目錄

第1講分數數列計算....................................................................................................................................................1

內容概述..........................................................................................................................................................................1

典型問題..........................................................................................................................................................................1

提高篇...........................................................................................................................................................1

拓展篇...........................................................................................................................................................3

超越篇...........................................................................................................................................................6

第2講比例解應用題................................................................................................................................................8

內容概述..........................................................................................................................................................................8

典型問題..........................................................................................................................................................................8

提高篇...........................................................................................................................................................8

拓展篇.........................................................................................................................................................10

第3講方程解應用題..............................................................................................................................................15

內容概述........................................................................................................................................................................15

典型問題........................................................................................................................................................................15

第4講濃度問題與經濟問題................................................................................................................................22

內容概述........................................................................................................................................................................22

典型問題........................................................................................................................................................................22

第5講立體幾何....................................................................................................................................................28

內容概述........................................................................................................................................................................28

典型問題........................................................................................................................................................................29

提高篇.........................................................................................................................................................29

拓展篇.........................................................................................................................................................31

超越篇.........................................................................................................................................................34

第6講邏輯推理（二）........................................................................................................................................36

內容概述........................................................................................................................................................................36

典型問題........................................................................................................................................................................37

提高篇.........................................................................................................................................................37

拓展篇.........................................................................................................................................................39

超越篇.........................................................................................................................................................42

第7講幾何綜合（一）........................................................................................................................................44

內容概述........................................................................................................................................................................44

典型問題........................................................................................................................................................................45

提高篇.........................................................................................................................................................45

拓展篇.........................................................................................................................................................47

超越篇.........................................................................................................................................................50

第8講數論綜合（一）........................................................................................................................................52

內容概述........................................................................................................................................................................52

典型問題........................................................................................................................................................................53

提高篇.........................................................................................................................................................53

拓展篇.........................................................................................................................................................55

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超越篇.........................................................................................................................................................58

第9講計算綜合（二）..........................................................................................................................................59

內容概述........................................................................................................................................................................59

典型問題........................................................................................................................................................................59

第十講行程問題（六）........................................................................................................................................67

內容概述........................................................................................................................................................................67

典型問題........................................................................................................................................................................67

提高篇.........................................................................................................................................................68

拓展篇.........................................................................................................................................................70

超越篇.........................................................................................................................................................73

第11講不定方程...................................................................................................................................................75

內容概述........................................................................................................................................................................75

典型問題........................................................................................................................................................................75

提高篇.........................................................................................................................................................75

拓展篇.........................................................................................................................................................78

超越篇.........................................................................................................................................................81

第12講進位制與取整符號..................................................................................................................................83

內容概述........................................................................................................................................................................83

典型問題........................................................................................................................................................................83

第13講應用題綜合（一）..................................................................................................................................91

內容概述........................................................................................................................................................................91

典型問題........................................................................................................................................................................91

提高篇.........................................................................................................................................................91

拓展篇.........................................................................................................................................................94

超越篇.........................................................................................................................................................98

第14講計數綜合（三）....................................................................................................................................101

內容概述......................................................................................................................................................................101

典型問題......................................................................................................................................................................101

提高篇......................................................................................................................................................101

拓展篇......................................................................................................................................................103

超越篇......................................................................................................................................................106

第15講幾何綜合（二）....................................................................................................................................108

內容概述......................................................................................................................................................................108

典型問題......................................................................................................................................................................108

提高篇......................................................................................................................................................108

拓展篇......................................................................................................................................................111

超越篇......................................................................................................................................................114

第16講最值問題（二）....................................................................................................................................117

內容概述......................................................................................................................................................................117

典型問題......................................................................................................................................................................117

提高篇......................................................................................................................................................117

拓展篇......................................................................................................................................................119

超越篇......................................................................................................................................................122

第17講應用題綜合（二）................................................................................................................................125

內容概述......................................................................................................................................................................125

典型問題......................................................................................................................................................................125

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提高篇......................................................................................................................................................125

拓展篇......................................................................................................................................................127

超越篇......................................................................................................................................................131

第18講數論綜合（二）....................................................................................................................................134

內容概述......................................................................................................................................................................134

典型問題......................................................................................................................................................................134

提高篇......................................................................................................................................................134

拓展篇......................................................................................................................................................136

超越篇......................................................................................................................................................139

第19講數字謎綜合（二）..................................................................................................................................141

內容概述......................................................................................................................................................................141

典型問題......................................................................................................................................................................141

提高篇......................................................................................................................................................141

拓展篇......................................................................................................................................................143

乙組的數□甲組的數○1=..........................................................................................................................................145

超越篇......................................................................................................................................................147

第20講計數綜合（四）......................................................................................................................................150

內容概述......................................................................................................................................................................150

典型問題......................................................................................................................................................................150

提高篇......................................................................................................................................................150

拓展篇......................................................................................................................................................152

超越篇......................................................................................................................................................155

第21講構造論證（二）....................................................................................................................................158

內容概述......................................................................................................................................................................158

典型問題......................................................................................................................................................................158

第22講數論綜合（三）....................................................................................................................................167

內容概述......................................................................................................................................................................167

典型問題......................................................................................................................................................................167

第23講概率初步................................................................................................................................................174

內容概述......................................................................................................................................................................174

典型問題......................................................................................................................................................................174

提高篇......................................................................................................................................................174

拓展篇......................................................................................................................................................177

超越篇......................................................................................................................................................180

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第1講分數數列計算

內容概述

建立抵消的思想，特別是靈話運用裂項的方法求解一些分數數列的計算問題．

典型問題

提高篇

111111111

1．計算：

1223344556677889910

22221111

2．計算：3.計算：

133557979924466898100

1111111111111

4.計算：.5.計算

612203042567290428701309700

1

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56677889910

6.計算：

56677889910

35791113151719

7.計算：

2612203042567290

2222

8.計算：

1232343459899100

151119209239

9.計算：

261220210240

2

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111111

3．計算：(1)(1)(1)(1)(1)(1)

223399

拓展篇

111111

1．計算：

122334455620072008

33333

2．計算：

2558811111498101

4812162024

3．計算：

133557799111113

3

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111111111

4．計算：(1)1357911131517;

2612203042567290

46810121416182076788082

(2)

132435465768798109113739384039414042

5．計算：

23410

1

1(12)(12)(123)(123)(1234)(129)(12910)

31123397598392356899899

6．計算：7.計算：

261220380420144771097100

4

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11111

8.計算：

224246246824620

1111

9.計算：

123234345484950

45611111

10.計算：11.計算：(1)(1)(1)

12323434589102232992

1111

12.計算：(1)(1)(1)(1)

13243520072009

5

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超越篇

12222232182192192202

1.計算：

122318191920

22142118212021

2.計算：.

22142118212021

241618

3.已知算式(1)(2)(8)(9)的結果是一個整數，那么它的末兩位數字是多少？

351719

35737

4.計算：

123234345181920

6

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12399

5.計算：（最后結果可以用階乘表示）

2!3!4!100!

11111

6.已知A,B，請比較A和B的大小。

88292102642

3!14!25!3102!100

7.計算：