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Ïðàâîîáëàäàòåëÿì

Ñáîðíèê çàäà÷ ïî àëãåáðå: ó÷åáíîå ïîñîáèå äëÿ 8-9 êë. ñ óãëóáëåííûì èçó÷åíèåì ìàòåìàòèêè.  Ãàëèöêèé Ì.Ë., Ãîëüäìàí À.Ì., Çâàâè÷ Ë.È.

7-å èçä., Ì.: Ïðîñâåùåíèå, 2001. - 271ñ. 





Êíèãà ïðåäñòàâëÿåò ñîáîé ñáîðíèê çàäà÷ ïî êóðñó àëãåáðû, ïðåäíàçíà÷åííûé äëÿ ó÷àùèõñÿ 8-9 êëàññîâ ñ óãëóáëåííûì èçó÷åíèåì ìàòåìàòèêè.  ïîñîáèè ñîäåðæàòñÿ çàäà÷è, ñïîñîáñòâóþùèå ñèñòåìàòè÷åñêîìó óãëóáëåíèþ èçó÷àåìîãî ìàòåðèàëà è ðàçâèòèþ íàâûêîâ ðåøåíèÿ ñëîæíûõ çàäà÷, à òàêæå ïîäãîòîâêå ê âñòóïèòåëüíûì ýêçàìåíàì â X êëàññ øêîë, ãèìíàçèé è ëèöååâ ñ óãëóáëåííûì èçó÷åíèåì ìàòåìàòèêè.

 ïîñîáèè ñîäåðæàòñÿ òðèíàäöàòü ïàðàãðàôîâ, îõâàòûâàþùèõ âñå îñíîâíûå òåìû êóðñà àëãåáðû 8 è 9 îáùåîáðàçîâàòåëüíûõ êëàññîâ è ðÿä äîïîëíèòåëüíûõ âîïðîñîâ, ñîîòâåòñòâóþùèõ ïðîãðàììå ìàòåìàòè÷åñêèõ êëàññîâ.  íà÷àëå êàæäîãî ïàðàãðàôà ïîìåùåíû ñïðàâî÷íûé ìàòåðèàë òåîðåòè÷åñêîãî õàðàêòåðà è ðåøåíèå íåñêîëüêèõ òèïîâûõ çàäà÷. Çàäà÷íèê ìîæåò áûòü èñïîëüçîâàí è â îáùåîáðàçîâàòåëüíûõ øêîëàõ è êëàññàõ.

(íà÷èíàÿ ñî ñòð. 226 - îòâåòû è óêàçàíèÿ)

 

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ÎÃËÀÂËÅÍÈÅ

Ïðåäèñëîâèå                                                                                                                 3

§ 1. Ïîâòîðåíèå è óãëóáëåíèå êóðñà àëãåáðû 7 êëàññà                                            4

§ 2. Ðàöèîíàëüíûå äðîáè                                                                                           11

Öåëûå âûðàæåíèÿ                                                                                                       13

Äðîáíûå âûðàæåíèÿ                                                                                                   15

§ 3. Äåëèìîñòü öåëûõ ÷èñåë                                                                                      20

Äåëèìîñòü ÷èñåë. Äåëèìîñòü ñóììû è ïðîèçâåäåíèÿ                                            22

Òåîðåìà î äåëåíèè ñ îñòàòêîì                                                                                   23

Âçàèìíî ïðîñòûå ÷èñëà                                                                                             25
Íàèáîëüøèé îáùèé äåëèòåëü. Íàèìåíüøåå îáùåå êðàòíîå. Ïðîñòûå ÷èñëà     —

Ïðèçíàêè äåëèìîñòè                                                                                                  27
Èñïîëüçîâàíèå ðàçëîæåíèÿ íà ìíîæèòåëè âûðàæåíèé âèäà õ"-à" è

x2k+i+a2k+i B çàäà÷àõ íà äåëèìîñòü

Óðàâíåíèå â öåëûõ ÷èñëàõ                                                                                        28

Ðàçíûå çàäà÷è                                                                                                             29

§ 4. Êâàäðàòíûå êîðíè                                                                                               30

Àðèôìåòè÷åñêèé êâàäðàòíûé êîðåíü                                                                       32

Èððàöèîíàëüíûå ÷èñëà                                                                                              34

Ôóíêöèÿ ó = -ó/õ è åå ãðàôèê                                                                                     36

Êâàäðàòíûé êîðåíü èç ïðîèçâåäåíèÿ è äðîáè                                                        37

Ñëîæåíèå è âû÷èòàíèå êîðíåé                                                                                3 8

Óìíîæåíèå è äåëåíèå êîðíåé                                                                                  

Óïðàæíåíèÿ íà âñå äåéñòâèÿ ñ êîðíÿìè                                                                  42

§ 5. Êâàäðàòíûå óðàâíåíèÿ                                                                                       44

Íåïîëíûå êâàäðàòíûå óðàâíåíèÿ                                                                             46

Ïîëíûå êâàäðàòíûå óðàâíåíèÿ                                                                                 47

Äðîáíûå ðàöèîíàëüíûå óðàâíåíèÿ                                                                          51

Óðàâíåíèÿ, ñâîäÿùèåñÿ ê êâàäðàòíûì                                                                     52

Òåîðåìà Âèåòà                                                                                                             53

Èññëåäîâàíèå êâàäðàòíîãî óðàâíåíèÿ                                                                      55

Çàäà÷è íà ñîñòàâëåíèå êâàäðàòíûõ óðàâíåíèé                                                       56

§ 6. Íåðàâåíñòâà                                                                                                         59

×èñëîâûå íåðàâåíñòâà è èõ ñâîéñòâà                                                                       60

Íåðàâåíñòâà ñ îäíîé ïåðåìåííîé è èõ ñèñòåìû                                                     70

§ 7. Ñòåïåíü ñ öåëûì ïîêàçàòåëåì                                                                            82

§ 8. Ôóíêöèÿ                                                                                                                 87

Êâàäðàòè÷íàÿ ôóíêöèÿ                                                                                                90

Íåðàâåíñòâà âòîðîé ñòåïåíè. Ðàöèîíàëüíûå íåðàâåíñòâà                                     94

Ýëåìåíòàðíîå èññëåäîâàíèå ôóíêöèè                                                                     101

§ 9. Óðàâíåíèÿ è ñèñòåìû óðàâíåíèé                                                                      107

Óðàâíåíèÿ âûñøèõ ñòåïåíåé                                                                                    111

Óðàâíåíèÿ ñ äâóìÿ ïåðåìåííûìè. Çàäàíèå ôèãóð íà êîîðäèíàòíîé                    114

ïëîñêîñòè óðàâíåíèÿìè è íåðàâåíñòâàìè

Ãðàôè÷åñêîå ðåøåíèå ñèñòåìû óðàâíåíèé                                                              116

Ñèñòåìû ëèíåéíûõ óðàâíåíèé è ñèñòåìû, ñâîäÿùèåñÿ ê íèì                             117

Íåëèíåéíûå ñèñòåìû óðàâíåíèé                                                                             119

§ 10. Òåêñòîâûå çàäà÷è                                                                                               129

§11. Ñòåïåíü ñ ðàöèîíàëüíûì ïîêàçàòåëåì                                                            143

Êîðåíü ï-é ñòåïåíè                                                                                                    146

Ñâîéñòâà àðèôìåòè÷åñêîãî êîðíÿ ï-é ñòåïåíè                                                       147

Ñòåïåíü ñ ðàöèîíàëüíûì ïîêàçàòåëåì                                                                    151

Ñâîéñòâà ñòåïåíè ñ ðàöèîíàëüíûì ïîêàçàòåëåì                                                    152

Èððàöèîíàëüíûå óðàâíåíèÿ                                                                                      156

Èððàöèîíàëüíûå íåðàâåíñòâà                                                                                  159

§ 12. Ïîñëåäîâàòåëüíîñòè è ïðîãðåññèè                                                                  160

Ïîñëåäîâàòåëüíîñòè                                                                                                   163

Ìåòîä ìàòåìàòè÷åñêîé èíäóêöèè                                                                             167

Àðèôìåòè÷åñêàÿ ïðîãðåññèÿ                                                                                      169

Ãåîìåòðè÷åñêàÿ ïðîãðåññèÿ                                                                                       173

Êîìáèíèðîâàííûå çàäà÷è íà àðèôìåòè÷åñêóþ è ãåîìåòðè÷åñêóþ                       175

ïðîãðåññèè

Ñóììèðîâàíèå                                                                                                            177

Ïðåäåë ïîñëåäîâàòåëüíîñòè. Áåñêîíå÷íàÿ ãåîìåòðè÷åñêàÿ ïðîãðåññèÿ               179

§ 13. Òðèãîíîìåòðè÷åñêèå âûðàæåíèÿ è èõ ïðåîáðàçîâàíèÿ                                183
Îïðåäåëåíèå ñèíóñà, êîñèíóñà, òàíãåíñà è êîòàíãåíñà. Ðàäèàííàÿ ìåðà óãëà 187
Çàâèñèìîñòü ìåæäó ôóíêöèÿìè îäíîãî àðãóìåíòà. Ôîðìóëû ïðèâåäåíèÿ        189

Òåîðåìû ñëîæåíèÿ                                                                                                     192

Ôîðìóëû äâîéíîãî è ïîëîâèííîãî àðãóìåíòà                                                        195
Ïðåîáðàçîâàíèå ñóììû òðèãîíîìåòðè÷åñêèõ ôóíêöèé â ïðîèçâåäåíèå è         199

îáðàòíî

Òåìàòè÷åñêèå ñåðèè äëÿ îðãàíèçàöèè çàêëþ÷èòåëüíîãî ïîâòîðåíèÿ                  202

Ïðèëîæåíèå. Îáîáùàþùèå ïðîâåðî÷íûå ðàáîòû                                                 213
Òåêñòû ýêçàìåíàöèîííûõ ðàáîò ïî àëãåáðå äëÿ IX êëàññîâ ñ óãëóáëåííûì       222

èçó÷åíèåì ìàòåìàòèêè

Îòâåòû. Óêàçàíèÿ. Ðåøåíèÿ                                                                                   226

 

 


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