8. Sınıf Öğreniyorum Serisi Matematik Soru Bankası

["Do\u011frular\u0131n \u00dczerindeki Noktalar Bir nokta bir do\u011fru \u00fczerindeyse o noktan\u0131n x ve y koordinatlar\u0131 do\u011frunun denkleminde yerine yaz\u0131ld\u0131\u011f\u0131nda e\u015fitlik sa\u011flan\u0131r. \u00d6rnek: A(4,2) noktas\u0131n\u0131n 2x + y = 10 do\u011frusunun \u00fczerinde olup olmad\u0131\u011f\u0131n\u0131 inceleyelim. A(4,2) \u2020 2x + y = 10 2\u00b74 + 2 = 10 E\u015fitlik do\u011fru oldu\u011funda A noktas\u0131 bu do\u011frunun \u00fczerindedir. xy 8 + 2 = 10 10 = 10 61 4. A\u015fa\u011f\u0131daki tabloda verilen noktalar, denklemleri verilen do\u011frunun \u00fczerinde ise uygun kutucu\u011fa 1. A\u015fa\u011f\u0131daki noktalar\u0131n kar\u015f\u0131lar\u0131nda verilen do\u011fru- \u201c\ufffd\u201d i\u015fareti koyunuz. nun \u00fczerinde olup olmad\u0131\u011f\u0131n\u0131 inceleyiniz. a) A(4,1) \u2020 y = x \u2013 3 x = 3 \u2013 y 2x + y = 4 x \u2013 2y = \u20131 (1,2) b) B(\u20132,4) \u2020 y + 2x \u2013 8 = 0 (2,3) (3,4) c) C(3,5) \u2020 y = 3x \u2013 4 2. K(a,6) noktas\u0131 y = 3x do\u011frusu \u00fczerinde ise a\u2019n\u0131n de\u011ferini bulunuz. 5. E(\u20135,n) noktas\u0131 x - y =0 do\u011frusu \u00fczerinde ol- 5 3 3. 2mx + 4y = \u20138 do\u011frusu A(1,1) noktas\u0131ndan ge\u00e7ti- du\u011funa g\u00f6re n\u2019nin de\u011ferini bulunuz. \u011fine g\u00f6re m\u2019nin de\u011ferini bulunuz. 250 8. S\u0131n\u0131f","Test Do\u011frusal Denklemlerin Grafi\u011fi Uyguluyorum 56 1. A\u015fa\u011f\u0131daki denklemlerden hangisine ait do\u011frunun 4. x = 4y do\u011frusunun grafi\u011fi a\u015fa\u011f\u0131dakilerden han- grafi\u011fi yanl\u0131\u015f \u00e7izilmi\u015ftir? gisidir? A) y B) y A) y B) y x=-2 4 2 y=2 x 1 O1 x O x -2 O x O4 C) y x=3 D) y C) y D) y 4 x O 3x Ox 1 x -3 y-3=0 -1 O -4 O 2. A\u015fa\u011f\u0131daki do\u011fru denklemlerinden hangisinin 5. 2x \u2013 y = 2 do\u011frusunun grafi\u011fi a\u015fa\u011f\u0131dakilerden grafi\u011fi ayn\u0131 zamanda y eksenidir? hangisidir? A) x \u2013 1 = 0 B) y + 1 = 0 A) y B) y C) x = 0 D) y = 0 2 O1 x O x 1 -2 3. I. x \u2013 5y = 0 II. 2x + y \u2013 6 = 0 C) y D) y x x -2 III. y = 4 1 Yukar\u0131daki denklemi verilen do\u011frulardan hangi- O O1 leri orijinden ge\u00e7er? -2 A) Yaln\u0131z I. B) I ve III. C) I ve II. D) II ve III. 8. S\u0131n\u0131f 251","Uyguluyorum Do\u011frusal Denklemlerin Grafi\u011fi Test 56 6. Denklemi 2y \u2013 8 = x olan do\u011frunun y eksenini 10. y kesti\u011fi nokta a\u015fa\u011f\u0131dakilerden hangisidir? m 2y=x+10 A) (0,\u20134) B) (0,4) 5 x C) (\u20138,0) D) (8,0) -10 O 20 7. A\u015fa\u011f\u0131daki noktalardan hangisi 7y + 2x = 0 do\u011fru- Yukar\u0131daki koordinat sisteminde verilenlere g\u00f6re su \u00fczerindedir? m ka\u00e7t\u0131r? A) (\u20137,2) B) (2,\u20137) A) 15 B) 20 C) 35 D) 40 C) (7,2) D) (\u20132,7) 8. y 11. A\u015fa\u011f\u0131daki koordinat sisteminde verilen karenin \u00e7evre uzunlu\u011fu 32 br\u2019dir. y m N 4M 6x x O -4 O K L x+y=6 Yukar\u0131da verilen m do\u011frusunun denklemi a\u015fa\u011f\u0131- dakilerden hangisidir? A) 2x + 3y = 0 B) 2x \u2013 3y = 0 Buna g\u00f6re bu karenin K k\u00f6\u015fesinin koordinatlar\u0131 C) \u20132x + 3y = 12 D) \u20132x + 3y = \u201312 a\u015fa\u011f\u0131dakilerden hangisidir? A) (\u20138,\u20134) B) (\u20136,\u20134) C) (\u20134,\u20138) D) (\u20134,\u20136) 9. 5y \u2013 3x = K denklemine ait do\u011fru orijinden ge\u00e7- 12. Bir koordinat sisteminde x = 7 ve y = a do\u011frular\u0131 ti\u011fine g\u00f6re K yerine a\u015fa\u011f\u0131dakilerden hangisi ya- 2x + y = 12 do\u011frusu \u00fczerinde kesi\u015fmektedir. z\u0131lamaz? A) 0 B) 2y C) \u20133x D) 1 Buna g\u00f6re a ka\u00e7t\u0131r? A) \u20135 B) \u20132 C) 2 D) 5 252 8. S\u0131n\u0131f","Do\u011frusal \u0130li\u015fki \u0130\u00e7eren Ger\u00e7ek Ya\u015fam Durumlar\u0131na Ait Denklem, Tablo ve Grafik Daha \u00f6nceki b\u00f6l\u00fcmlerde do\u011frusal ili\u015fkili de\u011fi\u015fkenlerin tablo ve denklem ile g\u00f6sterilmesini anlatt\u0131ktan sonra koordinat sisteminde do\u011fru grafiklerinin \u00e7izimlerini incelemi\u015ftik. Bu b\u00f6l\u00fcmde do\u011frusal ili\u015fkili de\u011fi\u015fkenlerin tablo ve denklem ile g\u00f6sterimine ek olarak grafikler ile g\u00f6sterimini anlataca\u011f\u0131z. \u00d6rnek: Yerden havaya b\u0131rak\u0131lan bir balon her dakikada yerden 25 m y\u00fckselmektedir. Ge\u00e7en s\u00fcreye g\u00f6re (x), balonun yerden y\u00fcksekli\u011fine (y) ait do\u011frusal ili\u015fkiyi tablo, denklem ve grafik ile g\u00f6sterelim. S\u00fcre Yerden \u0130li\u015fki S\u0131ral\u0131 \u0130kili y (x) Y\u00fcksekli\u011fi Yerden Y\u00fckseklik (m) 0\u00b725 (0,0) 100 0 (m) (y) 1\u00b725 (1,25) 1 0 2\u00b725 (2,50) 75 2 3\u00b725 (3,75) 50 3 25 25 ... ... ... 50 0 1234 x\u00b725 (x,25x) 75 ... x 25x x S\u00fcre (dakika) \u2022 Denklem: y = 25x 62 NOT: Do\u011frusal ili\u015fkili iki de\u011fi\u015fken aras\u0131ndaki do\u011fru grafi\u011fi \u0131\u015f\u0131n \u015feklindedir. 1. A\u015fa\u011f\u0131daki grafiklerden do\u011frusal ili\u015fki belirtenle- rin yan\u0131ndaki kutucu\u011fa \u201c\ufffd\u201d i\u015fareti koyunuz. e) y f) y a) y b) y xx xx c) y d) y x g) y h) y x x x 253 8. S\u0131n\u0131f","Do\u011frusal \u0130li\u015fki \u0130\u00e7eren Ger\u00e7ek Ya\u015fam Durumlar\u0131na Ait Denklem, Tablo ve Grafik 2. A\u015fa\u011f\u0131da verilen do\u011frusal ili\u015fkili de\u011fi\u015fkenlere ait b) Do\u011fdu\u011funda boyu 50 cm olan bir bebek do\u011fu- tablo, denklem ve grafi\u011fi olu\u015fturunuz. munun ilk y\u0131l\u0131nda her ay 4 cm uzam\u0131\u015ft\u0131r. a) Yeliz her g\u00fcn 40 sayfa kitap okumaktad\u0131r. S\u00fcre (ay) Boy (cm) \u0130li\u015fki S\u0131ral\u0131 \u0130kili (x) (y) S\u00fcre Toplam Sayfa \u0130li\u015fki S\u0131ral\u0131 \u0130kili (g\u00fcn) (x) Say\u0131s\u0131 (y) Ba\u011f\u0131ml\u0131 De\u011fi\u015fken : ........................................... Ba\u011f\u0131ml\u0131 De\u011fi\u015fken : ........................................... Ba\u011f\u0131ms\u0131z De\u011fi\u015fken : ........................................... Ba\u011f\u0131ms\u0131z De\u011fi\u015fken : ........................................... Denklem : ........................................... Denklem : ........................................... y y x x 254 8. S\u0131n\u0131f","Do\u011frusal \u0130li\u015fki \u0130\u00e7eren Ger\u00e7ek Ya\u015fam Durumlar\u0131na Ait Denklem, Tablo ve Grafik c) Puan\u0131 14 olan bir futbol tak\u0131m\u0131 bu andan itibaren d) Uzunlu\u011fu 44 cm olan bir mum yak\u0131lmaya ba\u015fla- oynad\u0131\u011f\u0131 her ma\u00e7tan 3 puan kazanm\u0131\u015ft\u0131r. d\u0131ktan sonra her 5 dakikada 3 cm k\u0131salmaktad\u0131r. Ma\u00e7 Puan (y) \u0130li\u015fki S\u0131ral\u0131 \u0130kili S\u00fcre (dk) Uzunluk \u0130li\u015fki S\u0131ral\u0131 \u0130kili Say\u0131s\u0131 (x) (x) (cm) (y) Ba\u011f\u0131ml\u0131 De\u011fi\u015fken : ........................................... Ba\u011f\u0131ml\u0131 De\u011fi\u015fken : ........................................... Ba\u011f\u0131ms\u0131z De\u011fi\u015fken : ........................................... Ba\u011f\u0131ms\u0131z De\u011fi\u015fken : ........................................... Denklem : ........................................... Denklem : ........................................... yy x x 8. S\u0131n\u0131f 255","Uyguluyorum Do\u011frusal \u0130li\u015fki \u0130\u00e7eren Ger\u00e7ek Ya\u015fam Durumlar\u0131 Test 57 1. Bir dondurma firmas\u0131, \u00fcretti\u011fi her 4 dondurmadan 3. A\u015fa\u011f\u0131daki grafik kareli zemin ile d\u00f6rt b\u00f6lgeye ayr\u0131l- 1\u2019ine hediye etiketi yap\u0131\u015ft\u0131rmaktad\u0131r. m\u0131\u015ft\u0131r. y Buna g\u00f6re firman\u0131n \u00fcretti\u011fi dondurma say\u0131s\u0131 (x) ile hediye etiketi yap\u0131\u015ft\u0131rd\u0131\u011f\u0131 dondurma say\u0131s\u0131 (y) aras\u0131ndaki do\u011frusal ili\u015fkiyi g\u00f6steren tablo a\u015fa\u011f\u0131- dakilerden hangisidir? A) y B) y 8 4 2 1234 x x0 4 8 x 02 Buna g\u00f6re ka\u00e7\u0131nc\u0131 b\u00f6lgede yer alan grafik do\u011fru- C) y D) y 8 sal ili\u015fki g\u00f6stermektedir? A) 1. B) 2. C) 3. D) 4. 4 2 1 0 4 x 0 12 x 8 4. A\u015fa\u011f\u0131daki do\u011frusal grafik Esin\u2019in banka hesab\u0131ndaki paras\u0131n\u0131n zamana g\u00f6re de\u011fi\u015fimini g\u00f6stermektedir. y 1800 1200 600 2. Deposunda 55 L yak\u0131t bulunan bir ara\u00e7 her 100 km 0 1234 x Zaman yol ald\u0131\u011f\u0131nda 7 L yak\u0131t t\u00fcketmektedir. (g\u00fcn) Buna g\u00f6re arac\u0131n deposunda bulunan yak\u0131t mik- Buna g\u00f6re; tar\u0131 (y) ile ald\u0131\u011f\u0131 yol (x) aras\u0131ndaki do\u011frusal ili\u015fkiyi I. Ba\u015flang\u0131\u00e7ta hesab\u0131nda \u2013300 TL vard\u0131r. g\u00f6steren denklem a\u015fa\u011f\u0131dakilerden hangisidir? II. Her iki ayda bir hesab\u0131ndaki para iki kat\u0131na \u00e7\u0131k- maktad\u0131r. A) y = 55 - 7x 7y 100 B) x = 55 - 100 C) 100y = 55 - 7x D) 100x = 55 - 7y III. 10. ay sonunda hesab\u0131nda 5400 TL bulunur. ifadelerinden hangileri do\u011frudur? A) Yaln\u0131z III. B) II ve III. C) I ve III. D) I, II ve III. 256 8. S\u0131n\u0131f","Test Do\u011frusal \u0130li\u015fki \u0130\u00e7eren Ger\u00e7ek Ya\u015fam Durumlar\u0131 Uyguluyorum 57 5. 20 cm uzunlu\u011fundaki bir mum yanmaya ba\u015flad\u0131ktan 8., 9., ve 10. sorular\u0131 a\u015fa\u011f\u0131daki bilgilere g\u00f6re ce- sonra her 2 saatte bir 3 cm k\u0131salmaktad\u0131r. vaplay\u0131n\u0131z. Buna g\u00f6re bu mum yanmaya ba\u015flad\u0131ktan 9 saat Bilgi: Bitkilerin boy uzunlu\u011fu toprak \u00fczerinde kalan sonra ka\u00e7 santimetre kal\u0131r? k\u0131s\u0131mlar\u0131ndan hesaplanmaktad\u0131r. A\u015fa\u011f\u0131da bir bitkinin tohum olarak topra\u011fa ekildikten A) 7,5 B) 7 C) 6,5 D) 6 sonra boy uzunlu\u011funun zamana ba\u011fl\u0131 olarak de\u011fi\u015fi- mini g\u00f6steren do\u011frusal grafik verilmi\u015ftir. 6. Bir eczane her ay e\u015fit miktarda serum satmaktad\u0131r. A\u015fa\u011f\u0131da bu eczanede sat\u0131lan ve kalan serum mikta- Uzunluk (cm) r\u0131n\u0131 g\u00f6steren do\u011frusal ili\u015fki verilmi\u015ftir. 12 Serum Adedi 1800 Sat\u0131lan Serum Say\u0131s\u0131 02 5 Hafta Kalan Serum -8 Say\u0131s\u0131 20 Ay Buna g\u00f6re ka\u00e7\u0131nc\u0131 ay sonunda eczanede 225 adet 8. Fidan\u0131n zamana g\u00f6re (x), uzunlu\u011funu (y) g\u00f6ste- serum kal\u0131r? ren do\u011frusal denklem a\u015fa\u011f\u0131dakilerden hangisi- A) 25 B) 30 C) 35 D) 40 dir? A) y = 8x + 12 B) y = 4x + 8 C) y = 2x \u2013 8 D) y = 4x \u2013 8 7. Ay cinsinden ge\u00e7en s\u00fcre (x), santimetre cinsinden 9. Fidan\u0131n ka\u00e7\u0131nc\u0131 hafta sonundaki uzunlu\u011fu 5. haf- boylar\u0131 (y) olmak \u00fczere iki farkl\u0131 bebe\u011fin boylar\u0131n\u0131n tadaki uzunlu\u011funun iki kat\u0131 olur? aylara g\u00f6re de\u011fi\u015fimini g\u00f6steren denklem a\u015fa\u011f\u0131da verilmi\u015ftir. A) 10 B) 9 C) 8 D) 7 1. Bebek 2. Bebek y = 10 + 5x y = 2 + 7x Buna g\u00f6re ka\u00e7\u0131nc\u0131 ay sonunda bebeklerin boylar\u0131 10. Fidan\u0131n 12. hafta sonundaki santimetre cinsinden birbirine e\u015fittir? uzunlu\u011funun rakamlar\u0131 toplam\u0131 ka\u00e7t\u0131r? A) 5 B) 4 C) 3 D) 2 A) 4 B) 7 C) 8 D) 11 8. S\u0131n\u0131f 257","Ba\u015far\u0131yorum Do\u011frusal \u0130li\u015fki \u0130\u00e7eren Ger\u00e7ek Ya\u015fam Durumlar\u0131na Test Ait Tablo, Grafik ve Denklemler 58 1. A\u015fa\u011f\u0131da g\u00f6sterilen \u00f6zde\u015f demir bloklar\u0131n tamam\u0131 bir kamyonla belirli bir noktaya ta\u015f\u0131nacakt\u0131r. 480 adet Ta\u015f\u0131ma i\u015flemi yap\u0131l\u0131rken kamyona 20\u2019\u015fer blok y\u00fcklenmektedir. Kamyonun y\u00fckleme i\u015flemi ile beraber 20 blo\u011fu b\u0131ra- k\u0131p geri d\u00f6nmesi ise her seferinde 40 dakika s\u00fcrmektedir. Buna g\u00f6re dakika cinsinden ge\u00e7en s\u00fcre (x), ta\u015f\u0131nmadan kalan blok say\u0131s\u0131 (y) aras\u0131ndaki do\u011frusal ili\u015fkiyi g\u00f6steren denklem a\u015fa\u011f\u0131dakilerden hangisidir? A) y \u2013 480 = 1 \u00b7x B) y = 480 - 1 \u00b7x C) y = 480 \u2013 40\u00b7x D) y \u2013 40\u00b7x = 480 2 2 2. Mert ve \u00c7etin iklim de\u011fi\u015fikli\u011fi ve yenilenebilir enerji faaliyetleri i\u00e7in bir \u015firket kurmu\u015ftur. A\u015fa\u011f\u0131da 220 000 TL serma- ye ile kurulan bu \u015firketin gelir gider durumunun zamana ba\u011fl\u0131 de\u011fi\u015fimini g\u00f6steren do\u011frusal grafik verilmi\u015ftir. Tutar (TL) 280 000 Gider 220 000 Gelir 160 000 0 4 Zaman (ay) Buna g\u00f6re bu \u015firket ilk olarak ka\u00e7\u0131nc\u0131 ayda k\u00e2r elde etmeye ba\u015flam\u0131\u015ft\u0131r? D) 10 A) 7 B) 8 C) 9 258 8. S\u0131n\u0131f","Test Do\u011frusal \u0130li\u015fki \u0130\u00e7eren Ger\u00e7ek Ya\u015fam Durumlar\u0131na Ba\u015far\u0131yorum 58 Ait Tablo, Grafik ve Denklemler 3 ve 4. sorular\u0131 a\u015fa\u011f\u0131daki bilgilere g\u00f6re cevaplay\u0131n\u0131z. A\u015fa\u011f\u0131da kareli zemin \u00fczerindeki T\u00fcrkiye iller haritas\u0131 \u00fczerine bir koordinat sistemi yerle\u015ftirilmi\u015ftir. y x O 3. Ersin bu haritada y = 1 ve x = \u20133 do\u011frular\u0131n\u0131n kesi\u015fim noktas\u0131n\u0131n bulundu\u011fu ilde ya\u015famaktad\u0131r. Buna g\u00f6re Ersin\u2019in ya\u015fad\u0131\u011f\u0131 \u015fehir a\u015fa\u011f\u0131dakilerden hangisidir? A) Ankara B) Bolu C) K\u0131r\u0131kkale D) Yozgat 4. Hakan bu haritada denklemi y=2x-2 olan do\u011frunun grafi\u011finin ge\u00e7ti\u011fi illerin isimlerini \u00f6zde\u015f kartlara yazarak bo\u015f bir torbaya at\u0131yor. Buna g\u00f6re bu torbadan rastgele se\u00e7ilen bir kartta yazan ilin ismi i\u00e7in a\u015fa\u011f\u0131dakilerden hangisi olas\u0131 durum- lardan biridir? A) Antalya B) Diyarbak\u0131r C) Eski\u015fehir D) Sivas 8. S\u0131n\u0131f 259","Ba\u015far\u0131yorum Do\u011frusal \u0130li\u015fki \u0130\u00e7eren Ger\u00e7ek Ya\u015fam Durumlar\u0131na Test Ait Tablo, Grafik ve Denklemler 59 1. Bir i\u015f yerinde kullan\u0131lan fotokopi makinelerinden 1. sinde A, 2. sinde ise B marka toner kullan\u0131lmaktad\u0131r. A\u015fa\u011f\u0131da \u00e7ekilen fotokopi say\u0131s\u0131na g\u00f6re makinelerde kalan toner miktar\u0131 aras\u0131ndaki ili\u015fkiyi g\u00f6steren do\u011frusal grafik verilmi\u015ftir. Grafik: \u00c7ekim Say\u0131s\u0131na G\u00f6re Kalan Toner Miktar\u0131 Kalan Toner (gram) 150 120 90 B A 0 3000 \u00c7ekim Say\u0131s\u0131 (adet) 130 graml\u0131k A marka tonerin fiyat\u0131 700 TL ve 90 graml\u0131k B marka tonerin fiyat\u0131 900 TL\u2019dir. Bir ay i\u00e7inde 1. makine ile 19 500 adet, 2. makine ile 27 000 adet fotokopi \u00e7ekildi\u011finde belirtilen ayda tonerler i\u00e7in toplam ka\u00e7 lira \u00f6deme yap\u0131lm\u0131\u015ft\u0131r? A) 4200 B) 4500 C)4800 D) 5100 2. A\u015fa\u011f\u0131daki do\u011frusal grafiklerden 1. si bir boya ustas\u0131n\u0131n zamana ba\u011fl\u0131 olarak boyad\u0131\u011f\u0131 duvar\u0131n alan\u0131n\u0131, 2. si ise za- mana ba\u011fl\u0131 olarak ustan\u0131n boya kutusunda kalan boya miktar\u0131n\u0131 g\u00f6stermektedir. Grafik: Boyanan Duvar\u0131n Alan\u0131n\u0131n Grafik: Kalan Boya Miktar\u0131n\u0131n Zamana G\u00f6re De\u011fi\u015fimi Zamana G\u00f6re De\u011fi\u015fimi Alan (m2) Miktar (kg) 100 75 45 0 5 Zaman 04 Zaman (saat) (saat) Buna g\u00f6re bu usta kutudaki boyan\u0131n tamam\u0131yla ka\u00e7 metrekarelik duvar boyayabilir? A) 185 B) 200 C) 215 D) 230 260 8. S\u0131n\u0131f","Test Do\u011frusal \u0130li\u015fki \u0130\u00e7eren Ger\u00e7ek Ya\u015fam Durumlar\u0131na Ba\u015far\u0131yorum 59 Ait Tablo, Grafik ve Denklemler 3 ve 4. sorular\u0131 a\u015fa\u011f\u0131daki bilgilere g\u00f6re cevaplay\u0131n\u0131z. Bir s\u00fct fabrikas\u0131nda \u015fi\u015felere doldurmak i\u00e7in depoda bulunan s\u00fct miktar\u0131n\u0131n zamana g\u00f6re de\u011fi\u015fimini g\u00f6steren do\u011fru- sal grafik a\u015fa\u011f\u0131da verilmi\u015ftir. Tabloda ise bu s\u00fctlerin \u015fi\u015felenmesinde kullan\u0131lan \u015fi\u015fe say\u0131lar\u0131 g\u00f6sterilmi\u015ftir. Miktar (L) Tablo: Kullan\u0131lan \u015ei\u015fe Say\u0131s\u0131 3500 S\u00fct Miktar\u0131 (L) 123 4 2500 16 \u015ei\u015fe Say\u0131s\u0131 (adet) 4 8 12 02 6 Zaman (saat) 3. Buna g\u00f6re ba\u015flang\u0131\u00e7ta fabrikada bulunan s\u00fct miktar\u0131 ka\u00e7 litredir? A) 4000 B) 4250 C) 4500 D) 4750 4. Fabrikada kullan\u0131lan s\u00fct miktar\u0131 ile kalan s\u00fct miktar\u0131n\u0131n e\u015fit oldu\u011fu anda s\u00fctlerin doldurulmas\u0131 i\u00e7in ka\u00e7 adet \u015fi\u015fe kullan\u0131lm\u0131\u015ft\u0131r? A) 10 000 B) 9000 C) 8000 D) 7000 5. Sabit h\u0131zla \u00e7al\u0131\u015fan iki arkada\u015f\u0131n bir at\u00f6lyede diktikleri g\u00f6mlek say\u0131lar\u0131n\u0131n zamana ba\u011fl\u0131 de\u011fi\u015fimini g\u00f6steren do\u011frusal grafik a\u015fa\u011f\u0131da verilmi\u015ftir. Say\u0131 Ay\u015fe Beren 7 5 0 36 Zaman (saat) Buna g\u00f6re iki arkada\u015f ayn\u0131 anda e\u015fit s\u00fcrelerde \u00e7al\u0131\u015farak 68 adet g\u00f6mle\u011fi ka\u00e7 saatte dikerler? A) 12 B) 18 C) 24 D) 30 8. S\u0131n\u0131f 261","E\u011fim Bir do\u011fru \u00fczerinde bulunan iki nokta aras\u0131ndaki dikey uzunlu\u011fun, yatay uzunlu\u011fa oran\u0131na e\u011fim denir. C E\u20acim = |BC | = Dikey uzunluk Dikey Uzunluk |AB | Yatay uzunluk AB Yatay Uzunluk \u2022 E\u011fim m harfi ile g\u00f6sterilir. \u00d6rnek: C 7 br m= Dikey uzunluk = 7 = 0, 7 = %70 Yatay uzunluk 10 AB 10 br 63 NOT: Hesaplanabilen e\u011fim de\u011ferleri rasyonel say\u0131 oldu\u011fu i\u00e7in ondal\u0131k g\u00f6sterim ya da y\u00fczde 1. A\u015fa\u011f\u0131da kareli zeminde verilen \u015fekillerin e\u011fimini sembol\u00fc ile ifade edilebilir. bulunuz. 2. A\u015fa\u011f\u0131da verilen \u015fekillerin e\u011fimlerini onlad\u0131k g\u00f6s- a) b) terim ve y\u00fczde sembol\u00fc ile ifade ediniz. a) b) m= m= 2 br 8 br 18 br c) d) m= 24 br c) m= d) m= m= 12 br 9 br 5 br 15 br m= m= 262 8. S\u0131n\u0131f","E\u011fim 3. A\u015fa\u011f\u0131daki kareli ka\u011f\u0131da e\u011fimi verilen rampa mo- b) dellerini \u00e7iziniz. m = 0,5 a) m = 3 28 dm 4 c) m = 1 3 b) m = 0,3 c) m = 2 d) 24 m 5 m = 0,5 2000 mm d) m = 1 5. A\u015fa\u011f\u0131da noktal\u0131 ka\u011f\u0131t \u00fczerideki A, B, C ve D b\u00f6- l\u00fcmlerinin e\u011fimini bularak b\u00fcy\u00fckten k\u00fc\u00e7\u00fc\u011fe s\u0131- ralay\u0131n\u0131z. 4. A\u015fa\u011f\u0131da e\u011fimleri verilen dik \u00fc\u00e7genlerin dikey ya D da yatay uzunluklar\u0131n\u0131 bulunuz. a) C m=7 8 B A 32 dm 8. S\u0131n\u0131f 263","Koordinat Sisteminde Do\u011frunun E\u011fimi \u2022 Koordinat sistemindeki grafi\u011fi sa\u011fa yat\u0131k olan do\u011frular\u0131n e\u011fimi pozitif, sola yat\u0131k olan do\u011frular\u0131n e\u011fimi negatiftir. yy (sa\u011fa yat\u0131k) f 3d 2 -10 10 3 x 23 x O O 3 (sola yat\u0131k) 3 f do\u011frusunun e\u011fimi - 2 \u2019t\u00fcr. d do\u011frusunun e\u011fimi 10 \u2019dur. 3 \u2022 x eksenine paralel olan do\u011frular\u0131n e\u011fimleri s\u0131f\u0131r (0) iken, y eksenine paralel olan do\u011frular\u0131n e\u011fimleri tan\u0131ms\u0131zd\u0131r. y ny Ox Ox m m do\u011frusunun e\u011fimi 0\u2019d\u0131r. n do\u011frusunun e\u011fimi tan\u0131ms\u0131zd\u0131r. 64 b) y x 7 9 1. A\u015fa\u011f\u0131daki do\u011frular\u0131n e\u011fimlerini bulunuz. a) y O 3 O 11 x m= m= 264 8. S\u0131n\u0131f","Koordinat Sisteminde Do\u011frunun E\u011fimi c) y d) y -3 O x O 9x -6 -4 m= m= 2. A\u015fa\u011f\u0131da verilen noktalardan ge\u00e7en do\u011fruyu \u00e7izerek e\u011fimini bulunuz. a) A(3,0) ve B(0,6) b) C(3,2) ve D(1,-2) c) E(0,0) ve F(4,7) yyy Ox Ox Ox m= m= m= NOT: y = ax + b bi\u00e7imindeki do\u011frusal denklemlerde x\u2019in katsay\u0131s\u0131 olan a de\u011feri do\u011frunun e\u011fimine e\u015fittir. \u00d6rnek: \u2022 3y \u2013 12x = 6 do\u011frusunun e\u011fimini bulmak i\u00e7in \u00f6nce \u2022 y = 5x + 2 do\u011frusunun e\u011fimi 5\u2019tir. y\u2019yi yaln\u0131z b\u0131rakal\u0131m. e\u011fim 3y = 6 + 12x 3 3 e\u011fim y = 2 + 4x 3. A\u015fa\u011f\u0131daki denklemleri verilen do\u011frular\u0131n e\u011fimini d) 20 + 2y = 8x bulal\u0131m. a) y = 4x \u2013 1 b) y = \u20137x e) 5x = 2y \u2013 3 c) y= 2x +1 f) x \u2013 5y + 1 = 0 7 g) 2x \u2013 4y + 6 = 0 \u00e7) y = \u2013x 8. S\u0131n\u0131f 265","Koordinat Sisteminde Do\u011frunun E\u011fimi 4. A\u015fa\u011f\u0131daki kartlarda yazan denklemin e\u011fimi ile ayn\u0131 e\u011fime sahip olan rampa modellerini e\u015fle\u015ftiriniz. y = 2x + 3 y = x -1 4y - 3x = 6 -6y + 3x = 10 3 5 br 6 br 8 br 7 br 8 br 4 br 15 br 14 br NOT: \u2022 Birbirine paralel olan iki do\u011frunun e\u011fimleri birbirine e\u015fittir. \u2022 Birbirine dik olan iki do\u011frunun e\u011fimleri \u00e7arp\u0131m\u0131 \u20131\u2019dir. 5. A\u015fa\u011f\u0131da denklemleri verilen iki do\u011frunun paralel \u00e7) 2 ya da dik olup olmama durumunu inceleyiniz. (8,4) noktas\u0131ndan ge\u00e7en ve e\u011fimi 3 olan do\u011fru- a) y = \u20132x + 1 ve y = \u20132x + 3 nun x eksenini kesti\u011fi noktay\u0131 bulunuz. b) y = 5x \u2013 4 ve 5y + x = 3 d) (4,6) noktas\u0131ndan ge\u00e7en ve e\u011fimi \u20132 olan do\u011fru- nun denklemini bulunuz. c) 2y \u2013 3 = 6x ve x = 2 \u2013 3y e) E\u011fimi -3 olan ve orijinden ge\u00e7en do\u011frunun 266 8. S\u0131n\u0131f 5 denklemini bulunuz.","Test E\u011fim Uyguluyorum 60 4. 1. 11 m 17 m 13 m Yukar\u0131da kareli zeminde verilen \u015feklin e\u011fimi ka\u00e7- t\u0131r? 3 B) 7 6 2 Yukar\u0131daki iki bina aras\u0131na gerilen telin e\u011fimi A) 5 11 C) 11 D) 3 ka\u00e7t\u0131r? 13 B) 11 7 6 A) 17 17 C) 13 D) 13 5. 2. A B 18 m C D 20 m Yukar\u0131daki rampa modelinin e\u011fimi y\u00fczde ka\u00e7t\u0131r? Yukar\u0131daki rampa modellerinin e\u011fimlerinin b\u00fc- y\u00fckten k\u00fc\u00e7\u00fc\u011fe s\u0131ralan\u0131\u015f\u0131 a\u015fa\u011f\u0131dakilerden hangi- A) 90 B) 80 C) 70 D) 60 sidir? A) B > A > D > C B) B > D > A > C C) C > D > A > B D) A > B > D > C 6. 3. 8 cm %50 x cm Yukar\u0131daki \u015feklin e\u011fimi 2 oldu\u011funa g\u00f6re x ka\u00e7t\u0131r? Ba\u015flang\u0131\u00e7ta yukar\u0131daki trafik i\u015faretinin bulundu- \u011fu bir yolda yatayda 70 m yol alan bir ara\u00e7 dikey A) 16 B) 12 C) 4 D) 2 do\u011frultuda ka\u00e7 metre y\u00fckselmi\u015ftir? A) 25 B) 35 C) 120 D) 140 8. S\u0131n\u0131f 267","Uyguluyorum E\u011fim Test 60 7. A\u015fa\u011f\u0131da bir evin \u00e7at\u0131s\u0131n\u0131n y\u00fcksekli\u011fi ve uzunlu\u011fu 10. modellenmi\u015ftir. 5m 16 m Buna g\u00f6re \u00e7at\u0131n\u0131n e\u011fimi ka\u00e7t\u0131r? 20 cm 16 cm 5 B) 1 5 7 A) 16 2 C) 8 D) 5 Yukar\u0131daki merdivenin e\u011fimi y\u00fczde ka\u00e7t\u0131r? A) 40 B) 60 C) 80 D) 100 8. BC 11. A A E D 9m Kareli ka\u011f\u0131tta u\u00e7lar\u0131 hangi iki nokta olan do\u011fru B 12 m C D par\u00e7as\u0131n\u0131n e\u011fimi 0,5\u2019tir? Yukar\u0131daki \u015fekilde 2|AB| = 3|CD|\u2019dir. A) A ile C B) A ile B 3 C) D ile B D) D ile C [CE]\u2019nin e\u011fimi 2 oldu\u011funa g\u00f6re [AC]\u2019nin e\u011fimi ka\u00e7t\u0131r? 3 B) 1 4 D) 3 A) 4 C) 3 12. Deniz seviyesinden itibaren bir da\u011f\u0131n zirvesine do\u011fru kurulan teleferi\u011fin e\u011fimi 0,75\u2019tir. 9. E\u011fimi 1 olan bir rampan\u0131n dikey uzunlu\u011fu yar\u0131s\u0131 Bu teleferi\u011fe deniz seviyesinde binen birisi tele- 4 ferik 150 m y\u00fckseldi\u011fi anda yatay do\u011frultuda ka\u00e7 metre yol al\u0131r? kadar azalt\u0131l\u0131rsa yeni rampan\u0131n e\u011fimi ka\u00e7 olur? A) 2 B) 1 C) 1 1 A) 200 B) 240 C) 300 D) 360 2 D) 8 268 8. S\u0131n\u0131f","Test E\u011fim Uyguluyorum 61 y III y y 1. I y II xx 4. 4 x Ox Yukar\u0131daki do\u011frulardan hangilerinin e\u011fimi pozi- -5 -1 tiftir? A) Yaln\u0131z I. B) I ve II. C) II ve III. D) I ve III. Yukar\u0131da verilen koordinat sistemindeki do\u011fru- 2. A\u015fa\u011f\u0131da grafikleri verilen do\u011frulardan hangisinin nun e\u011fimi ka\u00e7t\u0131r? 2 A) 1 4 C) - 1 D) \u20131 e\u011fimi - 3 \u2019t\u00fcr? B) 5 2 A) y B) y 4 6 -6 O x -4 O x 5. y 4L C) y D) y 1K 5x 4 6 O1 O 6x O 4x Yukar\u0131daki koordinat sisteminde belirtilen K ve L noktalar\u0131ndan ge\u00e7en do\u011frunun e\u011fimi ka\u00e7t\u0131r? 5 B) 1 4 3 A) 4 C) 5 D) 4 3. A\u015fa\u011f\u0131da denklemi verilen do\u011frulardan hangisinin 6. Orijinden ge\u00e7en ve e\u011fimi 3 olan do\u011frunun denk- e\u011fimi 0\u2019d\u0131r? lemi a\u015fa\u011f\u0131dakilerden hangisidir? A) x = 5 B) y = 4x A) 3y = x B) 3y = \u2013x C) y \u2013 2x = 0 D) y \u2013 1 = 0 x D) y = 3x C) y = 3 8. S\u0131n\u0131f 269","Uyguluyorum E\u011fim Test 61 7. y A 10. Bilgi: Birbirine dik kesi\u015fen iki do\u011frunun e\u011fimleri \u00e7ar- p\u0131m\u0131 \u20131\u2019dir. d y BO x e C Ox Yukar\u0131daki koordinat sisteminde verilen ABC \u00fc\u00e7ge- ninde [AB]\u2019nin e\u011fimi 1\u2019dir. Buna g\u00f6re [AC]\u2019nin e\u011fimi ka\u00e7t\u0131r? A) - 1 B) \u20131 C) 1 D) 2 Yukar\u0131daki koordinat sisteminde verilen e do\u011frusu- 2 2 nun e\u011fimi 0,6\u2019d\u0131r. Buna g\u00f6re d do\u011frusunun e\u011fimi ka\u00e7t\u0131r? A) - 5 B) - 5 C) - 5 D) - 1 3 4 6 2 8. A\u015fa\u011f\u0131dakilerden do\u011frulardan hangisinin e\u011fimi tan\u0131ms\u0131zd\u0131r? A) y B) y 11. y 5 Ox Ox 2 O1 x m n C) y D) y Ox Ox Yukar\u0131daki koordinat sisteminde verilen boyal\u0131 b\u00f6l- genin alan\u0131 14 br2\u2019dir. Buna g\u00f6re n do\u011frusunun e\u011fimi ka\u00e7t\u0131r? A) \u20132 B) - 6 C) - 5 D) - 2 5 6 3 9. ay \u2013 8x \u2013 10 = 0 do\u011frusunun e\u011fimi 4 oldu\u011funa 12. (1,6) noktas\u0131ndan ge\u00e7en y = ax + b do\u011frusunun e\u011fimi g\u00f6re a ka\u00e7t\u0131r? \u20132\u2019dir. A) \u20134 B) \u20132 C) 2 D) 4 Buna g\u00f6re b ka\u00e7t\u0131r? A) 5 B) 6 C) 7 D) 8 270 8. S\u0131n\u0131f","Test E\u011fim Ba\u015far\u0131yorum 62 1. E\u011fik d\u00fczlemlerde bir cisme belirli bir kuvvet uygulanarak cisim d\u00fczlem boyunca hareket ettirilir. D\u00fczlemin e\u011fimi artt\u0131k\u00e7a bu cisme uygulanmas\u0131 gereken kuvvet de artacakt\u0131r. Buna g\u00f6re a\u015fa\u011f\u0131da dik \u00fc\u00e7gen bi\u00e7imindeki e\u011fik d\u00fczlemlerden hangisinde \u00f6zde\u015f cismi hareket ettirmek i\u00e7in uygulanmas\u0131 gereken kuvvet en fazlad\u0131r? A) B) C) D) 10 m 15 m 11 m 10 m 10 m 20 m 4m 5m 2. A\u015fa\u011f\u0131da her bir basama\u011f\u0131n\u0131n y\u00fcksekli\u011fi 18 cm olan \u00f6zde\u015f basamaklardan olu\u015fan bir merdiven g\u00f6sterilmi\u015ftir. 90 cm 18 cm ? Bu merdivenin bir basama\u011f\u0131n\u0131n e\u011fimi 0,6 oldu\u011funa g\u00f6re \u201c?\u201d ile g\u00f6sterilen uzunluk ka\u00e7 santimetredir? A) 300 B) 270 C) 240 D) 210 3. Aralar\u0131nda 60 cm uzakl\u0131k bulunan \u00f6n y\u00fcz\u00fc \u00fc\u00e7gen \u015feklindeki mavi ve ye\u015fil iki levhan\u0131n tepe noktalar\u0131 aras\u0131na \u015fekil- deki gibi tahta bir \u00e7ubuk koyulmu\u015ftur. 1 Tahta \u00e7ubuk bu konumdayken e\u011fimi 8 \u2019dir. L K 25 cm 15 cm A B 5 cm C 60 cm D 15 cm E F 2 Ye\u015fil levha mavi levhaya do\u011fru x cm yakla\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda \u00e7ubu\u011fun e\u011fimi 9 olmu\u015ftur. Buna g\u00f6re x ka\u00e7t\u0131r? A) 15 B) 25 C) 35 D) 45 8. S\u0131n\u0131f 271","Ba\u015far\u0131yorum E\u011fim Test 62 4. A\u015fa\u011f\u0131daki do\u011frusal grafikte bir maraton ko\u015fucusunun her 10 kilometrede harcad\u0131\u011f\u0131 kalori miktar\u0131n\u0131n ko\u015ftu\u011fu yolun e\u011fimine g\u00f6re de\u011fi\u015fimi g\u00f6sterilmi\u015ftir. Kalori Miktar\u0131 (kcal) 720 C 600 50 m 400 A B? 0 0,25 0,4 E\u011fim Bu ko\u015fucu sabit h\u0131zla yukar\u0131da g\u00f6sterilen A ile B aras\u0131ndaki e\u011fimsiz yolda 8 km, B ile C aras\u0131ndaki e\u011fimli yolda 6 km ko\u015fmu\u015ftur. Ko\u015fucu A ile C aras\u0131ndaki yolda 752 kalori harcad\u0131\u011f\u0131na g\u00f6re B ile C noktalar\u0131 aras\u0131ndaki yatay uzunluk ka\u00e7 metredir? A) 175 B) 150 C) 125 D) 100 5. Bir koordinat sistemine a\u015fa\u011f\u0131daki gibi dokuz e\u015f kare ve bir d do\u011frusu \u00e7izilmi\u015ftir. d do\u011frusu x eksenini K noktas\u0131nda, karelerden birinin k\u00f6\u015fesini ise L noktas\u0131nda kesmektedir. yL OK x d K noktas\u0131n\u0131n orijine uzakl\u0131\u011f\u0131 3 br ve d do\u011frusunun e\u011fimi 5 oldu\u011funa g\u00f6re L noktas\u0131n\u0131n koordinatlar\u0131 a\u015fa- 3 \u011f\u0131dakilerden hangisidir? A) (15, 20) B) (20,15) C) (20,25) D) (25,20) 272 8. S\u0131n\u0131f","Birinci Dereceden Bir Bilinmeyenli E\u015fitsizlikleri Yazma <, >, \u2264, \u2265 sembolleri ile yaz\u0131lan matematiksel ifadelere e\u015fitsizlik denir. < : K\u00fc\u00e7\u00fck > : B\u00fcy\u00fck \u2264 : K\u00fc\u00e7\u00fck veya e\u015fit \u2265 : B\u00fcy\u00fck veya e\u015fit \u0130\u00e7inde birinci dereceden bir bilinmeyenli ifade bulunan e\u015fitsizliklere birinci dereceden bir bilinmeyenli e\u015fitsizlikler denir. \u00d6rnek: \u2022 10\u2019dan k\u00fc\u00e7\u00fck say\u0131lar: x < 10 \u2022 \u20138\u2019den b\u00fcy\u00fck veya e\u015fit say\u0131lar: x \u2265 \u20138 \u2022 2 fazlas\u0131 7\u2019den k\u00fc\u00e7\u00fck say\u0131lar: x + 2 < 7 \u2022 \u20134\u2019ten b\u00fcy\u00fck, 5\u2019ten k\u00fc\u00e7\u00fck veya e\u015fit say\u0131lar: \u20134 < x \u2264 5 65 d) Arkada\u015f\u0131m\u0131n boyu 165 cm\u2019den k\u00fc\u00e7\u00fckt\u00fcr. e) Gruptaki \u00f6\u011frencilerin en k\u00fc\u00e7\u00fc\u011f\u00fc 8 ya\u015f\u0131ndad\u0131r. 1. A\u015fa\u011f\u0131daki ifadelere kar\u015f\u0131l\u0131k gelen e\u015fitsizlikleri yaz\u0131n\u0131z. a) 3\u2019ten b\u00fcy\u00fck say\u0131lar. b) \u20132\u2019den k\u00fc\u00e7\u00fck veya e\u015fit say\u0131lar. f) Deneme s\u0131nav\u0131ndaki do\u011fru cevaplar\u0131m\u0131n say\u0131s\u0131 en az 14\u2019t\u00fcr. c) Kalemlerimin say\u0131s\u0131 12\u2019den fazlad\u0131r. g) Bu tiyatro salonunun kapasitesi 180\u2019dir. \u00e7) \u0130\u015fyeri ile ev aras\u0131ndaki uzakl\u0131k 4 km\u2019den fazla 10 \u011f) Bu asans\u00f6r en fazla 720 kg y\u00fck ta\u015f\u0131yabilir. km\u2019den azd\u0131r. 8. S\u0131n\u0131f 273","h) Bir dar a\u00e7\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc. Birinci Dereceden Bir Bilinmeyenli E\u015fitsizlikleri Yazma n) Yar\u0131s\u0131n\u0131n 4 fazlas\u0131 20\u2019den k\u00fc\u00e7\u00fck veya e\u015fit say\u0131lar. \u0131) Bir geni\u015f a\u00e7\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc. o) 12 eksi\u011fi 40\u2019tan b\u00fcy\u00fck veya e\u015fit say\u0131lar. i) \u015eehirleraras\u0131 yollarda ara\u00e7lar en fazla 120 km\/sa. 2. A\u015fa\u011f\u0131daki e\u015fitsizliklere uygun birer s\u00f6zel ifade h\u0131zla gidebilir. yaz\u0131n\u0131z. a) x > 7 j) Bu kre\u015fe ya\u015f\u0131 en az 3, en fazla 5 olan \u00e7ocuklar b) a < 0 kay\u0131t yapt\u0131rabilir. k) Bug\u00fcn hava s\u0131cakl\u0131\u011f\u0131 en az 12 \u00b0C, en fazla 21 \u00b0C c) y \u2013 3 \u2264 8 olacak. \u00e7) \u20135 \u2264 b < 3 d) 0 < 2x < 16 l) 2 kat\u0131n\u0131n 3 fazlas\u0131 23\u2019ten k\u00fc\u00e7\u00fck say\u0131lar. m) 5 eksi\u011finin 4 kat\u0131 \u201310\u2019dan b\u00fcy\u00fck say\u0131lar. e) 13 \u2264 4x \u2013 7 < 41 274 8. S\u0131n\u0131f","Test Birinci Dereceden Bir Bilinmeyenli Uyguluyorum 63 E\u015fitsizlikleri Yazma 1. \u201cS\u0131n\u0131ftaki erkek \u00f6\u011frenci say\u0131s\u0131 7\u2019den azd\u0131r.\u201d ifadesi- 5. A\u015fa\u011f\u0131daki terazilerden hangisinde modellenen ne uygun e\u015fitsizlik a\u015fa\u011f\u0131dakilerden hangisidir? e\u015fitsizlik \u201c2x + 5 > x + 2\u201d \u015feklinde g\u00f6sterilir? A) x < 7 B) x \u2264 7 A) 2 B) xx C) x > 7 D) x \u2265 7 x5 xx 2 x5 C) D) 5 2 x2 5 xx xx xx 2. \u201cBug\u00fcn en az 40 sayfa kitap okuyaca\u011f\u0131m.\u201d ifadesine uygun e\u015fitsizlik a\u015fa\u011f\u0131dakilerden hangisidir? A) x < 40 B) x \u2264 40 C) x > 40 D) x \u2265 40 3. \u201c7 fazlas\u0131 \u201315\u2019ten b\u00fcy\u00fck say\u0131lar\u201d ifadesine uygun 6. \u201c3 eksi\u011fi 3\u2019ten b\u00fcy\u00fck ve 13\u2019ten k\u00fc\u00e7\u00fck olan say\u0131lar\u201d e\u015fitsizlik a\u015fa\u011f\u0131dakilerden hangisidir? ifadesine uygun e\u015fitsizlik a\u015fa\u011f\u0131dakilerden hangi- sidir? A) x + 7 > \u201315 B) x + 7 \u2265 \u201315 A) 3 \u2013 x < 13 < x \u2013 3 B) 3 < x \u2013 3 < 13 C) x \u2013 15 > 7 D) x \u2013 15 \u2265 7 C) \u20133 < x < 13 D) 3 < x \u2013 13 < 13 4. \u201c2 kat\u0131n\u0131n 3 eksi\u011fi 21\u2019den k\u00fc\u00e7\u00fck veya e\u015fit say\u0131lar\u201d ifa- 7. \u201cBisikletin fiyat\u0131 en az 800 TL, en fazla 17 000 TL\u2019dir.\u201d desine uygun e\u015fitsizlik a\u015fa\u011f\u0131dakilerden hangisi- ifadesine uygun e\u015fitsizlik a\u015fa\u011f\u0131dakilerden hangi- dir? sidir? A) 2(x \u2013 3) \u2264 21 B) 2(x \u2013 3) < 21 A) 800 < x < 17 000 B) 800 \u2264 x < 17 000 C) 2x \u2013 3 \u2264 21 D) 2x \u2013 3 < 21 C) 800 < x \u2264 17 000 D) 800 \u2264 x \u2264 17 000 8. S\u0131n\u0131f 275","Uyguluyorum Birinci Dereceden Bir Bilinmeyenli Test E\u015fitsizlikleri Yazma 63 8. \u201c\u00d6\u011frencilerin haz\u0131rlad\u0131\u011f\u0131 program\u0131n s\u00fcresi 2 saatten 11. Bu sal\u00e7an\u0131n yap\u0131m\u0131nda fazla 2,5 saatten azd\u0131r.\u201d 3,5 kg\u2019dan fazla 5 kg\u2019dan az 1 KG Buna g\u00f6re program\u0131n dakika cinsinden s\u00fcresini Sal\u00e7a biber kullan\u0131lm\u0131\u015ft\u0131r. g\u00f6steren e\u015fitsizlik a\u015fa\u011f\u0131dakilerden hangisidir? A) 120 \u2264 x \u2264 150 B) 120 < x < 150 Yukar\u0131daki bilgiye g\u00f6re 2,5 kg sal\u00e7a yapmak i\u00e7in C) 90 \u2264 x \u2264 120 D) 90 < x < 120 kullan\u0131lmas\u0131 gereken kg cinsinden biber miktar- lar\u0131n\u0131 g\u00f6steren e\u015fitsizlik a\u015fa\u011f\u0131dakilerden hangi- sidir? A) 8,75 < x < 12,5 B) 8,75 \u2264 x \u2264 12,5 C) 7,5 < x < 10,75 D) 7,5 \u2264 x \u2264 10,75 9. Bu tart\u0131 25 kg ve fazlas\u0131n\u0131 tartamaz 12. A\u015fa\u011f\u0131daki asans\u00f6rde ta\u015f\u0131nabilecek y\u00fck s\u0131n\u0131r\u0131 g\u00f6ste- rilmi\u015ftir. 900 kg 05 Buna g\u00f6re bu tart\u0131n\u0131n gram cinsinden tartabile- ce\u011fi cisimlerin k\u00fctlesini g\u00f6steren e\u015fitsizlik a\u015fa- \u011f\u0131dakilerden hangisidir? A) x > 25 000 B) x \u2265 25 000 C) x < 25 000 D) x \u2264 25 000 Bu asans\u00f6rle k\u00fctlesi 80 kg olan bir usta kendisi ile beraber k\u00fctlesi 18 kg olan kolilerden x tane ta\u015f\u0131m\u0131\u015ft\u0131r. 10. Buna g\u00f6re asans\u00f6rle tek seferde usta ile beraber ka\u00e7 koli ta\u015f\u0131nabilece\u011fini g\u00f6steren e\u015fitsizlik a\u015fa- Nazan hafta i\u00e7i boyunca her g\u00fcn en az 30 en fazla \u011f\u0131dakilerden hangisidir? 50 soru \u00e7\u00f6zm\u00fc\u015ft\u00fcr. A) 18x \u2264 900 B) 18x < 900 C) 80 + 18x \u2264 900 D) 80 + 18x \u2265 900 Tahtadaki ifadeye g\u00f6re Nazan\u2019\u0131n bir haftada \u00e7\u00f6z- 13. Ayn\u0131 s\u0131nava giren \u00fc\u00e7 \u00f6\u011frenciden Ali 70 puan al\u0131rken, d\u00fc\u011f\u00fc toplam soru say\u0131s\u0131n\u0131 g\u00f6steren e\u015fitsizlik Bu\u011fra Ceyda\u2019dan 10 puan d\u00fc\u015f\u00fck alm\u0131\u015ft\u0131r. a\u015fa\u011f\u0131dakilerden hangisidir? En y\u00fcksek puan\u0131 Ceyda ald\u0131\u011f\u0131na g\u00f6re Bu\u011fra\u2019n\u0131n A) 150 \u2264 x \u2264 250 B) 150 < x < 250 puan\u0131n\u0131 ifade eden e\u015fitsizlik a\u015fa\u011f\u0131dakilerden C) 210 \u2264 x \u2264 350 D) 210 < x < 350 hangisidir? A) x > 60 B) x < 60 C) x > 80 D) x < 80 276 8. S\u0131n\u0131f","Birinci Dereceden Bir Bilinmeyenli E\u015fitsizlikleri Say\u0131 Do\u011frusunda G\u00f6sterme E\u015fitsizlik say\u0131 do\u011frusunda g\u00f6sterilirken \u201c<, >\u201d e\u015fitsizli\u011fi varsa s\u0131n\u0131r noktas\u0131n\u0131n i\u00e7i bo\u015f yap\u0131l\u0131r. \u201c\u2264, \u2265\u201d e\u015fitsizli\u011fi varsa s\u0131n\u0131r noktas\u0131n\u0131n i\u00e7i dolu yap\u0131l\u0131r. \u00d6rnek: x > 2 ve \u20133 \u2264 x < 4 e\u015fitsizliklerini say\u0131 do\u011frusunda g\u00f6sterelim. -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 2 dahil olmad\u0131\u011f\u0131 i\u00e7in -3 dahil oldu\u011fu i\u00e7in 4 dahil olmad\u0131\u011f\u0131 i\u00e7in noktan\u0131n i\u00e7i bo\u015f noktan\u0131n i\u00e7i dolu noktan\u0131n i\u00e7i bo\u015f 66 d) -2 < x < 4 1. A\u015fa\u011f\u0131daki e\u015fitsizlikleri say\u0131 do\u011frusunda g\u00f6steri- niz. a) x > 3 e) -3 < x \u2264 1 b) x < 2 c) x \u2265 -1 f) -5 \u2264 x < 0 \u00e7) x \u2264 0 g) -1 \u2264 x \u2264 5 8. S\u0131n\u0131f 277","Birinci Dereceden Bir Bilinmeyenli E\u015fitsizlikleri Say\u0131 Do\u011frusunda G\u00f6sterme 2. A\u015fa\u011f\u0131daki say\u0131 do\u011frular\u0131nda kal\u0131n k\u0131rm\u0131z\u0131 renkler- 3. A\u015fa\u011f\u0131da verilen s\u00f6zel ifadelere uygun e\u015fitsizlik- le g\u00f6sterilen yerleri ifade eden e\u015fitsizlikleri yaz\u0131- leri say\u0131 do\u011frusunda g\u00f6steriniz. n\u0131z. a) -1\u2019den k\u00fc\u00e7\u00fck say\u0131lar a) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 E\u015fitsizlik: b) b) 3\u2019ten b\u00fcy\u00fck veya e\u015fit say\u0131lar -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 E\u015fitsizlik: c) c) -4\u2019ten b\u00fcy\u00fck 2\u2019den k\u00fc\u00e7\u00fck say\u0131lar -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 E\u015fitsizlik: \u00e7) \u00e7) -3\u2019ten b\u00fcy\u00fck veya e\u015fit 1\u2019den k\u00fc\u00e7\u00fck say\u0131lar -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 E\u015fitsizlik: d) d) -1 ile 5 aras\u0131ndaki say\u0131lar -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 E\u015fitsizlik: e) e) 0\u2019dan 6\u2019ya kadar olan say\u0131lar -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 E\u015fitsizlik: 278 8. S\u0131n\u0131f","Birinci Dereceden Bir Bilinmeyenli E\u015fitsizlikleri \u00c7\u00f6zme \u2022 E\u015fitsizli\u011fin her iki taraf\u0131 ayn\u0131 say\u0131 ile topland\u0131\u011f\u0131nda e\u015fitsizlik y\u00f6n de\u011fi\u015ftirmez. \u00d6rnek: 2<5 2+3<5+3\u00a15<8 \u2022 E\u015fitsizli\u011fin her iki taraf\u0131ndan ayn\u0131 say\u0131 \u00e7\u0131kar\u0131ld\u0131\u011f\u0131nda e\u015fitsizlik y\u00f6n de\u011fi\u015ftirmez. \u00d6rnek: 7>3 7 \u2013 5 > 4 \u2013 5 \u00a1 2 > \u20131 \u2022 E\u015fitsizli\u011fin her iki taraf\u0131 ayn\u0131 pozitif say\u0131 ile \u00e7arp\u0131ld\u0131\u011f\u0131nda veya b\u00f6l\u00fcnd\u00fc\u011f\u00fcnde e\u015fitsizlik y\u00f6n de\u011fi\u015ftirmez. \u00d6rnek: 6<9 6\u00b74 < 9\u00b74 \u00a1 24 < 36 6<9 6:3<9:3\u00a12<3 \u2022E\u015fitsizli\u011fin her iki taraf\u0131 ayn\u0131 negatif say\u0131 ile \u00e7arp\u0131ld\u0131\u011f\u0131nda veya b\u00f6l\u00fcnd\u00fc\u011f\u00fcnde e\u015fitsizlik y\u00f6n de\u011fi\u015ftirir. \u00d6rnek: 8>6 8\u00b7(\u20133) > 6\u00b7(\u20133) \u00a1 \u201324 < \u201318 8>6 8 : (\u20132) > 6 : (\u20132) \u00a1 \u20134 < \u20133 !!! E\u015fitsizlikler \u00e7\u00f6z\u00fcl\u00fcrken denklem \u00e7\u00f6z\u00fcm\u00fcne benzer ad\u0131mlar takip edilir. 67 1. A\u015fa\u011f\u0131daki e\u015fitsizliklerin her iki taraf\u0131na 10 ekleye- 2. A\u015fa\u011f\u0131daki e\u015fitsizliklerin her iki taraf\u0131n\u0131 3 ve \u20133 ile rek ve 10 \u00e7\u0131kararak yeni e\u015fitsizlikler olu\u015fturunuz. \u00e7arparak yeni e\u015fitsizlikler olu\u015fturunuz. a) 7 < 9 7<9 a) 1 > \u20134 1 > \u20134 b) 11 > 6 11 > 6 b) \u20132 < \u20131 \u20132 < \u20131 c) \u20133 < 0 \u20133 < 0 c) 5 > \u20134 5 > \u20134 \u00e7) \u20135 > \u20138 \u20135 > \u20138 \u00e7) \u20133 < 3 \u20133 < 3 8. S\u0131n\u0131f 279","Birinci Dereceden Bir Bilinmeyenli E\u015fitsizlikleri \u00c7\u00f6zme 3. A\u015fa\u011f\u0131daki e\u015fitsizliklerin her iki taraf\u0131n\u0131 2 ve \u20132 ile \u00e7) \u20136x \u2264 24 b\u00f6lerek yeni e\u015fitsizlikler olu\u015fturunuz. a) 14 > 8 14 > 8 d) \u20133x > \u201333 b) 2 < 6 2<6 e) x >7 2 c) 18 > \u201310 18 > \u201310 f) x - \u2264 10 \u00e7) \u201316 < \u201312 \u201316 < \u201312 5 4. A\u015fa\u011f\u0131daki e\u015fitsizlikleri \u00e7\u00f6z\u00fcn\u00fcz. g) \u2013x + 3 \u2265 \u20139 a) 5x < 30 \u011f) 2(x \u20131) < \u20138 h) 3x + 7 \u2264 34 b) x \u2013 2 > 13 c) 2x + 1 \u2265 21 280 8. S\u0131n\u0131f","Birinci Dereceden Bir Bilinmeyenli E\u015fitsizlikleri \u00c7\u00f6zme \u0131) 3x \u2013 6 < 10 \u2013 x n) x - x >1 45 i) 7x \u2013 4 \u2265 8 \u20135x o) x 2x - \u2264 15 3 j) 5x \u2264 8x \u2013 24 \u00f6) x + 5 > 20 23 2x 2x - 1 \u2264 5 k) > - 12 3 3 p) l) x + 9 \u2264 x \u2013 15 r) x+6 -1\u2265 x+2 2 32 m) 2(x \u2013 2) \u2013 3(x + 2) < \u201311 s) x + 0, 5 > 0, 3 5 8. S\u0131n\u0131f 281","Birinci Dereceden Bir Bilinmeyenli E\u015fitsizlikleri \u00c7\u00f6zme 5. A\u015fa\u011f\u0131daki terazilerde modellenen e\u015fitsizlikleri yazarak \u00e7\u00f6zelim. a) 2 2 b) 3 37 x1 55 3 xx c) 1 2 \u00e7) 2x xx x3 xx 43 xx 6. \u20132x \u2013 15 \u2264 \u201313 \u2013 x e\u015fitsizli\u011finin \u00e7\u00f6z\u00fcm k\u00fcmesini 8. \u2022 x + 3 < 4 bularak say\u0131 do\u011frusu \u00fczerinde g\u00f6steriniz. \u2022 2\u2013x\u22646 e\u015fitsizliklerini birlikte sa\u011flayan \u00e7\u00f6z\u00fcm k\u00fcmesini bularak say\u0131 do\u011frusu \u00fczerinde g\u00f6steriniz. 7. \u201c3 kat\u0131n\u0131n 7 eksi\u011fi ayn\u0131 say\u0131n\u0131n 4 kat\u0131n\u0131n 6 eksi\u011finden k\u00fc\u00e7\u00fck olan say\u0131lar\u201d ifadesine uygun e\u015fitsizli\u011fin \u00e7\u00f6z\u00fcm\u00fcn\u00fc say\u0131 do\u011frusunda g\u00f6steriniz. 282 8. S\u0131n\u0131f","Birinci Dereceden Bir Bilinmeyenli E\u015fitsizlikleri \u00c7\u00f6zme 9. Bir geni\u015f a\u00e7\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc 2k + 10\u00b0 oldu\u011funa g\u00f6re k\u2019n\u0131n 12. alabilece\u011fi de\u011ferleri g\u00f6steren e\u015fitsizli\u011fi bulunuz. (4x-7)br Yukar\u0131daki karesel b\u00f6lgenin \u00e7evre uzunlu\u011fu 60 br\u2019den k\u00fc\u00e7\u00fck oldu\u011funa g\u00f6re x\u2019in birim cinsinden 10. alabilece\u011fi en b\u00fcy\u00fck tam say\u0131 de\u011ferini bulunuz. ? TL 8 TL 10 tane k\u0131rm\u0131z\u0131 makara i\u00e7in \u00f6denen \u00fccret 8 tane mavi 13. Bir elektronik e\u015fya ma\u011fazas\u0131nda t\u00fcm \u00fcr\u00fcnlerde %15 makara i\u00e7in \u00f6denen \u00fccretten fazlad\u0131r. ile %30 aras\u0131nda indirim uygulanmaktad\u0131r. Buna g\u00f6re k\u0131rm\u0131z\u0131 makaran\u0131n lira cinsinden fi- Bu ma\u011fazadaki en ucuz \u00fcr\u00fcn\u00fcn etiket fiyat\u0131 1400 TL, yat\u0131n\u0131n alabilece\u011fi en k\u00fc\u00e7\u00fck do\u011fal say\u0131 de\u011ferini en pahal\u0131 \u00fcr\u00fcn\u00fcn etiket fiyat\u0131 ise 8200 TL\u2019dir. bulunuz. Bu ma\u011fazadan indirimli bir \u00fcr\u00fcn alan m\u00fc\u015fterinin \u00f6demesi gereken lira cinsinden \u00fccretin alabilece- \u011fi de\u011fer aral\u0131\u011f\u0131n\u0131 g\u00f6steren e\u015fitsizli\u011fi yaz\u0131n\u0131z. 11. A\u015fa\u011f\u0131da e\u015f b\u00f6lmelendirilmi\u015f bir su kab\u0131 g\u00f6sterilmi\u015f- 14. \u0130ki farkl\u0131 gitar kursuna ait \u00fccretler a\u015fa\u011f\u0131daki tabloda tir. verilmi\u015ftir. Bu kaba 12 L su eklendi\u011finde kap dolmam\u0131\u015f, 18 L su Tablo: Kurslar\u0131n \u00dccretleri eklendi\u011finde ise su ta\u015fm\u0131\u015ft\u0131r. Buna g\u00f6re kab\u0131n tamamen dolu oldu\u011fu anda i\u00e7in- Kurslar Kay\u0131t \u00dccreti (TL) Ayl\u0131k \u00dccret (TL) deki su miktar\u0131n\u0131n litre cinsinden alabilece\u011fi de- 1. Kurs 510 70 \u011ferleri bulunuz. 2. Kurs 405 85 Bu kurslardan birine kat\u0131lmak isteyen bir ki\u015finin en az ka\u00e7 ay kursa gitmesi durumunda 1. kursa kat\u0131lmas\u0131 daha ekonomik olur? 8. S\u0131n\u0131f 283","Uyguluyorum Birinci Dereceden Bir Bilinmeyenli E\u015fitsizlikleri Test Say\u0131 Do\u011frusunda G\u00f6sterme 64 1. x > 4 e\u015fitsizli\u011fi a\u015fa\u011f\u0131daki say\u0131 do\u011frular\u0131ndan 4. hangisinde g\u00f6sterilmi\u015ftir? 14 A) 4 Yukar\u0131daki say\u0131 do\u011frusunda g\u00f6sterilen e\u015fitsizlik a\u015fa\u011f\u0131dakilerden hangisidir? B) 4 A) x \u2264 14 B) x + 2 \u2264 16 C) x \u2013 4 \u2264 10 D) x + 1 \u2265 15 C) 4 D) 4 2. x \u2264 \u20133 e\u015fitsizli\u011fi a\u015fa\u011f\u0131daki say\u0131 do\u011frular\u0131ndan 5. 12 hangisinde g\u00f6sterilmi\u015ftir? 0 A) -3 Yukar\u0131daki say\u0131 do\u011frusunda g\u00f6sterilen e\u015fitsizlik a\u015fa\u011f\u0131dakilerden hangisidir? B) -3 A) \u20132 \u2264 x \u2013 2 \u2264 10 B) 2 \u2264 x + 2 \u2264 10 C) 0 \u2264 x \u2013 2 \u2264 12 D) 0 \u2264 x + 2 \u2264 12 C) -3 D) -3 3. \u201c\u20134\u2019ten b\u00fcy\u00fck, 7\u2019den k\u00fc\u00e7\u00fck veya e\u015fit\u201d ifadesine kar- 6. Bir ara\u00e7 360 km\u2019lik bir yolda en fazla saatte 120 km \u015f\u0131l\u0131k gelen e\u015fitsizlik a\u015fa\u011f\u0131daki say\u0131 do\u011frular\u0131ndan h\u0131z yapm\u0131\u015ft\u0131r. hangisinde g\u00f6sterilmi\u015ftir? Buna g\u00f6re bu arac\u0131n bu yolu ka\u00e7 saatte ald\u0131\u011f\u0131n\u0131 A) 7 g\u00f6steren e\u015fitsizlik a\u015fa\u011f\u0131dakilerden hangisidir? -4 A) 3 B) 7 B) -4 3 C) 7 C) 3 -4 0 D) 7 D) 3 -4 0 284 8. S\u0131n\u0131f","Test Birinci Dereceden Bir Bilinmeyenli E\u015fitsizlikleri Uyguluyorum 64 Say\u0131 Do\u011frusunda G\u00f6sterme 7. 1 saatlik bir yar\u0131\u015fmada yar\u0131\u015fmay\u0131 en h\u0131zl\u0131 tamam- 10. \u201c2 fazlas\u0131n\u0131n 5 kat\u0131 25\u2019ten k\u00fc\u00e7\u00fck say\u0131lar\u201d ifadesine layan yar\u0131\u015fmac\u0131 18 dakikada tamamlam\u0131\u015ft\u0131r. B\u00fct\u00fcn ait e\u015fitsizli\u011fin \u00e7\u00f6z\u00fcm\u00fc a\u015fa\u011f\u0131daki say\u0131 do\u011frular\u0131n- yar\u0131\u015fmac\u0131lar ise yar\u0131\u015fma s\u00fcresi bitmeden tamamla- dan hangisinde g\u00f6sterilmi\u015ftir? m\u0131\u015ft\u0131r. A) Buna g\u00f6re yar\u0131\u015fmac\u0131lar\u0131n dakika cinsinden yar\u0131\u015f\u0131 5 tamamlama s\u00fcrelerini g\u00f6steren e\u015fitsizlik a\u015fa\u011f\u0131- daki say\u0131 do\u011frular\u0131ndan hangisinde verilmi\u015ftir? B) 5 A) 60 18 60 C) 60 3 B) D) C) 3 18 D) 18 11. \u201cAntalya\u2019da bug\u00fcn hava s\u0131cakl\u0131\u011f\u0131 en az 12 \u00b0C, en fazla 29 \u00b0C olmu\u015ftur.\u201d ifadesine ait e\u015fitsizli\u011fin \u00e7\u00f6- z\u00fcm\u00fc a\u015fa\u011f\u0131daki say\u0131 do\u011frular\u0131ndan hangisinde verilmi\u015ftir? 8. 3x \u2013 1 > 20 e\u015fitsizli\u011finin \u00e7\u00f6z\u00fcm\u00fcn\u00fcn say\u0131 do\u011fru- A) 29 sunda g\u00f6sterimi a\u015fa\u011f\u0131dakilerden hangisidir? 12 A) 21 B) 29 12 29 B) 21 C) 12 C) 7 D) 29 12 D) 7 12. \u00dc\u00e7 karde\u015ften en b\u00fcy\u00fc\u011f\u00fc 41 ya\u015f\u0131ndad\u0131r. En k\u00fc\u00e7\u00fck karde\u015f, en b\u00fcy\u00fck karde\u015ften 9 ya\u015f k\u00fc\u00e7\u00fckt\u00fcr. 9. Buna g\u00f6re ortanca karde\u015fin ya\u015f\u0131n\u0131n alabilece\u011fi 10 de\u011ferler a\u015fa\u011f\u0131daki say\u0131 do\u011frular\u0131ndan hangisin- de g\u00f6sterilmi\u015ftir? Yukar\u0131daki say\u0131 do\u011frusunda g\u00f6sterilen e\u015fitsizlik A) 41 32 41 B) 32 a\u015fa\u011f\u0131dakilerden hangisi olamaz? C) 41 x B) x \u2013 17 \u2264 \u20137 50 A) 5 \u2264 2 D) C) 50 \u2265 5x D) 13 \u2265 x \u2013 3 41 50 8. S\u0131n\u0131f 285","Uyguluyorum Birinci Dereceden Bir Bilinmeyenli Denklemlerin Test \u00c7\u00f6z\u00fcm\u00fc 65 1. 5. 4x + 9 < 37 x - 8 \u2264 10 2 e\u015fitsizli\u011finin \u00e7\u00f6z\u00fcm\u00fc a\u015fa\u011f\u0131dakilerden hangisi- e\u015fitsizli\u011finin \u00e7\u00f6z\u00fcm\u00fc a\u015fa\u011f\u0131dakilerden hangisi- dir? dir? A) x < 7 B) x \u2264 7 A) x \u2264 9 B) x < 9 C) x > 14 D) x \u2265 14 C) x \u2264 36 D) x < 36 2. \u20132x \u2013 6 \u2264 \u201316 e\u015fitsizli\u011finin \u00e7\u00f6z\u00fcm\u00fc a\u015fa\u011f\u0131dakilerden hangisi- 6. dir? 5x + 25 > \u201320 A) x < 5 B) x \u2264 5 e\u015fitsizli\u011finin \u00e7\u00f6z\u00fcm\u00fcne ait s\u00f6zel ifade a\u015fa\u011f\u0131daki- C) x > 5 D) x \u2265 5 lerden hangisidir? A) \u20131\u2019den b\u00fcy\u00fck say\u0131lar. B) \u20131\u2019den b\u00fcy\u00fck veya e\u015fit say\u0131lar. C) \u20139\u2019dan b\u00fcy\u00fck say\u0131lar. D) \u20139\u2019dan b\u00fcy\u00fck veya e\u015fit say\u0131lar. 3. 3(2x \u2013 1) \u2265 5(x + 3) e\u015fitsizli\u011finin \u00e7\u00f6z\u00fcm\u00fc a\u015fa\u011f\u0131dakilerden hangisi- 7. dir? 16 \u2013 4x > 3x + 9 A) x > 18 B) x \u2265 18 e\u015fitsizli\u011fini sa\u011flayan en b\u00fcy\u00fck x tam say\u0131s\u0131 ka\u00e7- C) x < 18 D) x \u2264 18 t\u0131r? A) \u20131 B) 0 C) 1 D) 2 4. 5x2 xxx x9 x x 13 Yukar\u0131da modellenen e\u015fitsizli\u011fin \u00e7\u00f6z\u00fcm\u00fc a\u015fa\u011f\u0131- 8. \u2022 x + 1 < 6 dakilerden hangisidir? \u2022 5x \u2013 4 \u2265 6 A) 15 > x B) 15 \u2265 x e\u015fitsizliklerini birlikte sa\u011flayan x tam say\u0131lar\u0131n- C) 15 < x D) 15 \u2264 x dan biri a\u015fa\u011f\u0131dakilerden hangisi de\u011fildir? A) 2 B) 3 C) 4 D) 5 286 8. S\u0131n\u0131f","Test Birinci Dereceden Bir Bilinmeyenli Denklemlerin Uyguluyorum 65 \u00c7\u00f6z\u00fcm\u00fc 9. 13. Sedat\u2019\u0131n ya\u015f\u0131n\u0131n 3 kat\u0131n\u0131n 5 eksi\u011fi 28\u2019den k\u00fc\u00e7\u00fckt\u00fcr. 4 12 > Buna g\u00f6re Sedat\u2019\u0131n ya\u015f\u0131n\u0131n alabilece\u011fi iki basa- 5x makl\u0131 ka\u00e7 do\u011fal say\u0131 de\u011feri vard\u0131r? e\u015fitsizli\u011fini sa\u011flayan en k\u00fc\u00e7\u00fck x\u2019in tam say\u0131 de- A) 4 B) 3 C) 2 D) 1 \u011feri ka\u00e7t\u0131r? A) 14 B) 15 C) 16 D) 17 10. \u2022 x-2 x-6< 3 \u2022 x+1> x-1 14. \u0130lk \u00fc\u00e7 s\u0131nav\u0131ndan 84, 88 ve 82 alan Ege\u2019nin 4. s\u0131nav 2 puan\u0131yla beraber ortalamas\u0131 86\u2019dan fazla olmu\u015ftur. e\u015fitsizliklerini birlikte sa\u011flayan x de\u011ferlerini g\u00f6s- Buna g\u00f6re Ege\u2019nin 4. s\u0131nav puan\u0131n\u0131n en k\u00fc\u00e7\u00fck teren e\u015fitsizlik a\u015fa\u011f\u0131daki say\u0131 do\u011frular\u0131ndan han- tam say\u0131 de\u011feri ka\u00e7t\u0131r? gisinde verilmi\u015ftir? A) 89 B) 90 C) 91 D) 92 A) 8 -3 B) 5 -2 C) 8 -3 D) 5 15. Kenar uzunluklar\u0131 santimetre cinsinden do\u011fal say\u0131 -2 olan bir dikd\u00f6rtgenin uzun kenar\u0131, k\u0131sa kenar\u0131n\u0131n 3 kat\u0131ndan 2 cm azd\u0131r. 11. A\u015fa\u011f\u0131daki e\u015fitsizliklerden hangisinde y = 3 i\u00e7in x\u2019in alabilece\u011fi en k\u00fc\u00e7\u00fck de\u011fer 0 olur? Bu dikd\u00f6rtgenin \u00e7evre uzunlu\u011fu en az 60 cm ol- du\u011funa g\u00f6re k\u0131sa kenar uzunlu\u011fu en az ka\u00e7 san- timetredir? A) 7 B) 8 C) 9 D) 10 A) 4y \u2013 12 < 4x B) 2x \u2013 3 \u2265 y C) 3x + 12 \u2265 4y D) 2y \u2013 6 > x 12. \u201c 1 \u2019\u00fcn\u00fcn 3 eksi\u011fi kendisinden b\u00fcy\u00fck olan say\u0131lar\u201d 16. (5x + 60) TL\u2019ye al\u0131nan bir \u00fcr\u00fcn, k\u00e2r elde edilemeden 3 (3x + 110) TL\u2019ye sat\u0131l\u0131yor. ifadesine ait e\u015fitsizli\u011fin \u00e7\u00f6z\u00fcm\u00fc a\u015fa\u011f\u0131dakilerden Buna g\u00f6re x\u2019in alabilece\u011fi en k\u00fc\u00e7\u00fck tam say\u0131 de- hangisidir? \u011feri ka\u00e7t\u0131r? A) x < \u20139 B) x \u2264 \u20139 A) 24 B) 25 C) 26 D) 27 C) x < \u20134,5 D) x \u2264 \u20134,5 8. S\u0131n\u0131f 287","Ba\u015far\u0131yorum E\u015fitsizlikler Test 66 1. A\u015fa\u011f\u0131da ayn\u0131 marka ve kaliteye ait iki bebek bezi kutusu ve bilgileri verilmi\u015ftir. 48 120 200 Adet TL TL 1. Kutu 2. Kutu Bu kutulardan birim fiyat olarak daha uygun olan\u0131n\u0131 se\u00e7mek isteyen bir baba 2. kutuyu tercih etmi\u015ftir. Buna g\u00f6re 2. kutuda en az ka\u00e7 tane bebek bezi vard\u0131r? A) 82 B) 81 C) 80 D) 79 2. A\u015fa\u011f\u0131da \u00fcst b\u00f6lmesinin hacmi, alt b\u00f6lmesinin hacminin 2 kat\u0131ndan fazla olacak bi\u00e7imde \u00fcretilen dikd\u00f6rtgenler priz- mas\u0131 bi\u00e7imindeki iki b\u00f6lmeli dolap g\u00f6sterilmi\u015ftir. (4x + 4) dm (x + 5) dm Buna g\u00f6re dolab\u0131n \u00fcst b\u00f6lmesinin desimetre cinsinden uzunlu\u011funun en k\u00fc\u00e7\u00fck do\u011fal say\u0131 de\u011feri ka\u00e7t\u0131r? A) 14 B) 15 C) 16 D) 17 288 8. S\u0131n\u0131f","Test E\u015fitsizlikler Ba\u015far\u0131yorum 66 3, 4 ve 5. sorular\u0131 a\u015fa\u011f\u0131daki bilgilere g\u00f6re cevaplay\u0131n\u0131z. A\u015fa\u011f\u0131daki tabloda bir hastanenin do\u011fumhane b\u00f6l\u00fcm\u00fcnde belirli bir zamanda do\u011fan bebeklerin do\u011fum k\u00fctlesi ve boylar\u0131 verilmi\u015ftir. KIZ ERKEK Boy (cm) K\u00fctle (gram) Boy (cm) K\u00fctle (gram) 52 2800 51 3200 51 3400 49 4000 50 3100 49 3500 47 2200 53 3300 47 2300 46 2300 45 2200 50 3300 43 3600 52 3700 53 3700 49 3100 52 3300 46 2400 48 4000 54 4100 Normal do\u011fum olarak adland\u0131r\u0131lan ve 40. haftada ger\u00e7ekle\u015fen do\u011fumlarda bebeklerin santimetre cinsinden bekle- nen ortalama boy ve kilogram cinsinden beklenen ortalama k\u00fctlelerini g\u00f6steren e\u015fitsizlikler ise \u015fu \u015fekildedir: Boy: 48 \u2264 x \u2264 52 K\u00fctle: 2,4 \u2264 x \u2264 3,9 Belirtilen normal do\u011fumlarda bebeklerin iki \u00f6zelli\u011fi de ta\u015f\u0131mas\u0131 beklenmektedir. 3. Buna g\u00f6re tablodaki bebeklerden ka\u00e7 tanesi normal do\u011fum zaman\u0131nda do\u011fmu\u015ftur? A) 7 B) 8 C) 9 D) 10 4. Normal do\u011fum zaman\u0131 d\u0131\u015f\u0131nda do\u011fan bir k\u0131z bebe\u011fin kilogram cinsinden k\u00fctlesinin alabilece\u011fi olas\u0131 durum- lar\u0131n say\u0131s\u0131 ka\u00e7t\u0131r? A) 1 B) 2 C) 3 D) 4 5. Normal do\u011fum zaman\u0131nda do\u011fan erkek bebeklerin santimetre cinsinden boylar\u0131n\u0131n de\u011ferlerini g\u00f6steren e\u015fitsizli\u011fe ait say\u0131 do\u011frusu a\u015fa\u011f\u0131dakilerden hangisidir? A) 52 B) 52 49 49 C) 52 D) 52 48 48 8. S\u0131n\u0131f 289","Ba\u015far\u0131yorum E\u015fitsizlikler Test 67 1. A\u015fa\u011f\u0131da bir oyuncak ma\u011fazas\u0131nda sat\u0131lan baz\u0131 oyuncaklar\u0131n lira cinsinden fiyatlar\u0131 verilmi\u015ftir. (4x + 8) TL (5x \u2013 30) TL (3x + 50) TL C) 176 Bu oyuncaklardan en pahal\u0131 olan\u0131 helikopter, en ucuz olan\u0131 ise arabad\u0131r. x bir tam say\u0131 oldu\u011funa g\u00f6re oyuncak ay\u0131n\u0131n fiyat\u0131 ka\u00e7 lirad\u0131r? A) 170 B) 173 C) 174 2. A\u015fa\u011f\u0131da baz\u0131lar\u0131n\u0131n renkleri ayn\u0131 ve kal\u0131nl\u0131klar\u0131 e\u015fit alt\u0131 \u00e7ubu\u011fun santimetre cinsinden uzunluklar\u0131n\u0131n \u00e7\u00f6z\u00fcmlenmi\u015f bi\u00e7imleri verilmi\u015ftir. 2\u00b7101 + 5\u00b710-1 2\u00b7101 + 2\u00b7100 + 2\u00b710-1 2\u00b7101 + 6\u00b7100 + 5\u00b710-1 2\u00b7101 + 4\u00b7100 2\u00b7101 + 7\u00b710-1 + 5\u00b710-2 2\u00b7101 + 2\u00b710-1 + 5\u00b710-2 Bu \u00e7ubuklardan iki tanesi al\u0131narak a\u015fa\u011f\u0131daki gibi birer kenar\u0131 \u00e7ak\u0131\u015facak bi\u00e7imde yerle\u015ftiriliyor. Buna g\u00f6re son durumda olu\u015fan \u015feklin santimetre cinsinden uzunlu\u011funun alabilece\u011fi de\u011ferleri g\u00f6steren e\u015fitsizli\u011fe ait say\u0131 do\u011frusu a\u015fa\u011f\u0131dakilerden hangisidir? A) 50,5 B) 51,5 40,75 41 C) 50,5 D) 51,5 41 41,25 290 8. S\u0131n\u0131f","Test E\u015fitsizlikler Ba\u015far\u0131yorum 67 3. A\u015fa\u011f\u0131da iki farkl\u0131 ampul t\u00fcr\u00fcn\u00fcn fiyatlar\u0131 ve ampullerden birer tanesinin 24 saatlik kullan\u0131mdaki faturaya yans\u0131yan kullan\u0131m bedelleri verilmi\u015ftir. Tasarufflu Amp\u00fcl Led Amp\u00fcl Fiyat : 15 TL Fiyat : 24 TL 24 Saatlik 24 Saatlik kullan\u0131m Kullan\u0131m bedeli : 2,16 TL bedeli : 0,75 TL Bir i\u015f yerinde ayd\u0131nlatma i\u00e7in toplam 32 adet ampul, s\u00fcrekli yanacak bi\u00e7imde kullan\u0131lmaktad\u0131r. Buna g\u00f6re bu i\u015f yerinde tasarruflu ampul yerine led ampul kullan\u0131l\u0131rsa en az ka\u00e7 g\u00fcn sonra ampullerin fatu- raya yans\u0131yan toplam kullan\u0131m bedelleri daha ekonomik olur? A) 5 B) 6 C) 7 D) 8 4. A\u015fa\u011f\u0131da iki farkl\u0131 d\u00fczenekte A, B ve 10 br\u2019lik a\u011f\u0131rl\u0131klar\u0131n e\u015fit kollu terazilerde olu\u015fturduklar\u0131 g\u00f6r\u00fcn\u00fcmler verilmi\u015ftir. AA 10 BA A ve B cisimlerinin br cinsinden k\u00fctleleri tam say\u0131d\u0131r. Buna g\u00f6re B cisminin k\u00fctlesi en az ka\u00e7 gramd\u0131r? A) 24 B) 23 C) 22 D) 21 8. S\u0131n\u0131f 291","5 \u00dcN\u0130TE \u00dc\u00c7GENLER E\u015eL\u0130K VE BENZERL\u0130K \u00dc\u00e7genler E\u015flik ve Benzerlik Kazan\u0131mlar; \u00dc\u00e7gende kenarortay, a\u00e7\u0131ortay ve y\u00fcksekli\u011fi in\u015fa eder. M.8.3.1.1 \u00dc\u00e7genin iki kenar uzunlu\u011funun toplam\u0131 veya fark\u0131 ile M.8.3.1.2 \u00fc\u00e7\u00fcnc\u00fc kenar\u0131n\u0131n uzunlu\u011funu ili\u015fkilendirir. M.8.3.1.3 \u00dc\u00e7genin kenar uzunluklar\u0131 ile bu kenarlar\u0131n kar\u015f\u0131s\u0131ndaki a\u00e7\u0131lar\u0131n \u00f6l\u00e7\u00fclerini ili\u015fkilendirir. Yeterli say\u0131da eleman\u0131n\u0131n \u00f6l\u00e7\u00fcleri verilen bir \u00fc\u00e7geni \u00e7izer. M.8.3.1.4 Pisagor ba\u011f\u0131nt\u0131s\u0131n\u0131 olu\u015fturur, ilgili problemleri \u00e7\u00f6zer. M.8.3.1.5 M.8.3.3.1 E\u015flik ve benzerli\u011fi ili\u015fkilendirir, e\u015f ve benzer \u015fekillerin M.8.3.3.2 kenar ve a\u00e7\u0131 ili\u015fkilerini belirler. Benzer \u00e7okgenlerin benzerlik oran\u0131n\u0131 belirler, bir \u00e7okgene e\u015f ve benzer \u00e7okgenler olu\u015fturur. 8. SINIF","\u00dc\u00e7gende Yard\u0131mc\u0131 Elemanlar - Kenarortay Kenarortay \u00dc\u00e7gende bir kenar\u0131n orta noktas\u0131n\u0131 kar\u015f\u0131 k\u00f6\u015feye birle\u015ftiren do\u011fru par\u00e7as\u0131na kenarortay denir. \u201cV\u201d sembol\u00fcyle g\u00f6s- terilir. \u00d6rnek: A YV |AY|=|YB| G |BZ|=|ZC| |AV|=|VC| BZ C AB kenar\u0131na ait kenarortay [YC], AC kenar\u0131na ait kenarortay [VB], BC kenar\u0131na ait kenarortay [ZA]\u2019d\u0131r. \u2022Kenarortaylar\u0131n \u00fc\u00e7genin i\u00e7inde kesi\u015fti\u011fi noktaya a\u011f\u0131rl\u0131k merkezi (G) denir. 68 1. A\u015fa\u011f\u0131daki kareli zeminde verilen \u00fc\u00e7genlerin istenen kenarlar\u0131na ait kenarortaylar\u0131 \u00e7iziniz. a) BC kenar\u0131na ait c) EF kenar\u0131na ait A D BC EF b) KL kenar\u0131na ait \u00e7) PR kenar\u0131na ait K P M R L S 8. S\u0131n\u0131f 293","\u00dc\u00e7gende Yard\u0131mc\u0131 Elemanlar - Kenarortay 2. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerde birer kenara ait kenarortay \u00e7i- 3. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerde baz\u0131 kenarlara ait kenarortay- zilmi\u015ftir. lar \u00e7izilmi\u015ftir. Buna g\u00f6re x\u2019lerin de\u011ferini bulunuz. a) A Buna g\u00f6re bu \u00fc\u00e7genlerin \u00e7evre uzunluklar\u0131n\u0131 bu- lunuz. B (x-2) cm K 12 cm C a) A 15 cm 6 cm E B 7 cm D C b) A b) E (x+8)cm C 3x cm C K (x+4) cm A B 7 cm 18 cm 8 cm D B c) A c) D (2x+2) cm K (3x-4) cm F D F E 11 cm 12 cm B 5 cm E C \u00e7) A (2x+1)cm E (3x-5)cm C \u00e7) F 13 cm 10 cm K (2x+8) cm E D F (4x-2) cm B D 294 8. S\u0131n\u0131f","\u00dc\u00e7gende Yard\u0131mc\u0131 Elemanlar - A\u00e7\u0131ortay A\u00e7\u0131ortay \u00dc\u00e7genin bir i\u00e7 a\u00e7\u0131s\u0131n\u0131 iki e\u015f par\u00e7aya b\u00f6len do\u011fru par\u00e7as\u0131na (\u00fc\u00e7genin o a\u00e7\u0131s\u0131na ait) a\u00e7\u0131ortay denir. A\u00e7\u0131ortaylar \u201cn\u201d harfi ile g\u00f6sterilir. \u00d6rnek: A m(BAE\u2211 ) = m(EA\u2211C) D F m(BC\u2211D) = m(DC\u2211A) m(ABF\u2211 ) = m(FBC\u2211 ) BEC A a\u00e7\u0131s\u0131na ait a\u00e7\u0131ortay [AE] = nA , B a\u00e7\u0131s\u0131na ait a\u00e7\u0131ortay [BF] = nB , C a\u00e7\u0131s\u0131na ait a\u00e7\u0131ortay [CD] = nC\u2019dir. Not: T\u00fcm \u00fc\u00e7gen t\u00fcrlerinde a\u00e7\u0131ortaylar daima \u00fc\u00e7genin i\u00e7 b\u00f6lgesinde \u00e7izilirler ve i\u00e7 b\u00f6lgede tek noktada kesi\u015firler. 69 \u00e7) F a\u00e7\u0131s\u0131na ait 1. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerde istenen a\u00e7\u0131lara ait a\u00e7\u0131or- D taylar\u0131 \u00e7iziniz ve a\u00e7\u0131 de\u011ferlerini bulunuz. 62\u00b0 a) A a\u00e7\u0131s\u0131na ait E 60\u00b0 A F 80\u00b0 C d) L a\u00e7\u0131s\u0131na ait B K 21\u00b0 b) C a\u00e7\u0131s\u0131na ait A 135\u00b0 LM B 40\u00b0 e) M a\u00e7\u0131s\u0131na ait C c) E a\u00e7\u0131s\u0131na ait K D 78\u00b0 M 56\u00b0 56\u00b0 E L F 8. S\u0131n\u0131f 295","\u00dc\u00e7gende Yard\u0131mc\u0131 Elemanlar - A\u00e7\u0131ortay 2. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerde baz\u0131 a\u00e7\u0131lara ait a\u00e7\u0131ortaylar \u00e7i- d) K zilmi\u015ftir. 30\u00b0 Buna g\u00f6re istenen a\u00e7\u0131 \u00f6l\u00e7\u00fclerini bulunuz. N a) A 55\u00b0 M 40\u00b0 L m(MN\u2211L)= BD C m(BA\u2211D)= e) K L m(KN\u2211L)= b) A N 60\u00b0 70\u00b0 M D C 70\u00b0 m(ACD\u2211 )= B f) P 41\u00b0 c) D 27\u00b0 T R 38\u00b0 m(RT\u2211S)= S 46\u00b0 F EG m(EG\u2211D)= \u00e7) g) P D (2x+20)\u00b0 33\u00b0 K G (x+5)\u00b0 41\u00b0 (x+5)\u00b0 S E R F m(PKS\u2211 )= m(EGF\u2211 )= 296 8. S\u0131n\u0131f","\u00dc\u00e7gende Yard\u0131mc\u0131 Elemanlar - Y\u00fckseklik Y\u00fckseklik \u00dc\u00e7genin herhangi bir k\u00f6\u015fesinden kar\u015f\u0131s\u0131ndaki kenara ya da kenar\u0131n uzant\u0131s\u0131na dik \u00e7izilen do\u011fru par\u00e7as\u0131na (o kenara ait) y\u00fckseklik denir. \u201ch\u201d sembol\u00fcyle g\u00f6sterilir. \u00d6rnek: Dar A\u00e7\u0131l\u0131 \u00dc\u00e7gende Y\u00fckseklik Dik A\u00e7\u0131l\u0131 \u00dc\u00e7gende Y\u00fckseklik Geni\u015f A\u00e7\u0131l\u0131 \u00dc\u00e7gende Y\u00fckseklik A P K DE T Y BF C R S V M L AB kenar\u0131na ait y\u00fckseklik [CD], PR kenar\u0131na ait y\u00fckseklik [RS], Z K BC kenar\u0131na ait y\u00fckseklik [AF], RS kenar\u0131na ait y\u00fckseklik [PR], AC kenar\u0131na ait y\u00fckseklik [BE]\u2019dir. PS kenar\u0131na ait y\u00fckseklik [RT]\u2019dir. \u2022 Y\u00fckseklikler \u00fc\u00e7genin i\u00e7 b\u00f6lgesinde \u2022 Y\u00fckseklikler \u00fc\u00e7genin dik k\u00f6\u015fesin- KM kenar\u0131na ait y\u00fckseklik [YL], KL kenar\u0131na ait y\u00fckseklik [MZ], kesi\u015fir. de kesi\u015fir. LM kenar\u0131na ait y\u00fckseklik [KV]\u2019dir. \u2022 Y\u00fcksekliklerin uzant\u0131lar\u0131 \u00fc\u00e7ge- \u2022 K noktas\u0131 diklik merkezidir. \u2022 R noktas\u0131 diklik merkezidir. nin d\u0131\u015f b\u00f6lgesinde ve tek noktada kesi\u015firler. \u2022 K noktas\u0131 diklik merkezidir. 70 c) K L M 1. A\u015fa\u011f\u0131daki kareli zemin \u00fczerinde verilen \u00fc\u00e7genle- rin t\u00fcm kenarlar\u0131na ait y\u00fckseklikleri \u00e7izerek y\u00fck- sekliklerin kesi\u015fti\u011fi noktay\u0131 bulunuz. a) A B C \u00e7) S b) D P EF R 297 8. S\u0131n\u0131f","\u00d6zel Durumlar \u2022 \u0130kizkenar \u00fc\u00e7gende, e\u015f olmayan \u2022 E\u015fkenar \u00fc\u00e7gende, herhangi bir \u2022 Dik \u00fc\u00e7gende, dik a\u00e7\u0131n\u0131n kar\u015f\u0131s\u0131n- a\u00e7\u0131dan kar\u015f\u0131 kenara \u00e7izilen y\u00fck- a\u00e7\u0131ya ait a\u00e7\u0131ortay, ayn\u0131 zamanda daki kenara ait kenarortay uzunlu- seklik, ayn\u0131 zamanda a\u00e7\u0131ortay ve y\u00fckseklik ve kenarortayd\u0131r. \u011fu, bu kenar\u0131n yar\u0131s\u0131 kadard\u0131r. kenarortayd\u0131r. A A A 30\u00b0DE D 30\u00b0 B 3300\u00b0 \u00b0 F 3300\u00b0\u00b0 C B C 30\u00b0 BDC [DC], [EB], [FA] hem y\u00fckseklik, hem |BD] = [AD] = [DC] a\u00e7\u0131ortay hem de kenarortayd\u0131r. [AD], A a\u00e7\u0131s\u0131na ait a\u00e7\u0131ortay; BC kenar\u0131na ait y\u00fckseklik ve kenaror- tayd\u0131r. 71 c) P S 1. A\u015fa\u011f\u0131daki \u00fc\u00e7genlerde istenen a\u00e7\u0131 \u00f6l\u00e7\u00fclerini ya da R |PT|= kenar uzunluklar\u0131n\u0131 bulunuz. \u00e7) T a) K 20 cm A 40\u00b0 ? m(NK\u2211M)= LNM 32\u00b0 C 32\u00b0 D m(DBC\u2211 )= b) B A d) 30\u00b0 14 cm K N 6 cm M 14 cm C \u00c7evre(KL\u2206M)= D |DC|= 13 cm B L 298 8. S\u0131n\u0131f","K\u00e2\u011f\u0131t Katlama Y\u00f6ntemiyle \u00dc\u00e7genin Elemanlar\u0131n\u0131 Elde Etme \u2022 Kenarortay A A A B B B KC C CK \u00dc\u00e7gen bi\u00e7imindeki k\u00e2\u011f\u0131d\u0131n C k\u00f6\u015fesi, B k\u00f6\u015fesi ile \u00e7ak\u0131\u015facak bi\u00e7imde katlan\u0131p a\u00e7\u0131ld\u0131\u011f\u0131nda olu\u015fan K noktas\u0131n\u0131 A k\u00f6\u015fe- siyle birle\u015ftirdi\u011fimizde BC kenar\u0131na ait kenarortay\u0131 olu\u015fur. \u201cV\u201d sembol\u00fc ile g\u00f6sterilir. Not: T\u00fcm \u00fc\u00e7gen t\u00fcrlerinde kenarortaylar i\u00e7 b\u00f6lgede ve tek noktada kesi\u015firler. \u2022 A\u00e7\u0131ortay A A A B\u0131 B CB K CB KC \u00dc\u00e7gen bi\u00e7imindeki k\u00e2\u011f\u0131d\u0131n AB kenar\u0131, AC kenar\u0131n\u0131n \u00fczerine gelecek bi\u00e7imde katlan\u0131p a\u00e7\u0131ld\u0131\u011f\u0131nda olu\u015fan [AK] kat izi A a\u00e7\u0131s\u0131na ait a\u00e7\u0131ortayd\u0131r. \u2022 Y\u00fckseklik A A A B CB K B\u0131 C B K C \u00dc\u00e7gen bi\u00e7imindeki k\u00e2\u011f\u0131d\u0131n B k\u00f6\u015fesi, BC kenar\u0131 \u00fczerine do\u011fru A noktas\u0131 ile ayn\u0131 hizaya gelene kadar katlan\u0131p a\u00e7\u0131l- d\u0131\u011f\u0131nda olu\u015fan [AK] kat izi BC kenar\u0131na ait y\u00fcksekliktir. 8. S\u0131n\u0131f 299"]