สอวน57 มอ..pdf
TRANSCRIPT
-
23 2557
1
( ..)
1 30 3
1.
=
+
+
2.
( )
= 8
= 45
3.
( ) ( )
4. ( )
=
( )
.
5.
-
2
6. =
( )
7. ( )
23 2557 ( ..) .
-
(.. 2557) 3
8.
=
=
=
= 15
9.
10. =
3,024
-
4 (.. 2557)
11. = 60
12. 10 8 8 6 6 4 4 2 2 0
13. 10 2 4 9 4499449949, 94949494 6
-
(.. 2557) 5
14. = ( ) = { | = }
15. 5 = {0, 2, 4, 6} = {1, 3, 5, 7} = { | = } = { | = }
16. A 13,500 B 10,000 7% A 20% B 15%
-
6 (.. 2557)
17. 10 50% 30% 20% 10 15% 10%
18. 5 2 14 3 5 17 4 5
19. 50 3 50 1 2
+ 1 = 9 50 1
-
(.. 2557) 7
20. ( ) = ( ) ( ) ( ) = 12 ( )
21. = = ,
22. = 1 = 7 = 2 =
= 5
-
8 (.. 2557)
23. = 0 1 3 4 2 , , ,
24. ABCD AB // CD AD = CD = BC 3B D = B D C D
25. TBC DAT 1:2 AB
A B
C
D
T
4
60 30
-
(.. 2557) 9
26. O AB C C BA E EC D DE = OA C B : D A
27. ABCDEFGH BG, DG BD BFCG, CDHG ABCD AB = 4 C BDG
28. Q Q Q 2 7 Q Q 1 2014
A B
C D
E F
G H
Q
-
10 (.. 2557)
29. 6 1 6 2
30. A, B, C, X, Y, Z 8 A X A Z
A
B
C
X Y Z
3 3 5
7 5 4
8 5 6
-
(.. 2557) 11
2 2 5 1. ABC AE, BF CD
FH = AE FH // AE BH HE BH = DC
2. 10 20 ( )
A B
C
D
E F
H
-
12 (.. 2557)
1. 146 9. 282 17. 0.65 25. 4 + 2 2. 9 10. 18. 14 26. 3 : 1 3. 64 11. 45 19. 626 27. 24 + 8 4. 121 12. 59 20.
28. 2010
5. 101 13. 4,444,444,494 21. 10 29.
6. 0.25 14. 2172.5 22. 11 30.
7. 4 15. 5 23.
1. -
8. 10 16. 18640.80 24. 22.5 2.
1. 146 = 4 + + 2 = 4 + + 2 = (4 + 1 + 2) = ( ) =
= 146
2. 9 = ( ) ( ) = ( )( ) = ( )( ) = 9( ) 9( ) = = ( ) = = 25 = = ( ) = 9
3. 64 = ( ) = ( )( ) ( )( ) = ( ) = = ( ) = = (3 + 1)(3 + 1)(3 + 1) = (4)(4)(4) = 64
4. 121 = 0
= 1
= 256 = 0 11 = 11 ( ) = ( ) = 121
5. 101 = ( ) = ( ) ( ) ( ) ( )( ) ( ) = ( )
( ) = ( ) (
) ( ) ( )
256 =
( ) = ( ) (
) ( ) ( )
0 = + + + +
-
(.. 2557) 13
= = = 101
6. 0.25
=
( )
( )
( )
( )
( )
=
( )( )
( )( )
( )( )
( )( )
( )( ) 2
1 99 , 2 98 , 3 97 9 51 ( 50 )
( )( )
( )( ) =
( )( ) =
( ( )( ) ) ( )( )
( )( ) =
( ) ( )( )
( )( )
= ( )( )
( )( ) =
( ( )( ))
( )( ) = 2
( )( )
( )( ) =
( )( ) =
( ) ( )( )
( )( )
= ( )( )
( )( ) =
( ( )( ))
( )( ) = 2
2 2 0 9 1 1 = 2
=
= 1
=
=
= 2 1 2 = 1 ( ) = (
)
=
= 0.25
7. 4 = 9 9 4 238 4 2 9 = 9 4 2537 4 1 = 2 ( ) = (9 ) = 4 2014 4 2 4 =
8. 10 = 15 , = 15 =
( ) ( ) ( ) ( )
= ( )
( ) =
= 10
9. 282 = ( )( ) = ( )( )( ) = ( )( )( )( ) = (257)( )( )( ) = 257 + 17 + 5 + 3 = 282
-
14 (.. 2557)
10. 1 , , , = ( )
=
( )
(2)
=
(1)
=
= 2(1007)
1007 = 19 53 2(1007) 2 : 1007 = 2 + 1007 = 1009
11. 45
60 =
=
60
60 = 2 2 3 5 1
2, 2, 3, 5
( 2 5
=
=
)
1: 3 3 2: 5 3 3: 2 2 ( ) 2 ( ) 1 2 + 2 + 1 = 5
= 3 3 5 = 45
12. 59 2 + 2 2 + 2 10, 8, 6, 4, 2 + 2 = ... 10, 8, 6, 4, 2 = = 120 = 120 2 = 118 > 1 = 2
= 59
13. 4,444,444,494 6 = 2 3 2 = 4 3 = 10 3 4 9 9 4 = 9(1) + 4(9) = 45 3 4,444,444,494
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(.. 2557) 15
14. 2172.5 = 66 ( ) = 66 < 66 = 1(66) , 2(33) , 3(22) , 6(11) ( ) (1, 65) , (2, 31) , (3, 19) , (6, 5) = { 65 1 , 31 2 , 19 3 , 5 6 } = { 65(66) , 31(33) , 19(22) , 5(11)}
= ( ) ( )
= ( )( )( )
=
= 2172.5
15. 5 1 5 = 0, 2, 4, 6 = 0, 2, 4 = {0, 2, 4} = 1, 3, 5, 7 = ( ) (1, 3) , (3, 4) , (5, 0) , (7, 1) { } (1, 3) , (7, 1) = {3, 1} 3 , 2 = 3 + 2 = 5
16. 18640.80 7% 100 7 107
A 13500 =
20% 120 100 A =
B =
B =
=
10514.02 + 8126.78 = 18640.80
17. 0.65 15% 10%
= 3 15%
= 0.45
= 2 10%
= 0.2
= 0.45 + 0.2 = 0.65
18. 14 14
=
( )
17
=
( )
5(1) ( ) =
9 =
( )( ) =
( )( ) =
( )( )
(1) =
( )( ) =
( )( ) =
( )( ) =
( )( )
-
16 (.. 2557)
4 5 = ( )( )
( )( ) =
( )( ) =
14
19. 626 1 2 , 2 50 1 50 : 2 ( 3 ) 50 4 + 1 = 47 4 ( 5 ) 45
48 ( 49 ) 5 1
( ) = (
)( )
= 50 + 576 = 626
20.
= 1, = 2
= 1, = 1
( ) (2) (1) :
21. 10
=
=
( ) = = ( ) ( ) = ( )
=
=
( ) = = ( ) ( ) = ( )
= = 1 = 1
A
= =
( ( )) (( ) ( ))
=
= 10
22. 11
=
7 = ( )
=
( )
2(2) (1) : 7 = =
= 2
(1) = = 5 =
( ) = ( ) ( ) ( )( ) ( )( ) 12 = ( ) ( ) 6 = ( ) ( ) ( )
( ) = ( ) ( ) ( )( ) ( )( ) ( ) = ( ) + 2 ( )
6 = ( ) ( ) 4 = 3 ( )
= ( )
1 = 0 =
= ( )( )
=
(1, 6)
(1,4)
(1+ , 1) (1 , 1)
-
(.. 2557) 17
= 5 = ( ) = 11
23.
: 4 2 = = 16 2 4 + 4 6 = 2 4 2 3 3 0, 1, 2 3 + 1 0 + 1 2 = 1 0 + 1 2 + 3 4 = 2
2 =
=
24. 22.5 AD = BC B D B D B D = B D = 3 A C = CDA = 3
= =
= 45
CBD C D =
= ( )
=
= 22.5
25. 4 + 2 ADT = 30 DAT ~ TBC TBC : DAT = 1:2 DAT ~ TBC TC : DT = 1:2 TC = DT = DTC
AT = DT cos 60 = 2(4)( ) = 4 TB = TC cos 30 = (4)(
) = 2
AB = AT + TB = 4 + 2
26. 3 : 1 OA = OD = OC = DE = OA DE = DEO D A = D A = DEO ODC = D A + D A = 2
ODC = ODC = 2 CEO C B = O C + = + 2 = 3 C B : D A = : = 3 : 1
A B
C D
( ) = ( )
5 = 80 = 4
A B
C
D
E O
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18 (.. 2557)
27. 24 + 8
BD = = 4 = DG = G BDG = ( )
= 8
= = 24
= 24 + 8
28. 2010 Q = 2 , Q = 3 , Q = Q = Q = 7 , Q = 8 , Q = 9 Q = = Q Q =
(Q )(Q )
(Q )(Q )
=
( )( )
( )( )
= ( )( )
( )( )
=
( ) ( )
=
=
= 2014 = 2014 = 2010
29.
2 6 = = 36 = 2 , = 12 2 12 4 9 4 9 (1,3), (2,2), (3,1) (3,6), (4,5), (5,4), (6,3) 7 =
30.
= 8 + 5 + 6 + 7 + 5 + 4 + 3 + 3 + 5 = 46 A Z ( )= 8 + 5 + 6 + 4 + 5 = 28 =
=
31. DE CH D E DE // AC ( )
DE = ( )
FH = AE FH // AE AEHF
EH // AF // AC EH = AF =
( )
(1), (2), (3) D, E, H DH // AC DH = AC ADHC CH = AD = DB CH // AD // DB DBHC BH = DC
Q
A B
C
D
E F
H
-
(.. 2557) 19
32.
= 10 , = = ( )( ) = 1000
. Pol Celona 11 Kheng Phongphun J 15
= 1000 = ( )( )( ) ( )( ) 10 = 4 ( )
=