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Ïðàâîîáëàäàòåëÿì

Çàäà÷è óñòíîãî ýêçàìåíà ïî ìàòåìàòèêå.  Ôåäîòîâ Ì.Â., Õàéëîâ Å.Í.

Ïîäãîòîâêà ê âñòóïèòåëüíûì ýêçàìåíàì â ÌÃÓ.

 

3-å èçä., ïåðåðàá. è äîï. -  Ì.: ôàêóëüòåò ÂÌèÊ ÌÃÓ, 2000. - 132ñ. 

Íàñòîÿùåå ïîñîáèå ñîñòàâëåíî äëÿ ïîäãîòîâèòåëüíûõ êóðñîâ ôàêóëüòåòà âû÷ìñëèòåëüíîé ìàòåìàòèêè è êèáåðíåòèêè ÌÃÓ èìåíè Ì.Â. Ëîìîíîñîâà. Ìîæåò áûòü ïîëåçíî àáèòóðèåíòàì ïðè ïîäãîòîâêå ê ïîñòóïëåíèþ êàê íà ôàêóëüòåò ÂÌèÊ, òàê è íà äðóãèå ôàêóëüòåòû ÌÃÓ, ãäå åñòü óñòíûé ýêçàìåí ïî ìàòåìàòèêå.

 

 

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Ñîäåðæàíèå

×àñòü I. Çàäà÷è ïî àëãåáðå

§ 1 Äåéñòâèòåëüíûå ÷èñëà                                                                                             7

ï. 1.1. Öåëûå ÷èñëà. Äåëèìîñòü                                                                                    7

ï. 1.2. Ðàöèîíàëüíûå è èððàöèîíàëüíûå ÷èñëà                                                     12

ï. 1.3. Ñðàâíåíèå ÷èñåë                                                                                                 15

§2. Êâàäðàòíûé òðåõ÷ëåí è åãî ñâîéñòâà. Òåîðåìà Âèåòà                                      18

§3. Òðèãîíîìåòðè÷åñêèå çàäà÷è                                                                                  23

§4. Ëîãàðèôìè÷åñêèå è ïîêàçàòåëüíûå çàäà÷è                                                        26

§5. Ðåøåíèå óðàâíåíèé è íåðàâåíñòâ                                                                        27

ï. 5.1. Ðàöèîíàëüíûå óðàâíåíèÿ è íåðàâåíñòâà                                                       29

ï. 5.2. Èððàöèîíàëüíûå óðàâíåíèÿ è íåðàâåíñòâà                                                   34

ï. 5.3. Òðèãîíîìåòðè÷åñêèå óðàâíåíèÿ è íåðàâåíñòâà                                             37

ï. 5.4. Ëîãàðèôìè÷åñêèå è ïîêàçàòåëüíûå óðàâíåíèÿ è íåðàâåíñòâà                49

ï. 5.5. Ðåøåíèå óðàâíåíèé è íåðàâåíñòâ â öåëûõ ÷èñëàõ                                        45

§6. Ðåøåíèå ñèñòåì óðàâíåíèé è íåðàâåíñòâ                                                           50

§7. Äîêàçàòåëüñòâà íåðàâåíñòâ è òîæäåñòâ                                                               57

§8. Çàäà÷è íà àðèôìåòè÷åñêèå è ãåîìåòðè÷åñêèå ïðîãðåññèè                            62

§9. Ôóíêöèè è èõ ãðàôèêè                                                                                              63

§10. Èçîáðàæåíèå ìíîæåñòâà òî÷åê íà ïëîñêîñòè                                                72

§11. Ìíîãî÷ëåíû                                                                                                            75

§12. Çàäà÷è ïîñëåäíèõ ëåò                                                                                          75

ï. 12.1. Ôàêóëüòåò ÂÌèÊ ÌÃÓ (1997 - 1999 ãã.)                                                        76

ï. 12. 2. Ãåîëîãè÷åñêèé ôàêóëüòåò ÌÃÓ (1997 - 1999 ãã.)                                       78

ï. 12.3. Ìåõàíèêî-ìàòåìàòè÷åñêèé ôàêóëüòåò ÌÃÓ (1998- 1999ãã.)                   80

Îòâåòû                                                                                                                               111

×àñòü Ï. Çàäà÷è ïî ãåîìåòðèè

§ 1. Çàäà÷è, ñâÿçàííûå ñ òðåóãîëüíèêàìè                                                                82

§2. Çàäà÷è, ñâÿçàííûå ñ ÷åòûðåõóãîëüíèêàìè                                                         90

§3. Çàäà÷è, ñâÿçàííûå ñ îêðóæíîñòüþ                                                                        94

§4. Ïëîùàäè ôèãóð                                                                                                       99

§5. Çàäà÷è íà ïîñòðîåíèå                                                                                          105

Îòâåòû                                                                                                                              127

 

 


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