2022年2020年小升初奥数知识点总结 .pdf

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1、1 2020 年小升初奥数知识点总结计算四则混合运算繁分数运算顺序分数、小数混合运算技巧一般而言：加减运算中，能化成有限小数的统一以小数形式；乘除运算中，统一以分数形式。带分数与假分数的互化繁分数的化简简便计算凑整思想基准数思想裂项与拆分提取公因数商不变性质改变运算顺序运算定律的综合运用连减的性质连除的性质同级运算移项的性质增减括号的性质2 变式提取公因数形如：1212.(.)nnabababaaab估算求某式的整数部分：扩缩法比较大小通分通分母通分子跟“中介”比利用倒数性质若111abc，则 cba.。形如：312123mmmnnn，则312123nnnmmm。定义新运算特殊数列求和运用相关

2、公式：21321nnn612121222nnnn21nan nnn412121222333nnnn131171001abcabcabcabcbababa221+2+3+4（n-1）+n+（n-1）+4+3+2+1=n2文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O

3、10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N

4、1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8

5、Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q

6、4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E

7、2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2

8、X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N1文档编码:CT4S2X8Y9O1 HA6B4A1Q4O10 ZT2R5G6E2N13 数论奇偶性问题奇奇=偶奇奇=奇奇偶=奇奇偶

9、=偶偶偶=偶偶偶=偶位值原则形如：abc=100a+10b+c 数的整除特征：整除数特征2 末尾是 0、2、4、6、8 3 各数位上数字的和是3 的倍数5 末尾是 0 或 5 9 各数位上数字的和是9 的倍数11 奇数位上数字的和与偶数位上数字的和，两者之差是11 的倍数4 和 25 末两位数是 4（或 25）的倍数8 和 125 末三位数是 8（或 125）的倍数7、11、13 末三位数与前几位数的差是7（或 11或 13）的倍数整除性质如果 c|a、c|b，那么 c|(ab)。文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E

10、1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1

11、 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文

12、档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P

13、9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6

14、O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y

15、3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K

16、8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y34 如果 bc|a，那么 b|a，c|a。如果 b|a，c|a，且（b,c）=1,那么 bc|a。如果 c|b,b|a,那么 c|a.a 个连续自然数中必恰有一个数能被a 整除。带余除法一般地，如果a 是整数，b 是整数（b0）,那么一定有另外两个整数q 和 r，0rb,使得 a=bq+r 当 r=0 时，我们称 a 能被 b 整除。当 r 0 时，我们称 a 不能被 b 整

17、除，r 为 a 除以 b 的余数，q 为 a 除以 b 的不完全商（亦简称为商）。用带余数除式又可以表示为ab=qr,0 rb a=bq+r 6.唯一分解定理任何一个大于 1 的自然数 n 都可以写成质数的连乘积，即n=p11a p22a.pkak约数个数与约数和定理设自然数 n 的质因子分解式如n=p11a p22a.pkak那么：n 的约数个数：d(n)=(a1+1)(a2+1).(ak+1)n 的所有约数和：（1+P1+P12+p11a）（1+P2+P22+p22a）（1+Pk+Pk2+pkak）同余定理 同余定义：若两个整数a，b 被自然数 m除有相同的余数，那么称a，b 对于模 m同

18、余，用式子表示为ab(mod m)若两个数 a，b 除以同一个数 c 得到的余数相同，则a，b 的差一定能被 c 整除。两数的和除以m的余数等于这两个数分别除以m的余数和。两数的差除以m的余数等于这两个数分别除以m的余数差。文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L

19、9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8

20、Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z

21、10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S

22、5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1

23、U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO

24、1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y35 两数的积除以m的余数等于这两个数分别

25、除以m的余数积。9完全平方数性质平方差：A2-B2=（A+B）（A-B），其中我们还得注意A+B，A-B 同奇偶性。约数：约数个数为奇数个的是完全平方数。约数个数为 3 的是质数的平方。质因数分解：把数字分解，使他满足积是平方数。平方和。10孙子定理（中国剩余定理）11辗转相除法12数论解题的常用方法：枚举、归纳、反证、构造、配对、估计几何图形平面图形多边形的内角和N边形的内角和=(N-2)180等积变形（位移、割补）三角形内等底等高的三角形平行线内等底等高的三角形公共部分的传递性极值原理（变与不变）三角形面积与底的正比关系文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1

26、U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO

27、1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV

28、2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9

29、V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:

30、CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1

31、HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 Z

32、I9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y36 S1S2=ab；S1S2=S4 S3 或者 S1S3=S2 S4 相似三角形性质（份数、比例）abchABCH ;S1S2=a2 A2 S1S3S2S4=a2b2abab;S=（a+b）2 燕尾定理SABG：SAGC SBGE：SGEC BE：EC；SBGA：SBGC SAGF：SGFC AF：FC；BCAFDGE文档编码:CO

33、1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV

34、2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9

35、V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:

36、CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1

37、HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 Z

38、I9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编

39、码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y37 SAGC：SBCG SADG：SDGB AD：DB；差不变原理知 5-2=3，则圆点比方点多3。隐含条件的等价代换例如弦图中长短边长的关系。组合图形的思考方法化整为零先补后去正反结合立体图形规则立体图形的表面积和体积公式不规则立体图形的表面积整体观照法体积的等积变形水中浸放

40、物体：V升水=V物测啤酒瓶容积：V=V空气+V水三视图与展开图最短线路与展开图形状问题染色问题几面染色的块数与“芯”、棱长、顶点、面数的关系。文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L

41、9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8

42、Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z

43、10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S

44、5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1

45、U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO

46、1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y38 典型应用题植树问题开放型与封闭型间隔与株数的关系方阵问题外层边长数-2=内层边长数（外层边长数-1）4=外周长数外层边

47、长数 2-中空边长数 2=实面积数列车过桥问题车长+桥长=速度时间车长甲+车长乙=速度和相遇时间车长甲+车长乙=速度差追及时间列车与人或骑车人或另一列车上的司机的相遇及追及问题车长=速度和相遇时间车长=速度差追及时间年龄问题差不变原理鸡兔同笼假设法的解题思想牛吃草问题文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档

48、编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9

49、E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O

50、1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3文档编码:CO1Z10K8P9E1 HV2S5L9O6O1 ZI9V1U8Y1Y3