higher-math_1st-paper_lecture-sheet by Atiq Isamee

D”PZi MwYZ 1g cÎ cvV-cwiKíbv I cÖfvlY cÎ wkÿvel©-2013-2014, cixÿv_x©-2015

MwYZ wefvM

†kªwY t GKv`kÑØv`k

cvV-cwiKíbv I cÖfvlY cÎ wkÿvel©-2013-2014 GBPGmwm cixÿv_x©-2015 weÁvb kvLv welq t D”PZi MwYZ 1g cÎ

cÖ_g el© cvV cwiKíbv †gvU K¬vm / wcwiqW : 100wU

3q Uvg© (K¬vm / wcwiqW msL¨v 30wU)

2q Uvg© (K¬vm / wcwiqW msL¨v 35 wU)

1g Uvg© (K¬vm / wcwiqW msL¨v 35 wU)

Uvg©

Aa¨vq bs

Aa¨v‡qi bvg

K¬vm / wcwiqW msL¨v 8wU

cÖ_g

g¨vwUª· I wbY©vqvK (Matrics & Determinants)

wØZxq

†f±i (Vectors)

8wU

Z…Zxq

mij‡iLv (Straight lines)

12wU

wÎ‡KvYwgwZK AbycvZ (Trigonometric ratios)

5wU

lô

wiwfkb K¬vm / wcwiqW

2wU

PZz_©

e„Ë (Circles)

9wU

cÂg

web¨vm I mgv‡ek (Permutations & Combinations)

7wU

mßg

mshy³ †Kv‡Yi wÎ‡KvYwgwZK AbycvZ (Trigonometric ratios of associated angles) dvskb I dvsk‡bi †jLwPÎ (Functions and graph of functions) wiwfkb K¬vm / wcwiqW

9wU 7wU

beg

AšÍixKiY (Differentiation)

14wU

`kg

†hvMRxKiY (Integrations)

Aóg

3wU

7wU

wiwfkb K¬vm / wcwiqW

9wU †gvU K¬vm / wcwiqW

100wU

1g el© mgvcwb cixÿv 1g Uvg©, 2q Uvg© Ges 3q Uv‡g©i welqe¯‘i Dci AbywôZ n‡e| c„ôv # 1

MwYZ wefvM

†kªwY t GKv`kÑØv`k

1g Uvg© (K¬vm / wcwiqW- 35wU) cÖ_g Aa¨vq Ñ g¨vwUª· I wbY©qvK (Matrics & Determinants): (K¬vm / wcwiqW- 08wU) K¬vm / wcwiqW K¬v‡mi weeiY: g¨vwUª‡·i msÁv Ges D`vniY, g¨vwUª‡·i cÖKvi‡f` (D`vniYmn)| 1g g¨vwUª‡·i mgZv, †hvM, we‡qvM c×wZ Av‡jvPbv Ges MvwYwZK mgm¨vejx| 2q g¨vwUª‡·i ¸Yb c×wZ Av‡jvPbv Ges MvwYwZK mgm¨vejx| 3q g¨vwUª‡·i ¸Yb m¤úwK©Z MvwYwZK mgm¨vejx| wbY©vq‡Ki msÁv I D`vniY, wbY©vq‡Ki gvb wbY©q, wbY©vq‡Ki Abyivwk I mn¸YK, 4_© wbY©vq‡Ki ag©vejx Ges MvwYwZK mgm¨vejx| 5g wbY©vq‡Ki MvwYwZK mgm¨vejx| 6ô

e¨wZµgx I Ae¨wZµgx g¨vwUª·, UªvÝ‡cvR g¨vwUª·, GWR‡q›U g¨vwUª·, eM©g¨vwUª·, wecixZ g¨vwUª·, eM©g¨vwUª‡·i wecixZ g¨vwUª· wbY©q c×wZ Ges MvwYwZK mgm¨vejx|

7g 8g

MvwYwZK mgm¨vejx| GKNvZ mgxKiY †RvU (†µgvic×wZ) Ges MvwYwZK mgm¨vejx|

wØZxq Aa¨vq Ñ †f±i (Vectors) (K¬vm / wcwiqW- 8wU) K¬vm / wcwiqW K¬v‡mi weeiY: mw`K ivwki cÖwZiƒc wn‡m‡e †f±i R¨vwgwZK †f±‡ii aviK, mgZv, wecixZ †f±i, k~b¨ †f±i 9g wØgvwÎK †f±‡ii †hvM, we‡qvM I †¯‹jvi ¸wYZK, wØgvwÎK †f±‡ii †hvM, we‡qvM I †¯‹jvi ¸wYZ‡Ki wewa | mgZ‡j †f±‡ii AskK, †f±i‡K Kv‡Z©mxq ¯’vbv‡¼ cÖKvk, GKK †f±i î , ˆj cÖKvk, 10Zg Ae¯’vb †f±i Ges wØgvwÎK †f±‡ii MvwYwZK mgm¨vejx| wØgvwÎK R¨vwgwZK mgm¨v mgvav‡b †f±i, wØgvwÎK †f±‡ii MvwYwZK mgm¨vejx| 11Zg wÎgvwÎK RM‡Z †f±‡ii AskK wbY©q, wÎgvwÎK RM‡Z GKK †f±i î , ˆj , kˆ 12Zg †f±i‡K î , ˆj , kˆ G gva¨‡g cÖKvk, wÎgvwÎK RM‡Z †f±‡ii †hvMdj I †¯‹jvi ¸wYZK‡K GKK †f±i î , ˆj , kˆ Gi gva¨‡g cÖKvk| 13Zg mij‡iLvq †f±i mgxKiY, †f±‡ii †¯‹jvi ¸Yb, †¯‹jvi ¸Y‡bi ag©| 14Zg †¯‹jvi ¸Y‡Ri MvwYwZK mgm¨vejx| 15Zg †f±‡ii †f±i ¸Yb, †f±i ¸Y‡Ri ag©, †f±i ¸YR| 16Zg †f±i ¸b‡Ri MvwYwZK mgm¨vejx|

c„ôv # 2

MwYZ wefvM

†kªwY t GKv`kÑØv`k

Z…Zxq Aa¨vq Ñ mij‡iLv (Straight lines) (K¬vm / wcwiqW- 12wU) K¬vm / wcwiqW K¬v‡mi weeiY: mgZ‡j Kv‡Z©mxq ¯’vbv¼ I †cvjvi ¯’vbv¼ Av‡jvPbv, Kv‡Z©mxq ¯’vbv¼ I †cvjvi 17Zg ¯’vbv‡¼i g‡a¨ m¤úK© Ges MvwYwZK mgm¨vejx| 18Zg `yBwU we›`yi ga¨eZ©x `~iZ¡ wbY©‡qi m~Î Ges MvwYwZK mgm¨vejx| †iLv wef³Kvix (AšÍwe©f³ I ewn©wef³) we›`yi ¯’vbv¼ wbY©q Ges MvwYwZK 19Zg mgm¨vejx| 20Zg wÎfz‡Ri †ÿÎdj wbY©‡qi m~Î cÖwZôv Ges MvwYwZK mgm¨vejx| wÎfz‡Ri †ÿÎdj msµvšÍ MvwYwZK mgm¨vejx Ges mÂvi c_ Ges MvwYwZK 21Zg mgm¨vejx| mij‡iLvi Xvj, `yBwU we›`yi ms‡hvRK †iLvi Xvj, A‡ÿi mgvšÍivj mij‡iLvi 22Zg mgxKiY Ges MvwYwZK mgm¨vejx| mij‡iLvi cÖwgZ mgxKiYmg~n, ax  by  c  0 mgxKiY GKwU mij‡iLv cÖKvk 23Zg K‡i (cÖgvY) †jLwP‡Î mij †iLv Dc¯’vcb Ges MvwYwZK mgm¨vejx| 24Zg MvwYwZK mgm¨vejx| `yBwU mij‡iLvi †Q`e›`y wbY©q c×wZ, `yBwU mij‡iLvi AšÍf©~³ †Kvb wbY©‡qi m~Î, 25Zg `yBwU mij‡iLvi ci¯úi mgvšÍivj ev j¤^ nIqvi kZ©, wewfbœ kZ©vax‡b mij‡iLvi mgxKiY wbY©q Ges MvwYwZK mgm¨vejx| 26Zg MvwYwZK mgm¨vejx| 27Zg †Kv‡bv we›`y †_‡K mij‡iLvi j¤^ `~iZ¡ wbY©q Ges MvwYwZK mgm¨vejx| 28Zg `yBwU mij‡iLvi AšÍf©~³ †Kv‡Yi wØLÐ‡Ki mgxKiY wbY©q Ges MvwYwZK mgm¨vejx| lô Aa¨vq Ñ wÎ‡KvYwgwZK AbycvZ (Trigonometric ratios) (K¬vm / wcwiqW- 5wU) wÎ‡KvYwgwZK †KvY, †Kv‡Yi wWwMÖ I †iwWqvb cwigvc, †iwWqvb cwigv‡c e„ËPv‡ci 29Zg •`N©¨ I e„ËKjvi †ÿÎd‡ji m~Î Ges MvwYwZK mgm¨vejx| 30Zg MvwYwZK mgm¨vejx| wÎ‡KvYwgwZK †Kv‡Yi AbycvZ, PZzfv© M Abyhvqx wÎ‡KvYwgwZK Abycv‡Zi wPý, 31Zg wÎ‡KvYwgwZK †Kv‡Yi AbycvZ mg~‡ni g‡a¨ m¤úK© I MvwYwZK mgm¨vejx| 32Zg MvwYwZK mgm¨vejx| 33Zg wÎ‡KvYwgwZK dvsk‡bi †jLwPÎ AsKb| 34Zg 35Zg

wiwfkb| wiwfkb|

c„ôv # 3

MwYZ wefvM

†kªwY t GKv`kÑØv`k

2q Uvg© (K¬vm / wcwiqW- 35wU) PZz_© Aa¨vq Ñ e„Ë (Circles) (K¬vm / wcwiqW- 09wU) K¬vm / wcwiqW K¬v‡mi weeiY: g~j we›`y‡Z †K›`ª wewkó e„‡Ëi mgxKiY, †K›`ª g~jwe›`y wewkó e„‡Ëi mgxKiY A¼b I 1g AÿØ‡qi mv‡_ †Q`we›`y wba©viY Ges MvwYwZK mgm¨vejx| 2q wbw`©ó †K›`ª I e¨vmva© wewkó e„‡Ëi mgxKiY wbY©q Ges MvwYwZK mgm¨vejx| 3q e„Ë m¤úwK©Z MvwYwZK mgm¨vejx| 4_© †cvjvi ¯’vbv‡¼ e„‡Ëi mgxKiY wbY©q Ges MvwYwZK mgm¨vejx| 5g e„Ë¯’ †Kv‡bv we›`y‡Z ¯úk©K I Awfj‡¤^i mgxKiY wbY©q Ges MvwYwZK mgm¨vejx| e„‡Ëi ewnt¯’ †Kv‡bv we›`y †_‡K Aw¼Z ¯úk©‡Ki mgxKiY wbY©q Ges MvwYwZK mgm¨vejx| 6ô 7g MvwYwZK mgm¨vejx| 8g MvwYwZK mgm¨vejx| 9g `yBwU e„‡Ëi mvaviY R¨v- Gi mgxKiY wbY©q Ges MvwYwZK mgm¨vejx| cÂg Aa¨vq Ñ web¨vm I mgv‡ek (Permutations & Combinations) (K¬vm / wcwiqW- 10wU) K¬vm / wcwiqW K¬v‡mi weeiY: MYbvi †hvRb I ¸Yb wewa e¨vL¨v, web¨v‡mi e¨vL¨v, n! e¨vL¨v, web¨v‡mi msL¨v wbY©‡qi 10Zg wewfbœ m~‡Îi cÖgvY I cÖ‡qvM| 11Zg web¨vm m¤úwK©Z MvwYwZK mgm¨vejx| 12Zg web¨vm m¤úwK©Z MvwYwZK mgm¨vejx| 13Zg web¨vm m¤úwK©Z MvwYwZK mgm¨vejx| mgv‡e‡ki e¨vL¨v, mgv‡ek msL¨v wbY©‡qi wewfbœ m~‡Îi cÖgvY I m¤ú~iK mgv‡e‡ki 14Zg msL¨vi m~‡Îi cÖgvY, n c r  n c r 1  n  1c r m~‡Îi cÖgvY I cÖ‡qvM| 15Zg kZ©vaxb mgv‡ek e¨vL¨v Ges Gi cÖ‡qvM, MvwYwZK mgm¨vejx| 16Zg mgv‡ek m¤úwK©Z MvwYwZK mgm¨vejx| mßg Aa¨vq Ñ mshy³ †Kv‡Yi wÎ‡KvYwgwZK AbycvZ (Trigonometric ratios of associated angles) (K¬vm / wcwiqW- 9wU) K¬vm / wcwiqW K¬v‡mi weeiY: 17Zg mshy³ †Kv‡Yi wÎ‡KvYwgwZK AbycvZ| 18Zg †hŠwMK †Kv‡Yi wÎ‡KvYwgwZK AbycvZ| 19Zg m~‡Îi iƒcvšÍi| 20Zg ¸wYZK †Kv‡Yi wÎ‡KvYwgwZK AbycvZ| 21Zg Dc¸wYZK †Kv‡Yi wÎ‡KvYwgwZK AbycvZ| 22Zg wÎ‡KvYwgwZK A‡f`vejx 23Zg wÎfz‡Ri mvBb m~Î Ges †KvmvBb m~‡Îi cÖgvY| 24Zg mvBb Ges †KvmvBb m~‡Îi cÖ‡qvM m¤úwK©Z MvwYwZK mgm¨vejx| 25Zg wÎfz‡Ri ¸Yvewj m¤úwK©Z MvwYwZK mgm¨vejx| c„ôv # 4

MwYZ wefvM

†kªwY t GKv`kÑØv`k

Aóg Aa¨vq Ñ dvskb I dvsk‡bi †jLwPÎ (Functions and graph of functions) (K¬vm / wcwiqW- 07wU) K¬vm / wcwiqW K¬v‡mi weeiY: Aš^q I dvskb D`vniYmn e¨vL¨v, dvsk‡bi †Wv‡gb I †iÄ wbY©q, †Wv‡gb I †iÄ 26Zg m¤úwK©Z MvwYwZK mgm¨vejx| 27Zg dvsk‡bi cÖKvi‡f` m¤úwK©Z Av‡jvPbv| 28Zg dvskb m¤úwK©Z MvwYwZK mgm¨vejx| 29Zg ciggvb dvskb, wØNvZ dvskb, m~PK dvskb Ges jMvwi`g dvsk‡bi †¯‹P| 30Zg dvsk‡bi Ges iƒcvšÍwiZ dvsk‡bi †¯‹P| 31Zg dvskb I Zvi wecixZ dvsk‡bi †¯‹P| 32Zg wÎ‡KvYwgwZK dvsk‡bi ch©vq wbY©q| 33Zg 34Zg 35Zg

wiwfkb| wiwfkb| wiwfkb|

1g el© mgvcwb (K¬vm / wcwiqW- 30wU) beg Aa¨vq Ñ AšÍixKiY (Differentiation) (K¬vm / wcwiqW- 14wU) K¬vm / wcwiqW K¬v‡mi weeiY: 1g wjwgU, Xvj, dvsk‡bi wjwgU, GKw`KeZx© wjwgU, Amxg wjwgU m¤ú‡K© aviYv| wjwg‡Ui ag©vejx, m¨vÛzBR Dccv‡`¨i eY©bv I 2q 3q 4_© 5g 6ô 7g 8g 9g 10Zg 11 Zg 12 Zg 13 Zg 14 Zg

lin sin x x0 x

Ges

lin tan x x0 x

lim e x  1 lim a x  1 , , x0 x x0 x

Gi cÖgvY|

MvwYwZK mgm¨vejx| dvskb, Awew”QbœZv, Awew”Qbœ dvsk‡bi ag©vejx, ga¨eZx© gvb Ges Mo gvb Dccv`¨| wjwgU wnmv‡e AšÍiR, ¯úk©‡Ki bwZ wn‡m‡e AšÍiR, g~j wbq‡g xn Gi AšÍiR Ges eûc`x dvsk‡bi AšÍixKiY| g~j wbq‡g wÎ‡KvYwgwZK dvskb, m~PK dvskb Ges jMvwi`wgK dvsk‡bi AšÍiR dvsk‡bi †hvMdj, we‡qvMdj, ¸Ydj I fvMd‡ji AšÍiR ms‡hvwRZ dvsk‡bi AšÍiR jMvwi`wgK dvsk‡bi AšÍiR wecixZ dvsk‡bi AšÍiR Ae¨³ dvskb Ges civwgwZK dvsk‡bi AšÍiR AšÍi‡Ri Av`k© cÖZxK wnmv‡e

f ' ( x), f '' ( x),

dy d 2 y , dx dx 2

BZ¨vw`i e¨envi Ges

ch©vqµwgK AšÍiR| ch©vqµwgK AšÍi‡Ri MvwYwZK mgm¨vejx µgea©gvb I µgn«vmgvb dvskb, Pigwe›`y, dvsk‡bi m‡e©v”P I me©wb¤œ gvb e¨vL¨v Ges MvwYwZK mgm¨vejx c„ôv # 5

MwYZ wefvM

†kªwY t GKv`kÑØv`k

`kg Aa¨vq Ñ †hvMRxKiY (Integrations) (K¬vm / wcwiqW- 7wU) K¬vm / wcwiqW K¬v‡mi weeiY: †hvMR, cÖwZ AšÍiR wn‡m‡e †hvMR, Awbw`©ó †hvM‡Ri †gŠwjK aviYv, †hvM‡Ri 15 Zg †gŠwjK ag©vejx Ges MvwYwZK mgm¨vejx| 16 Zg cÖwZ¯’vcb c×wZ‡Z Awbw`©ó †hvMR wbY©q| 17 Zg Av`k© †hvMR Ges Gi cÖ‡qvM K‡i †hvMR wbY©q| 18 Zg AvswkK fMœvsk, Askvqb m~‡Îi e¨envi K‡i Awbw`©ó †hvMR wbY©q| 19 Zg wbw`©ó †hvMR, wbw`©ó †hvMR m¤úwK©Z g~j Dccv`¨ Ges Gi cÖ‡qvM| 20 Zg wbw`©ó †hvMR wbY©q| 21Zg wbw`©ó †hvMR e¨envi K‡i †ÿÎdj wbY©q| 22Zg 23Zg 24Zg 25Zg 26Zg 27Zg 28Zg 29Zg 30Zg

c„ôv # 6