初中知识点总结(最新)

，，．0)07,233a2a与b数aaabab0．和a(a0)a0(a0)a(a0)bc20a0，b0，c0．aaa与b11a(a．aa和bab1。0a10n1a10a：ann例如：－40700＝－4.07×104，0.000043＝4.3×10ˉ5．ab0ab,ab0ab,ab0ababaa1a;1a;1a;bbabab。a2bab。2abba(ab)cabc)abba(ab)cabc)abc)151NANaaaaaaa（aa02aaa-a（aa0a2①a6263263．∵22∴2，262.4∴aaaa33a(a0)a(a)2a(a0)a(a0)a2aa(a0)aba•b(a0,b0)abaaab(ab0)bbb11baa.amanb⑴(aannn个①aaannna0aapp系数单项式次数整式项有理式代数式多项式次数排列分式无理式3、714ab313ab5abc是6323am•aa(m,n都是正整数)nmn（a）a(m,n都是正整数)mn(ab)ab(n都是正整数)nnn(ab)(ab)ab22(ab)a2abb222(ab)a2abb222amaa(m,n都是正整数,a0)nmn1a0a0);a(a为正整数)papa1abc)b(ab)(ab)22nn1nn1扩展：nn1nn1nn1②a22abb(ab)22a2abb(ab)222扩展：1111222aa2aa或22aaa2a2同理：或1111222x2xxx22xxx2x2aba2abb2a3b3aba2abb2a3b3a2b2ab③(＋)(－＋)＝＋．④(－)(＋＋)＝－；＋＝(＋)－2，(－)＝2abab2ab2ab(＋)－4．公式拓展：⑥(xyz)xyz3xy3xy3yz3yz3xz3xz6xyz3333222222⑦xyz3xyz(xyz)(xyzxyyzxz)333222⑧xxyy(xxyy)(xxyy)42242222n(n1)⑨123(n1)n2⑩135(2n3)(2n1)n2⑾246(2n2nn(na(cd)b(cd)(ab)(cd)(pq)apq(ap)(aq)a22344ABABBbbm=aambbbaaaacacacadad;;bdbdbdbcbcaaban()(()()pnpbbnababab;cccacadbcbdbd专题二一元一次方程整式方程一元二次方程有理方程方程*高次方程分式方程*无理方程只含有一个未知数，并且未知数的最高次数是1的整式方程叫做一元一次方程，其中方程b0x为未知数，axba和baxxb①a0x．a②a③a0b00b0，，CABs+s=s;ttCAB甲乙AB甲乙sss;tt甲乙()乙()→tBss;ttt甲乙甲乙船速水速v船速水速Vv;，）水顺逆顺逆aar)n1n1比y大或或与y1axbyc111axbyc222（a，b，c，a，b，c1112224代入法或加减法消元axbyczd1111axbyczd2222axbyczd3333代入法或加减法代入法或加减法消元消元x1axbaxba01得lbba0xxaaa0xbxbaaa0a0b0b0xabxbxaxbxbabxaxbab2ax2bxc0(a0)2ax(xa)bxa是bb0xab，2xaba222abb(ab)2axx2bxb(xb)。22bxc0(a0)ax2bb42xb40)22ab42axaxbxc0(a0)2bxc0(a0)b242b42①②③④00000a00a00a00a0cc022c0a0a02bacax2bxc0(a0)xxxxxx，121212ax2n0。xx,xxnx,x112122x21x(xx)2xx2221212(xx)(xx)4xx2212121211xxxxxx⑶21xx12a1212①a(1x)baaa(1x)a(1x)bn是nnb2xxyyabPP向Paxx向yybPbPbaP点xy0点xy0点xy0点xy0点xy0点yx0点xyP点x与y相等点x与yxyx点P(，y)(y)xPx．1点P(，y)yPxy．(，)2点P(，y)(y)Px．3点点xy点yx点x2y2y．yPQ．xx．PQA(x，y)B(x，y)P(x，y)，112200xxx1220yyy0122A(x，y)B(x，y)，1122AB(xx)(yy)221212和xyxx0ybyxybb为0yxkx①k0②k0x③k0yyxyxyABOxb2S2ky图1AkOBxyyA(x，y)B(x，y)k图2l，则12xx112212函数围正比例函数一次函数随x增k>0随x增k<0k>0ybykb号yx0yxy随x0xxy随x随xyb随x随xyk和ybyyktan21xx21kxyyyb)xb21x(xx)yxx1121yxxy1ab：ykxbll//lkkbb且。l：ykxbl若l11122212121212若llkk11212ybybd0000x，yk2(k10022ykykx1xxx0xyxky(k0)xkyyOxOxxx，y随xy随xykxkk设P(，y)ykP作xyx111OAPAxyk．222kPk4k2kyPBPBOAOAxEFyaxbxc(a,b,c是常数，a0)yx2yaxbxc(a,b,c是常数，a0)2xb2ayaxbxc2xyCxCyyaxbxc(a,b,c是常数，a0)2a(xh)k(a,h,k是常数，a0)2yaxbxc与xax2bxc02和xx12ax2bxca(xx)(xx)yaxbxc212ya(xx)(xx)12、、ca①a0②a0cyc0yx①c0②c0yx③bxb)2ay①b②b0y③by2bb，(．)aab4x2xxxa2ababc4abc、、y对称轴，用处多，三种式子ayb12ab2abyaxbxcxyaxbxcy22ya(x)b(x)cya(x)b(x)c22ya(xh)k2（10）结论：①二次函数yaxbxca与xx(2yyaxbxca(yyb0；2axbxcac0。(2yyaxbxca(2a(xh)k2、x轴xxyaxxxx1212xb2a4b2y。4axxxbxxx2a12124b24abyxxx2a12性，如果在此范围内，y随x的增大而增大，则当xx时，yaxbxc22xx，当时，221yax21bxc随xxxyax21bxcxx1112yaxbxc。222yax2bxc(a,b,c是常数，0)ayy0x0x（1bbb2a4b224a（2a4ab2ay随x2a的增大而减小；在对称轴的右侧，即当y随xb2ay随x的bb2ay2a4b24a4b24ayyax2bxc(a,b,c是常数，a0)a、b、cyaaabb2accy）xb24x当x当x当xyAB）1122则x22A12120x1B32y12a0开口向上函数有最小值顶点为最低点a0开口向下函数有最大值顶点为最高点bxhx12xa2)2b()21)，24当a0xxa0xxy最值4acb24a2ayxyb0xxyyaxbxc与xxx2yaxbxc2yaxbxca2(yaxbxc2点线面角1n把1把1’112b2180A2中线角平分线高线角边<：R＝C/25:22•)；a22212。13，斜边为2。24、角平分线(即内心)。5、垂直平分线(n2)•n(n。2S③④①②③④⑤SS4b2bS=a2正方形22①②①①②③等②对称性对面积边角角线轴中对心称对称1S2梯形ABCD；；圆切线的判定圆的切线和作法直线和圆的位置关系切线的性质圆柱、圆锥的侧面展开图ACDBEFOCDABCCDCBAOBOBOAAPO点P在⊙O内；AdrO点P在⊙O上；Bd点P在⊙O外。COllllrdrdd=rdrRR和图1drR图2drdrRR图3图4图5nna2RnnPRnnABcrlCn180OAB2S2SS弓形扇形1hlr2πr、S2SS2rr(rl)2底侧n2πrl、rhl222hr、、S圆锥侧圆锥表()SSrrrl、S2底侧•ACDPOBxxxyyy定义定判定OOambnacbddabbc或bb2abcdacbddcbadbcabdacem(bdfnbdfn是和的比例中项，叫做把线段AB2（3）传递性：若△ABC∽△A’B’C’，并且△A’B’C’∽△A’’B’’C’’，则△ABC∽△bdacacdcab或bacdadbcbdbcdabdacmaacbdnbdm(0)等比性质:nbdnb推论))相似三角形△321amcmm,()bndnn⑵''''⑶''bndn''°22ca22222•a22bc2①锐角A的对边与斜边的比叫做∠A的正弦，记为，即aAcbcbAbAaAααααα01024323°222112°312326424100AA122•sinAcosA在a22bc2ababbababsinA,cosA,tanA,cotA;sinB,cosB,tanB,cotBccbacca北ih西α东lα南111SabsinCbcsinAacsinB==22211Sabch22Rcabcr22abhcA在x在βαBQP即专题六统计与概率1nx,x,,x,x(xxx)n12nn12nxnxfxfxff1ffn122kk12kxfxfxfx，这样求得的平均数xk1122kn,f,