Tiêu đề Math 2020 Alll Board.pdf ✅

†mUK 1 XvKv †evW© 2020 welq †KvW : 1 0 9 mgq30 wgwbU MwYZ eûwbe©vPwb Afxÿv c~Y©gvb30 [we‡kl `aóe ̈ : mieivnK...Z eûwbe©vPwb Afxÿvi DËic‡Î cÖ‡kœi μwgK b¤^‡ii wecix‡Z cÖ`Ë eY©msewjZ e„Ëmg~n n‡Z mwVK/ m‡e©vrK...ó Dˇii e„ËwU ej c‡q›U Kjg Øviv m¤ú~Y© fivU Ki| cÖwZwU cÖ‡kœi gvb 1| mKj cÖ‡kœi DËi w`‡Z n‡e| cÖkœc‡Î †Kv‡bv cÖKvi `vM/wPý †`Iqv hv‡e bv|] 1. sin  = 1 2 n‡j, tan  = ? K 1 3 L 1 2 M 3 2 N 3 2. 0.  4  5 = KZ? K 41 99 L 5 11 M 41 90 N 1 2 3. 2x + y = 1 I x =  4 mgxKiY؇qi mgvavb we›`y †Kvb PZzf©v‡M Aew ̄’Z? K PZz_© L Z„Zxq M wØZxq N ca_g 4. 2 x = 1 8 n‡j, x = KZ? K  3 L  1 3 M 1 3 N 3 5. A = {3, 4} Ges B = {1, 2, 3} n‡j, B\A = KZ? K {1, 2} L {1, 3} M {2, 4} N {3, 4} 6. x 3  2x  4 ivwki Drcv`K †KvbwU? K (x  4) L (x  2) M (x + 2) N (x + 4) 7. P Q R 60 10 ‰KK PQ-Gi ˆ`N© ̈ KZ? K 10 3 GKK L 5 3 GKK M 10 3 GKK N 5 3 GKK 8. GKwU Abyμ‡gi mvaviY c` 1 3 n n‡j, wØZxq c` KZ? K 1 6 L 1 3 M 4 9 N 1 9 9. p, q, r μwgK mgvbycvZx n‡j, p 2 + q2 q 2 + r2 = KZ? K r p L p r M q p N q r 10. GKwU UavwcwRqv‡gi mgvšÍivj evûØq 32 wgUvi I 64 wgUvi Ges †ÿÎdj 768 eM©wgUvi n‡j, mgvšÍivj evû؇qi ga ̈eZ©x j¤^ `~iZ¡ KZ? K 64 wgUvi L 48 wgUvi M 16 wgUvi N 8 wgUvi 11. 3(5x  3) = 2(x + 2) n‡j, x = KZ? K  2 L  1 M 13 17 N 1 12. 0.0025 Gi eM©g~j †Kvb ai‡bi msL ̈v? K Ave„Ë `kwgK L Abve„Ë Amxg `kwgK M Amxg `kwgK N mmxg `kwgK 13. wP‡Î, O †K›`awewkó e„‡Ë PA I PB `yBwU ̄úk©K n‡j, AOB = KZ? B A O 55 P K 115 L 120 M 125 N 135 14. D A C B wP‡Î, O †K›`awewkó e„‡Ë ABCD AšÍwj©wLZ AvqZ‡ÿÎ hvi AB = 8 †m.wg. I BC = 6 †m.wg.| Mvp As‡ki †ÿÎdj KZ? K 266.16 eM©‡mwg L 250.16 eM©‡mwg M 78.54 eM©‡mwg N 30.54 eM©‡mwg  wb‡Pi Z‡_ ̈i Av‡jv‡K 15 I 16 bs cÖ‡kœi DËi `vI : †kawYe ̈vwß 4044 4549 5054 5559 6064 6569 MYmsL ̈v 6 10 16 20 13 5 15. ga ̈K wbY©‡qi †ÿ‡Î Fc Gi gvb KZ? K 13 L 16 M 32 N 65 16. caPziK wbY©‡qi †ÿ‡Î 1  + 2 Gi gvb KZ? K 0.88 L 0.64 M 0.57 N 0.36 17. 256 + 128 + 64 + .... avivwUi †Kvb c` 1 4 ? K 12 L 11 M 10 N 9 18. P Q R S T wP‡Î, ST || QR n‡j i. PS : SQ = PT : TR ii. PST I PQR m`„k‡KvYx iii. ST = 1 2 QR wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I iii N i, ii I iii 19. wb‡Pi †KvbwU GK gvÎvi N~Y©b cÖwZmgZv cÖ`k©b K‡i? K L M P N  cv‡ki Z‡_ ̈i Av‡jv‡K 20 I 21 bs cÖ‡kœi DËi `vI : wP‡Î, AB > AC Ges PA || CQ. B P C Q A x x 20. wb‡Pi †KvbwU mwVK? K AC : AB = PC : PB L BP = PC M AP : BP = AP : PC N  ABP   APC 21. wPÎvbymv‡i i. ACQ = CAP ii. BAP = AQC iii. -†ÿÎ ABP = -†ÿÎ ACP wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I iii N i, ii I iii 22. wb‡Pi †Kvb Z_ ̈ †`Iqv _vK‡j i¤^m A1⁄4b Kiv m¤¢e? K i¤^‡mi cwimxgv L GKwU KY© I evûi ˆ`N© ̈ M GKwU K‡Y©i ˆ`N© ̈ N evûi ˆ`N© ̈ 23. log3 ( ) 3 3. 3 = KZ? K 1 6 L 5 6 M 1 3 N 2 3 24. 35  2x  x 2 Gi Drcv`‡K we‡køwlZ iƒc wb‡Pi †KvbwU? K (7  x) (5 + x) L (7  x) (5  x) M (7 + x) (5  x) N (7 + x) (5 + x) 25. y 2 = 7y mgxKi‡Yi mgvavb †mU wb‡Pi †KvbwU? K {0,  7} L { 7} M {0, 7} N {0, 7} 26. P Q R S  PQR mgevû n‡j, wPÎvbymv‡i i. QS = SR ii. PQR = 30 iii. PS  QR wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I iii N i, ii I iii 27. A D B O P C ABCD AvqZ‡ÿ‡Îi KY©Ø‡qi †Q`we›`yO, OP = 4 †m.wg. Ges OA = 5 †m.wg. n‡j,BC = KZ? K 2 †m.wg. L 4 †m.wg. M 6 †m.wg. N 8 †m.wg. 28. x  2y = 5 I 2x  4y = 10 i. mgxKiY †RvU mgÄm ii. mgxKiY †RvU ci ̄úi wbf©ikxj iii. mgxKiY †RvUwUi AmsL ̈ mgvavb Av‡Q wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I iii N i, ii I iii 29. evwl©K kZKiv 5 UvKv nv‡i 500 UvKvi 3 eQ‡ii mij gybvdv KZ? K 15 UvKv L 45 UvKv M 60 UvKv N 75 UvKv 30. wb‡Pi †KvbwU g~j` msL ̈v? K 18 32 L 3 2 M 8 6 N 1 8 Self test 1 KLMN 2 KLMN 3 KLMN 4 KLMN 5 KLMN 6 KLMN 7 KLMN 8 KLMN 9 KLMN10 KLMN 11 KLMN 12 KLMN13 KLMN14 KLMN 15 KLMN 16 KLMN17 KLMN18 KLMN19 KLMN20 KLMN 21 KLMN22 KLMN23 KLMN24 KLMN25 KLMN 26 KLMN27 KLMN28 KLMN29 KLMN30 KLMN --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1 K 2 L 3 M 4 K 5 K 6 L 7 L 8 N 9 L 10 M 11 N 12 N 13 M 14 N 15 M 16 N 17 L 18 K 19 M 20 K 21 K 22 L 23 L 24 M 25 M 26 L 27 M 28 N 29 N 30 K

m„Rbkxj MwYZ : beg-`kg †kÖwY  3 †mUK 3 h‡kvi †evW© 2020 welq †KvW : 1 0 9 mgq30 wgwbU MwYZ eûwbe©vPwb Afxÿv c~Y©gvb30 [we‡kl `aóe ̈ : mieivnK...Z eûwbe©vPwb Afxÿvi DËic‡Î cÖ‡kœi μwgK b¤^‡ii wecix‡Z cÖ`Ë eY©msewjZ e„Ëmg~n n‡Z mwVK/ m‡e©vrK...ó Dˇii e„ËwU ej c‡q›U Kjg Øviv m¤ú~Y© fivU Ki| cÖwZwU cÖ‡kœi gvb 1| mKj cÖ‡kœi DËi w`‡Z n‡e| cÖkœc‡Î †Kv‡bv cÖKvi `vM/wPý †`Iqv hv‡e bv|] 1. 0.99973.....msL ̈vwUi wZb `kwgK ̄’vb ch©šÍ Avmbœ gvb wb‡Pi †KvbwU? K 0.999 ̇ L 0.99 ̇9 M 1.000 N 0.100 ̇ 2. A = {x  N : x2 < 25} B = {x  N : x †gŠwjK msL ̈v I x 2 < 25} C = {x  N : x2 = 25} n‡j (A  B)  C = KZ? K { } L {2, 3, 5} M {5, 2, 3, 5} N {1, 2, 3, 4, 5} 3. a 2 + 1  6a = 0 n‡j, a 3 + 1 a 3 Gi gvb KZ? K 0 L 3 3 M 3 6 N 5 6 4. i. log9 3 = 1 2 ii. 4 2x + 1 = 2 n‡j, x =  1 4 iii. (31 + 61 ) Gi gvb 1 2 wb‡Pi †KvbwU mwVK? K i I ii L ii I iii M i I iii N i, ii I iii 5. x Pj‡Ki Rb ̈ 4x3  5x  2 + a = 0| G mgxKi‡Yi aaæec` KZ? K  2 L 2 M a N a  2 6. 3  3 + 3  3 + ..... avivwUi 10Zg c` wb‡Pi †KvbwU? K 30 L  3 M 3 N 30 7. f + g + h + k + l + ..... mgvšÍi avivfz3 n‡j i. h = g +  2 ii. k = h + l 2 iii. g = f + h 2 wb‡Pi †KvbwU mwVK? K i I ii L ii I iii M i I iii N i, ii I iii 8. a 2  5a  6 Gi GKwU Drcv`K wb‡Pi †KvbwU? K a  3 L a  2 M a  1 N a + 1 9. R = {(3, 2), (3, 3), (4, 3)} Aš^‡qi †Wv‡gb wb‡Pi †KvbwU? K {2, 3} L {3, 4} M {3, 3, 4} N {2, 3, 3} 10. wb‡Pi †KvbwU A‡f`? K (x + 2)2 + (x  2)2 = 2x2 + 8 L (x + y)2 + (x  y)2 = 4xy M (x + y)2  (x  y)2 = 2(x2 + y2 ) N (x + 4)2 + (x  4)2 = 2x2 + 16 11. GKwU e‡M©i cwimxgv a 2 GKK| Gi †ÿÎdj wb‡Pi †KvbwU? K a 2 2 eM© GKK L a 2 4 eM© GKK M a 2 8 eM© GKK N a 2 64 eM© GKK 12. j, k, l I m μwgK mgvbycvZx n‡j i. j k = l m ii. j k = k l iii. k l = l m wb‡Pi †KvbwU mwVK? K i I ii L ii I iii M i I iii N i, ii I iii 13.  PQR G, Q = 90 Ges P = 30 n‡j wb‡Pi †Kvb m¤úK©wU mwVK? K PR = 2 QR L PR = 3 PQ M PR = 2QR N PR = 3QR 14. ̄’~j‡KvYx wÎfz‡Ri ̄’~j‡KvY Qvov evwK †KvY `yBwU KZ n‡j wÎfzR A1⁄4b m¤¢e? K 30 I 60 L 40 I 50 M 45 I 45 N 50 I 30  wb‡Pi Z‡_ ̈i Av‡jv‡K 15 I 16 bs cÖ‡kœi DËi `vI : wP‡Î O e„‡Ëi †K›`a| P S R Q 2x + 60 O 3x 15. QRS = KZ? K 30 L 45 M 60 N 135 16. PSR = 90 n‡j, QRS + PQR = KZ? K 100L 135 M 180 N 225 17. tan ( + 30) = 3 n‡j  Gi gvb KZ? K 0 L 30 M 60 N 90 18. †Kv‡bv `‡Ði Qvqvi ˆ`N© ̈ Zvi ˆ`‡N© ̈i KZ ̧Y n‡j DbœwZ †KvY 30 n‡e? K 1 3 L 1 2 M 2 N 3 19. 2x  3y = 8 Ges 4x  6y = 7 mgxKiYØq i. ci ̄úi AmgÄm ii. ci ̄úi wbf©ikxj iii. Gi †Kv‡bv mgvavb †bB wb‡Pi †KvbwU mwVK? K i I ii L ii I iii M i I iii N i, ii I iii  wb‡Pi Z‡_ ̈i Av‡jv‡K 20 I 21 bs cÖ‡kœi DËi `vI : P E Q R D 3 ˆm.wg. 2 ˆm.wg. 55 60 wP‡Î DE || QR Ges QR = 6.5 †m.wg.| 20. PDE = KZ? K 55 L 60 M 65 N 70 21. DE = KZ? K 1.6 †m.wg. L 2 †m.wg. M 2.6 †m.wg. N 3 †m.wg. 22. P B Q R A wP‡Î mgevû wÎfzR PQR G A, PQ Gi ga ̈we›`y Ges B, PR Gi ga ̈we›`y n‡j i.  PQR : PAB = 4 : 1 ii.  PQB : PQR = 1 : 2 iii.  PAB : ABQ = 1 : 1 wb‡Pi †KvbwU mwVK? K i I ii L ii I iii M i I iii N i, ii I iii 23. 13, 11, 8, 9, 15, 5 msL ̈v ̧‡jvi ga ̈K KZ? K 8.5 L 9 M 10 N 10.5 24.  ABC G, AB = AC n‡j, Gi cÖwZmvg ̈ †iLv KZwU? K 1 wU L 2 wU M 3 wU N 4 wU 25. †Kv‡bv e‡M© AšÍe©„Ë AvuK‡Z KqwU avc AbymiY Ki‡Z nq? K 2wU L 3wU M 4wU N 5wU 26. 6 ˆm.wg. 10 ˆm.wg. wP‡Î AvqZ‡ÿÎwUi Mvp wPý As‡ki †ÿÎdj KZ? K 28.27 eM© †m.wg. L 31.73 eM© †m.wg. M 33.27 eM© †m.wg. N 60 eM© †m.wg. 27. †kawY 10  14 15  19 20  24 25  29 MYmsL ̈v 5 6 7 2 cÖ`Ë mviwYi ga ̈K KZ? K 19.17 L 19.71 M 20.17 N 20.71 28. mgevû wÎfz‡Ri GKwU evû‡K Dfq w`‡K ewa©Z Ki‡j †h ewnt ̄’ †KvYØq Drcbœ nq, Zv‡`i mgwó KZ? K 120 L 180 M 240 N 270 29. A =  6 n‡j, tan 2A = KZ? K 3 2 L 1 3 M 1 N 3 30. ( 3) 2x + 1 = ( ) 3 3 x  1 n‡j, x = KZ? K  5 4 L  4 5 M 4 5 N 5 4 Self test 1 KLMN 2 KLMN 3 KLMN 4 KLMN 5 KLMN 6 KLMN 7 KLMN 8 KLMN 9 KLMN10 KLMN 11 KLMN 12 KLMN13 KLMN14 KLMN 15 KLMN 16 KLMN17 KLMN18 KLMN19 KLMN20 KLMN 21 KLMN22 KLMN23 KLMN24 KLMN25 KLMN 26 KLMN27 KLMN28 KLMN29 KLMN30 KLMN --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1 M 2 L 3 M 4 N 5 N 6 L 7 L 8 N 9 M 10 K 11 N 12 N 13 M 14 N 15 N 16 N 17 L 18 N 19 M 20 M 21 M 22 N 23 M 24 K 25 L 26 L 27 K 28 M 29 N 30 L
†mUM 4 Kzwgjøv †evW© 2020 welq †KvW : 1 0 9 mgq30 wgwbU MwYZ eûwbe©vPwb Afxÿv c~Y©gvb30 [we‡kl `aóe ̈ : mieivnK...Z eûwbe©vPwb Afxÿvi DËic‡Î cÖ‡kœi μwgK b¤^‡ii wecix‡Z cÖ`Ë eY©msewjZ e„Ëmg~n n‡Z mwVK/ m‡e©vrK...ó Dˇii e„ËwU ej c‡q›U Kjg Øviv m¤ú~Y© fivU Ki| cÖwZwU cÖ‡kœi gvb 1| mKj cÖ‡kœi DËi w`‡Z n‡e| cÖkœc‡Î †Kv‡bv cÖKvi `vM/wPý †`Iqv hv‡e bv|] 1. x 2  8 = 2 15 n‡j x = KZ? K 3 + 5 L 3 + 5 M 5 + 3 N 5  3 2. †KvbwU mg‡KvYx wÎfz‡Ri †KvY ̧‡jvi AbycvZ? K 6 : 13 : 18 L 1 : 5 : 9 M 3 : 5 : 10 N 7: 8 : 15  wb‡Pi Z‡_ ̈i Av‡jv‡K 3 I 4 bs cÖ‡kœi DËi `vI :  PQR mg‡KvYx wÎfz‡R R mg‡KvY| 3 tan P = 1. 3. P Gi gvb KZ? K 30 L 45 M 60 N 90 4. Dc‡ii Z_ ̈ Abymv‡i i. sin (P + Q) = 1 ii. PQ = 1 + 3 iii. cos P + sin Q = tan 60 wb‡Pi †KvbwU mwVK? K i I ii L ii I iii M i I iii N i, ii I iii 5. GKwU mgevû wÎfz‡Ri †ÿÎdj 25 3 eM© wg. n‡j wÎfzRwUi evûi ˆ`N© ̈ KZ? K 5 wg. L 10 wg. M 50 wg. N 100 wg. 6. f(x) = x4  mx2 + 5 Ges f(1) = 0 n‡j m = ? K 6 L 4 M 1 N  6 7. `yB A1⁄4wewkó msL ̈vi A1⁄4؇qi AšÍi 3| msL ̈vwUi A1⁄4Øq ̄’vb wewbgq Ki‡j †h msL ̈v cvIqv hvq Zv g~j msL ̈vwUi wØ ̧Y A‡cÿv 2 †ewk| msL ̈vwU KZ? K 25 L 36 M 41 N 63 8. {x  N : x †gŠwjK msL ̈v Ges x  5} †mUwUi ZvwjKv c×wZ wb‡Pi †KvbwU? K {1, 3, 5} L {5, 7, 11} M {2, 3, 5} N {3, 5, 7} 9. 25% jv‡f μqg~j ̈ I weμqg~‡j ̈i AbycvZ KZ? K 1 : 4 L 4 : 3 M 5 : 4 N 4 : 5 10. 42. 1  8  0.2  8 = KZ? K 0.1  3  2 L 12.1  8  5 M 13.2  5  0 N 11.8  1  0 11. x + 1 x = 5 n‡j, i. x 2  5x + 1 = 0 ii. x  1 x = 1 iii. x 2 + 1 x 2 = 5 wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I ii N i, ii I iii 12. ABE Gi gvb KZ? B C 30 E P A Q K 60 L 90 M 120 N 150 13. D”PZv 120 125 130 135 140 MYmsL ̈v 5 8 7 6 3 ca`Ë Dcv‡Ëi ga ̈K KZ? K 125 L 130 M 135 N 140 14. 1 2 , 2 3 , 3 4 , .... AbyμgwUi mvaviY c` †KvbwU? K 1 n L 1 2 n M 1 n + 1 N n n + 1 15. P F Q R E D wP‡Î PE = EQ, PF = FR, PD QPR Gi mgwØLÛK n‡j i. QR = 2 EF ii. QD DR = QE RF iii. EF || QR wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I iii N i, ii I iii 16. 3 cm wP‡Î i. eM©‡ÿ‡Îi evûi ˆ`N© ̈ 6 †m.wg. ii. e„‡Ëi cwiwa 12 †m.wg. iii. e„ˇÿÎ I eM©‡ÿ‡Îi †ÿÎd‡ji AbycvZ  : 4 wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I iii N i, ii I iii 17. †Kv‡bv e‡M©i evûi ˆ`N© ̈ 10% n«vm †c‡j Gi †ÿÎdj kZKiv KZ n«vm cv‡e? K 10%L 19% M 21% N 30% 18. 25 cm C 60 A D B h wP‡Î h Gi gvb KZ? K 25 3 †m.wg. L (25 + 3) †m.wg. M (25  3) †m.wg. N 25 3 †m.wg. 19. x 2  4 x 2 = 0 mgxKiYwUi i. Pj‡Ki m‡e©v”P NvZ 4 ii. `ywU g~j ( 2,  2) iii. aaæeK c` 4 wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I iii N i, ii I iii  wb‡Pi Z‡_ ̈i Av‡jv‡K 20 I 21 bs cÖ‡kœi DËi `vI : A D B E C 5 cm 12 cm 20. ABCD UavwcwRqv‡gi †ÿÎdj KZ? K 72 eM© †m.wg. L 102 eM© †m.wg. M 174 eM© †m.wg. N 204 eM© †m.wg. 21. ABED eM© I  CDE wÎfz‡Ri cwimxgvi AbycvZ KZ? K 3 : 4 L 5 : 7 M 5 : 8 N 8 : 5 22. 2x + y = 8 Ges 3x  2y = 5 mgxKiY؇qi †Q` we›`yi ̄’vbv1⁄4 †KvbwU? K (3, 2) L (2, 3) M ( 3, 2) N (2, 3) 23. 2x  5y = 3 I x  1 = 3y mgxKiY †RvUwU i. AmgÄm ii. ci ̄úi Awbf©ikxj iii. GKwU gvÎ mgvavb Av‡Q wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I iii N i, ii I iii 24. e„Ë ̄’ mvgvšÍwiK GKwU K i¤^m L eM© M AvqZ N UavwcwRqvg 25. wb‡Pi †KvbwU μwgK mgvbycvwZ? K 5 : 15 : 20 L 3 : 5 : 6 M 2 : 4 : 8 N 2 : 5 : 10 26. 4 sec A = 5 n‡j sin A = ? K 25 16 L 4 5 M 3 5 N 9 25  wb‡Pi Z‡_ ̈i Av‡jv‡K 27 I 28 bs cÖ‡kœi DËi `vI : loga x = 5 Ges loga y = 3 27. loga (xy) = KZ? K 2 L 5 M 8 N 15 28. logyx = KZ? K 3 5 L 5 3 M 8 N 15 29. P D C B A 2x x O O †K›`awewkó e„‡Ëi DP ̄úk©K i. BAD AwaPvc ii. BAD = 80 iii. OPD = 30 wb‡Pi †KvbwU mwVK? K i I ii L i I iii M ii I iii N i, ii I iii 30. 9 n + 1 = 243 n‡j n = ? K 5 2 L 3 2 M 2 3 N 5 9 Self test 1 KLMN 2 KLMN 3 KLMN 4 KLMN 5 KLMN 6 KLMN 7 KLMN 8 KLMN 9 KLMN10 KLMN 11 KLMN 12 KLMN13 KLMN14 KLMN 15 KLMN 16 KLMN17 KLMN18 KLMN19 KLMN20 KLMN 21 KLMN22 KLMN23 KLMN24 KLMN25 KLMN 26 KLMN27 KLMN28 KLMN29 KLMN30 KLMN --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1 M 2 N 3 K 4 M 5 L 6 K 7 K 8 M 9 N 10 L 11 K 12 M 13 L 14 N 15 N 16 L 17 L 18 K 19 K 20 M 21 N 22 K 23 M 24 M 25 M 26 M 27 M 28 L 29 L 30 L