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  • 1. Äàðààõ çóðãààñ òýãø ºíöºãò ãóðâàëæíû ºíöã¿¿ä áîëîí òàëóóäûã íýðëý . A B CÊîñèíóñ íü 12 – òýé òýíöýõ ºíöºã áàéãóóë.Èëýðõèéëëèéã õÿëáàð÷èë. tan2α + cos2α + sin2α =cosα = 1112 áîë sinα= ? tanα=? cotα=?ABC òýãø ºíöºãò ãóðâàëæíû íýã ºíöºã íü 60° áà AB =43 áîë BC=? AC=?
  • 2. Äàðààõ òýãø ºíöºãò ãóðâàëæíû õóâüä Ïèôàãîðûí òåîðåì áè÷. A B CÑèíóñ íü 22 - òýé òýíöýõ ºíöºã áàéãóóë .Èëýðõèéëëèéã õÿëáàð÷èë.
  • 3. cot2α +cotα · tanα=sinα = 610 áîë cosα=? tanα=? cotα= ?C òýãø ºíöºãòýé ABC ãóðâàëæíû ∠A = 30° áà AB = 12 áîë AC=?,BC=?1510 · 2322- 572 +16 567 -11315 · 2528 èëýðõèéëëèéã õÿëáàð÷èë.à) y = x2 +2x -15 á) y = (2-x) (x + 6) â) y = -9+4x2 ôóíêöûíãðàôèêèéã áàéãóóë.x2 – (3à +2)x + à2 =0 òýãøèòãýëèéí ÿçãóóðóóä íü x1 áà x2 áºãººä x1= 9x2õàìààðàëòàé áîë à òîî áà x1 , x2 –èéã îë.à) y = x2+2xx2+5x+6 á) y= x2-2x+84-x â) y=x2 – x+1x2-1 ôóíêöûíòîäîðõîéëîãäîõ ìóæèéã îë.13-10 · 27-3 + (0.2)- 4 · 25-1· 25-2 + (64 -1/9 ) -3 èëýðõèéëëèéã õÿëáàð÷èë.Õî¸ð àæèë÷èí õàìòðàí 4 öàã àæèëëàæ áàñ I àæèë÷èí 3.5 öàã íýìæàæèëëàâàë 290 äåòàëü ¿éëäâýðëýõ áàéâ.Õýðýâ òýä õàìòðàí 5öàã àæèëëàâàë¿ëäñýí õýñãèéã II àæèë÷èí 2öàã 30 ìèíóòàä ã¿éöýòãýíý.Àæèë÷èí öàã òóòàìäõýäýí äåòàëü ¿éëäâýðëýõ âý?3 õºâã¿¿í 3 îõèíûã íýã ýãíýýíä çîãñîîõäîî îõèä áà õºâã¿¿äèéã ñàëààâ÷ëàíçîãñîîñîí áîë òýä õýäýí ÿíçààð çîãñîõ âý?
  • 4. Òðàïåöûí ñóóðèóä 5:9 õàðüöààòàé , õàæóó òàëóóäûí íýã íü 16ñì .ͺ㺺õàæóó òàëûí ¿ðãýëæëýëòýé îãòëîëöóóëàõûí òóëä ýíý õàæóó òàëûã õè÷íýýí¿ðãýëæë¿¿ëýõ âý?Öýãýýñ øóëóóíä ïåðïåíäèêóëÿð áà õî¸ð íàëóó òàòàâ.Õýðýâ íàëóóíóóä 41ñìáà 50ñì áà øóëóóí äýýðõ ïðîåêöóóä íü 3:1 õàðüöààòàé ïåðïåíäèêóëÿðûíóðòûã îë.Àäèë õàæóóò òýãø ºíöºãò ãóðâàëæèíä õî¸ð îðîé íü ãåïîòåíóç äýýð, õî¸ðîðîé íü êàòåòóóä äýýð îðøèõ òýãø ºíöºãò áàãòààâ.Ãóðâàëæíû ãèïîòåíóç45ñì òýãø ºíöºãòèéí òàëóóäûí õàðüöàà 5:2 áîë òàëóóäûã îë.Òðàïåöûí õàæóó òàëóóäûã 6 òýíö¿¿ õýñýãò õóâààæ õóâààëòûí öýã¿¿äèéãäàéðóóëàí ñóóðüòàé ïàðàëëåëààð íºãºº õàæóó òàëòàé õýð÷ìýýð õîëáîâ.Õýðýâòðàïåöûí ñóóðèóä 10ñì 28 ñì áîë ýäãýýð õýð÷ì¿¿äèéí óðòûã îë.à ñóóðüòàé àäèë õàæóóò òýãø ºíöºãò ãóðâàëæíû õàæóó òàëûã îë.ACB ãóðâàëæíû òýãø ºíöãèéí îðîé C-ýýñ CD áèññåêòðèññ òàòàâ.Õýðýâ∠CDB =105° , AC=3 áîë DB – ã îë.
  • 5. Ãóðâàëæíû a áà â óðòòàé òàëóóäûí õîîðîíäîõ ºíöºã α áîëíî.α íü 45° ,60°,90° ¿åä ãóðàâäàõü òàëûã îë.ABCD òðàïåöûí B îðîéãîîñ õàæóó òàë CD –òýé ïàðàëëåëü øóëóóí òàòàõàäAD-ã E öýãò îãòîëíî.ABE ãóðâàëæíû ïåðèìåòð 10äì ED=3äì áîë òðàïåöûíïåðèìåòðèéã îë.30ñì ñóóðüòàé 10ñì ºíäºðòýé ãóðâàëæèíä 63ñì2 òàëáàéòàé òýãø ºíöºãòáàãòàâ.Òýãø ºíöºãòèéí òàëóóäûã îë.À(-2;0) B(0;3) C(2;0) D(0;-3) öýã¿¿äýýð ºãºãäñºí ä¿ðñèéí õýëáýðèéãòîäîðõîéë.AOB ãóðâàëæèíä OC ìåäèàí òàòæýý. Ñ öýãèéí êîîðäèíàòûã òîäîðõîéëA (-5;0) B( 0;-3 )A òºâòýé R ðàäèóñòàé òîéðãèéí òýãøèòãýë çîõèî.A (7;11) R= 5
  • 6. Äàðààõ òýãøèòãýëýýð ºãºãäñºí øóëóóíóóä êîîðäèíàòûí òýíõëýã¿¿äòýéîãòëîëöîõ öýãèéã îë.à) x+y-7=0 á) 3x-4y-8=0Êîîðäèíàòûí ýõýýñ m øóëóóí õ¿ðòýëõ çàé 3-òàé òýíö¿¿ m øóëóóí x2 + ¿2=16òîéðîãòîé îãòëîëöîõ óó?õ2 + ¿2 -8õ-6¿+7=0 òîéðîã OX òýíõëýãòýé îãòëîëöîõ öýãèéí êîîðäèíàòûã îë.À(-3;0) B(0;4) C(3;0) öýã¿¿äýýð ºãºãäñºí ä¿ðñèéí õýëáýðèéãòîäîðõîéë.AOB ãóðâàëæèíä OC ìåäèàí òàòæýý. Ñ öýãèéí êîîðäèíàòûã òîäîðõîéë.A (0;-4) B( 5;-2 )A òºâòýé R ðàäèóñòàé òîéðãèéí òýãøèòãýë çîõèî. A (-9;4) R= 7
  • 7. Äàðààõ òýãøèòãýëýýð ºãºãäñºí øóëóóíóóä êîîðäèíàòûí òýíõëýã¿¿äòýéîãòëîëöîõ öýãèéã îë. à)õ-y+4=0 á) 3õ+4y-16=0x2 + ¿2=9 òýãøèòãýëòýé òîéðãèéí òºâººñ a øóëóóí õ¿ðòýëõ çàé 5-òàé òýíö¿¿áîë òîéðîãòîé îãòîëöîõ óó?õ2 + ¿2 -6õ-4¿-3=0 òîéðîã OY òýíõëýãòýé îãòëîëöîõ öýãèéí êîîðäèíàòûã îë.1. Êâàäðàòûã òàëààð íü áàéãóóë.2. Êîñèíóñ áà òàíãåíñûí òîäîðõîéëîëòûã áè÷.3. Òðèãîíîìåòðûí ¿íäñýí 6 àäèëòãàëóóäûã áè÷.4. Äàðààõ óòãóóäûã áºãëºíº ¿¿? 0 30 45 60° 90° ° ° ° sinα ctg α5. a) 26°, 31° ,108°, 199 ° á) 90°, 100 °, 90°, 100° äºðâºíºíöºãò áàéõ óó? ¯íäýñëýëòýé
  • 8. òàéëáàðëà.6. ßìàð äºðâºí ºíöºãòèéã òðàïåö ãýäýã âý? Õàðèóëòûã ¿ãýýð áè÷ýýä çóðàãä¿ðñëýëýýð èëýðõèéëýýðýé7. äàðààõ ºã¿¿ëáýðèéã ã¿éöýýãýýðýé a) ïàðàëëåëîãðàììûí ýñðýã òàëóóä áà ……………….. á) …………………….. …………. îãòëîëöëûíõîî öýãýýð õàãàñëàíõóâààãäàíà. â) ïàðàëëåëîãðàììûí …………..õîñ õîñîîðîî ïàðàëëåëü áàéíà.8. Òýãø ºíöºãòèéí íýã òàë íü 15 ñì ,äèàãîíàë íü 17 ñì òýãø ºíöºãòèéíòàëáàéã îë.9. Ðîìáûí òàë íü 4 ñì íýã ºíöºã íü 60° áîë äèàãîíàëèóäûã îë.Êâàäðàòûã äèàãîíàëèàð íü áàéãóóë.Êîñèíóñ áà òàíãåíñûí òîäîðõîéëîòûã áè÷.Òðèãîíîìåòðûí ¿íäñýí 6 àäèëòãàëóóäûã áè÷.
  • 9. Äàðààõ óòãóóäûã áºãëºíº ¿¿? 0 30 45 60 90 ° ° ° ° ° cos α tgαà) 81°, 99° ,81°, 99° á) 50°, 112 °, 98°, 100° äºðâºí ºíöºãò áàéõóó? ¯íäýñëýëòýé òàéëáàðëà.ßìàð äºðâºí ºíöºãòèéã ïàðàëëåëîãðàìì ãýäýã âý? Õàðèóëòûã ¿ãýýð áè÷ýýäçóðàã ä¿ðñëýëýýð èëýðõèéëýýðýé 7. Äàðààõ ºã¿¿ëáýðèéã ã¿éöýýãýýðýé à) Òðàïåöûã …………….íü õàæóó ãýäýã. á) Òðàïåöûí ýñðýã õî¸ð îðîéã õîëáîñîíûã ……….. â) Òðàïåöûí õî¸ð õàæóóãèéí …………………. äóíäàæ øóãàìãýíý. 8. Òýãø ºíöºãò õýëáýðòýé ãàçðûí ïåðèìåòð 78 ì ,òàëáàé íü 324 ì 2áîë òàëóóäûã îë. 9. Ðîìáûí äèàãîíàëü 16 ì ,12 ì áîë ðîìáûí òàëóóäûã îë.