Mathimatika A Gymnasioy

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Σχολικά Βοηθήματα (Τσουκάλες)

Transcript of Mathimatika A Gymnasioy

2008 41 & , . 210 3608065, Fax: 210 3608197 www.volonaki.gr, e-mail: info@volonaki.gr : : : , . 35, , . 26510 20069 , . ISBN 978-960-381-391-0

. . . . : 3 . : , , , , , ( ) , ( ). , , . , , . , 20/06/2008

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: 1: 1.1 - ............................ 16 1.2 , ................. 28 1.3 ........................................................................... 39 1.4 ....................................................................................... 49 1.5 . . . . . . ............................................................................. 57

2:

2.1 ................................................................................. 74 2.2 ..................................................................................... 82 2.3 ..................................................................................... 93 2.4 ............................................................ 101 2.5 ...................................................................... 113 2.6 ..................................................................................... 121

3:

3.1 ....................................................................................... 136 3.2 ...... 147 3.3 ............................................ 156 3.4 ........................................................ 157 3.5 ........................................................................................ 160

4:

4.1 : + x = , x = , x = , x = , : x = x : = ............................................................... 178 4.2 .................................................................................. 187

5:

5.1 ......................................................................................................... 198 5.2 ............................................................................... 208

11 6: 6.1 .................................................................. 224 6.2 ..................................................................... 229 6.3 ................................................. 233 6.4 ......................................................... 237 6.5 ................................................................................. 244 6.6 ........................................................................... 247

7:

7.1 ( ) ............................................................................................... 254 7.2 ............................ 258 7.3 ............................................................................. 264 7.4 .............................................................................. 269 7.5 ............................................................................... 273 7.6 .................................................................... 279 7.7 .................................................................... 283 7.8 ...................................................287 7.9 ................................................. 291 7.10 ................................... 297

: 1.1 ......................................................................................................... 302 1.2 .......................................................................................................309 1.3 , ............................................................ 316 1.4 ....................................... 321 1.5 , ....................... 327 1.6 ..................................................................... 331 1.7 ...................................... 335 1.8 ......................................................................................... 341 1.9 ........................................................................... 349 1.10 .......................... 353 1.11 .................................................................. 357

1:

121.12 .................................................................................................. 362 1.13 ........................................................................... 367

2:

2.1 ............................................................................... 378 2.2 ......................................................................................... 382 2.3 ........................................................... 385 2.4 ............................................................................. 391 2.5 ......................................................................................... 393 2.6 .............................. 396

3: ,

3.1 .......................................... 406 3.2 .......................................... 411 3.3 .......................................................................................... 419 3.4 .................................................................. 424

& ............................. 437

-

15

1

1, 2, 3, 4, 5, 6, 7, 8, ...99, 100

16

1

1.1

.

1, 2 , 3 , 4 , 5 , ... , 99 , 100 , 101 , 102 ,... , 999 , 1000 ,... . () (). 2 . 0 , 2 , 4 , 6 , 8 1, 3 , 5 ,7 , 9.

: 0 , 2 , 4 ,, 10 ,... , 102 ,... , 998 , ..., 2004 ,... :1, 3 , 5 ,... , 11,... , 205 ,... , 999 ,... , 2007 ,... N N 1 N + 1 . 0 ( 1), . N , : : A N = 6 (), N 1 = 5 ()

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N + 1 = 7 (). A N = 55 (), N 1 = 54 () N + 1 = 56 (). 0,1,2,3,4,5,6, 7, 8, 9. () ., , , ...:254.897

7 , 9 , 8 , 4 , 5 , 2 .

.. : > . < = . .

, . .:100 > 89 , 1010 > 1000 , 500 = 500

0 0 .

18

1

. . 0 1 2 3 4

, , ..,. : 0 , 1, 2 , 3 , 4 . : 13.637 . 6 3 , 6 13.600 . 5 , 6 , 7 , 8 , 9 . : 13.637 . 3 6 , 3 4 14.000 .

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9 , 0 1.:202.987 .

9 1 0 2 3 . 203.000 . , ,...

1. : . 455 , . 203 , . 860 , . 2007 .

, 2 .

. 455 227 2 + 1 , 2 . . 203 101 2 + 1 , 2 . . 860 430 2 , 2 . . 2007 1003 2 + 1 , 2 .

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1

2. . 2 9 . . 2 9 . : = + 1 . ( , ) : = 1. : = . .: 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 . ,: = 9 2 +1 = 8 .

. : 3 , 4 , 5 , 6 , 7 , 8 . ,: = 9 2 1 = 6 .

3. : . 400 4.000 , . 789 987 , . 10.100 10.010 .

. , , . . 400 4.000 ,:400 < 4.000 .

.: 7 < 9 .:789 < 987 .

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. , 8 > 0 ,:80.800 > 80.080 .

4.. 4.402, 4.204, 4.420 ,4.240 .

. 50.500, 50.005, 50.050, 55.000. ( ) ( ) , . .( 4 ). , 4.402 4.420 4.204 4.240 . ,: 4.402 < 4.420 4.204 < 4.240 .

:4.420 > 4.402 > 4.240 > 4.204 .

., :50.005 < 50.050 < 50.500 < 55.000 .

5. 5 , 35 , 65 95 : . , .

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1

,,,10 1. 5 , 5 5 ( 10 ). , 35 5 (40),655(70) 95 5 (100). 6. : . : 196959 , : 4.344m , : 1.255 , : 1020kg ,

2651095637 . . ; . . , , , , , . . , . . 1.300 , 2 5 . 4.300m , 3 4 . 1.000kg, 0 2 .

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23

13. 1.. 205 . 732 . 20.813 .

2. .. .. .. 3. 289 288 , 287 286, 290 291 . 4.,:3.508 > 3.515 > 3.620 > 4.800 > 4.801

5.. 45 = 45

. 38 > 36

. 456 < 465

. 8.765 < 8.970 . 90.876 < 86.945 . 345 < 5.690

6.

2cm 0 1 2

3 4

5

6

7 8

= 2cm 1 , 6cm : 6cm = 3 3, 2cm 3 .

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1

,,,( = 10cm , = 12cm , = 14cm ) 5 , 6 , 7 . 7. .().1o 0 , . .(). 0 2 4 , . .(). .().1 1,1 2 ,2 3 ,2 4 , 1 (1) 9 (5), 2 , 4 , 6 , 8 , . .(). . (). 7 , 7 , 8 = 7 + 1 ,. .(). .(). .(). 75 , 375 . .(). .(). 1.275 . .(). 2.025 . 8. 345 300 , 4 . 761 800 , 6 . 659 700 ,

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5 . 2.567 2.600 , 6 . 9.532 9.500 , 3 . 123.564 123.600 , 6 . 34.564 34.600 , 6 . 31.549 31.500 , 4 . 8.765 8.800 , 6 . 9.. 7.568.350 ,9. . 7.568.300 , 4 . . 7.568.000 , 3 . . 7.570.000 , 8 . . 7.600.000 , 6 .

1.()().

26

1

.11 24 12 . () . 3 . () . 23 26 . () . 26 14 6 > 4 . () . . () .1 0 ,. () .. () 2..:22, 567 , 1.453 , 1.921,49.870 , 567.532 , 1.234.709 .

.,, . 3..: 233 , 8455 ,332 , 1234 , 700 , 12 , 0 , 32.459 .

. . 4.. 5 500 .

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. 21 2007. 5.( >, =, < ) :34 .. 43 457 ..0457 1.234 .. 1.324 6.010 .. 6.001 4.568 .. 4.659 5.944 .. 59.440

6..: 3.124 , 1.243 , 4.312,4.213 , 2.134 , 2.431 , 1.234 .

.: 5.678 , 6.786 , 8.576 ,8.765 , 5.687 , 6.587 , 7.685 .

7. . 5 , 6 , 7 . . . . .. 8. 50 5