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MATH-800 ﾐ｡ﾐ榧ﾐ侑 29 ﾐ孟侑ｨﾐ侑 ﾐ頒籍籍嶢寅籍漬籍 ﾐｦﾐｭﾐ寅ｦﾐ｢ﾐｭﾐ ﾐ燐ｨﾐ ﾐ｡ﾐｭﾐ｢ﾐ寅ｭﾐ･ ﾐ斷ｬ ﾐ慴籍｢ﾐ片慴籍｢ﾐ侑墟｢ ﾐ｡ﾐ｣ﾐﾐ籍嶢ｦﾐ籍･ﾐ籍籍｡ ﾐｭﾐ･ﾐｭﾐ嶢頒ｭﾐ 1 ﾐ籍ｼﾐｶﾐｸﾐｻﾑ ﾑﾒｯﾑﾑ糊ｵ! ﾐ･ﾑσｳﾐｰﾑﾐｰﾐｰ 100 ﾐｼﾐｸﾐｽﾑτ I ﾑﾑ采ﾑ災ｳ. ﾐ｡ﾐｾﾐｽﾐｳﾐｾﾑ ﾑひｵﾑﾑ 1. ( ) 2 3 1 1 4 z z z + 竏 竏 ﾐｸﾐｻﾑ采ﾑﾐｸﾐｹﾐｻﾐｻﾐｸﾐｹﾐｳ ﾑﾑ紹ｻﾐｱﾐｰﾑﾑﾐｸﾐｻ. A. 1 1 z竏 B. 2 4 z z竏 C. 1 2 z+ D. 1 2z 竏 E. 1 2 z竏 2. 10 0 ln x 竕､ ﾑび災ｽﾑﾑ采ひｳﾑ災ｻ ﾐｱﾐｸﾑ威ｸﾐｹﾐｽ ﾐｱﾒｯﾑ ﾑ威ｸﾐｹﾐｴﾐｸﾐｹﾐｳ ﾐｾﾐｻ. A.] [0;e B.] [0;1 C.] [1;竏 D.] [ ] [0;1 1;竏ｪ 竏 E.] ]0;1 3. 1 2 1 1 , 3 4 x x= = 竏 ﾑひｾﾐｾﾐｽﾑτσｴ ﾑ威ｸﾐｹﾐｴ ﾐｽﾑ ﾐｱﾐｾﾐｻﾐｾﾑ ﾐｱﾒｯﾑﾑ災ｻ ﾐｺﾐｾﾑ采ﾑﾐｸﾑﾐｸﾐｵﾐｽﾑびび災ｹ ﾐｺﾐｲﾐｰﾐｴﾑﾐｰﾑ ﾑび災ｳﾑ威ｸﾑひｳﾑ災ｻ ﾐｰﾐｻﾑ ﾐｽﾑ ﾐｲﾑ? A. 2 12 1 0x x竏 竏 = B. 2 1 1 0 12 12 x x竏 竏 = C. 2 1 1 0 12 12 x x+ 竏 = D. 2 12 1 0x x+ + = E. 2 144 1 0x x+ + = 4. ( )4 3 4f x x竏 = + ﾐｱﾐｾﾐｻ ( )f x -ﾐｳ ﾐｾﾐｻ. A. ( ) 19 4 x f x 竏 = B. ( ) 4f x x= + C. ( ) 4 3f x x= 竏 D. ( ) 19 4 x f x + = E. ( ) 4 3f x x= + 5. ( ) ( )( ) 23 3 1 sin 1 cosctg tgﾎｱ ﾎｱ ﾎｱ ﾎｱ+ 站 + + 站 ﾐｸﾐｻﾑ采ﾑﾐｸﾐｹﾐｻﾐｻﾐｸﾐｹﾐｽ ﾑτひｳﾑ巾ｳ ﾐｾﾐｻ. ` A.1 B.1 sin cosﾎｱ ﾎｱ+ 站 C.1 cos2ﾎｱ竏 D.1 cos2ﾎｱ+ E.1 sin 2ﾎｱ+ 6. 2 ﾑﾐｰﾐｴﾐｸﾑτﾑひｰﾐｹ ﾑひｾﾐｹﾑﾐｾﾐｳﾑ AB ﾑﾓｩﾐｲﾑ ﾑひｰﾑひｰﾐｲ. ﾐ･ﾑ采ﾑ災ｲ ﾑひｾﾐｹﾑﾐｳﾐｸﾐｹﾐｽ N ﾑﾑ災ｳﾑ采采 ﾑ災ｽﾑ采ﾒｯﾒｯ ﾑﾓｩﾐｲﾑﾐｸﾐｹﾐｳ 45ﾂｰ ﾓｩﾐｽﾑﾐｳﾓｩﾓｩﾑ ﾑﾐｰﾑﾐｰﾑ ﾐｱﾐｾﾐｻ ﾑﾓｩﾐｲﾑﾐｸﾐｹﾐｽ ﾑτﾑび巾ｳ ﾐｾﾐｻ. A. 2 B. 2 C. 4 D.1 E. 2 2 7. 3 2 23 5 7 3 lim 4 3x x x x x x竊停 + + + + + ﾑﾑ紹ｷﾐｳﾐｰﾐｰﾑﾑ巾ｳ ﾐｾﾐｻ. A. 2竏 B. 0 C. 2 D. 4 E. 1竏 8. ﾐ頒ｾﾐｻﾐｾﾐｾ ﾑﾐｾﾐｽﾐｾﾐｳﾐｸﾐｹﾐｽ ﾐｰﾐｳﾐｰﾐｰﾑﾑ巾ｽ ﾑひｵﾐｼﾐｿﾐｵﾑﾐｰﾑびτﾑ巾ｳ ﾑﾑ災ｼﾐｶﾐｸﾐｶ ﾐｴﾐｰﾑﾐｰﾐｰﾑ ﾑﾒｯﾑﾐｽﾑ災ｳﾑび災ｽﾐｴ ﾒｯﾐｷﾒｯﾒｯﾐｻﾑ災ｲ. ﾐｭﾐｽﾑ采ﾒｯﾒｯ ﾑぴｯﾒｯﾐｲﾑﾐｸﾐｹﾐｽ ﾐｴﾑσｽﾐｴﾐｰﾐｶ, ﾐｼﾐｾﾐｾﾐｴ, ﾐｼﾐｵﾐｴﾐｸﾐｰﾐｽﾑ巾ｳ ﾐｾﾐｻ. ﾓｨﾐｴﾓｩﾑ 1 2 3 4 5 6 7 ﾐ｢ﾐｵﾐｼﾐｿﾐｵﾑﾐｰﾑびτ 30 C 4 0 C 5 0 C 7 0 C 6 0 C 5 0 C 5 0 C A. ﾐ飯σｽﾐｴﾐｰﾐｶ 5, ﾐｼﾐｾﾐｾﾐｴ 6, ﾐｼﾐｵﾐｴﾐｸﾐｰﾐｽ 6 B. ﾐ飯σｽﾐｴﾐｰﾐｶ 5, ﾐｼﾐｾﾐｾﾐｴ 5, ﾐｼﾐｵﾐｴﾐｸﾐｰﾐｽ 5 C. ﾐ飯σｽﾐｴﾐｰﾐｶ 5, ﾐｼﾐｾﾐｾﾐｴ 6, ﾐｼﾐｵﾐｴﾐｸﾐｰﾐｽ 5 D. ﾐ飯σｽﾐｴﾐｰﾐｶ 4, ﾐｼﾐｾﾐｾﾐｴ 6, ﾐｼﾐｵﾐｴﾐｸﾐｰﾐｽ 5 E. ﾐ飯σｽﾐｴﾐｰﾐｶ 6, ﾐｼﾐｾﾐｾﾐｴ 5, ﾐｼﾐｵﾐｴﾐｸﾐｰﾐｽ 65 9. 0, 2, 3, 9 ﾑﾐｸﾑﾑﾒｯﾒｯﾐｴﾑ采采 ﾑひｾﾐｳﾑひｾﾑ 3-ﾐｴ ﾑﾑσｲﾐｰﾐｰﾐｳﾐｴﾐｴﾐｰﾐｳ 3 ﾐｾﾑﾐｾﾐｽﾑひｾﾐｹ ﾑひｾﾐｾ ﾑﾑ災ｴ ﾐｱﾐｰﾐｹﾑ ﾐｲﾑ? A. 2 B. 45 C.19 D.192 E. 27
MATH-800 ﾐ｡ﾐ榧ﾐ侑 29 ﾐ孟侑ｨﾐ侑 ﾐ頒籍籍嶢寅籍漬籍 ﾐ･ﾐｭﾐ ﾐ｡ﾐ籍厰 ﾐ･ﾓｨﾐ晩ｨﾐ嶢慱ｨﾐﾐ嶮ｨﾐ ﾐ岱籍厰斷 ﾐ｢ﾐｭﾐ ﾐ籍慴孟侑嶢｢ﾐ籍斷 ﾐ･ﾒｮﾐﾐ頒ｭﾐ 2 10. 2 0a b> > ﾒｯﾐｵﾐｴ 2 2 2 2 2 2 2 a b b ab ｣ｫ ｣ｶ + 竏 +｣ｬ ｣ｷ ｣ｬ ｣ｷ ｣ｭ ｣ｸ ﾐｸﾐｻﾑ采ﾑﾐｸﾐｹﾐｻﾐｻﾐｸﾐｹﾐｳ ﾐｱﾐｾﾐｴ. A. 2 a B. ( ) 2 2 4b a竏 C. ( ) 2 4 2 b a竏 D. 2 2 a E. 2 2 a 11. ( )2 4 6 ... 2 72 5 5 ;n n+ + + + < 竏遺 ﾑび災ｽﾑﾑ采ひｳﾑ災ｻ ﾐｱﾐｸﾑ ﾑﾑ災ｴﾑ災ｽ ﾑ威ｸﾐｹﾐｴﾑび災ｹ ﾐｲﾑ? A.7 B.18 C.17 D.8 E.6 12. log 2a b = ﾐｱﾐｾﾐｻ 5 2 2log logb a b b a a + ﾐｸﾐｻﾑ采ﾑﾐｸﾐｹﾐｻﾐｻﾐｸﾐｹﾐｽ ﾑτひｳﾑ巾ｳ ﾐｾﾐｻ. A. 9 5 B.1 C. 3 10 竏 D. 1竏 E. 11 5 13. ﾐｦﾑ采ﾐｳﾒｯﾒｯﾐｴ 5 ﾑ災ｳﾐｽﾑ采 ﾐｱﾐｾﾐｻﾐｾﾐｽ ﾐｶﾐｰﾐｳﾑﾐｰﾑﾐｰﾐｴ 7 ﾑ災ｳﾐｽﾑ采 ﾐｱﾐｾﾐｻﾐｾﾐｽ ﾐｶﾐｰﾐｳﾑﾑﾐｰﾐｽﾐｰﾐｰﾑﾐｰﾐｰ 4 -ﾓｩﾓｩﾑ ﾐｾﾐｻﾐｾﾐｽ ﾐｼﾓｩﾑ ﾐｱﾐｾﾐｻﾐｶ ﾐｱﾐｰﾐｹﾐｲ. ﾐ斷ｸﾐｹﾑ ﾑﾑ災ｴﾑ災ｽ ﾑﾑ采ﾑ災ｳ ﾐｱﾐｰﾐｹﾑﾐｰﾐｽ ﾐｱﾑ? A.35 B.105 C.{ }35;70 D.140 E.70 14. 10 2x x竏 = + ﾑび災ｳﾑ威ｸﾑひｳﾑ災ｻﾐｸﾐｹﾐｽ ﾑ威ｸﾐｹﾐｴﾐｸﾐｹﾐｽ ﾐｾﾐｻﾐｾﾐｽﾐｻﾐｾﾐｳﾐｸﾐｹﾐｳ ﾐｷﾐｰﾐｰ. A.{ }1 B. 1 33 2 ｣ｱ ｣ｼ竏 +｣ｴ ｣ｴ ｣ｲ ｣ｽ ｣ｴ ｣ｴ｣ｳ ｣ｾ C.{ }1;4 D.{ }1; 6竏 E.{ }6竏 15. a -ﾐｸﾐｹﾐｽ ﾑ紹ｼﾐｰﾑ ﾑτひｳﾐｰﾐｽﾐｴ ( ) sinf x ax x= + ﾐｱﾑττﾐｴﾐｰﾐｳ ﾑﾑσｽﾐｺﾑ ﾐｱﾐｰﾐｹﾑ ﾐｲﾑ? A. 1a 竕･ B. 1a < 竏 C. 1a 竕､ 竏 D. 1a 竕､ E. 1a < 16. S ﾑﾑ災ｳ ﾐｽﾑ ﾑび災ｳﾑ ﾓｩﾐｽﾑﾓｩﾐｳﾑひｸﾐｹﾐｽ ﾐｾﾑﾐｾﾐｹ ﾐｱﾒｯﾑﾑ采采 10 ﾑﾐｼ, ﾑび災ｳﾑ ﾓｩﾐｽﾑﾓｩﾐｳﾑひｸﾐｹﾐｽ ﾑﾐｰﾐｲﾑひｳﾐｰﾐｹﾐｳﾐｰﾐｰﾑ 8 ﾑﾐｼ ﾐｷﾐｰﾐｹﾐｴ ﾐｾﾑﾑ威ｸﾐｽﾐｾ. ﾐ｢ﾑ災ｳﾐｲﾑ災ｻ ﾑび災ｳﾑ ﾓｩﾐｽﾑﾓｩﾐｳﾑひｸﾐｹﾐｽ ﾐｴﾐｸﾐｰﾐｳﾐｾﾐｽﾐｰﾐｻﾐｸﾐｹﾐｽ ﾑτﾑび巾ｳ ﾐｾﾐｻ. A. 46 ﾑﾐｼ B. 6 ﾑﾐｼ C. 26 ﾑﾐｼ D.12 ﾑﾐｼ E. 2 26 ﾑﾐｼ 17. ﾐ績ﾐｸﾑﾐｼﾐｵﾑひｸﾐｺ ﾐｿﾑﾐｾﾐｳﾑﾐｵﾑﾑﾐｸﾐｹﾐｽ ﾑ采ﾐｽﾐｸﾐｹ n ﾐｳﾐｸﾑ惟ｯﾒｯﾐｽﾐｸﾐｹ ﾐｽﾐｸﾐｹﾐｻﾐｱﾑ采ﾐｸﾐｹﾐｳ 2 5nS n n= + ﾑひｾﾐｼﾑ袴岱ｾﾐｳﾐｾﾐｾﾑ ﾐｾﾐｻﾐｴﾐｾﾐｳ ﾐｱﾐｾﾐｻ ﾐｵﾑﾓｩﾐｽﾑﾐｸﾐｹ ﾐｳﾐｸﾑ惟ｯﾒｯﾐｽﾐｸﾐｹ ﾑひｾﾐｼﾑ袴岱ｾ ﾐｰﾐｻﾑ ﾐｲﾑ? A. 5 1nb n= + B. 10 4nb n= 竏 C. 5 10nb n= 竏 D. 5 1nb n= 竏 E. 10 6nb n= + 18. [ 9;8]竏 ﾐｷﾐｰﾐｲﾑﾐｰﾑﾑ ﾑひｾﾐｴﾐｾﾑﾑﾐｾﾐｹﾐｻﾐｾﾐｳﾐｴﾑﾐｾﾐｽ ( )y f x= ﾑﾑσｽﾐｺﾑﾐｸﾐｹﾐｽ ﾑσｻﾐｰﾐｼﾐｶﾐｻﾐｰﾐｻﾑ巾ｽ ﾐｳﾑﾐｰﾑﾐｸﾐｺ ﾓｩﾐｳﾓｩﾐｴﾐｶﾑ采. ﾐ績ﾐｳﾑσｼﾐｵﾐｽﾑび巾ｽ ﾑ紹ｼﾐｰﾑ ﾑτひｳﾑτσｴﾐｰﾐｴ ( )y f x= ﾑﾑσｽﾐｺﾑ ﾐｼﾐｸﾐｽﾐｸﾐｼﾑσｼ ﾑτひｳﾐｰﾐｰ ﾐｰﾐｲﾐｰﾑ ﾐｲﾑ? A. 0x = B. 5; 6x x= 竏 = C. 8; 3; 7,5; 0x x x x= 竏 = = = D. 4,5; 2; 6,5x x x= 竏 = = E. 8; 3; 7,5x x x= 竏 = =
MATH-800 ﾐ｡ﾐ榧ﾐ侑 29 ﾐ孟侑ｨﾐ侑 ﾐ頒籍籍嶢寅籍漬籍 ﾐｦﾐｭﾐ寅ｦﾐ｢ﾐｭﾐ ﾐ燐ｨﾐ ﾐ｡ﾐｭﾐ｢ﾐ寅ｭﾐ･ ﾐ斷ｬ ﾐ慴籍｢ﾐ片慴籍｢ﾐ侑墟｢ ﾐ｡ﾐ｣ﾐﾐ籍嶢ｦﾐ籍･ﾐ籍籍｡ ﾐｭﾐ･ﾐｭﾐ嶢頒ｭﾐ 3 19. (0;0), (0;2), (2;2), (2;0)A B C D ﾑﾑ災ｳﾒｯﾒｯﾐｴﾑ災ｴ ﾐｾﾑﾐｾﾐｹﾑひｾﾐｹ ﾐｺﾐｲﾐｰﾐｴﾑﾐｰﾑ ﾐｴﾑσｳﾑσｹﾐｴ ﾐｱﾐｰﾐｳﾑひｶﾑ采. ﾐｭﾐｽﾑ采ﾒｯﾒｯ ﾐｴﾑσｳﾑσｹ ﾐｴﾐｾﾑびﾐｾﾐｾﾑ ﾑﾐｰﾐｽﾐｰﾐｼﾑﾐｰﾑﾐｳﾒｯﾐｹﾐｳﾑ采采 ﾐｽﾑ災ｳ ﾑﾑ災ｳ ﾐｰﾐｲﾐｰﾑﾐｰﾐｴ ﾑσｳ ﾑﾑ災ｳ ﾐｺﾐｲﾐｰﾐｴﾑﾐｰﾑ ﾐｴﾐｾﾑひｾﾑ ﾐｾﾑﾑ威ｸﾑ ﾐｼﾐｰﾐｳﾐｰﾐｴﾐｻﾐｰﾐｻﾑ巾ｳ ﾐｾﾐｻ. A. 2 ﾏ B. 2 ﾏ C. 4 ﾏ D. 4 ﾏ E.1 4 ﾏ 竏 20. ( ) ( ) 3 3 2 2 2 2 68 x x x 竏 + = ﾑび災ｳﾑ威ｸﾑひｳﾑ災ｻ ﾐｱﾐｾﾐｴ. A. 2 B. 1 2 竏 C. 1 2 D. 2竏 E. 0 21. 3 1, 2 8 x y y x= + = 竏 ﾐｱﾐｰ 2, 0y y= = ﾑ尉σｳﾐｰﾐｼﾑτσｴﾐｰﾐｰﾑ ﾑﾒｯﾑﾑ采災ｻﾑ災ｳﾐｴﾑﾑ災ｽ ﾐｴﾒｯﾑﾑﾐｸﾐｹﾐｽ ﾑひｰﾐｻﾐｱﾐｰﾐｹﾐｳ ﾐｾﾐｻ A.12 B. 1 9 3 C. 1 1 3 D. 4 E. 2 6 3 22. sin 2cos sinx x x+ = ﾑび災ｳﾑ威ｸﾑひｳﾑ災ｻ ﾐｱﾐｾﾐｴ. A. , , ( , ) 2 4 n k n k ﾏ ﾏ ﾏ ﾏ ｣ｱ ｣ｼ + 竏 + 竏茨｣ｲ ｣ｽ ｣ｳ ｣ｾ 邃､ B. 2 , 2 , ( , ) 2 4 n k n k ﾏ ﾏ ﾏ ﾏ ｣ｱ ｣ｼ + 竏 + 竏茨｣ｲ ｣ｽ ｣ｳ ｣ｾ 邃､ C. 3 2 , 2 , ( , ) 2 4 n k n k ﾏ ﾏ ﾏ ﾏ ｣ｱ ｣ｼ 竏 + 竏 + 竏茨｣ｲ ｣ｽ ｣ｳ ｣ｾ 邃､ D. 3 2 , 2 , ( , ) 2 4 n k n k ﾏ ﾏ ﾏ ﾏ ｣ｱ ｣ｼ + 竏 + 竏茨｣ｲ ｣ｽ ｣ｳ ｣ｾ 邃､ E. 3 2 , , ( , ) 2 4 n k n k ﾏ ﾏ ﾏ ﾏ ｣ｱ ｣ｼ + + 竏茨｣ｲ ｣ｽ ｣ｳ ｣ｾ 邃､ 23. ( )y f x= ﾑﾑσｽﾐｺﾑﾐｸﾐｹﾐｽ ﾐｳﾑﾐｰﾑﾐｸﾐｺ ( )3;1竏 ﾑﾑ災ｳﾐｸﾐｹﾐｽ ﾑﾑσｲﾑ糊ｴ ﾑび災ｳﾑ ﾑﾑ災ｼﾑび災ｹ. ﾐ頒ｰﾑﾐｰﾐｰﾑ ﾑﾑσｽﾐｺﾑﾒｯﾒｯﾐｴﾐｸﾐｹﾐｽ ﾐｰﾐｻﾑ ﾐｽﾑ ﾑﾐｾﾐｽﾐｴﾐｳﾐｾﾐｹ ﾑﾑσｽﾐｺﾑ ﾐｲﾑ? A. ( )3 1y f x= 竏 + B. ( )3 1y f x= 竏 竏 C. ( )3 1y f x= + + D. ( )3 1y f x= + 竏 E. ( )y f x= 24. ABCD ﾑﾐｾﾐｼﾐｱﾐｾﾐｴ ﾐｱﾐｰﾐｳﾑびﾐｰﾐｽ ﾑひｾﾐｹﾑﾐｾﾐｳ AB ﾐｱﾐｰ BC ﾑひｰﾐｻﾑτσｴﾑ巾ｳ ﾑﾐｰﾑﾐｳﾐｰﾐｻﾐｷﾐｰﾐｽ M ﾐｱﾐｰ P ﾑﾑ災ｳﾒｯﾒｯﾐｴﾑ災ｴ ﾑ惟ｯﾑﾐｳﾑ采 ﾐｱﾓｩﾐｳﾓｩﾓｩﾐｴ 60ADC =竏｡ ﾐｱﾐｰﾐｹﾐｲ. ﾐ･ﾑ采ﾑ災ｲ ﾑひｾﾐｹﾑﾐｳﾐｸﾐｹﾐｽ ﾑﾐｰﾐｴﾐｸﾑτ ﾐｽﾑ 27 ﾐｱﾐｾﾐｻ ﾑﾐｾﾐｼﾐｱﾑ巾ｽ ﾐｿﾐｵﾑﾐｸﾐｼﾐｵﾑびﾐｸﾐｹﾐｳ ﾐｾﾐｻ. A.12 ﾑﾐｼ B.16 27 ﾑﾐｼ C.48 ﾑﾐｼ D. 24 ﾑﾐｼ E.8 27 ﾑﾐｼ 25. 1 1 1ABCA BC ﾑ尉σｻﾑτσｽ ﾐｿﾑﾐｸﾐｷﾐｼﾐｸﾐｹﾐｽ ﾑﾑττﾑ ﾐｽﾑ ﾑび災ｳﾑ ﾓｩﾐｽﾑﾓｩﾐｳﾑ ﾐｳﾑτﾐｲﾐｰﾐｻﾐｶﾐｸﾐｽ ﾐｱﾓｩﾐｳﾓｩﾓｩﾐｴ ﾐｺﾐｰﾑひｵﾑびτσｴ ﾐｽﾑ 3, 4AC CB= = ﾐｱﾐｰ ﾐｿﾑﾐｸﾐｷﾐｼﾐｸﾐｹﾐｽ ﾑﾐｰﾐｶﾑτ ﾐｸﾑﾐｼﾑ災ｳ ﾐｽﾑ 11 ﾐｱﾐｰﾐｹﾐｲ. ﾐ湲ﾐｸﾐｷﾐｼﾐｴ AC ﾐｸﾑﾐｼﾑ災ｳ ﾐｱﾐｰ 1B ﾐｾﾑﾐｾﾐｹﾐｳ ﾐｴﾐｰﾐｹﾑﾑﾐｰﾐｽ ﾐｾﾐｳﾑひｻﾐｾﾐｻ ﾐｼﾓｩﾐｽ 1CC ﾐｸﾑﾐｼﾑ災ｳ ﾐｱﾐｰ 1AB ﾐｸﾑﾐｼﾑ災ｳﾐｸﾐｹﾐｽ ﾐｴﾑσｽﾐｴﾐｰﾐｶﾐｸﾐｹﾐｳ ﾐｴﾐｰﾐｹﾑﾑﾐｰﾐｽ ﾐｱﾐｰﾑ ﾐｽﾑ災ｳ ﾐｾﾐｳﾑひｻﾐｾﾐｻ ﾑひｰﾑひｰﾐｲ. ﾐｭﾐｴﾐｳﾑ采采 ﾐｾﾐｳﾑひｻﾐｾﾐｻﾑτσｴﾑ巾ｽ ﾐｵﾑﾓｩﾐｽﾑﾐｸﾐｹ ﾑﾑ采ﾑ災ｳ ﾐｱﾐｾﾐｻﾐｾﾑ ﾑﾑ采ﾑﾐｼﾐｸﾐｹﾐｽ ﾑτﾑび巾ｳ ﾐｾﾐｻ. A. 4,5 ﾑﾐｼ B.3 ﾑﾐｼ C. 11 ﾑﾐｼ 2 D. 2,5 ﾑﾐｼ E.9 ﾑﾐｼ
MATH-800 ﾐ｡ﾐ榧ﾐ侑 29 ﾐ孟侑ｨﾐ侑 ﾐ頒籍籍嶢寅籍漬籍 ﾐ･ﾐｭﾐ ﾐ｡ﾐ籍厰 ﾐ･ﾓｨﾐ晩ｨﾐ嶢慱ｨﾐﾐ嶮ｨﾐ ﾐ岱籍厰斷 ﾐ｢ﾐｭﾐ ﾐ籍慴孟侑嶢｢ﾐ籍斷 ﾐ･ﾒｮﾐﾐ頒ｭﾐ 4 II ﾑﾑ采ﾑ災ｳ. ﾐ旁ｩﾑﾓｩﾑ ﾑひｵﾑﾑ 2.1. ﾐ林τﾐｰﾐｳﾑ ﾒｯﾐｷﾒｯﾒｯﾐｻﾑﾑ災ｽ ABC ﾐｷﾓｩﾐｲ ﾐｳﾑτﾐｲﾐｰﾐｻﾐｶﾐｽﾑ ,A C ﾐｾﾑﾐｾﾐｹﾐｽﾑτσｴﾐｰﾐｰﾑ ﾑﾑττﾑ袴ひｰﾐｹ 15 ﾐｱﾐｰ 30 ﾓｩﾐｽﾑﾓｩﾐｳ ﾒｯﾒｯﾑﾐｳﾑ采 ﾑﾐｾﾑ帯, ﾑﾐｾﾑ帯 ﾑﾐｰﾑﾑﾐｰﾐｳ ﾑひｰﾑひｰﾐｲ. 0,5AC = ﾑﾐｼ ﾐｱﾐｾﾐｻ a b ED c 竏 = ﾐｱﾐｰﾐｹﾐｽﾐｰ. ﾐ慱ｩﾐｽ 3 KMLE d e S fg 竏 = ﾐｱﾐｾﾐｻﾐｽﾐｾ. 2.2. ﾐ渙ｸﾑﾐｰﾐｼﾐｸﾐｴﾑ巾ｽ ﾑﾑττﾑ ﾐｽﾑ 60 ﾓｩﾐｽﾑﾓｩﾐｳﾑび災ｹ ﾑﾐｾﾐｼﾐｱﾐｾ. ﾐ･ﾑ采ﾑ災ｲ ﾑぴｯﾒｯﾐｽﾐｸﾐｹ ﾑﾑττﾑ ﾐｴﾐｰﾑﾑ 2 ﾑひｰﾐｻﾑﾑ ﾓｩﾐｽﾑﾓｩﾐｳ ﾐｽﾑ 60 ﾐｱﾐｰ ﾐｿﾐｸﾑﾐｰﾐｼﾐｸﾐｴﾐｰﾐｴ ﾐｱﾐｰﾐｳﾑびﾐｰﾐｽ ﾐｱﾓｩﾐｼﾐｱﾓｩﾑﾑﾓｩﾐｳﾐｸﾐｹﾐｽ ﾑﾐｰﾐｴﾐｸﾑτ 3 ﾐｱﾐｾﾐｻ ﾑﾑττﾐｸﾐｹﾐｽ ﾑひｰﾐｻﾐｱﾐｰﾐｹ cS ab c= , ﾐｿﾐｸﾑﾐｰﾐｼﾐｸﾐｴﾑ巾ｽ ﾑ災ｷﾑ災ｻﾑﾒｯﾒｯﾐｽ V def g= ﾐｱﾐｰﾐｹﾐｽﾐｰ. 2.3. 1 ﾑﾐｼ ﾑﾐｰﾐｴﾐｸﾑτﾑひｰﾐｹ ﾐｱﾓｩﾐｼﾐｱﾓｩﾑﾑﾐｳﾐｸﾐｹﾐｽ ﾑﾐｰﾐｴﾐｸﾑτ ﾐｽﾑ 2 ﾑﾐｼ/ﾑﾐｵﾐｺ ﾑﾑτﾐｴﾑひｰﾐｹﾐｳﾐｰﾐｰﾑ ﾑτﾑびﾐｰﾐｶ ﾑ采ﾐｻﾑ災ｲ. ﾐﾐｰﾐｴﾐｸﾑτ ﾐｽﾑ 13 ﾑﾐｼ ﾐｱﾐｾﾐｻﾐｾﾑ ﾒｯﾐｵﾐｴ ﾑ災ｷﾑ災ｻﾑﾒｯﾒｯﾐｽ ﾑび災ｻﾑ采 ﾑﾑτﾐｴ ﾐｽﾑ 3 ﾑﾐｼ /ﾑﾐｵﾐｺabcd ﾏ , ﾐｳﾐｰﾐｴﾐｰﾑﾐｳﾑτσｳﾐｸﾐｹﾐｽ ﾑひｰﾐｻﾐｱﾐｰﾐｹ ﾐｸﾑﾑﾑ采 ﾑﾑτﾐｴ ﾐｽﾑ 2 ﾑﾐｼ /ﾑﾐｵﾐｺe f g ﾏ ﾐｱﾐｰﾐｹﾐｽﾐｰ. 2.4. ﾐ･ﾐｰﾐｹﾑﾑﾐｰﾐｳﾑ 5 ﾑﾑ災ｽﾑﾑ采, 4 ﾑσｻﾐｰﾐｰﾐｽ ﾐｱﾐｰ 6 ﾑﾐｰﾐｳﾐｰﾐｰﾐｽ ﾐｱﾓｩﾐｼﾐｱﾓｩﾐｳ ﾐｱﾐｰﾐｹﾐｲ. ﾐ･ﾐｰﾐｹﾑﾑﾐｰﾐｳﾐｽﾐｰﾐｰﾑ ﾑﾐｰﾑﾐｰﾐｻﾐｳﾒｯﾐｹﾐｳﾑ采采 ﾐｴﾐｰﾑﾐｰﾐｰﾐｻﾐｰﾐｽ ﾐｳﾑτﾐｲﾐｰﾐｽ ﾐｱﾓｩﾐｼﾐｱﾓｩﾐｳ ﾐｰﾐｲﾑ ﾐｱﾐｰﾐｹﾑﾐｰﾐｽ ﾐｱﾐｰ ﾐｰﾐｲﾑﾐｽﾑ巾ｳﾐｰﾐｰ ﾐｱﾑτﾐｰﾐｰﾐｶ ﾑﾐｸﾐｹﾑﾐｳﾒｯﾐｹ ﾐｱﾐｰﾐｹﾐｲ. - ﾐ･ﾑ采ﾑ災ｲ ﾑ采ﾐｽﾐｸﾐｹ ﾐｰﾐｲﾐｰﾐｻﾑひｰﾐｰﾑ ﾑﾑ災ｽﾑﾑ采 ﾐｱﾓｩﾐｼﾐｱﾓｩﾐｳ ﾐｰﾐｲﾐｰﾑ ﾒｯﾐｷﾑ災ｳﾐｴﾐｻﾐｸﾐｹﾐｳ A, - ﾐ･ﾐｾﾑ帯 ﾐｴﾐｰﾑﾑ ﾐｰﾐｲﾐｰﾐｻﾑひｰﾐｰﾑ ﾑσｻﾐｰﾐｰﾐｽ ﾐｱﾓｩﾐｼﾐｱﾓｩﾐｳ ﾐｰﾐｲﾐｰﾑ ﾒｯﾐｷﾑ災ｳﾐｴﾐｻﾐｸﾐｹﾐｳ B , - ﾐ｡ﾒｯﾒｯﾐｻﾐｸﾐｹﾐｽ ﾐｰﾐｲﾐｰﾐｻﾑひｰﾐｰﾑ ﾑﾐｰﾐｳﾐｰﾐｰﾐｽ ﾐｱﾓｩﾐｼﾐｱﾓｩﾐｳ ﾐｰﾐｲﾐｰﾑ ﾒｯﾐｷﾑ災ｳﾐｴﾐｻﾐｸﾐｹﾐｳ C ﾐｳﾑ災ｲﾑ災ｻ ( ) , ( | ) , ( | )P A a c e P B A P C AB b d fg = = = ﾐｱﾐｰﾐｹﾑ ﾐｱﾐｰ ( ) 4 P ABC hi = ﾐｱﾐｰﾐｹﾐｽﾐｰ.

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  • 1. MATH-800 ﾐ｡ﾐ榧ﾐ侑 29 ﾐ孟侑ｨﾐ侑 ﾐ頒籍籍嶢寅籍漬籍 ﾐｦﾐｭﾐ寅ｦﾐ｢ﾐｭﾐ ﾐ燐ｨﾐ ﾐ｡ﾐｭﾐ｢ﾐ寅ｭﾐ･ ﾐ斷ｬ ﾐ慴籍｢ﾐ片慴籍｢ﾐ侑墟｢ ﾐ｡ﾐ｣ﾐﾐ籍嶢ｦﾐ籍･ﾐ籍籍｡ ﾐｭﾐ･ﾐｭﾐ嶢頒ｭﾐ 1 ﾐ籍ｼﾐｶﾐｸﾐｻﾑ ﾑﾒｯﾑﾑ糊ｵ! ﾐ･ﾑσｳﾐｰﾑﾐｰﾐｰ 100 ﾐｼﾐｸﾐｽﾑτ I ﾑﾑ采ﾑ災ｳ. ﾐ｡ﾐｾﾐｽﾐｳﾐｾﾑ ﾑひｵﾑﾑ 1. ( ) 2 3 1 1 4 z z z + 竏 竏 ﾐｸﾐｻﾑ采ﾑﾐｸﾐｹﾐｻﾐｻﾐｸﾐｹﾐｳ ﾑﾑ紹ｻﾐｱﾐｰﾑﾑﾐｸﾐｻ. A. 1 1 z竏 B. 2 4 z z竏 C. 1 2 z+ D. 1 2z 竏 E. 1 2 z竏 2. 10 0 ln x 竕､ ﾑび災ｽﾑﾑ采ひｳﾑ災ｻ ﾐｱﾐｸﾑ威ｸﾐｹﾐｽ ﾐｱﾒｯﾑ ﾑ威ｸﾐｹﾐｴﾐｸﾐｹﾐｳ ﾐｾﾐｻ. A.] [0;e B.] [0;1 C.] [1;竏 D.] [ ] [0;1 1;竏ｪ 竏 E.] ]0;1 3. 1 2 1 1 , 3 4 x x= = 竏 ﾑひｾﾐｾﾐｽﾑτσｴ ﾑ威ｸﾐｹﾐｴ ﾐｽﾑ ﾐｱﾐｾﾐｻﾐｾﾑ ﾐｱﾒｯﾑﾑ災ｻ ﾐｺﾐｾﾑ采ﾑﾐｸﾑﾐｸﾐｵﾐｽﾑびび災ｹ ﾐｺﾐｲﾐｰﾐｴﾑﾐｰﾑ ﾑび災ｳﾑ威ｸﾑひｳﾑ災ｻ ﾐｰﾐｻﾑ ﾐｽﾑ ﾐｲﾑ? A. 2 12 1 0x x竏 竏 = B. 2 1 1 0 12 12 x x竏 竏 = C. 2 1 1 0 12 12 x x+ 竏 = D. 2 12 1 0x x+ + = E. 2 144 1 0x x+ + = 4. ( )4 3 4f x x竏 = + ﾐｱﾐｾﾐｻ ( )f x -ﾐｳ ﾐｾﾐｻ. A. ( ) 19 4 x f x 竏 = B. ( ) 4f x x= + C. ( ) 4 3f x x= 竏 D. ( ) 19 4 x f x + = E. ( ) 4 3f x x= + 5. ( ) ( )( ) 23 3 1 sin 1 cosctg tgﾎｱ ﾎｱ ﾎｱ ﾎｱ+ 站 + + 站 ﾐｸﾐｻﾑ采ﾑﾐｸﾐｹﾐｻﾐｻﾐｸﾐｹﾐｽ ﾑτひｳﾑ巾ｳ ﾐｾﾐｻ. ` A.1 B.1 sin cosﾎｱ ﾎｱ+ 站 C.1 cos2ﾎｱ竏 D.1 cos2ﾎｱ+ E.1 sin 2ﾎｱ+ 6. 2 ﾑﾐｰﾐｴﾐｸﾑτﾑひｰﾐｹ ﾑひｾﾐｹﾑﾐｾﾐｳﾑ AB ﾑﾓｩﾐｲﾑ ﾑひｰﾑひｰﾐｲ. ﾐ･ﾑ采ﾑ災ｲ ﾑひｾﾐｹﾑﾐｳﾐｸﾐｹﾐｽ N ﾑﾑ災ｳﾑ采采 ﾑ災ｽﾑ采ﾒｯﾒｯ ﾑﾓｩﾐｲﾑﾐｸﾐｹﾐｳ 45ﾂｰ ﾓｩﾐｽﾑﾐｳﾓｩﾓｩﾑ ﾑﾐｰﾑﾐｰﾑ ﾐｱﾐｾﾐｻ ﾑﾓｩﾐｲﾑﾐｸﾐｹﾐｽ ﾑτﾑび巾ｳ ﾐｾﾐｻ. A. 2 B. 2 C. 4 D.1 E. 2 2 7. 3 2 23 5 7 3 lim 4 3x x x x x x竊停 + + + + + ﾑﾑ紹ｷﾐｳﾐｰﾐｰﾑﾑ巾ｳ ﾐｾﾐｻ. A. 2竏 B. 0 C. 2 D. 4 E. 1竏 8. ﾐ頒ｾﾐｻﾐｾﾐｾ ﾑﾐｾﾐｽﾐｾﾐｳﾐｸﾐｹﾐｽ ﾐｰﾐｳﾐｰﾐｰﾑﾑ巾ｽ ﾑひｵﾐｼﾐｿﾐｵﾑﾐｰﾑびτﾑ巾ｳ ﾑﾑ災ｼﾐｶﾐｸﾐｶ ﾐｴﾐｰﾑﾐｰﾐｰﾑ ﾑﾒｯﾑﾐｽﾑ災ｳﾑび災ｽﾐｴ ﾒｯﾐｷﾒｯﾒｯﾐｻﾑ災ｲ. ﾐｭﾐｽﾑ采ﾒｯﾒｯ ﾑぴｯﾒｯﾐｲﾑﾐｸﾐｹﾐｽ ﾐｴﾑσｽﾐｴﾐｰﾐｶ, ﾐｼﾐｾﾐｾﾐｴ, ﾐｼﾐｵﾐｴﾐｸﾐｰﾐｽﾑ巾ｳ ﾐｾﾐｻ. ﾓｨﾐｴﾓｩﾑ 1 2 3 4 5 6 7 ﾐ｢ﾐｵﾐｼﾐｿﾐｵﾑﾐｰﾑびτ 30 C 4 0 C 5 0 C 7 0 C 6 0 C 5 0 C 5 0 C A. ﾐ飯σｽﾐｴﾐｰﾐｶ 5, ﾐｼﾐｾﾐｾﾐｴ 6, ﾐｼﾐｵﾐｴﾐｸﾐｰﾐｽ 6 B. ﾐ飯σｽﾐｴﾐｰﾐｶ 5, ﾐｼﾐｾﾐｾﾐｴ 5, ﾐｼﾐｵﾐｴﾐｸﾐｰﾐｽ 5 C. ﾐ飯σｽﾐｴﾐｰﾐｶ 5, ﾐｼﾐｾﾐｾﾐｴ 6, ﾐｼﾐｵﾐｴﾐｸﾐｰﾐｽ 5 D. ﾐ飯σｽﾐｴﾐｰﾐｶ 4, ﾐｼﾐｾﾐｾﾐｴ 6, ﾐｼﾐｵﾐｴﾐｸﾐｰﾐｽ 5 E. ﾐ飯σｽﾐｴﾐｰﾐｶ 6, ﾐｼﾐｾﾐｾﾐｴ 5, ﾐｼﾐｵﾐｴﾐｸﾐｰﾐｽ 65 9. 0, 2, 3, 9 ﾑﾐｸﾑﾑﾒｯﾒｯﾐｴﾑ采采 ﾑひｾﾐｳﾑひｾﾑ 3-ﾐｴ ﾑﾑσｲﾐｰﾐｰﾐｳﾐｴﾐｴﾐｰﾐｳ 3 ﾐｾﾑﾐｾﾐｽﾑひｾﾐｹ ﾑひｾﾐｾ ﾑﾑ災ｴ ﾐｱﾐｰﾐｹﾑ ﾐｲﾑ? A. 2 B. 45 C.19 D.192 E. 27
  • 2. MATH-800 ﾐ｡ﾐ榧ﾐ侑 29 ﾐ孟侑ｨﾐ侑 ﾐ頒籍籍嶢寅籍漬籍 ﾐ･ﾐｭﾐ ﾐ｡ﾐ籍厰 ﾐ･ﾓｨﾐ晩ｨﾐ嶢慱ｨﾐﾐ嶮ｨﾐ ﾐ岱籍厰斷 ﾐ｢ﾐｭﾐ ﾐ籍慴孟侑嶢｢ﾐ籍斷 ﾐ･ﾒｮﾐﾐ頒ｭﾐ 2 10. 2 0a b> > ﾒｯﾐｵﾐｴ 2 2 2 2 2 2 2 a b b ab ｣ｫ ｣ｶ + 竏 +｣ｬ ｣ｷ ｣ｬ ｣ｷ ｣ｭ ｣ｸ ﾐｸﾐｻﾑ采ﾑﾐｸﾐｹﾐｻﾐｻﾐｸﾐｹﾐｳ ﾐｱﾐｾﾐｴ. A. 2 a B. ( ) 2 2 4b a竏 C. ( ) 2 4 2 b a竏 D. 2 2 a E. 2 2 a 11. ( )2 4 6 ... 2 72 5 5 ;n n+ + + + < 竏遺 ﾑび災ｽﾑﾑ采ひｳﾑ災ｻ ﾐｱﾐｸﾑ ﾑﾑ災ｴﾑ災ｽ ﾑ威ｸﾐｹﾐｴﾑび災ｹ ﾐｲﾑ? A.7 B.18 C.17 D.8 E.6 12. log 2a b = ﾐｱﾐｾﾐｻ 5 2 2log logb a b b a a + ﾐｸﾐｻﾑ采ﾑﾐｸﾐｹﾐｻﾐｻﾐｸﾐｹﾐｽ ﾑτひｳﾑ巾ｳ ﾐｾﾐｻ. A. 9 5 B.1 C. 3 10 竏 D. 1竏 E. 11 5 13. ﾐｦﾑ采ﾐｳﾒｯﾒｯﾐｴ 5 ﾑ災ｳﾐｽﾑ采 ﾐｱﾐｾﾐｻﾐｾﾐｽ ﾐｶﾐｰﾐｳﾑﾐｰﾑﾐｰﾐｴ 7 ﾑ災ｳﾐｽﾑ采 ﾐｱﾐｾﾐｻﾐｾﾐｽ ﾐｶﾐｰﾐｳﾑﾑﾐｰﾐｽﾐｰﾐｰﾑﾐｰﾐｰ 4 -ﾓｩﾓｩﾑ ﾐｾﾐｻﾐｾﾐｽ ﾐｼﾓｩﾑ ﾐｱﾐｾﾐｻﾐｶ ﾐｱﾐｰﾐｹﾐｲ. ﾐ斷ｸﾐｹﾑ ﾑﾑ災ｴﾑ災ｽ ﾑﾑ采ﾑ災ｳ ﾐｱﾐｰﾐｹﾑﾐｰﾐｽ ﾐｱﾑ? A.35 B.105 C.{ }35;70 D.140 E.70 14. 10 2x x竏 = + ﾑび災ｳﾑ威ｸﾑひｳﾑ災ｻﾐｸﾐｹﾐｽ ﾑ威ｸﾐｹﾐｴﾐｸﾐｹﾐｽ ﾐｾﾐｻﾐｾﾐｽﾐｻﾐｾﾐｳﾐｸﾐｹﾐｳ ﾐｷﾐｰﾐｰ. A.{ }1 B. 1 33 2 ｣ｱ ｣ｼ竏 +｣ｴ ｣ｴ ｣ｲ ｣ｽ ｣ｴ ｣ｴ｣ｳ ｣ｾ C.{ }1;4 D.{ }1; 6竏 E.{ }6竏 15. a -ﾐｸﾐｹﾐｽ ﾑ紹ｼﾐｰﾑ ﾑτひｳﾐｰﾐｽﾐｴ ( ) sinf x ax x= + ﾐｱﾑττﾐｴﾐｰﾐｳ ﾑﾑσｽﾐｺﾑ ﾐｱﾐｰﾐｹﾑ ﾐｲﾑ? A. 1a 竕･ B. 1a < 竏 C. 1a 竕､ 竏 D. 1a 竕､ E. 1a < 16. S ﾑﾑ災ｳ ﾐｽﾑ ﾑび災ｳﾑ ﾓｩﾐｽﾑﾓｩﾐｳﾑひｸﾐｹﾐｽ ﾐｾﾑﾐｾﾐｹ ﾐｱﾒｯﾑﾑ采采 10 ﾑﾐｼ, ﾑび災ｳﾑ ﾓｩﾐｽﾑﾓｩﾐｳﾑひｸﾐｹﾐｽ ﾑﾐｰﾐｲﾑひｳﾐｰﾐｹﾐｳﾐｰﾐｰﾑ 8 ﾑﾐｼ ﾐｷﾐｰﾐｹﾐｴ ﾐｾﾑﾑ威ｸﾐｽﾐｾ. ﾐ｢ﾑ災ｳﾐｲﾑ災ｻ ﾑび災ｳﾑ ﾓｩﾐｽﾑﾓｩﾐｳﾑひｸﾐｹﾐｽ ﾐｴﾐｸﾐｰﾐｳﾐｾﾐｽﾐｰﾐｻﾐｸﾐｹﾐｽ ﾑτﾑび巾ｳ ﾐｾﾐｻ. A. 46 ﾑﾐｼ B. 6 ﾑﾐｼ C. 26 ﾑﾐｼ D.12 ﾑﾐｼ E. 2 26 ﾑﾐｼ 17. ﾐ績ﾐｸﾑﾐｼﾐｵﾑひｸﾐｺ ﾐｿﾑﾐｾﾐｳﾑﾐｵﾑﾑﾐｸﾐｹﾐｽ ﾑ采ﾐｽﾐｸﾐｹ n ﾐｳﾐｸﾑ惟ｯﾒｯﾐｽﾐｸﾐｹ ﾐｽﾐｸﾐｹﾐｻﾐｱﾑ采ﾐｸﾐｹﾐｳ 2 5nS n n= + ﾑひｾﾐｼﾑ袴岱ｾﾐｳﾐｾﾐｾﾑ ﾐｾﾐｻﾐｴﾐｾﾐｳ ﾐｱﾐｾﾐｻ ﾐｵﾑﾓｩﾐｽﾑﾐｸﾐｹ ﾐｳﾐｸﾑ惟ｯﾒｯﾐｽﾐｸﾐｹ ﾑひｾﾐｼﾑ袴岱ｾ ﾐｰﾐｻﾑ ﾐｲﾑ? A. 5 1nb n= + B. 10 4nb n= 竏 C. 5 10nb n= 竏 D. 5 1nb n= 竏 E. 10 6nb n= + 18. [ 9;8]竏 ﾐｷﾐｰﾐｲﾑﾐｰﾑﾑ ﾑひｾﾐｴﾐｾﾑﾑﾐｾﾐｹﾐｻﾐｾﾐｳﾐｴﾑﾐｾﾐｽ ( )y f x= ﾑﾑσｽﾐｺﾑﾐｸﾐｹﾐｽ ﾑσｻﾐｰﾐｼﾐｶﾐｻﾐｰﾐｻﾑ巾ｽ ﾐｳﾑﾐｰﾑﾐｸﾐｺ ﾓｩﾐｳﾓｩﾐｴﾐｶﾑ采. ﾐ績ﾐｳﾑσｼﾐｵﾐｽﾑび巾ｽ ﾑ紹ｼﾐｰﾑ ﾑτひｳﾑτσｴﾐｰﾐｴ ( )y f x= ﾑﾑσｽﾐｺﾑ ﾐｼﾐｸﾐｽﾐｸﾐｼﾑσｼ ﾑτひｳﾐｰﾐｰ ﾐｰﾐｲﾐｰﾑ ﾐｲﾑ? A. 0x = B. 5; 6x x= 竏 = C. 8; 3; 7,5; 0x x x x= 竏 = = = D. 4,5; 2; 6,5x x x= 竏 = = E. 8; 3; 7,5x x x= 竏 = =
  • 3. MATH-800 ﾐ｡ﾐ榧ﾐ侑 29 ﾐ孟侑ｨﾐ侑 ﾐ頒籍籍嶢寅籍漬籍 ﾐｦﾐｭﾐ寅ｦﾐ｢ﾐｭﾐ ﾐ燐ｨﾐ ﾐ｡ﾐｭﾐ｢ﾐ寅ｭﾐ･ ﾐ斷ｬ ﾐ慴籍｢ﾐ片慴籍｢ﾐ侑墟｢ ﾐ｡ﾐ｣ﾐﾐ籍嶢ｦﾐ籍･ﾐ籍籍｡ ﾐｭﾐ･ﾐｭﾐ嶢頒ｭﾐ 3 19. (0;0), (0;2), (2;2), (2;0)A B C D ﾑﾑ災ｳﾒｯﾒｯﾐｴﾑ災ｴ ﾐｾﾑﾐｾﾐｹﾑひｾﾐｹ ﾐｺﾐｲﾐｰﾐｴﾑﾐｰﾑ ﾐｴﾑσｳﾑσｹﾐｴ ﾐｱﾐｰﾐｳﾑひｶﾑ采. ﾐｭﾐｽﾑ采ﾒｯﾒｯ ﾐｴﾑσｳﾑσｹ ﾐｴﾐｾﾑびﾐｾﾐｾﾑ ﾑﾐｰﾐｽﾐｰﾐｼﾑﾐｰﾑﾐｳﾒｯﾐｹﾐｳﾑ采采 ﾐｽﾑ災ｳ ﾑﾑ災ｳ ﾐｰﾐｲﾐｰﾑﾐｰﾐｴ ﾑσｳ ﾑﾑ災ｳ ﾐｺﾐｲﾐｰﾐｴﾑﾐｰﾑ ﾐｴﾐｾﾑひｾﾑ ﾐｾﾑﾑ威ｸﾑ ﾐｼﾐｰﾐｳﾐｰﾐｴﾐｻﾐｰﾐｻﾑ巾ｳ ﾐｾﾐｻ. A. 2 ﾏ B. 2 ﾏ C. 4 ﾏ D. 4 ﾏ E.1 4 ﾏ 竏 20. ( ) ( ) 3 3 2 2 2 2 68 x x x 竏 + = ﾑび災ｳﾑ威ｸﾑひｳﾑ災ｻ ﾐｱﾐｾﾐｴ. A. 2 B. 1 2 竏 C. 1 2 D. 2竏 E. 0 21. 3 1, 2 8 x y y x= + = 竏 ﾐｱﾐｰ 2, 0y y= = ﾑ尉σｳﾐｰﾐｼﾑτσｴﾐｰﾐｰﾑ ﾑﾒｯﾑﾑ采災ｻﾑ災ｳﾐｴﾑﾑ災ｽ ﾐｴﾒｯﾑﾑﾐｸﾐｹﾐｽ ﾑひｰﾐｻﾐｱﾐｰﾐｹﾐｳ ﾐｾﾐｻ A.12 B. 1 9 3 C. 1 1 3 D. 4 E. 2 6 3 22. sin 2cos sinx x x+ = ﾑび災ｳﾑ威ｸﾑひｳﾑ災ｻ ﾐｱﾐｾﾐｴ. A. , , ( , ) 2 4 n k n k ﾏ ﾏ ﾏ ﾏ ｣ｱ ｣ｼ + 竏 + 竏茨｣ｲ ｣ｽ ｣ｳ ｣ｾ 邃､ B. 2 , 2 , ( , ) 2 4 n k n k ﾏ ﾏ ﾏ ﾏ ｣ｱ ｣ｼ + 竏 + 竏茨｣ｲ ｣ｽ ｣ｳ ｣ｾ 邃､ C. 3 2 , 2 , ( , ) 2 4 n k n k ﾏ ﾏ ﾏ ﾏ ｣ｱ ｣ｼ 竏 + 竏 + 竏茨｣ｲ ｣ｽ ｣ｳ ｣ｾ 邃､ D. 3 2 , 2 , ( , ) 2 4 n k n k ﾏ ﾏ ﾏ ﾏ ｣ｱ ｣ｼ + 竏 + 竏茨｣ｲ ｣ｽ ｣ｳ ｣ｾ 邃､ E. 3 2 , , ( , ) 2 4 n k n k ﾏ ﾏ ﾏ ﾏ ｣ｱ ｣ｼ + + 竏茨｣ｲ ｣ｽ ｣ｳ ｣ｾ 邃､ 23. ( )y f x= ﾑﾑσｽﾐｺﾑﾐｸﾐｹﾐｽ ﾐｳﾑﾐｰﾑﾐｸﾐｺ ( )3;1竏 ﾑﾑ災ｳﾐｸﾐｹﾐｽ ﾑﾑσｲﾑ糊ｴ ﾑび災ｳﾑ ﾑﾑ災ｼﾑび災ｹ. ﾐ頒ｰﾑﾐｰﾐｰﾑ ﾑﾑσｽﾐｺﾑﾒｯﾒｯﾐｴﾐｸﾐｹﾐｽ ﾐｰﾐｻﾑ ﾐｽﾑ ﾑﾐｾﾐｽﾐｴﾐｳﾐｾﾐｹ ﾑﾑσｽﾐｺﾑ ﾐｲﾑ? A. ( )3 1y f x= 竏 + B. ( )3 1y f x= 竏 竏 C. ( )3 1y f x= + + D. ( )3 1y f x= + 竏 E. ( )y f x= 24. ABCD ﾑﾐｾﾐｼﾐｱﾐｾﾐｴ ﾐｱﾐｰﾐｳﾑびﾐｰﾐｽ ﾑひｾﾐｹﾑﾐｾﾐｳ AB ﾐｱﾐｰ BC ﾑひｰﾐｻﾑτσｴﾑ巾ｳ ﾑﾐｰﾑﾐｳﾐｰﾐｻﾐｷﾐｰﾐｽ M ﾐｱﾐｰ P ﾑﾑ災ｳﾒｯﾒｯﾐｴﾑ災ｴ ﾑ惟ｯﾑﾐｳﾑ采 ﾐｱﾓｩﾐｳﾓｩﾓｩﾐｴ 60ADC =竏｡ ﾐｱﾐｰﾐｹﾐｲ. ﾐ･ﾑ采ﾑ災ｲ ﾑひｾﾐｹﾑﾐｳﾐｸﾐｹﾐｽ ﾑﾐｰﾐｴﾐｸﾑτ ﾐｽﾑ 27 ﾐｱﾐｾﾐｻ ﾑﾐｾﾐｼﾐｱﾑ巾ｽ ﾐｿﾐｵﾑﾐｸﾐｼﾐｵﾑびﾐｸﾐｹﾐｳ ﾐｾﾐｻ. A.12 ﾑﾐｼ B.16 27 ﾑﾐｼ C.48 ﾑﾐｼ D. 24 ﾑﾐｼ E.8 27 ﾑﾐｼ 25. 1 1 1ABCA BC ﾑ尉σｻﾑτσｽ ﾐｿﾑﾐｸﾐｷﾐｼﾐｸﾐｹﾐｽ ﾑﾑττﾑ ﾐｽﾑ ﾑび災ｳﾑ ﾓｩﾐｽﾑﾓｩﾐｳﾑ ﾐｳﾑτﾐｲﾐｰﾐｻﾐｶﾐｸﾐｽ ﾐｱﾓｩﾐｳﾓｩﾓｩﾐｴ ﾐｺﾐｰﾑひｵﾑびτσｴ ﾐｽﾑ 3, 4AC CB= = ﾐｱﾐｰ ﾐｿﾑﾐｸﾐｷﾐｼﾐｸﾐｹﾐｽ ﾑﾐｰﾐｶﾑτ ﾐｸﾑﾐｼﾑ災ｳ ﾐｽﾑ 11 ﾐｱﾐｰﾐｹﾐｲ. ﾐ湲ﾐｸﾐｷﾐｼﾐｴ AC ﾐｸﾑﾐｼﾑ災ｳ ﾐｱﾐｰ 1B ﾐｾﾑﾐｾﾐｹﾐｳ ﾐｴﾐｰﾐｹﾑﾑﾐｰﾐｽ ﾐｾﾐｳﾑひｻﾐｾﾐｻ ﾐｼﾓｩﾐｽ 1CC ﾐｸﾑﾐｼﾑ災ｳ ﾐｱﾐｰ 1AB ﾐｸﾑﾐｼﾑ災ｳﾐｸﾐｹﾐｽ ﾐｴﾑσｽﾐｴﾐｰﾐｶﾐｸﾐｹﾐｳ ﾐｴﾐｰﾐｹﾑﾑﾐｰﾐｽ ﾐｱﾐｰﾑ ﾐｽﾑ災ｳ ﾐｾﾐｳﾑひｻﾐｾﾐｻ ﾑひｰﾑひｰﾐｲ. ﾐｭﾐｴﾐｳﾑ采采 ﾐｾﾐｳﾑひｻﾐｾﾐｻﾑτσｴﾑ巾ｽ ﾐｵﾑﾓｩﾐｽﾑﾐｸﾐｹ ﾑﾑ采ﾑ災ｳ ﾐｱﾐｾﾐｻﾐｾﾑ ﾑﾑ采ﾑﾐｼﾐｸﾐｹﾐｽ ﾑτﾑび巾ｳ ﾐｾﾐｻ. A. 4,5 ﾑﾐｼ B.3 ﾑﾐｼ C. 11 ﾑﾐｼ 2 D. 2,5 ﾑﾐｼ E.9 ﾑﾐｼ
  • 4. MATH-800 ﾐ｡ﾐ榧ﾐ侑 29 ﾐ孟侑ｨﾐ侑 ﾐ頒籍籍嶢寅籍漬籍 ﾐ･ﾐｭﾐ ﾐ｡ﾐ籍厰 ﾐ･ﾓｨﾐ晩ｨﾐ嶢慱ｨﾐﾐ嶮ｨﾐ ﾐ岱籍厰斷 ﾐ｢ﾐｭﾐ ﾐ籍慴孟侑嶢｢ﾐ籍斷 ﾐ･ﾒｮﾐﾐ頒ｭﾐ 4 II ﾑﾑ采ﾑ災ｳ. ﾐ旁ｩﾑﾓｩﾑ ﾑひｵﾑﾑ 2.1. ﾐ林τﾐｰﾐｳﾑ ﾒｯﾐｷﾒｯﾒｯﾐｻﾑﾑ災ｽ ABC ﾐｷﾓｩﾐｲ ﾐｳﾑτﾐｲﾐｰﾐｻﾐｶﾐｽﾑ ,A C ﾐｾﾑﾐｾﾐｹﾐｽﾑτσｴﾐｰﾐｰﾑ ﾑﾑττﾑ袴ひｰﾐｹ 15 ﾐｱﾐｰ 30 ﾓｩﾐｽﾑﾓｩﾐｳ ﾒｯﾒｯﾑﾐｳﾑ采 ﾑﾐｾﾑ帯, ﾑﾐｾﾑ帯 ﾑﾐｰﾑﾑﾐｰﾐｳ ﾑひｰﾑひｰﾐｲ. 0,5AC = ﾑﾐｼ ﾐｱﾐｾﾐｻ a b ED c 竏 = ﾐｱﾐｰﾐｹﾐｽﾐｰ. ﾐ慱ｩﾐｽ 3 KMLE d e S fg 竏 = ﾐｱﾐｾﾐｻﾐｽﾐｾ. 2.2. ﾐ渙ｸﾑﾐｰﾐｼﾐｸﾐｴﾑ巾ｽ ﾑﾑττﾑ ﾐｽﾑ 60 ﾓｩﾐｽﾑﾓｩﾐｳﾑび災ｹ ﾑﾐｾﾐｼﾐｱﾐｾ. ﾐ･ﾑ采ﾑ災ｲ ﾑぴｯﾒｯﾐｽﾐｸﾐｹ ﾑﾑττﾑ ﾐｴﾐｰﾑﾑ 2 ﾑひｰﾐｻﾑﾑ ﾓｩﾐｽﾑﾓｩﾐｳ ﾐｽﾑ 60 ﾐｱﾐｰ ﾐｿﾐｸﾑﾐｰﾐｼﾐｸﾐｴﾐｰﾐｴ ﾐｱﾐｰﾐｳﾑびﾐｰﾐｽ ﾐｱﾓｩﾐｼﾐｱﾓｩﾑﾑﾓｩﾐｳﾐｸﾐｹﾐｽ ﾑﾐｰﾐｴﾐｸﾑτ 3 ﾐｱﾐｾﾐｻ ﾑﾑττﾐｸﾐｹﾐｽ ﾑひｰﾐｻﾐｱﾐｰﾐｹ cS ab c= , ﾐｿﾐｸﾑﾐｰﾐｼﾐｸﾐｴﾑ巾ｽ ﾑ災ｷﾑ災ｻﾑﾒｯﾒｯﾐｽ V def g= ﾐｱﾐｰﾐｹﾐｽﾐｰ. 2.3. 1 ﾑﾐｼ ﾑﾐｰﾐｴﾐｸﾑτﾑひｰﾐｹ ﾐｱﾓｩﾐｼﾐｱﾓｩﾑﾑﾐｳﾐｸﾐｹﾐｽ ﾑﾐｰﾐｴﾐｸﾑτ ﾐｽﾑ 2 ﾑﾐｼ/ﾑﾐｵﾐｺ ﾑﾑτﾐｴﾑひｰﾐｹﾐｳﾐｰﾐｰﾑ ﾑτﾑびﾐｰﾐｶ ﾑ采ﾐｻﾑ災ｲ. ﾐﾐｰﾐｴﾐｸﾑτ ﾐｽﾑ 13 ﾑﾐｼ ﾐｱﾐｾﾐｻﾐｾﾑ ﾒｯﾐｵﾐｴ ﾑ災ｷﾑ災ｻﾑﾒｯﾒｯﾐｽ ﾑび災ｻﾑ采 ﾑﾑτﾐｴ ﾐｽﾑ 3 ﾑﾐｼ /ﾑﾐｵﾐｺabcd ﾏ , ﾐｳﾐｰﾐｴﾐｰﾑﾐｳﾑτσｳﾐｸﾐｹﾐｽ ﾑひｰﾐｻﾐｱﾐｰﾐｹ ﾐｸﾑﾑﾑ采 ﾑﾑτﾐｴ ﾐｽﾑ 2 ﾑﾐｼ /ﾑﾐｵﾐｺe f g ﾏ ﾐｱﾐｰﾐｹﾐｽﾐｰ. 2.4. ﾐ･ﾐｰﾐｹﾑﾑﾐｰﾐｳﾑ 5 ﾑﾑ災ｽﾑﾑ采, 4 ﾑσｻﾐｰﾐｰﾐｽ ﾐｱﾐｰ 6 ﾑﾐｰﾐｳﾐｰﾐｰﾐｽ ﾐｱﾓｩﾐｼﾐｱﾓｩﾐｳ ﾐｱﾐｰﾐｹﾐｲ. ﾐ･ﾐｰﾐｹﾑﾑﾐｰﾐｳﾐｽﾐｰﾐｰﾑ ﾑﾐｰﾑﾐｰﾐｻﾐｳﾒｯﾐｹﾐｳﾑ采采 ﾐｴﾐｰﾑﾐｰﾐｰﾐｻﾐｰﾐｽ ﾐｳﾑτﾐｲﾐｰﾐｽ ﾐｱﾓｩﾐｼﾐｱﾓｩﾐｳ ﾐｰﾐｲﾑ ﾐｱﾐｰﾐｹﾑﾐｰﾐｽ ﾐｱﾐｰ ﾐｰﾐｲﾑﾐｽﾑ巾ｳﾐｰﾐｰ ﾐｱﾑτﾐｰﾐｰﾐｶ ﾑﾐｸﾐｹﾑﾐｳﾒｯﾐｹ ﾐｱﾐｰﾐｹﾐｲ. - ﾐ･ﾑ采ﾑ災ｲ ﾑ采ﾐｽﾐｸﾐｹ ﾐｰﾐｲﾐｰﾐｻﾑひｰﾐｰﾑ ﾑﾑ災ｽﾑﾑ采 ﾐｱﾓｩﾐｼﾐｱﾓｩﾐｳ ﾐｰﾐｲﾐｰﾑ ﾒｯﾐｷﾑ災ｳﾐｴﾐｻﾐｸﾐｹﾐｳ A, - ﾐ･ﾐｾﾑ帯 ﾐｴﾐｰﾑﾑ ﾐｰﾐｲﾐｰﾐｻﾑひｰﾐｰﾑ ﾑσｻﾐｰﾐｰﾐｽ ﾐｱﾓｩﾐｼﾐｱﾓｩﾐｳ ﾐｰﾐｲﾐｰﾑ ﾒｯﾐｷﾑ災ｳﾐｴﾐｻﾐｸﾐｹﾐｳ B , - ﾐ｡ﾒｯﾒｯﾐｻﾐｸﾐｹﾐｽ ﾐｰﾐｲﾐｰﾐｻﾑひｰﾐｰﾑ ﾑﾐｰﾐｳﾐｰﾐｰﾐｽ ﾐｱﾓｩﾐｼﾐｱﾓｩﾐｳ ﾐｰﾐｲﾐｰﾑ ﾒｯﾐｷﾑ災ｳﾐｴﾐｻﾐｸﾐｹﾐｳ C ﾐｳﾑ災ｲﾑ災ｻ ( ) , ( | ) , ( | )P A a c e P B A P C AB b d fg = = = ﾐｱﾐｰﾐｹﾑ ﾐｱﾐｰ ( ) 4 P ABC hi = ﾐｱﾐｰﾐｹﾐｽﾐｰ.