Transcription of 本校數理資優班考試參考書目： - wlsh.tyc.edu.tw
1 1. 2. 3. PDF created with pdfFactory trial version 1 . A B A B=A A>B A B=B 1 B=1 B (1)0<B<1 (2)B<1 (3)0<B 1 (4)B 1 (5)B 1 2 . 100 ( 1 100) 2 3 4 .. 100 (1) 20 (2) 36 (3) 38 (4) 60 (5) 95 3 . 100 (1)1627384950 (2)2345678910 (3)4692581470 (4)3579111300 (5)5815937260 4 . S H E A. B. 13 C. S H S E S H (1) 2 (2) 3 (3) 4 (4) 5 (5) 5 . 1 (1)22+ (2) 3 (3)21+ (4) 32+ (5) 4 Ans (1) PDF created with pdfFactory trial version 6 (1)6 (2) 7 (3)8 (4) 9 (5) 10 Ans (4) 7.
2 6 1~6 ( ) 6 6 2 (1) 0 (2) 14 (3) 13 (4) 12 (5) 23 Ans (1) 8. a b 123456789=(11111+a)(11111 b) (1) a (2) b (3) a b (4) a < b (5) a b 4 Ans (5) PDF created with pdfFactory trial version A. 4 2 2 1 1 1 2 B. 0 , 1 , 2 ,.. , 9 D C. 20cm 50cm 60cm 30cm 50cm ( ) D. ABCD AB=24 AD=243 M N AB AD = E. S=1+1 2+1 2 3+..+1 2 3 .. 100 S F. 10 6 CD C AB C DE A C B E D G F D D D 5 6 7 8 9 10 11 12 13 14 3 15 3 16 17 18 19 PDF created with pdfFactory trial version G.
3 ( ISBN ) a1 a2 a3 a4 a5 a6 a7 a8 a9 1 a1+2 a2+3 a3+..+9 a9 11 10 ISBN ISBN 986 7 9 103 4 H. ABCD AB=AD BCD = 60 ADC = 100 BAC I. 0 0 1 1 0 2 1 1 3 0 1 4 0 2 5 1 2 6 2 2 7 2 1 8 2 0 9 2000 J. 4 ABCDEF AB BC CD DE EF FA A B C D E F 3 P Q R S T U PQRSTU ABCDEF ABPFEDCUTSRQ A B C D 20 21 22 23 24 25 26 , ( ) 27 28 16 1 2 3 4 1 2 3 4 O x y PDF created with pdfFactory trial version 0 1 2 3 K.
4 10 5 20 L. (0,3) (9,0) (0,3) (4,0) (9,0) (,)xy x + y = M. A E F B C D 1 G ( =13 ) BFEDACG N. 0 1 2 3 1 5 13 25 50 O. ABCD F G AB AFFGGB== E DC AC EF H EG J ABCD 70 EHJ DCBAEFGHJ 29 30 4 31 . 32 33 34 39 36 37 38 35 PDF created with pdfFactory trial version A M D N B C P. P(n) n S(n) n P(23)=6 S(23)=5 N N=P(N)+S(N) N A. 15 34 Ans 6 B. n 3n 80 n = Ans 8 C.
5 1 ABCD N DC M AD D MBCNMB = AM= Ans 3 D. x [ x ] x [ ] = 3 [ ] = 8 [773+x] = 4 x Ans 3 E. O,(1,3),(3,)ABxx 0x> OAB 310 x Ans 34 F. 1 88 747 2002 10001 10101 .. 78987 Ans 690 40 5 6 8 9 10 12 13 11 1 7 PDF created with pdfFactory trial version 10 6 ( ) 6 Ans 6 H. P F :2Ly= A B AB F 18AB= C D A B x CD=12 ACDB Ans 84 I. O ABC AB ABC 5 29 Ans 107 14 15 16 A B C O D E 17 18 7 PDF created with pdfFactory trial version 5 L M 5 18 8 Ans:12 K.
6 X y 22064yxx= + .x y (,)xy Ans:11 L. ()fx ()gx 2242[()][()]323fxgxxxx =+ + ()fx 2x x Ans: 22x+ M. 1 2 A A ( ) Ans:43 N. ABCD 8AB= PBPC= PBD 48 PBC Ans 32 19 20 L M 21 22 23 24 25 26 27 28 29 PDF created with pdfFactory trial version ABCD P CD 12 DPPC= APD 8 ABCP Ans 40 P. n 22(1)1nnn+ = n Ans 4 Q. a1,a2,a3,..,an,.. a1 a2 a3 .. an .. a7=120 an+2=an+an+1(n 1) a8= Ans:194 R. 1 4 7 10 .. 697 700 1 3 700 0 200307150000 0 4 Ans: 60 S. 4 6 AB Ans 20 30 31 33 34 32 A B 36 37 35 38 39 PDF created with pdfFactory trial version f(x) f(x) f(1 x) 1 01x 2101[()]99f+ 2111[()]99f+ 2121[()]99f+.
7 21981[()]99f+ 21991[()]99f+ Ans 50 U. ABCD //ABCD 3 CDAB= //EFCD EF ABCD AEED Ans:512+ 1 ABCDEF40 41 42 + 43 PDF created with pdfFactory trial version 1. ( ) ABC B=900 AC BC AC E D AB=4 CE=5 ABC __(1)___ 2. ( ) A B C D AB=4 CD AB CD=5 sin ACB=__(2)__ 3. 4 12 2 2 10 10 ?__(3)___ 4. <an> a1+a2+..+a100=100 a101+a102+..+a200=200 a2 a1=__(4)__ 5. 13 19 20 25 31( ) ___(5)____ 6. f x > 0 f(x)+2f(2002x)=3x f(2)=__(6)____ 7. 8 ( ) 1 =_(7)_ 8. 1 2 3 4 ( ) ?__(8)__ 9. 20 ( ) __(9)___ 10 10. ?
8 __(10)___ 11. a b c xab ybc zca x y z 0 12. 23xy+ 44xy+ 6xyz+ z 5 13. 0 a b ab 1 2222()4()4()4()4abababab + + +++ a2 14. a b 2ab+ 4 6 462+ 5 a (3 7) 6 a 7 A B C E D ( ) A B C D ( ) ( ) PDF created with pdfFactory trial version ABCD AD//BC AD BC 3 AC 3 BD 6 ABCD 322 16. 15 4 4 4 7 5 5 5 6 6 3 7 7 1 17. ( ) 7 18. (x 1)8 ax8 bx7 cx6 dx5 e x4 fx3 gx2 hx i a b c d e f g h i b c d e f g h -2 19. (3 1)(32+1)(34+1)(38+1)(316+1) 12(332 1) 20. 21911 21. f(x) x f(x) 4f(100x) x f(4) 9615 22. ( ) 10 5 5 1 1 10 1 A 44 B 66 C 59 D 95 E 115 E 23.
9 ( ) (A) 4 (B)6 (C)9 (D)10 (E)16 D PDF created with pdfFactory trial version 1. 2000 800 400 ? 2. ABC B=2 C BC=a CA=b AB=c b2=c(a+c) 3. ( ) ( ) _____ 4. 10 199 x=? ( ) 5. ( ) BAC A O O BAC B C O D DE O D ACsuur E (1)2 BDABCE= (2) BD32= DECE12+= AB32AC= DE 6. (1) 315132xxxx ++=+ (2) 222252320xyxxyy += = 11 x 72 A B C a b c O A B C E D ( ) PDF created with pdfFactory trial version 8 8 12 12 (1) 8 a1 , a2 , .. , a8 0 a1 a2 .. a8 a5+a6+a7+a8 8 (2) (1) 4 4 12 4 4 8.
10 (1) ( ) L M 150cm A L P1 P2 P3 .. M 1AP L +======cm A L 45o M M 45o L M 45o M P1 P2 P3 .. ? (2) 260cm 150cm A B C D E F ABBCDEEF130====cm A AC 45o ( ( )) 45o ? 9. (1) ( ) 27 3 3 3 3 9 9 9 7 20 ( ( )) (2) 20 7 1 1 1 1 2 8 1 2 8 A L M P1 P2 P3 P4 45o 45o 45o ( ) A B C D E F 45o 45o ( ) ( ) ( ) PDF created with pdfFactory trial version a b c a 1b b 1c c 1a a2b2c2 1 11. ACD BCD CD A B( ) A B C D 12. x 1 42723xx+ + 27x+ 23x+ 2 1 27x+ 23x+ 35x+ 31x+ x 2 13. 1 ABC M BC 2222122 ABACAMBC+=+ A(a b) B( c 0) C(c 0) M(0 0) 2 ABCD BDAC , M, N 22222224 MNBDACDACDBCAB++=+++ 1 14.
