____ _. ___ 53-54.pdf

...

.. 2553-2554

...

.. 2553-2554

ISBN 978-616-202-598-3

.. 2555

2,000

2/931- 10800 0-2587-31370-2587-3295

(

.. 2553-2554)

.. 2553-2554

(

..2553-2554)

.. 2553-2554

3

1...

..2553-2554

2...

..2553-2554

3 ...

..2553-2554

(

..2553-2554)

.. 2553-2554

........................................................7

..2553

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..2553

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..2553

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..2553

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..2554

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..2554

.........................................................81

..2554

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..2554

.. 2553

.. 2553

.. 2553

.. 2553

23 .. 2553 9.30 .-11.30 .

1. () 5

2

2. 30 120

3

1 1 10 3 30 2 11 20 4 40 3 21 30 5 50 3. 1 -

4.

5.

6.

7. 1

8.

... ( 2553) : 10

1. ...84,90120

2. 9

3. 91125

4. 5654

5.

6. A = B = AB =

7. 5, 4, 3, 2 4, 3, 2, 1

11

8.

9. m 10 5 n 10 2 3m-2n 5 pp+3

10. ABC

ABC ()

1 1-10 3

11 .. 2553-2554 :

11. 2,000 1,400 20%

30%

12.

13. 5

12

(pi)

14.AB,AC=8.BC=6.

DABDABACE DE(2)

15. ABCD AB=50BC=40 ECD ADE

16. 4

311

7 x 7

17. ADABCPQ , RSBC

PQRSADMN

AM = MN = ND PQSR24

ABC

18. 3

19. a, b, c 3 2x 3x kx 12 03 2x 3x kx 12 03 2x 3x kx 12 0x 3x kx 12 0 x 3x kx 12 0 x 3x kx 12 0 k a b 6a b 6 a b 6 20. k y 2x k 0y 2x k 0y 2x k 0y 2x k 0 y 2x k 0 2 2x y 202 2x y 202 2 2 2 2 2x y 20 x y 202 2x y 202 2 2 2x y 202 2

0, 2 , 3 , 4 , 5 , 6 , 7

a,b,c

2 11-20 4

... ( 2553) : 12

22. 67723 22 yxykxyx k

23. 3 1 14

24. O 34 AB CD X AB 2 2532 2532 253 OX 10 CX XD

25. 10321032 100

26. 26. bba, 00201201,...,44,33,22,1111AA a bb AA b a , 4ba ba,

27. N 1......21! NNNN 12345!5 !100...!7!6!5!4!3!2!1 A C A D

10A C +C +C D

28. n Sum(n) n Sum(976) = 9+7+6 = 22

1287714714714714 16

1161

21

41

21

81

41

161

81

n

Sum(n)

29. yx, z 20724860808610 zyxzxyzxyxyz zyx 432

30. 2009 bad a d c dcb c b a

4991111 badadcdcbcba

cba

dbad

cadc

bdcb

a

22.

k

21. 7 (

722 )

3 21-30 5

*******************************

.. 2553

.. 2553

... ( 2553) : 14

1. ... 84, 90 120

237

10157)5

304521)3

604542)2

1209084)2

... 2375322 2520 2520 2. 9

1002319171311753223,19,17,13,11,7,5,3,2

100 3. 91125

1

3)3

9)3

27)3

81)3

243)3

729)3

3645)518225)5

91125)5

4533591125

333333555911253

45

92, 3, 5, 7, 11 , 13, 17, 19, 23

2+3+5+7+11+13+17+19+23=100

1. ... 84, 90 120

237

10157)5

304521)3

604542)2

1209084)2

... 2375322 2520

2520

2. 9

100

92, 3, 5, 7, 11 , 13, 17, 19, 23

2+3+5+7+11+13+17+19+23=100

3. 91125

1

3)3

9)3

27)3

81)3

243)3

729)3

3645)518225)5

91125)5

4533591125

333333555911253

45

15 .. 2553-2554 :

4. 5 654 5 99999

5911318189932703459654

152(99999)654

99999 591 = 99408 99408 5. ABCD

48AB 50AC

2

222

222

222

1419698248504850

4850BC

BC4850BCABAC

14BC . 1448ABCD 672 2 672 2

A B

CD

1308

4. 5 654

5 99999

5911318189932703459654

152(99999)654

99999 591 = 99408 99408

1308

ABCDAB=48AC=505.

A B

CD

ABCDAB=48AC=50AC=50AC

... ( 2553) : 16

6. A = 932 xx B = 932 xx AB = cbxax 24 cba 932 xxA

9181,9,1819

9811839

39399393

93

24

224

222

22

22

2

cbacba

xxxxx

xx

xxxxxxxxAB

xxB

91 7. N 5, 4, 3, 2 4, 3, 2, 1 N

11 45 pN

1282334

NrNqN

1N 60

539540194554415331522151115015

1115

1155

11

160601

NN

aa

aaaaa

aaNaNaN

539


9181,9,1819

9811839

39399393

93

24

224

222

22

22

2

cbacba

xxxxx

xx

xxxxxxxxAB

xxB

91 7. N 5, 4, 3, 2 4, 3, 2, 1 N

11 45 pN

1282334

NrNqN

1N 60

539540194554415331522151115015

1115

1155

11

160601

NN

aa

aaaaa

aaNaNaN

539


9181,9,1819

9811839

39399393

93

24

224

222

22

22

2

cbacba

xxxxx

xx

xxxxxxxxAB

xxB

91 7. N 5, 4, 3, 2 4, 3, 2, 1 N

11 45 pN

1282334

NrNqN

1N 60

539540194554415331522151115015

1115

1155

11

160601

NN

aa

aaaaa

aaNaNaN

539

2 S + 1

45 pN

1282334

NrNqN

1N 60

1115

1155

11

160601

aaNaNaN

53954054011

NNN

539

2 S + 1

6. A = 932 xx B = 932 xx AB = cbxax 24 cba

932 xxA

9181,9,1819

98118 3 9

3 9 3 9 9 3 9 3

93

24

224

22 2 2 2 2 2

2

cbacba

xxxxx

x x x x x x x x x x AB

xxB

91

5a - 1 = 0 ; a =5a - 1 = 11 ; a =5a - 1 = 22 ; a =

5a - 1 = 33 ; a =

5a - 1 = 44 ; a =

15125235345455

7. 5,4,3,24,3,2,1

11

17 .. 2553-2554 :

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

8. 76x

2142

x

x

22

2 121x

xx

x

222 1242142

xx

xx

42169

4284852

4285

42424936

267

76

7612

76

76

1276

2

2

169498436672

7642

7612

7642

2142

x

x = 169

169

1 2

... ( 2553) : 18

9. m 10 5 n 10 2 3m-2n 5

p p+3 am

10 5 510 am

...15303 am .. bn

10 2 210 bn

...4202 bn . - ; 11203023 banm 12465 ba nm 23 5 1 P = 1 P+3 = 4 4 10. ABC 4:5:2:: CABCAB ABC CFBEAD :: () BECAADBCCFAB ...

xCAxBCxABCABCAB

4,5,24:5:2::

BExADxCFx 452

10:5:4::2:1:5:4:452

CFBEADCFBEBEAD

BEADCF

4:5:10

A

D

E F

BC

9. m 10 5 n 10 2 3m-2n 5

p p+3 am

10 5 510 am

...15303 am .. bn

10 2 210 bn

...4202 bn . - ; 11203023 banm 12465 ba nm 23 5 1 P = 1 P+3 = 4 4 10. ABC 4:5:2:: CABCAB ABC CFBEAD :: () BECAADBCCFAB ...

xCAxBCxABCABCAB

4,5,24:5:2::

BExADxCFx 452

10:5:4::2:1:5:4:452

CFBEADCFBEBEAD

BEADCF

4:5:10

A

D

E F

BC

10. ABCABCABC AB : BC : CA = 2 : 5 : 4 ABC (AD : BE : CF)()

ABCF = BCAD = CABE

19 .. 2553-2554 :

11. 2,000 1,400 20% 30% %5

000,2)914((000,2

000,2)60030()400,120(

5 5 12. 2 2x 2x 2 x 2x 10 x 0

2 2 2

2

2 2

x 2x 2 x 2x 10 x2 x 2x 10 2x

x 2x 10 x x 5

5

11. 2,000 1,400 20% 30% %5

000,2)914((000,2

000,2)60030()400,120(

5 5 12. 2 2x 2x 2 x 2x 10 x 0

2 2 2

2

2 2

x 2x 2 x 2x 10 x2 x 2x 10 2x

x 2x 10 x x 5

5

%5000,2

)914((000,2000,2

)60030()400,120(

5

11.2,0001,400

20%30%

x2 + 2x - 2 x2 - 2x + 10 = x2 2 x2 - 2x + 10 = 2x x2 - 2x + 10 = x2 x = 5

5

... ( 2553) : 20

355

h

12

5126056012

1212

5

rh

hr

hr

512602 rrrr

r r 12 60 5

2 rr

35

321 r

351260

925

5

9200

40 5 9

9 = 200

200

13.321 5

12

(pi)

21 .. 2553-2554 :

14. ABC AB 8, ACAB . 6BC .

D AB D AB AC E DE ( 2 )

366468 22 AB 10100 5 BDAD AED ~ ABC

BCAC

DE5

68

75.3830 DE ..

3.75 15. ABCD 50AB 40BC

E CD EACCAB ADE

1. AE CF AE F AFCABC 2. EFCEDA ( 90 ) CFAD FECDEA () CFEADE (...) xCEAE 50

9160010025004050

22

222

xxxxxx

.. 94021 ADE

= 180 180

E

D

A

C B

40

x

40

B

CD

F

E

A



366468 22 AB 10100 5 BDAD AED ~ ABC

BCAC

DE5

68

75.3830 DE ..

3.75 15. ABCD 50AB 40BC

E CD EACCAB ADE


9160010025004050

22

222

xxxxxx

.. 94021 ADE

= 180 180

E

D

A

C B

40

x

40

B

CD

F

E

A



366468 22 AB 10100 5 BDAD AED ~ ABC

BCAC

DE5

68

75.3830 DE ..

3.75 15. ABCD 50AB 40BC

E CD EACCAB ADE


9160010025004050

22

222

xxxxxx

.. 94021 ADE

= 180 180

E

D

A

C B

40

x

40

B

CD

F

E

A



366468 22 AB 10100 5 BDAD AED ~ ABC

BCAC

DE5

68

75.3830 DE ..

3.75 15. ABCD 50AB 40BC

E CD EACCAB ADE


9160010025004050

22

222

xxxxxx

.. 94021 ADE

= 180 180

E

D

A

C B

40

x

40

B

CD

F

E

A



366468 22 AB 10100 5 BDAD AED ~ ABC

BCAC

DE5

68

75.3830 DE ..

3.75 15. ABCD 50AB 40BC

E CD EACCAB ADE


9160010025004050

22

222

xxxxxx

.. 94021 ADE

= 180 180

E

D

A

C B

40

x

40

B

CD

F

E

A



366468 22 AB 10100 5 BDAD AED ~ ABC

BCAC

DE5

68

75.3830 DE ..

3.75 15. ABCD 50AB 40BC

E CD EACCAB ADE


9160010025004050

22

222

xxxxxx

.. 94021 ADE

= 180 180

E

D

A

C B

40

x

40

B

CD

F

E

A

22

A

14.AB,AC=8.AC=8.AC BC=6.BC=6.BC=6

DABDABACACAC E

DE(2)DE(2)DE

.



366468 22 AB 10100 5 BDAD AED ~ ABC

BCAC

DE5

68

75.3830 DE ..

3.75 15. ABCD 50AB 40BC

E CD EACCAB ADE


9160010025004050

22

222

xxxxxx

.. 94021 ADE

= 180 180

E

D

A

C B

40

x

40

B

CD

F

E

A



366468 22 AB 10100 5 BDAD AED ~ ABC

BCAC

DE5

68

75.3830 DE ..

3.75 15. ABCD 50AB 40BC

E CD EACCAB ADE


9160010025004050

22

222

xxxxxx

.. 94021 ADE

= 180 180

E

D

A

C B

40

x

40

B

CD

F

E

A

(..)

... ( 2553) : 22

16. 4 3 1 1 77

35

!4!3!4567

!4!3!7

35

35

!4!3!4567

!4!3!7

35

16. 4

3

117 X 7

23 .. 2553-2554 :

17. AD ABC PQ , RS BC

PQ RS AD M N

SR

QP

N

M

B D C

A

AM = MN = ND PQSR 24 ABC

.. PQSR

21

2421

RSPQMN

72

723482

1BC:AD

2

1

348BCAD

48BC3

2

3

2AD

3

1

48RS2

3MN

48RSPQMN

17. AD ABC PQ , RS BC PQ RS AD M N

SR

QP

N

M

B D C

A AM = MN = ND PQSR 24 ABC

.. PQSR

21

2421

RS PQ MN

72

MN !MN " PQ + RS( ) = 48

MN 32

RS = 48#$%

&

'(

13

AD#$%

&

'( 32

"23

BC#$%

&

'( = 48

AD ) BC = 48" 312

AD BC = 12" 48" 3 = 72

RS

!MN " PQ + RS( ) = 48

MN 32

RS = 48#$%

&

'(

13

AD#$%

&

'( 32

"23

BC#$%

&

'( = 48

AD ) BC = 48" 312

AD BC = 12" 48" 3 = 72

= 48

!MN " PQ + RS( ) = 48

MN 32

RS = 48#$%

&

'(

13

AD#$%

&

'( 32

"23

BC#$%

&

'( = 48

AD ) BC = 48" 312

AD BC = 12" 48" 3 = 72

AD BC = 48 x 3

!MN " PQ + RS( ) = 48

MN 32

RS = 48#$%

&

'(

13

AD#$%

&

'( 32

"23

BC#$%

&

'( = 48

AD ) BC = 48" 312

AD BC = 12" 48" 3 = 72

= 48

!MN " PQ + RS( ) = 48

MN 32

RS = 48#$%

&

'(

13

AD#$%

&

'( 32

"23

BC#$%

&

'( = 48

AD ) BC = 48" 312

AD BC = 12" 48" 3 = 72

... ( 2553) : 24

18. 30,2,3,4,5,6,7

0 6 5 1 = 30 0 5 5 3 = 75 30+75=105

105

19.a, b, cx3 - 3x2 + kx - 12 = 0kkk a b = - 6

-16

20. k y - 2x - k = 0x2 + y2 = 20

y = 2x + kx2 + y2 = 20x2 + 4x2 + 4kx + k2 k2 k - 20 = 0

5x2 + 4kx + k2 k2 k - 20 = 0

16 k2k2k - 20 (k2 k2 k - 20) = 0 16k2 k2 k - 20 (k2 k2 k - 20) = 0 k = 10k = 10k k = 10k = 10k

10

25 .. 2553-2554 :

21. 7

( 722 )

= 2 .. + ..

196308

1414777222

= 504 504

21. 7

( 722 )

= 2 .. + ..

196308

1414777222

= 504 504

21. 7

( 722 )

= 2 .. + ..

196308

1414777222

= 504 504

21. 7 (

722 )

= 504

504

= 2+

= (2 X

21. 7

( 722 )

= 2 .. + ..

196308

1414777222

= 504 504

X 7 X 7) + (14 X 14)

= 308 + 196= 504

... ( 2553) : 26

22. 67723 22 yxykxyx

k 67723 22 yxykxyx

3,

32

03230673637637

37,7,2

73,3,6

3333

2

2

22

C

CCCCCCCCCB

BDACADBCkADBC

BCBDyBxACyADyAxyxCxyDxCDyxBAyx

2;3 BC 7 BDAC ...723 DA

DA 2

kADAD

D

DDDD

DD

DD

51631,2

2,23

02320672

762

726

2

2

5

22. 67723 22 yxykxyx

k 67723 22 yxykxyx

3,

32

03230673637637

37,7,2

73,3,6

3333

2

2

22

C

CCCCCCCCCB

BDACADBCkADBC


2;3 BC 7 BDAC ...723 DA

DA 2

kADAD

D

DDDD

DD

DD

51631,2

2,23

02320672

762

726

2

2

5

22. 67723 22 yxykxyx

k 67723 22 yxykxyx

3,

32

03230673637637

37,7,2

73,3,6

3333

2

2

22

C

CCCCCCCCCB

BDACADBCkADBC


2;3 BC 7 BDAC ...723 DA

DA 2

kADAD

D

DDDD

DD

DD

51631,2

2,23

02320672

762

726

2

2

5

22. 67723 22 yxykxyx

k 67723 22 yxykxyx

3,

32

03230673637637

37,7,2

73,3,6

3333

2

2

22

C

CCCCCCCCCB

BDACADBCkADBC


2;3 BC 7 BDAC ...723 DA

DA 2

kADAD

D

DDDD

DD

DD

51631,2

2,23

02320672

762

726

2

2

5

22. 67723 22 yxykxyx

k 67723 22 yxykxyx

3,

32

03230673637637

37,7,2

73,3,6

3333

2

2

22

C

CCCCCCCCCB

BDACADBCkADBC


2;3 BC 7 BDAC ...723 DA

DA 2

kADAD

D

DDDD

DD

DD

51631,2

2,23

02320672

762

726

2

2

5

22. 67723 22 yxykxyx

k 67723 22 yxykxyx

3,

32

03230673637637

37,7,2

73,3,6

3333

2

2

22

C

CCCCCCCCCB

BDACADBCkADBC


2;3 BC 7 BDAC ...723 DA

DA 2

kADAD

D

DDDD

DD

DD

51631,2

2,23

02320672

762

726

2

2

5

3x2 + kxy - 2y2 - 7x + 7y - 6

= (3x + Ay + B)(x + Dy + C)

= 3x2 + 3xyD + 3xC + Axy + ADy2 + ACy + Bx + BDy + BC

BC = -6, 3D + A = k, 3C + B = - 7

AD = - 2, AC + BD = 7,

B = - 7 - 3C

(- 7 - 3C) C = - 6

- 7C - 3C2 = - 6

3C2 + 7C - 6 = 0

(3C - 2) (C + 3) = 0

C = 2 , - 3

C = - 3 ; B = 2 AC+BD=7

- 3A + 2D = 7 ...

22. 67723 22 yxykxyx

k 67723 22 yxykxyx

3,

32

03230673637637

37,7,2

73,3,6

3333

2

2

22

C

CCCCCCCCCB

BDACADBCkADBC


2;3 BC 7 BDAC ...723 DA

DA 2

kADAD

D

DDDD

DD

DD

51631,2

2,23

02320672

762

726

2

2

5

A =

22. 67723 22 yxykxyx

k 67723 22 yxykxyx

3,

32

03230673637637

37,7,2

73,3,6

3333

2

2

22

C

CCCCCCCCCB

BDACADBCkADBC


2;3 BC 7 BDAC ...723 DA

DA 2

kADAD

D

DDDD

DD

DD

51631,2

2,23

02320672

762

726

2

2

5

22. 67723 22 yxykxyx

k 67723 22 yxykxyx

3,

32

03230673637637

37,7,2

73,3,6

3333

2

2

22

C

CCCCCCCCCB

BDACADBCkADBC


2;3 BC 7 BDAC ...723 DA

DA 2

kADAD

D

DDDD

DD

DD

51631,2

2,23

02320672

762

726

2

2

5

3

27 .. 2553-2554 :

10

17253

X

O

A

B

CD

P

23. 3 1 14 266, 662, 626, 356, 365, 536, 563, 635, 653, 446, 464, 644, 455, 545, 554

15 24. O 34 AB

CD X AB 2 253 OX 10 CX XD

18964253

8253,8253,8

362532892

XBAXXDCXXBAXPX

OP

189

25. 10321032 100 1032 100 32 21032 100 24 31032 100 68 41032 100 76 10321032 100 76 76

10

17253

X

O

A

B

CD

P

23. 3 1 14 266, 662, 626, 356, 365, 536, 563, 635, 653, 446, 464, 644, 455, 545, 554

15 24. O 34 AB


18964253

8253,8253,8

362532892

XBAXXDCXXBAXPX

OP

189

25. 10321032 100 1032 100 32 21032 100 24 31032 100 68 41032 100 76 10321032 100 76 76

10

17253

X

O

A

B

CD

P

23. 3 1 14 266, 662, 626, 356, 365, 536, 563, 635, 653, 446, 464, 644, 455, 545, 554

15 24. O 34 AB


18964253

8253,8253,8

362532892

XBAXXDCXXBAXPX

OP

189

25. 10321032 100 1032 100 32 21032 100 24 31032 100 68 41032 100 76 10321032 100 76 76

10

17253

X

O

A

B

CD

P

23. 3 1 14 266, 662, 626, 356, 365, 536, 563, 635, 653, 446, 464, 644, 455, 545, 554

15 24. O 34 AB


18964253

8253,8253,8

362532892

XBAXXDCXXBAXPX

OP

189

25. 10321032 100 1032 100 32 21032 100 24 31032 100 68 41032 100 76 10321032 100 76 76

10

17253

X

O

A

B

CD

P

23. 3 1 14 266, 662, 626, 356, 365, 536, 563, 635, 653, 446, 464, 644, 455, 545, 554

15 24. O 34 AB


18964253

8253,8253,8

362532892

XBAXXDCXXBAXPX

OP

189

25. 10321032 100 1032 100 32 21032 100 24 31032 100 68 41032 100 76 10321032 100 76 76

23. 3 1 14

266, 662, 626, 356, 365, 536, 563, 635, 653, 446, 464, 644, 455, 545, 554

15

10

17253

XX

O

A

B

CD

P

18964253

8253,8253,8

362532892

XBAXXDCXXBAXPX

OP

189

24.O 34 AB CD

XAB OX10

CXXD

... ( 2553) : 28

26. ba, 0201,...,4,3,2,1A a b A

ba, 4ba ba, 1 ba 2010,2009,...,4,3,3,2,2,1 2009,2010,...,3,42,3,1,2 401822009 2ba 2010,2008,...5,3,4,2,3,1 2008,2010,...,3,5,2,4,1,3 401620082 3ba 2010,2007,...,6,3,5,2,4,1 2007,2010,...,3,6,2,5,1,4 401420072 4ba 2006,2010,...,3,7,2,2,1,52010,2006,...7,3,6,2,5,1 401220062 0ba 2010,2010,...,3,3,2,2,1,1 2010 = 4018 + 4016 + 4014 + 4012 + 2010 18070 27. N 1...21! NNNN 12345!5

!100...!7!6!5!4!3!2!1 A C A D

10A C + D

1! = 1 6! = 720 2! = 2 7! = 5,040 3! = 6 8! = 40,320 4! = 24 9! = 362,880 5! = 120 10! = 3,628,800 11! 1! + 2!++10! 913 C = 3 913 1 10 1 D = 1 413 DC 4

26. ba, 0201,...,4,3,2,1A a b A


!100...!7!6!5!4!3!2!1 A C A D

10A C + D

1! = 1 6! = 720 2! = 2 7! = 5,040 3! = 6 8! = 40,320 4! = 24 9! = 362,880 5! = 120 10! = 3,628,800 11! 1! + 2!++10! 913 C = 3 913 1 10 1 D = 1 413 DC 4

26. ba, 0201,...,4,3,2,1A a b A


!100...!7!6!5!4!3!2!1 A C A D

10A C + D

1! = 1 6! = 720 2! = 2 7! = 5,040 3! = 6 8! = 40,320 4! = 24 9! = 362,880 5! = 120 10! = 3,628,800 11! 1! + 2!++10! 913 C = 3 913 1 10 1 D = 1 413 DC 4

26. ba, 0201,...,4,3,2,1A a b A


!100...!7!6!5!4!3!2!1 A C A D

10A C + D

1! = 1 6! = 720 2! = 2 7! = 5,040 3! = 6 8! = 40,320 4! = 24 9! = 362,880 5! = 120 10! = 3,628,800 11! 1! + 2!++10! 913 C = 3 913 1 10 1 D = 1 413 DC 4

26. ba, 0201,...,4,3,2,1A a b A


!100...!7!6!5!4!3!2!1 A C A D

10A C + D

1! = 1 6! = 720 2! = 2 7! = 5,040 3! = 6 8! = 40,320 4! = 24 9! = 362,880 5! = 120 10! = 3,628,800 11! 1! + 2!++10! 913 C = 3 913 1 10 1 D = 1 413 DC 4

26. ba, 0201,...,4,3,2,1A a b A


!100...!7!6!5!4!3!2!1 A C A D

10A C + D

1! = 1 6! = 720 2! = 2 7! = 5,040 3! = 6 8! = 40,320 4! = 24 9! = 362,880 5! = 120 10! = 3,628,800 11! 1! + 2!++10! 913 C = 3 913 1 10 1 D = 1 413 DC 4

26. ba, 0201,...,4,3,2,1A a b A


!100...!7!6!5!4!3!2!1 A C A D

10A C + D

1! = 1 6! = 720 2! = 2 7! = 5,040 3! = 6 8! = 40,320 4! = 24 9! = 362,880 5! = 120 10! = 3,628,800 11! 1! + 2!++10! 913 C = 3 913 1 10 1 D = 1 413 DC 4

26. ba, 0201,...,4,3,2,1A a b A


!100...!7!6!5!4!3!2!1 A C A D

10A C + D

1! = 1 6! = 720 2! = 2 7! = 5,040 3! = 6 8! = 40,320 4! = 24 9! = 362,880 5! = 120 10! = 3,628,800 11! 1! + 2!++10! 913 C = 3 913 1 10 1 D = 1 413 DC 4

26. ba, 0201,...,4,3,2,1A a b A


!100...!7!6!5!4!3!2!1 A C A D

10A C + D

1! = 1 6! = 720 2! = 2 7! = 5,040 3! = 6 8! = 40,320 4! = 24 9! = 362,880 5! = 120 10! = 3,628,800 11! 1! + 2!++10! 913 C = 3 913 1 10 1 D = 1 413 DC 4

26. ba, 0201,...,4,3,2,1A a b A


!100...!7!6!5!4!3!2!1 A C A D

10A C + D

1! = 1 6! = 720 2! = 2 7! = 5,040 3! = 6 8! = 40,320 4! = 24 9! = 362,880 5! = 120 10! = 3,628,800 11! 1! + 2!++10! 913 C = 3 913 1 10 1 D = 1 413 DC 4

29 .. 2553-2554 :

28. n Sum(n)

n Sum(976) = 9+7+6 = 22

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

Sum(n)

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

1 1 1 116 16 2 2

1 18 16

2

(7 )(28 1)(14 7 )(14 7 )n(14 7 )

14 7 189sum(189) 18

18 29. yx, z

20724860808610 zyxzxyzxyxyz zyx 432 20724860808610 zyxzxyzxyxyz 25524804860808610 zyxzxyzxyxyz 291181086 zyx yx, z 98,76 yx 1110 z 118,86 yx 2910 z

897694432193,2

zyxzyx

89

28. n Sum(n)

n Sum(976) = 9+7+6 = 22

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

Sum(n)

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

1 1 1 116 16 2 2

1 18 16

2

(7 )(28 1)(14 7 )(14 7 )n(14 7 )

14 7 189sum(189) 18

18 29. yx, z


897694432193,2

zyxzyx

89

28. n Sum(n)

n Sum(976) = 9+7+6 = 22

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

Sum(n)

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

1 1 1 116 16 2 2

1 18 16

2

(7 )(28 1)(14 7 )(14 7 )n(14 7 )

14 7 189sum(189) 18

18 29. yx, z


897694432193,2

zyxzyx

89

28. n Sum(n)

n Sum(976) = 9+7+6 = 22

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

Sum(n)

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

1 1 1 116 16 2 2

1 18 16

2

(7 )(28 1)(14 7 )(14 7 )n(14 7 )

14 7 189sum(189) 18

18 29. yx, z


897694432193,2

zyxzyx

89

28. n Sum(n)

n Sum(976) = 9+7+6 = 22

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

Sum(n)

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

1 1 1 116 16 2 2

1 18 16

2

(7 )(28 1)(14 7 )(14 7 )n(14 7 )

14 7 189sum(189) 18

18 29. yx, z


897694432193,2

zyxzyx

89

28. n Sum(n)

n Sum(976) = 9+7+6 = 22

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

Sum(n)

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

1 1 1 116 16 2 2

1 18 16

2

(7 )(28 1)(14 7 )(14 7 )n(14 7 )

14 7 189sum(189) 18

18 29. yx, z


897694432193,2

zyxzyx

89

28. n Sum(n)

n Sum(976) = 9+7+6 = 22

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

Sum(n)

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

1 1 1 116 16 2 2

1 18 16

2

(7 )(28 1)(14 7 )(14 7 )n(14 7 )

14 7 189sum(189) 18

18 29. yx, z


897694432193,2

zyxzyx

89

28. n Sum(n)

n Sum(976) = 9+7+6 = 22

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

Sum(n)

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

1 1 1 116 16 2 2

1 18 16

2

(7 )(28 1)(14 7 )(14 7 )n(14 7 )

14 7 189sum(189) 18

18 29. yx, z


897694432193,2

zyxzyx

89

28. n Sum(n)

n Sum(976) = 9+7+6 = 22

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

Sum(n)

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

1 1 1 116 16 2 2

1 18 16

2

(7 )(28 1)(14 7 )(14 7 )n(14 7 )

14 7 189sum(189) 18

18 29. yx, z


897694432193,2

zyxzyx

89

28. n Sum(n)

n Sum(976) = 9+7+6 = 22

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

Sum(n)

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

1 1 1 116 16 2 2

1 18 16

2

(7 )(28 1)(14 7 )(14 7 )n(14 7 )

14 7 189sum(189) 18

18 29. yx, z


897694432193,2

zyxzyx

89

28. n Sum(n)

n Sum(976) = 9+7+6 = 22

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

Sum(n)

1 1 1 1 11 1 1 18 16 8 16 164 2 4 2n (14 7 )(14 7 )(14 7 )(14 7 )(7 )(28 1)

1 1 1 116 16 2 2

1 18 16

2

(7 )(28 1)(14 7 )(14 7 )n(14 7 )

14 7 189sum(189) 18

18 29. yx, z


897694432193,2

zyxzyx

89

x = 2, y = 3 z = 19

... ( 2553) : 30

30. 2009 badadcdcbcba


cba

dbad

cadc

bdcb

a

1233

2009499

32009

baddcba

adcdcba

dcbdcba

cbadcba

dcba

1231111 badc

adcb

dcba

cbad

bad

cadc

bdcb

acba

d = 119

119



cba

dbad

cadc

bdcb

a

1233

2009499

32009

baddcba

adcdcba

dcbdcba

cbadcba

dcba

1231111 badc

adcb

dcba

cbad

bad

cadc

bdcb

acba

d = 119

119



cba

dbad

cadc

bdcb

a

1233

2009499

32009

baddcba

adcdcba

dcbdcba

cbadcba

dcba

1231111 badc

adcb

dcba

cbad

bad

cadc

bdcb

acba

d = 119

119



cba

dbad

cadc

bdcb

a

1233

2009499

32009

baddcba

adcdcba

dcbdcba

cbadcba

dcba

1231111 badc

adcb

dcba

cbad

bad

cadc

bdcb

acba

d = 119

119



cba

dbad

cadc

bdcb

a

1233

2009499

32009

baddcba

adcdcba

dcbdcba

cbadcba

dcba

1231111 badc

adcb

dcba

cbad

bad

cadc

bdcb

acba

d = 119

119

(a+b+c)+(b+c+d)+(c+d+a)+(d+a+b) = 2009 a+b+c+d = a+b+c+d = 2009

(a+b+c+d) x 1 1 1 1

()()()()()b()ba()ad()da()ad()dc()cd()dc()cb()bc()cb()ba()a ()()()()()()()()()()() = 32009

499

3

.. 2553

.. 2553

.. 2553

.. 2553

6 .. 2553 9.30 . - 11.30 .

1. () 6

2

2. 30 120

3

1 1 10 3 30 2 11 20 4 40 3 21 30 5 50 3. 2 -

4.

5.

6.

7. 1

8.

... ( 2553) : 34

1. 1 0.5

0.75

2. n 24 + 27 + 2n n 3. ABC E AB ECA = BCA

47

D AC BD CBE BD CE P BC = BP = CP BAC

4. A 0,0 , B 5,0 , C 5,5 , D 0,5 ABCD E (0, 2) F CD EF ABCD 2 EF X P

PAEA

5. ABCD BE = 4 DF = 6

6

4

F

E

A

D C

B

AEF 25 ABCD

6. 3 2 (ab)c, a(bc) 4 5 (a(bc))d,

((ab)c)d, (ab)(cd), a((bc)d), a(b(cd)) 5 7. abc2)ac(ca)cb(bc)ba(ab 8. d,c,b,a 0dcba 1cb,1da 2222

31bdac

)cdab(23 9. x )12x)(x4(2y y 10. 2, 3, 4, 6 9 346 692 ( 23496

23469 ) 11.

505500,,

10023,

10032,

10041

12. a, b

4bxx

ax4xx)x(f 2

223

a 5 , b 5

(a, b) f (1) = 0

1 1-10 3

35 .. 2553-2554 :

6. 3 2 (ab)c, a(bc) 4 5 (a(bc))d,


31bdac

)cdab(23 9. x )12x)(x4(2y y 10. 2, 3, 4, 6 9 346 692 ( 23496

23469 ) 11.

505500,,

10023,

10032,

10041

12. a, b

4bxx

ax4xx)x(f 2

223

a 5 , b 5

(a, b) f (1) = 0

6. 3 2 (ab)c, a(bc) 4 5 (a(bc))d,


31bdac

)cdab(23 9. x )12x)(x4(2y y 10. 2, 3, 4, 6 9 346 692 ( 23496

23469 ) 11.

505500,,

10023,

10032,

10041

12. a, b

4bxx

ax4xx)x(f 2

223

a 5 , b 5

(a, b) f (1) = 0

13. ABC BAC

oY'

X'

BXA

Y

C

AB AC X Y XX YY 6AB ( = 3.14)

14. ABC D BC DAB = DAC AB = 5 AC = 6 AD = 4 BD DC 15. AP AD C 7 P D

BD 24 BC // AP () ( 227 ) 16. x

320104x2553320104x2553

x201048x2553x201048x2553

25x4x2 17. a, b, c 03x27x8x 23

cb

bc

ca

ac

ab

ba

18. P(x)

x1PxP

x1PxP

1615

21P

, 8180

31P

P(1) + P(2) + P(3) + P(4)

P

D

C

BA

13. ABC BAC

oY'

X'

BXA

Y

C



BD 24 BC // AP () ( 227 ) 16. x

320104x2553320104x2553

x201048x2553x201048x2553

25x4x2 17. a, b, c 03x27x8x 23

cb

bc

ca

ac

ab

ba

18. P(x)

x1PxP

x1PxP

1615

21P

, 8180

31P

P(1) + P(2) + P(3) + P(4)

P

D

C

BA

2 11-20 4

... ( 2553) : 36

13. ABC BAC

oY'

X'

BXA

Y

C



BD 24 BC // AP () ( 227 ) 16. x

320104x2553320104x2553

x201048x2553x201048x2553

25x4x2 17. a, b, c 03x27x8x 23

cb

bc

ca

ac

ab

ba

18. P(x)

x1PxP

x1PxP

1615

21P

, 8180

31P

P(1) + P(2) + P(3) + P(4)

P

D

C

BA

19. c,b,a 6cba 18cba 222 4cba abc9

20. 3

323232 )13x7x(8)20x9x()6x5x(

ba ... a b 1 a + b

21. 20092008

2009

200820081A 2

22 103A

22. n 1255325532553 81624 n2 n

23. ABC AB = 108 BC = 1009 CA = 1043

O ABC AOB

24. P Q R S ABCD BD AB P Q BD P Q R S CD R S P R 4 Q S ABCD ba b ba

R

Q

PS

CB

DA


20. 3

323232 )13x7x(8)20x9x()6x5x(

ba ... a b 1 a + b

21. 20092008

2009

200820081A 2

22 103A

22. n 1255325532553 81624 n2 n

23. ABC AB = 108 BC = 1009 CA = 1043

O ABC AOB


R

Q

PS

CB

DA

3 21-30 5

37 .. 2553-2554 :


20. 3

323232 )13x7x(8)20x9x()6x5x(

ba ... a b 1 a + b

21. 20092008

2009

200820081A 2

22 103A

22. n 1255325532553 81624 n2 n

23. ABC AB = 108 BC = 1009 CA = 1043

O ABC AOB


R

Q

PS

CB

DA

25. ABCD 999 PABC, QABD, RACD SBCD ABCD PQRS

26. b,a 1. abba 2. aaa 3. baabbaba 6*8 27. n 99

10n9n)1(

541

431

321

21149

9n

28. z,y,x w

10373xyzw8)wzyx()wzyx(2 222224444 wxzwyzxy

29. nn37 n 30. ABCDE A CD,BC DE 3293

4628 3588 A BE *******************************

.. 2553

.. 2553

... ( 2553) : 40

1. 1 0.5 0.75

t

0 5t 0 75t 1000t 800

. .

800 2. n 24 + 27 + 2n n 24 + 27 + 2n = 24 (1+ 23 + 2n-4 ) = 24 (9 + 2n-4 ) = 24 (9 + 28-4 ) = 24 (25) 8 3. ABC E AB ECA = BCA

47


P

DE

B C

A BC = BP = CP PCB = PBC = 60 BCA = 80 CBA = 60 CAB = 180 140 = 40

40

1. 1 0.5 0.75

t

0 5t 0 75t 1000t 800

. .


47


P

DE

B C


40

1. 1 0.5 0.75

t

0 5t 0 75t 1000t 800

. .


47


P

DE

B C


40

1. 1 0.5 0.75

t

0 5t 0 75t 1000

t 800 0 5t 0 75t 1000 0 5t 0 75t 1000

t 800t 8000 5t 0 75t 1000. .0 5t 0 75t 10000 5t 0 75t 1000 0 5t 0 75t 1000. .0 5t 0 75t 1000 0 5t 0 75t 1000

800

2. n 2 2 4 + 27 + 2n n 24 + 27 + 2n = 24 (1+ 23 + 2n-4 ) = 24 (9 + 2n-4 ) = 24 (9 + 28-4 ) = 24 (25)

3. ABC E AB ECA = BCA47


P

DE

B C

A BC = BP = CP PCB = PBC = 60 BCA = 80 CBA = 60 CCAABB = 180 140 = 40 = 180 140 = 40

40

n(a+2n-4)

n=8

8

41 .. 2553-2554 :


PAEA

2,0 CD 3,5F ABCD 2 3,5,2,0

5032

0x2y

51

PAEA

PAEA = 6

6 5. ABCD BE = 4 DF = 6

6

4

F

E

A

D C

B

AEF 25 ABCD

x BC y DC .. xy4x6y

21y2x3AEF

xy74xy224y4x6xyy4x650

xy24y4x6xy21y2x325

74 74

3

32

2

A (0,0)

B (0,5)

D (5,0)

E (0,2)

C (5,5)

F

P X

Y


PAEA

2,0 CD 3,5F ABCD 2 3,5,2,0

5032

0x2y

51

PAEA

PAEA = 6

6 5. ABCD BE = 4 DF = 6

6

4

F

E

A

D C

B

AEF 25 ABCD

x BC y DC .. xy4x6y

21y2x3AEF


xy24y4x6xy21y2x325

74 74

3

32

2

A (0,0)

B (0,5)

D (5,0)

E (0,2)

C (5,5)

F

P X

Y


PAEA

2,0 CD 3,5F ABCD 2 3,5,2,0

5032

0x2y

51

PAEA

PAEA = 6

6 5. ABCD BE = 4 DF = 6

6

4

F

E

A

D C

B

AEF 25 ABCD

x BC y DC .. xy4x6y

21y2x3AEF


xy24y4x6xy21y2x325

74 74

3

32

2

A (0,0)

B (0,5)

D (5,0)

E (0,2)

C (5,5)

F

P X

Y


PAEA

2,0 CD 3,5F ABCD 2 3,5,2,0

5032

0x2y

51

PAEA

PAEA = 6

6 5. ABCD BE = 4 DF = 6

6

4

F

E

A

D C

B

AEF 25 ABCD

x BC y DC .. xy4x6y

21y2x3AEF


xy24y4x6xy21y2x325

74 74

3

32

2

A (0,0)

B (0,5)

D (5,0)

E (0,2)

C (5,5)

F

P X

Y


PAEA

2,0 CD 3,5F ABCD 2 3,5,2,0

5032

0x2y

51

PAEA

PAEA = 6

6 5. ABCD BE = 4 DF = 6

6

4

F

E

A

D C

B

AEF 25 ABCD

x BC y DC .. xy4x6y

21y2x3AEF


xy24y4x6xy21y2x325

74 74

3

32

2

A (0,0)

B (0,5)

D (5,0)

E (0,2)

C (5,5)

F

P X

Y


PAEA

2,0 CD 3,5F ABCD 2 3,5,2,0

5032

0x2y

51

PAEA

PAEA = 6

6 5. ABCD BE = 4 DF = 6

6

4

F

E

A

D C

B

AEF 25 ABCD

x BC y DC .. xy4x6y

21y2x3AEF


xy24y4x6xy21y2x325

74 74

3

32

2

A (0,0)

B (0,5)

D (5,0)

E (0,2)

C (5,5)

F

P X

Y


PAEA

2,0 CD 3,5F ABCD 2 3,5,2,0

5032

0x2y

51

PAEA

PAEA = 6

6 5. ABCD BE = 4 DF = 6

6

4

F

E

A

D C

B

AEF 25 ABCD

x BC y DC .. xy4x6y

21y2x3AEF


xy24y4x6xy21y2x325

74 74

3

32

2

A (0,0)

B (0,5)

D (5,0)

E (0,2)

C (5,5)

F

P X

Y


PAEA

2,0 CD 3,5F ABCD 2 3,5,2,0

5032

0x2y

51

PAEA

PAEA = 6

6 5. ABCD BE = 4 DF = 6

6

4

F

E

A

D C

B

AEF 25 ABCD

x BC y DC .. xy4x6y

21y2x3AEF


xy24y4x6xy21y2x325

74 74

3

32

2

A (0,0)

B (0,5)

D (5,0)

E (0,2)

C (5,5)

F

P X

Y

4. A 0 , 0 , B 5 , 0 , C 5 , 5 , D 0 , 5 ABCD E (0, 2)

3

32

2

A (0,0) (0,0)

B (0,5)

D (5,0)

E (0,2)

C (5,5)

F

P X

Y 2,0 CD 3 , 5 F ABCD 2

3,5,2,0

5032

0x2y

51

PAEA

PAEA = 6

6

= xy

= xy

= 2xy

74 = xy

.. ABCD = AEF + ADF + FCE + ABE

FCDEFABCD2

EFXP

... ( 2553) : 42

6. 3 2 (ab)c, a(bc) 4 5 (a(bc))d,

((ab)c)d, (ab)(cd), a((bc)d), a(b(cd)) 5 (abcd)e 6 ((ab)(cd))e, (ab)((cd)e), ((a(bc))d)e, (a((bc)d))e, (((ab)c)d)e,

(a(b(cd)))e

a(bcde) 6 a((bc)(de)), (a(bc))(de) , a(((bc)d)e), a(b(c(de))), (a((bc)d)e), a((b(cd))e)

((ab)c)(de), (ab)(c(de)) 14 7. abc2)ac(ca)cb(bc)ba(ab abc2)ac(ca)cb(bc)ba(ab

)ba)(cb)(ca(

cabcbab)ca(

ca)cba(b)ca()ac(ca)bcab)(cba(

)ac(ca)cba(bc)cba(ab

2

)ba)(cb)(ca(

6. 3 2 (ab)c, a(bc) 4 5 (a(bc))d,


(a(b(cd)))e



)ba)(cb)(ca(

cabcbab)ca(



2

)ba)(cb)(ca(

6. 3 2 (ab)c, a(bc) 4 5 (a(bc))d,


(a(b(cd)))e



)ba)(cb)(ca(

cabcbab)ca(



2

)ba)(cb)(ca(

6. 3 2 2 (ab)c, a(bc)

4 5 (a(bc))d, ((ab)c)d, (ab)(cd), a((bc)d), a(b(cd)) 5 (abcd)e 6 ((ab)(cd))e, (ab)((cd)e), ((a(bc))d)e, (a((bc)d))e, (((ab)c)d)e, (a(b(cd)))e


((ab)c)(de), (ab)(c(de)) 14

7. abc2)ac(ca)cb(bc)ba(ab abc2)ac(ca)cb(bc)ba(ab

)ba)(cb)(ca(

ca bc b ab )ca( ca ) c b a ( b )ca()ac(ca)bcab)(cba(


2

)ba)(cb)(ca(

= ab (a+b)+bc(b+c)+ca(c+a)+abc+abc

43 .. 2553-2554 :

8. d,c,b,a 0dcba 1cb,1da 2222 31bdac

)cdab(23

98

3111

bdaccbdacdab2

222222

0dcba 0cdab

322cdab

)cdab(23 = 4 4 9. x )12x)(x4(2y y

x = 4 )12x)(x4(2y 128 128

10. 2, 3, 4, 6 9 346 692 ( 23496

23469 ) 54321 = 120 346 321 = 6 692 321 = 6 346 692 1 2, 3, 4, 6, 9 346 692 120 - 13 = 107 107


)cdab(23

98

3111

bdaccbdacdab2

222222

0dcba 0cdab

322cdab

)cdab(23 = 4 4 9. x )12x)(x4(2y y

x = 4 )12x)(x4(2y 128 128

10. 2, 3, 4, 6 9 346 692 ( 23496

23469 ) 54321 = 120 346 321 = 6 692 321 = 6 346 692 1 2, 3, 4, 6, 9 346 692 120 - 13 = 107 107


)cdab(23

98

3111

bdaccbdacdab2

222222

0dcba 0cdab

322cdab

)cdab(23 = 4 4 9. x )12x)(x4(2y y

x = 4 )12x)(x4(2y 128 128

10. 2, 3, 4, 6 9 346 692 ( 23496

23469 ) 54321 = 120 346 321 = 6 692 321 = 6 346 692 1 2, 3, 4, 6, 9 346 692 120 - 13 = 107 107


)cdab(23

98

3111

bdaccbdacdab2

222222

0dcba 0cdab

322cdab

)cdab(23 = 4 4 9. x )12x)(x4(2y y

x = 4 )12x)(x4(2y 128 128

10. 2, 3, 4, 6 9 346 692 ( 23496

23469 ) 54321 = 120 346 321 = 6 692 321 = 6 346 692 1 2, 3, 4, 6, 9 346 692 120 - 13 = 107 107


)cdab(23

98

3111

bdaccbdacdab2

222222

0dcba 0cdab

322cdab

)cdab(23 = 4 4 9. x )12x)(x4(2y y

x = 4 )12x)(x4(2y 128 128

10. 2, 3, 4, 6 9 346 692 ( 23496

23469 ) 54321 = 120 346 321 = 6 692 321 = 6 346 692 1 2, 3, 4, 6, 9 346 692 120 - 13 = 107 107

8. d,c,b,a 0dcba da 22 )cdab(23

1cb 22 31bdac

98

31 1 1 2

0dcba 0cdab

322cdab

)cdab(23 = 4 4


)cdab(23

98

3111

bdaccbdacdab2

222222

0dcba 0cdab

322cdab

)cdab(23 = 4 4 9. x )12x)(x4(2y y

x = 4 )12x)(x4(2y 128 128

10. 2, 3, 4, 6 9 346 692 ( 23496

23469 ) 54321 = 120 346 321 = 6 692 321 = 6 346 692 1 2, 3, 4, 6, 9 346 692 120 - 13 = 107 107

8. d , c , b , a 0 d c b a 1 c b , 1 d a

2 2 2 2

3

1

bd ac

) cd ab ( 2 3

9

8

3

1

1 1

bd ac c b d a cd ab

2

2 2 2 2 2 2

0 d c b a

0 cd ab

3

2 2

cd ab

) cd ab ( 2 3 = 4

4

9. x ) 12 x )( x 4 ( 2 y y

x = 4 ) 12 x )( x 4 ( 2 y 128

128

10. 2, 3, 4, 6 9

346 692 ( 23496

23469 )

54321 = 120

346 321 = 6

692 321 = 6

346 692 1

2, 3, 4, 6, 9 346 692

120 - 13 = 107

107

9. x )12x)(x4(2y y x = 4 )12x)(x4(2y 128 128

10. 2, 3, 4, 6 9 346 692 ( 23496

23469 ) 54321 = 120 346 321 = 6 692 321 = 6 346 692 1 2, 3, 4, 6, 9 346 692 120 - 13 = 107 107 107

1 ,

... ( 2553) : 44

11.

505500,,

10023,

10032,

10041

505500,,

10023,

10032,

10041

5001005500,,

310053,

210052,

110051

67531005 1 500 3, 5, 67

1675

500

2673

500

3353

500

767500

1005

500

1663

500

3 5 67 500 = 237 500 237 = 263 263 12. a, b

4bxx

ax4xx)x(f 2

223

a 5 , b 5

(a, b) f (1) = 0

3 2 2 2

21 1 4 a a 4f (1) 0

1 b 4 b 5

a2 4 = 0 a = 2, -2 b = -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 (a,b) 20 20

67

10

2

6633

4

131

53 3

5

67

11. 505500,,

10023,

10032,

10041

505500,,

10023,

10032,

10041

5001005

500,,31005

3,21005

2,11005

1

67531005 1 500 3, 5, 67

1675

500

2673

500

3353

500

767500

1005

500

1663

500

3 5 67 500 = 237 500 237 = 263 263

10

2

6633

4

131

3 3 3 5

67 67

45 .. 2553-2554 :

13. ABC BAC

oY'

X'

BXA

Y

C


114 14. ABC D BC DAB = DAC AB = 5 AC = 6 AD = 4 BD DC

ABC AD E CE ABD AEC AB AD AB AC AD AE AD(AD DE)

AE AC

2 2AB AC AD DE AD AD BD CD 56 = 42 + BDDC BDDC = 14

14

4

5

6

D

C

A

E

B

O r rYOXO 90YOX YOX ~ CAB 2r .. = )22(

41 .. YXO

= 22214

41

= 2 = 3.14 2 = 1.14 = 114

r

r

6x

y

C

BA

x'

Oy'

13. ABC BAC

oY'

X'

BXA

Y

C




AE AC


14

4

5

6

D

C

A

E

B


41 .. YXO

= 22214

41

= 2 = 3.14 2 = 1.14 = 114

r

r

6x

y

C

BA

x'

Oy'

13. ABC BAC

oY'

X'

BXA

Y

C




AE AC


14

4

5

6

D

C

A

E

B


41 .. YXO

= 22214

41

= 2 = 3.14 2 = 1.14 = 114

r

r

6x

y

C

BA

x'

Oy'

13. ABC BAC

oY'

X'

BXA

Y

C




AE AC


14

4

5

6

D

C

A

E

B


41 .. YXO

= 22214

41

= 2 = 3.14 2 = 1.14 = 114

r

r

6x

y

C

BA

x'

Oy'

ABCADECE

56=42+BDDC

BDDC=14

14

13. ABC BAC

oY'

X'

BXA

Y

C AB AC X Y XX YY 6AB ( = 3.14)

114

O O r

rYOXO 90YOX

YOX ~ CAB 2r .. = )22(

41 .. YXO

= 2221 4

41

= 2 = 3.14 2 = 1.14 = 114

r

r

6x

y

C

BA

x'

Oy'

14. ABC D BC DAB = DAC AB = 5 AC = 6 AD = 4 BD DC

ABD AEC AB AD AB AC AD AE AD(AD DE)AE AC

AB AC AD AE AD(AD DE) AB AC AD AE AD(AD DE) 2 2AB AC AD DE AD AD BD CD 2 2 2 2AB AC AD DE AD AD BD CD AB AC AD DE AD AD BD CD2 2AB AC AD DE AD AD BD CD2 2 2 2AB AC AD DE AD AD BD CD2 2

4

5

6

D

A

E

B

ABCADECE

56=4 56=4 56=4 56=4 56=4 56=4 56=4 56=42+BDDC

BDDC=14 BDDC=14 BDDC=14 BDDC=14 BDDC=14E BDDC=14E

14

ABCADECEABCADECE

c

... ( 2553) : 46

15. AP AD C 7 P D BD 24 BC // AP ()

( 227

)

CP CD P D 90 BC E 25FP BF PC

2,205

.. 21APCB

BCAP721

2592549721

.. 27360

90PCE

= 4941

.. = 259 38.5 = 220.5 2,205

P

D

C

BA

AF = X

49xAB

49xAB

2

22

ADAP

24x48x2

492x1x22x492x1x

492x2425x

C

BA

E

F

P

725

7 7

24 D

15. AP AD C 7 P D BD 24 BC // AP ()

( 227

)


2,205

.. 21APCB

BCAP721

2592549721

.. 27360

90PCE

= 4941

.. = 259 38.5 = 220.5 2,205

P

D

C

BA

AF = X

49xAB

49xAB

2

22

ADAP

24x48x2

492x1x22x492x1x

492x2425x

C

BA

E

F

P

725

7 7

24 D

15. AP AD C 7 P D BD 24 BC // AP () ( 22

7 )

P

D

C

BA


.. 21APCB

BC AP 721

259 25 49 721

.. 2 7 360

90PCE = 49

41

.. = 259 38.5 = 220.5 2,205

AF = AF = X

49xAB

49xAB

2

22

ADAP

24x48x2

492x1x22x492x1x

492x2425x

C

BA

E

F

P

725

7 7

24 D

2,205

47 .. 2553-2554 :

16. X 320104x2553320104x2553

x201048x2553x201048x2553

25x4x2

34x

x48x

345

21324212x25x4x

16x09x16x0144x7x

x4x144x3

22

2

2

345 17. a, b, c 03x27x8x 23

cb

bc

ca

ac

ab

ba

a b c a c b

b a a c b c a a b b c c

b c a c a b

1 1 1 1 1 1a b cb c a c a b

1 1 1 1 1 1 1 1 1a b c 3a b c a b c a b c

1 1 1 bc ac aba b c 3 a b c 3a b c abc

27 8 3 693

69

Documents

____ _. ___ 53-54.pdf