff09
\u80fd\u76f8\u4e58\u5417\uff1f \uff08\u80fd\uff0c\u4f46\u6709\u6761\u4ef6\uff09
3\u3001\u4e24\u4e2a\u6b63\u6570\u7684\u5747\u503c\u4e0d\u7b49\u5f0f\u662f\uff1a
\u4e09\u4e2a\u6b63\u6570\u7684\u5747\u503c\u4e0d\u7b49\u5f0f\u662f\uff1a
n\u4e2a\u6b63\u6570\u7684\u5747\u503c\u4e0d\u7b49\u5f0f\u662f\uff1a
4\u3001\u4e24\u4e2a\u6b63\u6570 \u7684\u8c03\u548c\u5e73\u5747\u6570\u3001\u51e0\u4f55\u5e73\u5747\u6570\u3001\u7b97\u672f\u5e73\u5747\u6570\u3001\u5747\u65b9\u6839\u4e4b\u95f4\u7684\u5173\u7cfb\u662f
6\u3001 \u53cc\u5411\u4e0d\u7b49\u5f0f\u662f\uff1a
\u5de6\u8fb9\u5728 \u65f6\u53d6\u5f97\u7b49\u53f7\uff0c\u53f3\u8fb9\u5728 \u65f6\u53d6\u5f97\u7b49\u53f7\u3002
\u4e94\u3001 \u6570\u5217
1\u3001\u7b49\u5dee\u6570\u5217\u7684\u901a\u9879\u516c\u5f0f\u662f \uff0c\u524dn\u9879\u548c\u516c\u5f0f\u662f\uff1a = \u3002
2\u3001\u7b49\u6bd4\u6570\u5217\u7684\u901a\u9879\u516c\u5f0f\u662f \uff0c
\u524dn\u9879\u548c\u516c\u5f0f\u662f\uff1a
3\u3001\u5f53\u7b49\u6bd4\u6570\u5217 \u7684\u516c\u6bd4q\u6ee1\u8db3 <1\u65f6\uff0c =S= \u3002\u4e00\u822c\u5730\uff0c\u5982\u679c\u65e0\u7a77\u6570\u5217 \u7684\u524dn\u9879\u548c\u7684\u6781\u9650 \u5b58\u5728\uff0c\u5c31\u628a\u8fd9\u4e2a\u6781\u9650\u79f0\u4e3a\u8fd9\u4e2a\u6570\u5217\u7684\u5404\u9879\u548c\uff08\u6216\u6240\u6709\u9879\u7684\u548c\uff09\uff0c\u7528S\u8868\u793a\uff0c\u5373S= \u3002
4\u3001\u82e5m\u3001n\u3001p\u3001q\u2208N\uff0c\u4e14 \uff0c\u90a3\u4e48\uff1a\u5f53\u6570\u5217 \u662f\u7b49\u5dee\u6570\u5217\u65f6\uff0c\u6709 \uff1b\u5f53\u6570\u5217 \u662f\u7b49\u6bd4\u6570\u5217\u65f6\uff0c\u6709 \u3002
5\u3001 \u7b49\u5dee\u6570\u5217 \u4e2d\uff0c\u82e5Sn=10\uff0cS2n=30\uff0c\u5219S3n=60\uff1b
6\u3001\u7b49\u6bd4\u6570\u5217 \u4e2d\uff0c\u82e5Sn=10\uff0cS2n=30\uff0c\u5219S3n=70\uff1b
\u516d\u3001 \u590d\u6570
1\u3001 \u600e\u6837\u8ba1\u7b97\uff1f\uff08\u5148\u6c42n\u88ab4\u9664\u6240\u5f97\u7684\u4f59\u6570\uff0c \uff09
2\u3001 \u662f1\u7684\u4e24\u4e2a\u865a\u7acb\u65b9\u6839\uff0c\u5e76\u4e14\uff1a
3\u3001 \u590d\u6570\u96c6\u5185\u7684\u4e09\u89d2\u5f62\u4e0d\u7b49\u5f0f\u662f\uff1a \uff0c\u5176\u4e2d\u5de6\u8fb9\u5728\u590d\u6570z1\u3001z2\u5bf9\u5e94\u7684\u5411\u91cf\u5171\u7ebf\u4e14\u53cd\u5411\uff08\u540c\u5411\uff09\u65f6\u53d6\u7b49\u53f7\uff0c\u53f3\u8fb9\u5728\u590d\u6570z1\u3001z2\u5bf9\u5e94\u7684\u5411\u91cf\u5171\u7ebf\u4e14\u540c\u5411\uff08\u53cd\u5411\uff09\u65f6\u53d6\u7b49\u53f7\u3002
4\u3001 \u68e3\u83ab\u4f5b\u5b9a\u7406\u662f\uff1a
5\u3001 \u82e5\u975e\u96f6\u590d\u6570 \uff0c\u5219z\u7684n\u6b21\u65b9\u6839\u6709n\u4e2a\uff0c\u5373\uff1a
\u5b83\u4eec\u5728\u590d\u5e73\u9762\u5185\u5bf9\u5e94\u7684\u70b9\u5728\u5206\u5e03\u4e0a\u6709\u4ec0\u4e48\u7279\u6b8a\u5173\u7cfb\uff1f
\u90fd\u4f4d\u4e8e\u5706\u5fc3\u5728\u539f\u70b9\uff0c\u534a\u5f84\u4e3a \u7684\u5706\u4e0a\uff0c\u5e76\u4e14\u628a\u8fd9\u4e2a\u5706n\u7b49\u5206\u3002
6\u3001 \u82e5 \uff0c\u590d\u6570z1\u3001z2\u5bf9\u5e94\u7684\u70b9\u5206\u522b\u662fA\u3001B\uff0c\u5219\u25b3AOB\uff08O\u4e3a\u5750\u6807\u539f\u70b9\uff09\u7684\u9762\u79ef\u662f \u3002
7\u3001 = \u3002
8\u3001 \u590d\u5e73\u9762\u5185\u590d\u6570z\u5bf9\u5e94\u7684\u70b9\u7684\u51e0\u4e2a\u57fa\u672c\u8f68\u8ff9\uff1a
\u2460 \u8f68\u8ff9\u4e3a\u4e00\u6761\u5c04\u7ebf\u3002
\u2461 \u8f68\u8ff9\u4e3a\u4e00\u6761\u5c04\u7ebf\u3002
\u2462 \u8f68\u8ff9\u662f\u4e00\u4e2a\u5706\u3002
\u2463 \u8f68\u8ff9\u662f\u4e00\u6761\u76f4\u7ebf\u3002
\u2464 \u8f68\u8ff9\u6709\u4e09\u79cd\u53ef\u80fd\u60c5\u5f62\uff1aa)\u5f53 \u65f6\uff0c\u8f68\u8ff9\u4e3a\u692d\u5706\uff1bb)\u5f53 \u65f6\uff0c\u8f68\u8ff9\u4e3a\u4e00\u6761\u7ebf\u6bb5\uff1bc)\u5f53 \u65f6\uff0c\u8f68\u8ff9\u4e0d\u5b58\u5728\u3002
\u2465 \u8f68\u8ff9\u6709\u4e09\u79cd\u53ef\u80fd\u60c5\u5f62\uff1aa)\u5f53 \u65f6\uff0c\u8f68\u8ff9\u4e3a\u53cc\u66f2\u7ebf\uff1bb) \u5f53 \u65f6\uff0c\u8f68\u8ff9\u4e3a\u4e24\u6761\u5c04\u7ebf\uff1bc) \u5f53 \u65f6\uff0c\u8f68\u8ff9\u4e0d\u5b58\u5728\u3002
\u4e03\u3001 \u6392\u5217\u7ec4\u5408\u3001\u4e8c\u9879\u5f0f\u5b9a\u7406
1\u3001 \u52a0\u6cd5\u539f\u7406\u3001\u4e58\u6cd5\u539f\u7406\u5404\u9002\u7528\u4e8e\u4ec0\u4e48\u60c5\u5f62\uff1f\u6709\u4ec0\u4e48\u7279\u70b9\uff1f
\u52a0\u6cd5\u5206\u7c7b\uff0c\u7c7b\u7c7b\u72ec\u7acb\uff1b\u4e58\u6cd5\u5206\u6b65\uff0c\u6b65\u6b65\u76f8\u5173\u3002
2\u3001\u6392\u5217\u6570\u516c\u5f0f\u662f\uff1a = = \uff1b
\u6392\u5217\u6570\u4e0e\u7ec4\u5408\u6570\u7684\u5173\u7cfb\u662f\uff1a
\u7ec4\u5408\u6570\u516c\u5f0f\u662f\uff1a = = \uff1b
\u7ec4\u5408\u6570\u6027\u8d28\uff1a = + =
= =
3\u3001 \u4e8c\u9879\u5f0f\u5b9a\u7406\uff1a \u4e8c\u9879\u5c55\u5f00\u5f0f\u7684\u901a\u9879\u516c\u5f0f\uff1a
\u516b\u3001 \u89e3\u6790\u51e0\u4f55
1\u3001 \u6c99\u5c14\u516c\u5f0f\uff1a
2\u3001 \u6570\u8f74\u4e0a\u4e24\u70b9\u95f4\u8ddd\u79bb\u516c\u5f0f\uff1a
3\u3001 \u76f4\u89d2\u5750\u6807\u5e73\u9762\u5185\u7684\u4e24\u70b9\u95f4\u8ddd\u79bb\u516c\u5f0f\uff1a
4\u3001 \u82e5\u70b9P\u5206\u6709\u5411\u7ebf\u6bb5 \u6210\u5b9a\u6bd4\u03bb\uff0c\u5219\u03bb=
5\u3001 \u82e5\u70b9 \uff0c\u70b9P\u5206\u6709\u5411\u7ebf\u6bb5 \u6210\u5b9a\u6bd4\u03bb\uff0c\u5219\uff1a\u03bb= = \uff1b
=
=
\u82e5 \uff0c\u5219\u25b3ABC\u7684\u91cd\u5fc3G\u7684\u5750\u6807\u662f \u3002
6\u3001\u6c42\u76f4\u7ebf\u659c\u7387\u7684\u5b9a\u4e49\u5f0f\u4e3ak= \uff0c\u4e24\u70b9\u5f0f\u4e3ak= \u3002
7\u3001\u76f4\u7ebf\u65b9\u7a0b\u7684\u51e0\u79cd\u5f62\u5f0f\uff1a
\u70b9\u659c\u5f0f\uff1a \uff0c \u659c\u622a\u5f0f\uff1a
\u4e24\u70b9\u5f0f\uff1a \uff0c \u622a\u8ddd\u5f0f\uff1a
\u4e00\u822c\u5f0f\uff1a
\u7ecf\u8fc7\u4e24\u6761\u76f4\u7ebf \u7684\u4ea4\u70b9\u7684\u76f4\u7ebf\u7cfb\u65b9\u7a0b\u662f\uff1a
8\u3001 \u76f4\u7ebf \uff0c\u5219\u4ece\u76f4\u7ebf \u5230\u76f4\u7ebf \u7684\u89d2\u03b8\u6ee1\u8db3\uff1a
\u76f4\u7ebf \u4e0e \u7684\u5939\u89d2\u03b8\u6ee1\u8db3\uff1a
\u76f4\u7ebf \uff0c\u5219\u4ece\u76f4\u7ebf \u5230\u76f4\u7ebf \u7684\u89d2\u03b8\u6ee1\u8db3\uff1a
\u76f4\u7ebf \u4e0e \u7684\u5939\u89d2\u03b8\u6ee1\u8db3\uff1a
9\u3001 \u70b9 \u5230\u76f4\u7ebf \u7684\u8ddd\u79bb\uff1a
10\u3001\u4e24\u6761\u5e73\u884c\u76f4\u7ebf \u8ddd\u79bb\u662f
11\u3001\u5706\u7684\u6807\u51c6\u65b9\u7a0b\u662f\uff1a
\u5706\u7684\u4e00\u822c\u65b9\u7a0b\u662f\uff1a
\u5176\u4e2d\uff0c\u534a\u5f84\u662f \uff0c\u5706\u5fc3\u5750\u6807\u662f
\u601d\u8003\uff1a\u65b9\u7a0b \u5728 \u548c \u65f6\u5404\u8868\u793a\u600e\u6837\u7684\u56fe\u5f62\uff1f
12\u3001\u82e5 \uff0c\u5219\u4ee5\u7ebf\u6bb5AB\u4e3a\u76f4\u5f84\u7684\u5706\u7684\u65b9\u7a0b\u662f
\u7ecf\u8fc7\u4e24\u4e2a\u5706
\uff0c
\u7684\u4ea4\u70b9\u7684\u5706\u7cfb\u65b9\u7a0b\u662f\uff1a
\u7ecf\u8fc7\u76f4\u7ebf \u4e0e\u5706 \u7684\u4ea4\u70b9\u7684\u5706\u7cfb\u65b9\u7a0b\u662f\uff1a
13\u3001\u5706 \u4e3a\u5207\u70b9\u7684\u5207\u7ebf\u65b9\u7a0b\u662f
\u4e00\u822c\u5730\uff0c\u66f2\u7ebf \u4e3a\u5207\u70b9\u7684\u5207\u7ebf\u65b9\u7a0b\u662f\uff1a \u3002\u4f8b\u5982\uff0c\u629b\u7269\u7ebf \u7684\u4ee5\u70b9 \u4e3a\u5207\u70b9\u7684\u5207\u7ebf\u65b9\u7a0b\u662f\uff1a \uff0c\u5373\uff1a \u3002
\u6ce8\u610f\uff1a\u8fd9\u4e2a\u7ed3\u8bba\u53ea\u80fd\u7528\u6765\u505a\u9009\u62e9\u9898\u6216\u8005\u586b\u7a7a\u9898\uff0c\u82e5\u662f\u505a\u89e3\u7b54\u9898\uff0c\u53ea\u80fd\u6309\u7167\u6c42\u5207\u7ebf\u65b9\u7a0b\u7684\u5e38\u89c4\u8fc7\u7a0b\u53bb\u505a\u3002
14\u3001\u7814\u7a76\u5706\u4e0e\u76f4\u7ebf\u7684\u4f4d\u7f6e\u5173\u7cfb\u6700\u5e38\u7528\u7684\u65b9\u6cd5\u6709\u4e24\u79cd\uff0c\u5373\uff1a
\u2460\u5224\u522b\u5f0f\u6cd5\uff1a\u0394>0\uff0c=0\uff0c<0\uff0c\u7b49\u4ef7\u4e8e\u76f4\u7ebf\u4e0e\u5706\u76f8\u4ea4\u3001\u76f8\u5207\u3001\u76f8\u79bb\uff1b
\u2461\u8003\u67e5\u5706\u5fc3\u5230\u76f4\u7ebf\u7684\u8ddd\u79bb\u4e0e\u534a\u5f84\u7684\u5927\u5c0f\u5173\u7cfb\uff1a\u8ddd\u79bb\u5927\u4e8e\u534a\u5f84\u3001\u7b49\u4e8e\u534a\u5f84\u3001\u5c0f\u4e8e\u534a\u5f84\uff0c\u7b49\u4ef7\u4e8e\u76f4\u7ebf\u4e0e\u5706\u76f8\u79bb\u3001\u76f8\u5207\u3001\u76f8\u4ea4\u3002
15\u3001\u629b\u7269\u7ebf\u6807\u51c6\u65b9\u7a0b\u7684\u56db\u79cd\u5f62\u5f0f\u662f\uff1a
16\u3001\u629b\u7269\u7ebf \u7684\u7126\u70b9\u5750\u6807\u662f\uff1a \uff0c\u51c6\u7ebf\u65b9\u7a0b\u662f\uff1a \u3002
\u82e5\u70b9 \u662f\u629b\u7269\u7ebf \u4e0a\u4e00\u70b9\uff0c\u5219\u8be5\u70b9\u5230\u629b\u7269\u7ebf\u7684\u7126\u70b9\u7684\u8ddd\u79bb\uff08\u79f0\u4e3a\u7126\u534a\u5f84\uff09\u662f\uff1a \uff0c\u8fc7\u8be5\u629b\u7269\u7ebf\u7684\u7126\u70b9\u4e14\u5782\u76f4\u4e8e\u629b\u7269\u7ebf\u5bf9\u79f0\u8f74\u7684\u5f26\uff08\u79f0\u4e3a\u901a\u5f84\uff09\u7684\u957f\u662f\uff1a \u3002
17\u3001\u692d\u5706\u6807\u51c6\u65b9\u7a0b\u7684\u4e24\u79cd\u5f62\u5f0f\u662f\uff1a \u548c
\u3002
18\u3001\u692d\u5706 \u7684\u7126\u70b9\u5750\u6807\u662f \uff0c\u51c6\u7ebf\u65b9\u7a0b\u662f \uff0c\u79bb\u5fc3\u7387\u662f \uff0c\u901a\u5f84\u7684\u957f\u662f \u3002\u5176\u4e2d \u3002
19\u3001\u82e5\u70b9 \u662f\u692d\u5706 \u4e0a\u4e00\u70b9\uff0c \u662f\u5176\u5de6\u3001\u53f3\u7126\u70b9\uff0c\u5219\u70b9P\u7684\u7126\u534a\u5f84\u7684\u957f\u662f \u548c \u3002
20\u3001\u53cc\u66f2\u7ebf\u6807\u51c6\u65b9\u7a0b\u7684\u4e24\u79cd\u5f62\u5f0f\u662f\uff1a \u548c
\u3002
21\u3001\u53cc\u66f2\u7ebf \u7684\u7126\u70b9\u5750\u6807\u662f \uff0c\u51c6\u7ebf\u65b9\u7a0b\u662f \uff0c\u79bb\u5fc3\u7387\u662f \uff0c\u901a\u5f84\u7684\u957f\u662f \uff0c\u6e10\u8fd1\u7ebf\u65b9\u7a0b\u662f \u3002\u5176\u4e2d \u3002
22\u3001\u4e0e\u53cc\u66f2\u7ebf \u5171\u6e10\u8fd1\u7ebf\u7684\u53cc\u66f2\u7ebf\u7cfb\u65b9\u7a0b\u662f \u3002\u4e0e\u53cc\u66f2\u7ebf \u5171\u7126\u70b9\u7684\u53cc\u66f2\u7ebf\u7cfb\u65b9\u7a0b\u662f \u3002
23\u3001\u82e5\u76f4\u7ebf \u4e0e\u5706\u9525\u66f2\u7ebf\u4ea4\u4e8e\u4e24\u70b9A(x1\uff0cy1)\uff0cB(x2\uff0cy2)\uff0c\u5219\u5f26\u957f\u4e3a \uff1b
\u82e5\u76f4\u7ebf \u4e0e\u5706\u9525\u66f2\u7ebf\u4ea4\u4e8e\u4e24\u70b9A(x1\uff0cy1)\uff0cB(x2\uff0cy2)\uff0c\u5219\u5f26\u957f\u4e3a \u3002
24\u3001\u5706\u9525\u66f2\u7ebf\u7684\u7126\u53c2\u6570p\u7684\u51e0\u4f55\u610f\u4e49\u662f\u7126\u70b9\u5230\u51c6\u7ebf\u7684\u8ddd\u79bb\uff0c\u5bf9\u4e8e\u692d\u5706\u548c\u53cc\u66f2\u7ebf\u90fd\u6709\uff1a \u3002
25\u3001\u5e73\u79fb\u5750\u6807\u8f74\uff0c\u4f7f\u65b0\u5750\u6807\u7cfb\u7684\u539f\u70b9 \u5728\u539f\u5750\u6807\u7cfb\u4e0b\u7684\u5750\u6807\u662f\uff08h\uff0ck\uff09\uff0c\u82e5\u70b9P\u5728\u539f\u5750\u6807\u7cfb\u4e0b\u7684\u5750\u6807\u662f \u5728\u65b0\u5750\u6807\u7cfb\u4e0b\u7684\u5750\u6807\u662f \uff0c\u5219 = \uff0c = \u3002
\u4e5d\u3001 \u6781\u5750\u6807\u3001\u53c2\u6570\u65b9\u7a0b
1\u3001 \u7ecf\u8fc7\u70b9 \u7684\u76f4\u7ebf\u53c2\u6570\u65b9\u7a0b\u7684\u4e00\u822c\u5f62\u5f0f\u662f\uff1a \u3002
2\u3001 \u82e5\u76f4\u7ebf \u7ecf\u8fc7\u70b9 \uff0c\u5219\u76f4\u7ebf\u53c2\u6570\u65b9\u7a0b\u7684\u6807\u51c6\u5f62\u5f0f\u662f\uff1a \u3002\u5176\u4e2d\u70b9P\u5bf9\u5e94\u7684\u53c2\u6570t\u7684\u51e0\u4f55\u610f\u4e49\u662f\uff1a\u6709\u5411\u7ebf\u6bb5 \u7684\u6570\u91cf\u3002
\u82e5\u70b9P1\u3001P2\u3001P\u662f\u76f4\u7ebf \u4e0a\u7684\u70b9\uff0c\u5b83\u4eec\u5728\u4e0a\u8ff0\u53c2\u6570\u65b9\u7a0b\u4e2d\u5bf9\u5e94\u7684\u53c2\u6570\u5206\u522b\u662f \u5219\uff1a \uff1b\u5f53\u70b9P\u5206\u6709\u5411\u7ebf\u6bb5 \u65f6\uff0c \uff1b\u5f53\u70b9P\u662f\u7ebf\u6bb5P1P2\u7684\u4e2d\u70b9\u65f6\uff0c \u3002
3\u3001\u5706\u5fc3\u5728\u70b9 \uff0c\u534a\u5f84\u4e3a \u7684\u5706\u7684\u53c2\u6570\u65b9\u7a0b\u662f\uff1a \u3002
3\u3001 \u82e5\u4ee5\u76f4\u89d2\u5750\u6807\u7cfb\u7684\u539f\u70b9\u4e3a\u6781\u70b9\uff0cx\u8f74\u6b63\u534a\u8f74\u4e3a\u6781\u8f74\u5efa\u7acb\u6781\u5750\u6807\u7cfb\uff0c\u70b9P\u7684\u6781\u5750\u6807\u4e3a \u76f4\u89d2\u5750\u6807\u4e3a \uff0c\u5219 \uff0c \uff0c \u3002
4\u3001 \u7ecf\u8fc7\u6781\u70b9\uff0c\u503e\u659c\u89d2\u4e3a \u7684\u76f4\u7ebf\u7684\u6781\u5750\u6807\u65b9\u7a0b\u662f\uff1a \uff0c
\u7ecf\u8fc7\u70b9 \uff0c\u4e14\u5782\u76f4\u4e8e\u6781\u8f74\u7684\u76f4\u7ebf\u7684\u6781\u5750\u6807\u65b9\u7a0b\u662f\uff1a \uff0c
\u7ecf\u8fc7\u70b9 \u4e14\u5e73\u884c\u4e8e\u6781\u8f74\u7684\u76f4\u7ebf\u7684\u6781\u5750\u6807\u65b9\u7a0b\u662f\uff1a \uff0c
\u7ecf\u8fc7\u70b9 \u4e14\u503e\u659c\u89d2\u4e3a \u7684\u76f4\u7ebf\u7684\u6781\u5750\u6807\u65b9\u7a0b\u662f\uff1a \u3002
5\u3001 \u5706\u5fc3\u5728\u6781\u70b9\uff0c\u534a\u5f84\u4e3ar\u7684\u5706\u7684\u6781\u5750\u6807\u65b9\u7a0b\u662f \uff1b
\u5706\u5fc3\u5728\u70b9 \u7684\u5706\u7684\u6781\u5750\u6807\u65b9\u7a0b\u662f \uff1b
\u5706\u5fc3\u5728\u70b9 \u7684\u5706\u7684\u6781\u5750\u6807\u65b9\u7a0b\u662f \uff1b
\u5706\u5fc3\u5728\u70b9 \uff0c\u534a\u5f84\u4e3a \u7684\u5706\u7684\u6781\u5750\u6807\u65b9\u7a0b\u662f \u3002
6\u3001 \u82e5\u70b9M \u3001N \uff0c\u5219 \u3002
\u5341\u3001 \u7acb\u4f53\u51e0\u4f55
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5\u3001 \u5408\u6bd4\u5b9a\u7406\uff1b
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7\u3001 \u5408\u5206\u6bd4\u5b9a\u7406\uff1a
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