SH. A. Alimov, O. R. Xolmuhamedov, M. A. Mirzaahmedov
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algebra 7 qqr
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x x − − = + − 2) + + = 1 3 4 . 2 N N 3. Satwsh zatn 20 % in 40 % payda menen satt. Jámi satwdan 32 % payda kóriw ushn ol qal®an zatn neshe procent payda menen satw kerek? 49 I I b a p q a t i y i s l i s h n ® w l a r 114. 1) 1 kg 200 swmnan aln®an júzimni 3 kg nan 1 kg sherbet alnp, 720 swm®a satld. Júzimni bahas 50 swm®a arzanlad. Isbilermen dáslepki paydan saqlap qalmaqsh. Sherbetti ja a bahas dáslepkiden neshe swm®a arzan bolw kerek? 2) 20 % li sherbet tayarlamaqshsz. Neshe litr qayna®an suw®a 200 gramm qumsheker qosasz? 115. 1) dsta dáslep belgili mu®darda suw bar edi. Eger dsqa a litr suw quylsa, dst 1 8 bólegi tolad. Eger dsta® dáslepki suwdan a litr alp taslansa, dst 3 20 bólegi tolq bolad. Dáslep dst qansha bólegi tolq bol®an? 2) dst 1 5 bólegi bos. Axmet dst toltrmaqsh. Ol ds- ta® suwd qansha bólegine shekem suw quysa, ds tolad? O®an járdem beri . 116. Jerdi birinshi eki jasalma joldasn massas 592,4 kg d qurad. Birinshi jasalma joldas úshinshisinen 1243,4 kg je il, al ekinshisi 818,2 kg je il. Jerdi birinshi úsh jasalma joldasn hárqayssn massasn tab . 117. Qayq dáryan a®s boynsha 2,4 saat hám a®sqa qars 3,2 saat júzdi. Qayqt a®s boynsha basp ótken jol a®sqa qars ótken jolnan 13,2 km artq bold. Eger dárya a®sn tezligi 3,5 km/saat bolsa, qayqt aqpay tur®an suwda® tezligin tab . 118. Bostan menen Gulistan awllar arasnda® aralq 72 km. Bul awllardan eki sayaxatsh bir waqtta jol®a shqt. Birini tezligi saatna v kilometr, ekinshisiniki bolsa saatna u kilometr. 2 saattan so olar arasnda® aralq neshe kilometr bolad? Barlq ja®daylard qara hám talqla . 4 Algebra, 7- klass 50 Qadan 3 bólekke bóliw ushn 12 minut kerek. Sol qadan 4 bólekke bóliw ushn neshe minut kerek? 119. dst 1 3 bólegi suw menen tol. Bul suwd 1 4 bólegi paydalan®annan keyin o®an 45 litr suw quylsa, dst 1 8 bólegi bos bolad. dsqa barl® neshe litr suw ketedi? 120. Snaqta 60 soraw berildi, hárbir durs juwapqa 5 ball qoyld. 4 nadurs juwapqa jariyma spatnda bir durs juwap biykar etiledi. Bul snaqta barlq sorawlard belgilegen bir oqwsh 225 ball al®an bolsa, ol neshe soraw®a durs juwap bergen? II bapqa tiyisli snaq shn®wlar testler 1. − − = + + 5 3 11 3 8 2 4 3 N N N te lemesini koreni x 0 bolsa, 2 0 1 N + a latpasn san mánisin tab . A) 50; B) 10; C) 5; D) 37. 2. + − + + = + 2 1 3 2 1 3 2 3 2 N N N te lemesini koreni x 0 bolsa, 18 : x 0 a latpan esapla . A) 6; B) 7; C) − 7; D) 2 7 46 . 3. + − = ( 3) :( 2) 5 :3 N N te lemesini koreni x 0 bolsa, 2x 0 + 61 a latpasn san mánisin tab . A) − 80; B) 70; C) 80; D) 81. 4. + = − 4 :(2 5) 2 :(3 2) N N te lemesini koreni x 0 bolsa, 4x 0 + 11 a latpasn san mánisin tab . A) − 18; B) − 20; C) 19; D) 20. 5. 0,8 . (1,5x − 2) − 0,4x = 0, 3 . (6x − 5) − 2,6 te lemesini koreni x 0 bolsa, − 2 0 0 0,5 x x a latpasn san mánisin tab . A) 5; B) 1,25; C) 6,25; D) − 5. ¹ 4 51 6. Úsh tekshede barl® bolp 385 kitap bar. Birinshi tekshede ekinshisine qara®anda 8 ge kóp, biraq úshinshi tekshedegi- -den 9 ®a kem kitap bar. Hárbir tekshede neshe kitaptan bar? A) 128; 120; 137; B) 127; 119; 139; C) 127; 122; 136; D) 126; 134; 125. 7. Te qaptall úshmúyeshlikti perimetri 51 sm ge te . Ultan qaptal tárepinen 6 sm uzn. Us úshmúyeshlikti qaptal tárepini ultanna qatnasn tab . A) 7 : 5; B) 5 : 7; C) 2 : 3; D) 10 : 7. 8. Te qaptall úshmúyeshlikti perimetri 42 sm ge te . Qaptal tárepi ultann 2 3 bólimin qurayd. Us úshmúyeshlikti ultan qaptal tárepinen neshe santimetr uzn? A) 7,5 sm; B) 6,5 sm; C) 6 sm; D) 7 sm. 9. Usta buyrtpan 8 kúnde ornlaw kerek edi. Ol hár kúni rejeden tsqar 6 ónim tayarlap, buyrtpan 5 kúnde ornlap ®ana qoymastan, al artqsha jáne 12 ónim tayarlad. Usta reje boynsha bir kúnde neshe ónim tayarlaw kerek edi? A) 6; B) 4; C) 5; D) 7. Te lemeni sheshi (1011): 10. + − = − + 8( 2) 5 2( 4,5). N N N A) − 5; B) 5; C) 6; D) − 4,5. 11. 6 . (2,3x − 1) − 3,5x + 0, 7x = 0,5(x − 14). A) − 2 21 ; B) 10,5; C) 2 21 ; D) 7. 12. Úshmúyeshlikti bir tárepi ekinshi tárepinen 3 sm uzn, úshinshi tárepinen bolsa 5 sm qsqa. Eger úshmúyeshlikti perimetri 41 sm bolsa, on e uzn tárepi e qsqa tárepinen neshe ese uzn? A) 2; B) 1,5; C) 1,3; D) 1,8. 52 13. Birinshi topta 75 m, ekinshi topta 120 m atlas bar edi. Ekinshi toptan birinshisinen satl®anna qara®anda 3 ese kóp atlas satld. Nátiyjede, birinshi topta ekinshisine qara®anda 2 ese kóp atlas qald. Hárbir toptan neshe metrden atlas satl®an? A) 24 m; 72 m; B) 30 m; 90 m; C) 15 m 45 sm; D) 33 m; 99 m. 14. Te lemeni sheshi : + − + = − + 3( 2) 2( 3) 7 5( 1). N N N A) − 1 3 ; B) 1 3 ; C) − 1; D) 2. T a r i y x y m a ® l w m a t l a r Muhammed ibn Musa al-Xorezmiy «Al-jabr val-muqobala hisobi haqida qisqacha kitob» sh®armasnda kirgizilgen «al-jabr», «val-muqobala» qa®ydalarn biz 7-§ de te lemeni tiykar® qá- siyetleri spatnda bayan ettik. Algebrada 3 túrli sanlar menen jums kóriledi, deydi al Xorezmiy. Olar: koren yamasa zat (te lemedegi belgisiz san x); kvadrat (mol) (belgisizdi kvadrat x 2 ); ápiway san (bunda natural san názerde tutlad). Xorezmiydi us 3 túrli shamalar arasnda® baylanslard analizleydi hám tómendegi te lemelerdi sheshiw usllarn kórsetedi: 1) = 2 ?N >N kvadratlar korenlerge te ; 2) = 2 ?N = kvadratlar sanlar®a te ; 3) = >N = korenler san®a te ; 4) + = 2 ?N >N = kvadratlar hám korenler sanlar®a te ; 5) + = 2 ?N = >N kvadratlar hám san korenlerge te ; 6) + = 2 >N = ?N korenler hám san kvadratlar®a te . Biz 7-klasta tek szql te lemelerdi úyrenemiz [3) bánttegi te leme]. Qal®anlar 8-klasta úyreniledi. Hárqanday szql yaki kvadrat te leme «al-jabr», «val-muqobala» túrlendiriwleri nátiy- jesinde joqarda® 6 te lemeni birine keltiriliwi múmkin. 53 BIRAZALÍLAR HÁM KÓPAZALÍLAR Natural kórsetkishli dáreje Birdey sanlard qoswd kóbeytiw menen almastrw múmkin: 3 3 3 3 3 3 5 + + + + = ⋅ 1442443 5 márte a a a a a a n + + + + + = ⋅ K 144424443 márte n Birdey sanlard kóbeymesin de kópshilik ja®daylarda q- shamraq jazw menen almastrw maqsetke muwapq bolad. Tárepini uznl® 5 birlikke te bol®an kvadratt qarayq (6-súwret). Ol 5 . 5 = 25 birlik kvadrattan ibarat. Tárepini uznl® 5 birlikke te kub (7-súwret) bolsa 5 . 5 . 5 = 125 birlik kubt óz ishine alad. Sizge belgili, 5 . 5 kóbeymesi 5 2 (oqlw: «besti kvadrat»); 5 . 5 . 5 kóbeymesi 5 3 (oqlw: «besti kub») dep belgilenedi: 5 · 5 = 5 2 , 5 · 5 · 5 = 5 3 . Tap usnday etip, kóbeytiwshileri bir qyl sanlardan ibarat kóbeymeni ja a ámel dárejege kóteriw menen almastrw múmkin: 5 3 3 3 3 3 3 + + + + = 1442443 5 márte 9 1 1 1 1 1 , 7 7 7 7 7 ⋅ ⋅ ⋅ ⋅ = K 144244 3 5 márte 0,4 = (0,4) 1 . Ulwma, birdey n kóbeytiwshilerdi kóbeymesin belgilew ushn a n jazwnan paydalanlad: a a a a a a ⋅ ⋅ ⋅ ⋅ ⋅ = K 1442443 márte n n III BAP 9- 54 Ol blaynsha oqlad: «a sann n kórsetkishli dárejesi». Ádette, qsqasha etip: «a n n dárejesi» dep aytlad. a sann n natural kórsetkishli dárejesi dep, hárbiri a ®a te bol®an n kóbeytiwshini kóbeymesine aytlad: a a a a a = ⋅ ⋅ ⋅ ⋅ K 14 4244 3 márte n n a san (tákirarlanwsh kóbeytiwshi) dárejeni tiykar, n san (kóbeytiwshini neshe márte tákirarlanwn kórsetiwshi san) dáreje kórsetkishi dep atalad. Máselen, 3 4 = 3 · 3 · 3 · 3 = 81, bul jerde 3 dárejeni tiykar, 4 dáreje kórsetkishi, al 81 bolsa 3 4 dárejesini mánisi. Tiykarnan, sann birinshi dárejesi dep, us sann ózine aytlad: a 1 = a. Máselen, ( ) = = = 1 1 1 1 1 7 7 5 5, 25 25, . Dárejeni tiykar qálegen san bolw múmkin, máselen, ( ) ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ = = = 3 5 2 2 2 8 2 5 5 5 5 125 2 2 2 2 2 2 32; ; − = − ⋅ − ⋅ − ⋅ − ⋅ − = − 5 ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) 32; ( ) ( ) ( ) ( ) ( ) − = − ⋅ − ⋅ − ⋅ − = 4 2 2 2 2 2 16 3 3 3 3 3 81 ; = ⋅ ⋅ = 3 0,2 0,2 0,2 0,2 0,008; − = − ⋅ − ⋅ − ⋅ − ⋅ − ⋅ − = 6 ( 1) ( 1) ( 1) ( 1) ( 1) ( 1) ( 1) 1; = ⋅ ⋅ = = ⋅ ⋅ ⋅ = 3 4 0 0 0 0 0; 10 10 10 10 10 10 000. 6-súwret. 7-súwret. 55 Dárejege kóteriw ámeli úshinshi basqsh ámeli bolad. Eger a latpada qawsrmalar bolmasa, onda dáslep úshinshi basqsh ámeller, keyin ekinshi basqsh ámeller (kóbeytiw hám bóliw) hám aqrnda, birinshi basqsh ámeller (qosw hám alw) ornlanatu®nn esletip ótemiz. Másele. Esapla : 7 . 2 4 . 2 7 . 2 4 − 5 . 3 2 = 7 . 16 − 5 . 9 = 112 − 45 = 67. Sanlard dáreje járdeminde jazwdan kópshilik ja®daylarda, máselen, natural sanlard ta ba (razryad) birliklerini qosnds kórinisinde jazw ushn paydalanlad: = ⋅ + ⋅ + ⋅ + = ⋅ + ⋅ + ⋅ + 3 2 . 3245 3 1000 2 100 4 10 5 3 10 2 10 4 10 5 Úlken sanlard jazw ushn kóbinese 10 sann dárejeleri qollanlad. Máselen, Jerden Quyashqa shekemgi aralq shama menen 150 mln km ge te bolp, ol 1,5 . 10 8 km kórinisinde jazlad: Jer sharn radius shama menen 6,37 mln m ge te , bul 6,37 . 10 6 m kórinisinde jazlad; Jerden e jaqn juldz®a (α Sentavr) shekemgi aralq 4 . 10 13 km kórinisinde jazlad. 10 nan úlken bol®an hárbir sand a . 10 n kórinisinde jazw múmkin, bunda 1 ≤ a < 10 hám n natural san. Bunday jazw sann standart kórinisi dep atalad. Máselen, 4578 = 4,578 · 10 3 , 45,78 = 4,578 · 10, 103000 = 1,03 · 10 5 . Fizika hám ximiya pánlerin úyreniwde, mikrokalkulyatorda esaplawlarda hám basqa da kópshilik ja®daylarda sann standart kórinisindegi jazwnan paydalanlad. Qosndn kóbeyme kórinisinde jaz (121122): 121. 1) + + + + 4 4 4 4 4; 3) + + ; c c c 2) + + + 6 6 6 6; 4) + + + + . a a a a a S h n ® w l a r 5 3 . − 56 122. 1) + + 2 2 2 ; m m m 5) 3 3 3; + + + K 14243 21 márte 2) + + 17 17 17 ; ab ab ab 6) 5 5 5; + + + K 14243 17 márte 3) − + − ( 2 ) ( 2 ); c d c d 7) ; m m m + + + K 1442443 márte n 4) − + − + − (3 ) (3 ) (3 ); b a b a b a 8) ; K 144244 3 márte k b+ b+ + b Kóbeymeni dáreje túrinde jaz (123125): 123. 1) ⋅ ⋅ ⋅ ⋅ 2 2 2 2 2; 2) ⋅ ⋅ ⋅ ⋅ 1 1 1 1 1 ; 3 3 3 3 3 3) ( ) ( ) ( ) ⋅ ⋅ 3 3 3 4 4 4 ; 4) − ⋅ − ⋅ − ⋅ − ( 2,7) ( 2,7) ( 2,7) ( 2,7). 124. 1) ⋅ ⋅ ⋅ ⋅ ; x x x x x 3) ⋅ ⋅ (2 ) (2 ) (2 ); a a a 2) ⋅ ⋅ ⋅ ⋅ ; m m m m m 4) − ⋅ − ⋅ − ⋅ − ( 3 ) ( 3 ) ( 3 ) ( 3 ). b b b b 125. 1) − ⋅ − ⋅ − ( ) ( ) ( ); x y x y x y 3) ⋅ 3 3 2 2 ; x x 2) + ⋅ + ( ) ( ); a b a b 4) ⋅ ⋅ ⋅ ⋅ . m m m m m n n n n n Kóbeymeni dáreje túrindegi jazwnan paydalanp, a latpan ápiwaylastr (126128): 126. 1) 2 . 2 . 2 . 15; 3) 5 . 5 . 8 . 8 . 8 . 2 . 2; 2) 4 . 4 . 4 . 4 . 21; 4) 6 . 6 . 7 . 7 . 3 . 3 . 3. 127. 1) 1,2 . 1,2 . 2 . 2 . 5 . 5; 2) 0,5 . 0,5 . 0,5 . 2 . 2 . 4 . 4; 3) ⋅ ⋅ ⋅ ⋅ ⋅ 1 1 1 1 7 7 7 7 0,3 0,3 ; 4) ⋅ ⋅ ⋅ ⋅ 2 2 2 3 3 3 2,3 2,3. 128. 1) 9 . 9 . 9 . a . a . a; 3) − ⋅ − ⋅ ⋅ ( ) ( ) ; x x x y y y x y x y 2) x . x . x . x . 3 . 3; 4) − ⋅ − ⋅ − ⋅ ⋅(8 ) (8 ) (8 ) . a a b b a b a b a b 57 A latpan ápiwaylastr (129130): 129. 1) p . p . p . p + q . q; 3) a . a + a . a + a . a; 2) a . a + b . b . b . b; 4) x . x . x + x . x . x. 130. 1) ; c c c c c c ⋅ + ⋅ + + ⋅ K 144424443 márte k 3) ; a a a b b b ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ K K 14243 14243 márte márte k m 2) ; a a a a a a a a a ⋅ ⋅ + ⋅ ⋅ + + ⋅ ⋅ K 1444442444443 n márte 4) 5 5 5 a a a ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ K K 14243 14243 k márte 17 márte 131. A latpan oq , dárejeni tiykarn, dáreje kórsetkishin ayt : 1) 3 2 ; 3) ( ) − 41 2 9 ; 5) + 15 (4 ) ; m n 2) ( ) 3 3 8 1 ; 4) − 39 ( 1,2) ; 6) ( ) 7 2 3 . a b Esapla (132139): 132. 1) 2 3 ; 2) 3 2 ; 3) 4 4 ; 4) 5 3 . 133. 1) 1 5 ; 2) ( − 1) 7 ; 3) 0 15 ; 4) 0 5 . 134. 1) ( ) 3 2 3 ; 2) ( ) 2 3 5 ; 3) ( ) 2 2 7 1 ; 4) ( ) 3 1 3 2 . 135. 1) (2,5) 2 ; 2) (1,7) 2 ; 3) ( − 0,2) 3 ; 4) ( − 0,2) 4 . 136. 1) ( − 5) 3 ; 2) − 5 3 ; 3) ( ) − 2 1 4 ; 2 4) ( ) − 2 1 4 . 2 137. 1) − 4 5 ( 0,2) (0,1) ; 2) − 3 4 (0,3) ( 0,1) ; 3) 2 2 (3,2) (1,6) ; 4) 2 2 (2,6) (1,3) . 138. 1) 2 . ( − 3) 2 ; 2) − 5 . ( − 2) 3 ; 3) − ⋅ − 2 1 2 ( 4) ; 4) − ⋅ − 2 2 3 ( 3) . 139. 1) ( ) − ⋅ − 2 3 5 ( 5) ; 2) ( ) − ⋅ − 3 2 3 ( 3) ; 3) − − ⋅ 2 3 ( 3) 2 ; 4) − − ⋅ − 2 3 ( 3) ( 2) . 58 140. − − − 2 2 3 ; ( ) ; ( ) x x x a latpan mánisin = − 1 2 1 ; 5 x de tab . 141. x 2 a latpasn mánisin x ti kestede kórsetilgen mánisleri ushn esapla : 142. x 3 a latpasn mánisin x ti kestede kórsetilgen mánisleri ushn esapla : 143. Tómendegi pikirlerdi qays biri durs, qays biri nadurs? Sebebin túsindiri . Pikir nadurs dep aytsa z, on biykar etiwshi msal tab . 1) eki sann kvadratlar te bolsa, bul sanlard ózleri de te ; 2) eki sann kublar te bolsa, bul sanlard ózleri de te ; 3) eger teris san®a on kvadrat qoslsa, o san payda bolad; 4) eger teris sannan on kvadrat alnsa, teris san payda bolad; 5) eger o sannan on kvadrat alnsa, o san payda bolad. Tómendegi pikirlerdi qays biri durs, qays biri nadurs? Sebebin túsindiri . Sáykes msallar dúzi (144145): 144. 1) natural sann kvadrat qálegen san menen tamamlanw múmkin; 2) natural sann kub qálegen san menen tamamlanw múmkin. 145. 1) natural sann tórtinshi dárejesi tek 0; 1; 5; 6 san- larnan biri menen tamamlanw múmkin. 2) natural sann besinshi dárejesi sol san qays san me- nen tamamlan®an bolsa, sol san menen tamamlanad. x x 2 0 1 −1 2 −2 3 −3 4 −4 5 −5 6 −6 x x 3 0 1 −1 2 −2 3 −3 4 −4 5 −5 6 −6 59 10- Natural kórsetkishli dárejeni qásiyetleri Dárejege kóteriw birneshe áhmiyetli qásiyetlerge iye. 1-qásiyet. + ⋅ = . m n m n a a a Tiykarlar birdey dárejelerdi kóbeytiwde tiykar ózgerissiz qalad, dáreje kórsetkishleri bolsa qoslad. Natural kórsetkishli dárejeni anqlamasna muwapq { 2 3 2 2 (2 2) (2 2 2) ⋅ = ⋅ ⋅ ⋅ ⋅ = 1 424 3 2 márte 3 márte ( ) ( ) m n a a a a a a a a a a ⋅ = ⋅ ⋅ ⋅ ⋅ × ⋅ ⋅ ⋅ ⋅ K K 1442443 1442443 márte márte m n kóbeytiwdi gruppalaw nzamna muwapq 2 2 2 2 2 = ⋅ ⋅ ⋅ ⋅ = 14243 5 márte a a a a = ⋅ ⋅ ⋅ ⋅ = K 14 4244 3 márte (m+n) natural kórsetkishli dárejeni anqlamasna muwapq = 2 5 . = a m + n . Solay etip, 2 2 · 2 3 = 2 2+3 . a m · a n = a m + n . 2-qásiyet. − = > ≠ : , , 0 m n m n a a a m n a . Tiykarlar birdey dárejelerdi bóliwde tiykar ózgerissiz qalad, dáreje kórsetkishleri bolsa alnad. Shártke muwapq 5 > 3. m > n, a ≠ 0. Dárejeni birinshi qásiyeti boynsha 2 5 3 . 2 3 = 2 5 . a m n . a n = a m . Son ushn 2 5 3 = 2 5 : 2 3 . a m n = a m : a n . 60 Solay etip, 2 5 : 2 3 = 2 5 3 . a m : a n = a m n , m > n, a ≠ 0. = ≠ 1, 0 n n a a a ekenin aytp ótemiz. 3-qásiyet. = ( ) m n mn a a . Dárejeni dárejege kóteriwde tiykar ózgerissiz qalad, dáreje kórsetkishleri bolsa óz ara kóbeytiledi. Natural kórsetkishli dárejeni anqlamasna muwapq = ⋅ = 3 2 3 3 (2 ) 2 2 ( ) Download 1.97 Mb. Do'stlaringiz bilan baham: 
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