8. Sınıf Öğreniyorum Serisi Matematik Soru Bankası

["\u0130ki Kare Fark\u0131 \u00d6zde\u015fli\u011finin Modellenmesi a-b b b a b a-b a-b b a a-b a a Yukar\u0131daki \u015fekilde boyal\u0131 b\u00f6lgenin alan\u0131: a2 - b2 = ^a + bh\u00b7^a - bh 49 \u00e7) y y y 1. A\u015fa\u011f\u0131daki \u015fekillerde boyal\u0131 b\u00f6lgelerin alan\u0131n\u0131 g\u00f6steren \u00f6zde\u015flikleri yaz\u0131n\u0131z. y a) 5 2x 5 y x y x 2x b) 2a 2a b d) 6 b 3a 6 c) 8 2n 8 3m 2n 3a 3m 200 8. S\u0131n\u0131f","\u0130ki Kare Fark\u0131 \u00d6zde\u015fli\u011finin Modellenmesi 2. A\u015fa\u011f\u0131daki \u00f6zde\u015fliklerde bo\u015f b\u0131rak\u0131lan yerlere ya- 3. x + y = 16 ve x \u2013 y = 6\u2019d\u0131r. z\u0131lmas\u0131 gereken ifadeleri bulunuz. Buna g\u00f6re x2 \u2013 y2 ifadesinin de\u011ferini bulunuz. a) (2x + 3y)2 = .......... x2 + .......... xy + .......... y2 b) (3a \u2013 b)2 = .......... a2 \u2013 .......... ab + b2 4. a\u00b7b = 60 ve a2 + b2 = 136\u2019d\u0131r. c) 4x2 \u2013 y2 = (2x + y)\u00b7(..........) Buna g\u00f6re a + b ifadesinin alabilece\u011fi de\u011ferleri bulunuz. \u00e7) (2x \u2013 5)2 = 4x2 \u2013 .......... x + .......... 5. x \u2013 y = 15 ve x\u00b7y = 100\u2019d\u00fcr. d) (.......... + 3y)2 = 9x2 + .......... xy + .......... Buan g\u00f6re x2 + y2 ifadesinin de\u011ferini bulunuz. e) x2 \u2013 .......... =(x \u2013 7)\u00b7(x + 7) 6. f) (.......... \u2013 5)2 = 2a2 \u2013 .......... + 25 g) 9x2 \u2013 16y2 = (.......... x \u2013 4y)\u00b7(.......... + ..........) 5x \u011f) (3a + 2b)\u00b7(3a \u2013 ..........) = .......... a2 \u2013 4b2 O 3y Yukar\u0131da i\u00e7 i\u00e7e ge\u00e7mi\u015f O merkezli iki dairenin yar\u0131- \u00e7aplar\u0131 verilmi\u015ftir. Buna g\u00f6re ye\u015fil boyal\u0131 b\u00f6lgenin alan\u0131n\u0131 ifade eden cebirsel ifadeyi bulunuz. (\u220f yerine 3 al\u0131n\u0131z.) h) (3a + 4)2 = .......... a2 + .......... a + .......... 8. S\u0131n\u0131f 201","Uyguluyorum \u00d6zde\u015flikler Test 47 1. A\u015fa\u011f\u0131daki e\u015fitliklerden hangisi \u00f6zde\u015fliktir? A) 6x + 4 = 3x \u2013 5 5. B) 2(x \u2013 3) = x + 2x \u2013 6 (3a \u2013 5)2 C) 3\u00b7(x \u2013 2) = 12 D) 5\u00b7(x + 2) = 6x \u2013 x + 10 ifadesi a\u015fa\u011f\u0131dakilerden hangisine e\u015fittir? A) 3a2 \u2013 15a + 5 B) 9a2 \u2013 15a + 25 C) 9a2 \u2013 30a + 25 D) 9a2 \u2013 30a + 10 2. I. a + a + a + a = 4a 6. A\u015fa\u011f\u0131daki dikd\u00f6rtgenin kenar uzunluklar\u0131 birim cin- sinden verilmi\u015ftir. II. (a + 1)\u00b7(a \u2013 1) = a2 \u2013 1 24x+18 III. 3a\u00b72a = 6a 8x2 8x2 Yukar\u0131daki e\u015fitliklerden hangileri de\u011fi\u015fkenin ala- bilece\u011fi t\u00fcm de\u011ferler i\u00e7in do\u011fru olamaz? A) Yaln\u0131z III B) I ve II C) I ve III D) II ve III 24x+18 Buna g\u00f6re bu dikd\u00f6rtgenin birim cinsinden \u00e7evre uzunlu\u011fu a\u015fa\u011f\u0131dakilerden hangisine e\u015fittir? 3. A) (8x + 6)2 B) (8x + 3)2 \ufffd\u00b7(2a \u2013 5) = 15 \u2013 6a C) (4x + 6)2 D) (4x + 3)2 Yukar\u0131daki e\u015fitlik \u00f6zde\u015flik oldu\u011funa g\u00f6re \ufffd ka\u00e7- t\u0131r? A) 3a B) 3 C) \u20133 D) \u20133a 7. (a+5) cm a cm 4. a cm 7m\u00b7(3 + a) = 21m \u2013 28m2 (a-5) cm Yukar\u0131daki e\u015fitlik \u00f6zde\u015flik oldu\u011funa g\u00f6re a ka\u00e7- Yukar\u0131daki karesel b\u00f6lgenin alan\u0131, dikd\u00f6rtgensel t\u0131r? b\u00f6lgenin alan\u0131ndan ka\u00e7 santimetrekare fazlad\u0131r? A) 4m B) 4 C) \u20134 D) \u20134m A) 25 B) 10 C) 5 D) 0 202 8. S\u0131n\u0131f","Test \u00d6zde\u015flikler Uyguluyorum 47 8. 13. (3a \u2013 7)\u00b7(3a + 7) 6x2 \u2013 21x \u2013 x\u00b7(3x + 1) = 3x2 + \ufffd ifadesinin \u00f6zde\u015fi a\u015fa\u011f\u0131dakilerden hangisidir? e\u015fitli\u011finin \u00f6zde\u015flik olabilmesi i\u00e7in \ufffd yerine a\u015fa- \u011f\u0131dakilerden hangisi gelmelidir? A) 9a2 \u2013 42a \u2013 49 B) 9a2 \u2013 42a + 49 C) 9a2 \u2013 49 D) 9a2 + 49 A) 22x \u2013 1 B) \u2013x2 \u2013 22x C) \u201322x D) x2 \u201322x 9. 16 m2 49 n2 28 mn -56 mn 14. 2x 3y 3y 2x 4x2 6xy 6xy Yukar\u0131daki balonlardan hangisi patlat\u0131l\u0131rsa kalan Yukar\u0131da modellenen \u00f6zde\u015flik a\u015fa\u011f\u0131dakilerden balonlarda yazan cebirsel ifadelerin toplam\u0131 tam- hangisidir? kare ifade olur? A) 2x\u00b7(2x + 6y) = 4x2 + 12xy A) Sar\u0131 B) K\u0131rm\u0131z\u0131 C) Mavi D) Mor B) 2x\u00b7(2x + 3y) = 4x2 + 6xy 10. 4x2 + 48 + 9y2 = (2x + 3y)2 C) 2x\u00b7(6y \u2013 2x) = 12xy \u2013 4x D) 2x\u00b73y = 6xy e\u015fitli\u011fi bir \u00f6zde\u015flik oldu\u011funa g\u00f6re x\u00b7y ka\u00e7t\u0131r? 15. 102\u00b798 i\u015fleminin sonucu a\u015fa\u011f\u0131daki i\u015flemlerden A) 2 B) 4 C) 8 D) 12 hangisinin sonucuna e\u015fittir? 11. A) 1002 + 4 B) 1002 \u2013 2 (m + 7)2 \u2013 14m C) 1002 \u2013 4 D) 102 \u2013 2 ifadesi a\u015fa\u011f\u0131dakilerden hangisi ile \u00f6zde\u015ftir? A) m2 \u201372 B) (m \u20137)2 16. Bir kenar uzunlu\u011fu a br olan karenin i\u00e7inden bir ke- C) (m \u20137)\u00b7(m \u2013 7) D) m2 + 72 nar uzunlu\u011fu 3b br olan 9 adet kare \u00e7\u0131kar\u0131lm\u0131\u015ft\u0131r. a + 9b = 38 ve kalan b\u00f6lgenin alan\u0131 76 br2 oldu\u011fu- 12. x2 \u2013 8 ifadesi a\u015fa\u011f\u0131dakilerden hangisi ile toplan\u0131r- na g\u00f6re a \u2013 9b ka\u00e7t\u0131r? sa elde edilen sonu\u00e7 (x \u2013 3)\u00b7(x + 3) ile \u00f6zde\u015f olur? A) 1 B) 2 C) 3 D) 4 A) 2x B) x C) \u20131 D) \u20132 8. S\u0131n\u0131f 203","\u00c7arpanlara Ay\u0131rma Cebirsel ifadelerin \u00e7arpanlar\u0131n\u0131n \u00e7arp\u0131m\u0131 \u015feklinde yaz\u0131lmas\u0131na \u00e7arpanlara ay\u0131rma denir. Bu s\u0131n\u0131f d\u00fczeyinde bir ce- birsel ifadeyi \u00e7arpanlara ay\u0131rmak i\u00e7in \u015fu y\u00f6ntemlerden faydalanaca\u011f\u0131z; \u2022 Ortak \u00e7arpan parantezine alma \u2022 \u0130ki kare fark\u0131 \u00f6zde\u015fli\u011fini kullanma \u2022 Tam kare \u00f6zde\u015fliklerini kullanma Ortak \u00c7arpan Parantezine Alma \u0130ki veya daha fazla terimden olu\u015fan bir cebirsel ifadede t\u00fcm terimlerdeki ortak \u00e7arpan, \u00e7arpan olarak parantez d\u0131\u015f\u0131na yaz\u0131l\u0131r. Ortak \u00e7arpan, parantez d\u0131\u015f\u0131na al\u0131n\u0131rken \u00e7arpma i\u015fleminin da\u011f\u0131lma \u00f6zelli\u011finden yararlan\u0131l\u0131r. \u00d6rnek: \u2022 3a + 3b ifadesinde 3 ortak \u00e7arpand\u0131r. O y\u00fczden; 3a + 3b = 3\u00b7(a + b) \u015feklinde yaz\u0131labilir. \u2022 15a2 \u201310a = 5a\u00b73a \u2013 5a\u00b72 \u2022 8x + 12 = 4\u00b72x + 4\u00b73 = 4\u00b7(2x + 3) = 5a\u00b7(3a \u2013 2) 50 e) 20x2y + 10x = .................................................... f) 9a3 \u2013 6a2 = ........................................................ 1. A\u015fa\u011f\u0131daki cebirsel ifadeleri ortak \u00e7arpan y\u00f6nte- miyle \u00e7arpanlar\u0131na ay\u0131r\u0131n\u0131z. a) 8x + 10 = ........................................................... b) 3a + 12 =........................................................... g) 12ab2 + 8ab = ................................................... \u011f) a3 + a2 + a = ..................................................... c) 16x2 \u2013 4x =........................................................ h) 15x2 + 5x + 10x3 =............................................. \u0131) 12a2 \u2013 4ab \u2013 8ab2 =........................................... \u00e7) 6a2 + 24a = ....................................................... i) \u20136m2n \u2013 mn2 \u2013 mn = ......................................... d) x2 + 7x = ........................................................... NOT: Ortak \u00e7arpan parantezine al\u0131nan terimle- rin katsay\u0131lar\u0131n\u0131n EBOB\u2019u ortak \u00e7arpan olarak parantez d\u0131\u015f\u0131na al\u0131n\u0131r. 204 8. S\u0131n\u0131f","\u00c7arpanlara Ay\u0131rma c) 2. A\u015fa\u011f\u0131daki e\u015fitliklerde bo\u015f b\u0131rak\u0131lan yerlere yaz\u0131l- mas\u0131 gereken e\u015fitlikleri bulunuz. a) 9a + 21 = .......... \u00b7(3a + 7) b) 8 m2 \u2013 6m = .......... \u00b7(4m \u2013 3) \u00e7) c) 30a3 + 5a2 = 5a2\u00b7(.......... + 1) \u00e7) 6x2y3 \u20132xy = .......... \u00b7(3xy2 \u20131) d) a3 \u2013 a + a2 = a\u00b7(.......... \u2013 .......... + .......... ) 4. A\u015fa\u011f\u0131da alanlar\u0131 ve bir kenar uzunluklar\u0131 verilen e) 3x2 + 5x3 + 4x = .......... \u00b7(3x + 5x2 + 4) dikd\u00f6rtgensel b\u00f6lgelerin verilmeyen kenar uzun- luklar\u0131n\u0131 bulunuz. a) x-2 b) ? ? 2a 3. x 1 x 1 1 Alan = 2x2-4x Alan = 18a+4a2 x2 x 11 Yukar\u0131da verilen cebir karolar\u0131 ile modellenen c) ? \u00e7) ? a\u015fa\u011f\u0131daki cebirsel ifadeleri \u00e7arpanlar\u0131na ay\u0131r\u0131n\u0131z. a) 2a y\u20133 b) Alan = 12a2-2a+6ab Alan = x.(y-3)+4.(y-3) 8. S\u0131n\u0131f 205","\u0130ki Kare Fark\u0131 \u00d6zde\u015fli\u011finden Faydalanarak \u00c7arpanlara Ay\u0131rma \u0130ki terimin kareleri fark\u0131 \u015feklinde verilen bir ifadenin \u00e7arpanlar\u0131na ayr\u0131lm\u0131\u015f \u015fekli \u015fu \u015fekildedir. a2 - b2 = ^a + bh\u00b7^a - bh \u00d6rnek: \u2022 6xx2 - 54 = x2 - 4 = ^x + 2h\u00b7^x - 2h \u2022 49a2 - 9b2 = ^7ah2 - ^3bh2 = ^7a + 3bh\u00b7^7a - 3bh 14472a443 9 2 3b 51 g) 144 \u2013 25x2 = ..................................................... \u011f) 4m2 \u2013 169n2 =................................................... 1. A\u015fa\u011f\u0131daki cebirsel ifadeleri iki kare fark\u0131 \u00f6zde\u015fli- \u011finden faydalanarak \u00e7arpanlar\u0131na ay\u0131r\u0131n\u0131z. a) x2 \u2013 9 = ............................................................. b) a2 \u2013 25 =........................................................... h) x2 \u2013 1 =........................................................... c) 36 \u2013 x2 = ........................................................... 4 \u0131) 4 - 16a2 = ....................................................... 25 \u00e7) 1 \u2013 49b2 = ......................................................... i) 100x2 \u2013 64 =....................................................... d) 9x2 \u2013 100y2 = .................................................... j) m4 \u2013 n4 =............................................................ e) 64a2 \u2013 36b2 =.................................................... k) 25a2b2 \u2013 225c2d2 = ........................................... f) 81a2 \u2013 144b2 = ................................................... l) 81x4y4 \u2013 16a2b2 = ............................................... 206 8. S\u0131n\u0131f","\u0130ki Kare Fark\u0131 \u00d6zde\u015fli\u011finden Faydalanarak \u00c7arpanlara Ay\u0131rma 2. A\u015fa\u011f\u0131da verilen karesel ya da dikd\u00f6rtgensel b\u00f6l- 3. A\u015fa\u011f\u0131daki e\u015fitliklerde bo\u015f b\u0131rak\u0131lan yerlere yaz\u0131l- gelerde boyal\u0131 k\u0131s\u0131mlar\u0131n alan\u0131n\u0131 bulup \u00e7arpanla- mas\u0131 gereken cebirsel ifadeleri bulunuz. r\u0131na ay\u0131r\u0131n\u0131z. a) 81x2 \u2013 100y2 = (9x + 10y)\u00b7(..........) a) a a b) 36 \u20134a2 = (..........)\u00b7(\u20132a + 6) 3 c) 16m2 \u2013 .......... = (4m + 7)\u00b7(4m \u2013 7) \u00e7) 225x2 \u2013 1 = (..........)\u00b7(15x + 1) 3 d) a2b2 \u2013 144 = (ab + 12)\u00b7(..........) e) .......... \u2013 64y4 = (16x2 \u2013 8y2)\u00b7(16x2 + 8y2) b) 5 2x 5 2x c) 4 10a 4 3 4. 672 \u2013 432 i\u015fleminin sonucunu iki kare fark\u0131 \u00f6zde\u015f- li\u011finden faydalanarak bulunuz. 3 5. 10a (400a2-196b4) \u00e7) Yukar\u0131da metrekare cinsinden bir y\u00fcz\u00fcn\u00fcn alan\u0131 verilen dikd\u00f6rtgen \u015feklindeki afi\u015fin \u00e7evre uzun- y lu\u011fu ka\u00e7 metredir? 7y 9x 6y 6y 2y 3y 4x 8. S\u0131n\u0131f 207","Tam Kare \u00d6zde\u015fliklerden Faydalanarak \u00c7arpanlara Ay\u0131rma \u0130ki terimin Toplam\u0131n\u0131n Karesi \u0130ki terimin toplam\u0131n\u0131n karesi \u015feklinde verilen bir ifadenin \u00e7arpanlar\u0131na ayr\u0131lm\u0131\u015f h\u00e2li \u015fu \u015fekildedir. a2 + 2ab + b2 = ^a + bh\u00b7^a + bh \u00d6rnek: \u2022 84x2 + 12xy + 9y2 = ^2x + 3yh\u00b7^2x + 3yh ; 8 ^2xh2 2\u00b72x\u00b73y ^3yh2 52 g) 9m2 + 72mn + 144n2 =...................................... \u011f) 4x2 + 12x + 9 =.................................................. 1. A\u015fa\u011f\u0131daki cebirsel ifadeleri tam kare \u00f6zde\u015flikler- den faydalanarak \u00e7arpanlar\u0131na ay\u0131r\u0131n\u0131z. a) x2 + 2xy + y2 = .................................................. b) a2 + 4ab + 4b2 = ............................................... h) 25a2 + 30ab + 9b2 = ......................................... c) 9 + 6m + m2 = ................................................... \u0131) x2 + 20x + 100 =................................................. \u00e7) x2 + 16xy+ 64y2 =.............................................. d) 16x2 + 8xy + y2 =............................................... i) 81a2 + 72ab + 16b2 = ......................................... e) 4a2 + 20ab + 25b2 =.......................................... j) 64x2 + 32x + 4 = ................................................ f) 25 + 10a + a2 = .................................................. k) 36m2 + 84mn + 49n2 =...................................... 208 8. S\u0131n\u0131f","\u0130ki Terimin Fark\u0131n\u0131n Karesi \u0130ki terimin fark\u0131n\u0131n karesi \u015feklinde verilen bir ifadenin \u00e7arpanlar\u0131na ayr\u0131lm\u0131\u015f \u015fekli \u015fu \u015fekildedir. a2 - 2ab + b2 = ^a - bh\u00b7^a - bh \u00d6rnek: \u00d6rnek: \u2022 x2 - 6x +9 = ^x - 3h\u00b7^x - 3h \u2022 9x2 \u2013 12xy + 4y2 = (3x \u2013 2y)\u00b7(3x + 2y) 6 6 7 ^xh2 -2\u00b7x\u00b73 ^3h2 (3x)2 \u2013 2\u00b73x\u00b7y + (2y)2 53 2. A\u015fa\u011f\u0131daki e\u015fitliklerde bo\u015f b\u0131rak\u0131lan yerlere yaz\u0131l- mas\u0131 gereken ifadeleri yaz\u0131n\u0131z. 1. A\u015fa\u011f\u0131daki cebirsel ifadeleri tam kare \u00f6zde\u015flikler- den faydalanarak \u00e7arpanlar\u0131na ay\u0131r\u0131n\u0131z. a) x2 + 6x + 9 = (x + 3)\u00b7(.........................) a) 4x2 \u2013 4xy + y2 = ................................................ b) 1 \u2013 6a + 9a2 = ................................................... b) 4a2 \u2013 20a + 25 = (2a \u2013 5) (.........................) c) 16m2 \u2013 40mn + 25n2 = ...................................... c) (.................) + 12mn + 4n2 = (3m + 2n)\u00b7(3m + 2n) \u00e7) 4x2 \u2013 24xy + 36y2 = .......................................... \u00e7) 64a2 \u2013 (.....................) + 9b2 = (8a \u20133b)\u00b7(8a \u2013 3b) d) 100a2 \u2013 100ab + 25b2 = .................................... d) 36x2 \u2013 60x + (........................) = (6x \u2013 5)\u00b7(6x \u2013 5) e) 64 \u2013 112m + 49m2 =.......................................... f) 81 \u2013 18xy+ x2y2 = ............................................... f) 81a2 + 180ab + 100b2 = (......................)\u00b7(9a + 10b) 8. S\u0131n\u0131f 209","\u0130ki Terimin Fark\u0131n\u0131n Karesi 3. A\u015fa\u011f\u0131da alan\u0131 verilen karesel \u015fekillerin \u00e7evre 5. A\u015fa\u011f\u0131daki cebirsel ifadeleri \u00f6nce ortak parante- uzunluklar\u0131n\u0131 bulunuz. zine al\u0131p daha sonra \u00f6zde\u015fliklerden faydalanarak \u00e7arpanlar\u0131na ay\u0131r\u0131n\u0131z. a) b) a) 4a2 + 8ab + 4b2 =.............................................. 9x2 \u2013 30x + 25 64a2 \u2013 48ab + 9b2 \u00c7evre = \u00c7evre = b) 8x2 \u2013 16x + 8 =.................................................. c) \u00e7) 49 \u2013 140m2 + 100m4 144m2n2 \u2013 24mnr + r2 \u00c7evre = c) a3 \u2013 36a = ......................................................... \u00e7) 45x2 \u201380y2 = ..................................................... \u00c7evre = d) 2x3 + 32x2y + 128xy2 = ..................................... 4. A\u015fa\u011f\u0131daki ifadelerin tam kare olabilmesi i\u00e7in \ufffd yerine yaz\u0131labilecek de\u011ferleri bulunuz. a) a2 \u2013 \ufffda + 9 b) 4 + \ufffdx + x2 c) 9x2 \u2013 24x + \ufffd e) 3 \u2013 147a2 = ....................................................... \u00e7) \ufffd + 8a + 4 f) 20x2 \u2013 180y2 = ................................................... d) \ufffda2 \u2013 8a + 16 e) x2 + \ufffdx + 25 g) 147m3 \u2013 3mn2 =................................................ 210 8. S\u0131n\u0131f","\u0130ki Terimin Fark\u0131n\u0131n Karesi 6. A\u015fa\u011f\u0131daki \u00e7arpan a\u011fa\u00e7lar\u0131nda bo\u015f b\u0131rak\u0131lan kutu- 7. x = 98 oldu\u011funa g\u00f6re x2 + 4x + 4 i\u015fleminin sonu- lara yaz\u0131lmas\u0131 gereken ifadeleri bulunuz. cunu bulunuz. a) 2a2-8ab+8b2 2 8. 452 \u2013 2\u00b745\u00b715 + 152 i\u015fleminin sonucunu bulunuz. b) 256m4-81 9. m + n = 5 ve m\u00b7n = 6 Buna g\u00f6re m2 + n2 ifadesinin de\u011ferini bulunuz. 10. a2 \u2013 b2 = 400 ve a + b = 25 Buna g\u00f6re a \u2013 b ifadesinin de\u011ferini bulunuz. c) 3x3+18x2+27x 3x 11. ab \u2013 ac = 24 ve b \u2013 c= 8 Buna g\u00f6re a + b \u2013 c ifadesinin de\u011ferini bulunuz. 8. S\u0131n\u0131f 211","Uyguluyorum \u00c7arpanlara Ay\u0131rma Test 48 1. 5. 6a3 + 30a x2 x2 x2 x2 -x -x -x cebirsel ifadesinin \u00e7arpanlar\u0131na ayr\u0131lm\u0131\u015f \u015fekli x x x x -1 -1 -1 a\u015fa\u011f\u0131dakilerden hangisidir? x x x x -1 -1 -1 x x x x -1 -1 -1 A) 6a(a2 + 5) B) 6a(a + 5) C) 6(a2 + 5) D) 6(a + 5) Cebirsel karolar\u0131 ile modellenen \u00e7arpma i\u015flemi a\u015fa\u011f\u0131dakilerden hangisidir? A) (3x \u2013 2)\u00b7(x + 3) B) (3x \u2013 2)\u00b7(x \u2013 3) C) (4x \u2013 3)\u00b7(x + 3) D) (4x \u2013 3)\u00b7(x \u2013 3) 2. 4x2 \u2013 \ufffd = (2x \u2013 3)\u00b7(2x + 3) e\u015fitli\u011fine g\u00f6re \ufffd yerine yaz\u0131lmas\u0131 gereken say\u0131 6. ka\u00e7t\u0131r? A) \u20139 B) \u20133 C) 3 D) 9 a2 + \ufffda + 36 ifadesi tam kare oldu\u011funa g\u00f6re \ufffd yerine yaz\u0131labi- lecek tam say\u0131lar\u0131n \u00e7arp\u0131m\u0131 ka\u00e7t\u0131r? A) \u2013256 B) \u2013196 C) \u2013144 D) \u2013100 3. 16x2+40x+25 A\u015fa\u011f\u0131dakilerden hangisi yukar\u0131daki tahtada ya- 7. (13 + m)2 = x2 + ym + m2 zan cebirsel ifadenin \u00e7arpanlar\u0131ndan biri de\u011fil- e\u015fitli\u011fine g\u00f6re x + y ka\u00e7t\u0131r? dir? A) 4x + 5 B) \u20134x \u2013 5 A) 26 B) 39 C) 52 D) 65 C) 1 D) 4x \u2013 5 8. 9542 \u2013 142 = 968\u00b7\ufffd 4. Bir tanesi 3a \u2013 1 olan iki cebirsel ifadenin \u00e7arp\u0131m\u0131 oldu\u011funa g\u00f6re \ufffd yerine yaz\u0131lmas\u0131 gereken say\u0131 9a2 \u2013 6a + 1\u2019dir. ka\u00e7t\u0131r? Buna g\u00f6re di\u011fer cebirsel ifade a\u015fa\u011f\u0131dakilerden A) 920 B) 930 C) 940 D) 950 hangisidir? A) 3a + 1 B) 3a \u2013 1 C) 9a + 1 D) 9a \u2013 1 212 8. S\u0131n\u0131f","Test \u00c7arpanlara Ay\u0131rma Uyguluyorum 48 9. A\u015fa\u011f\u0131da alan\u0131 verilen dikd\u00f6rtgen \u015feklindeki kartonun 12. 2x2 + 16 cebirsel ifadesi x\u00b7(8 \u2013 x) ifadesiyle top- uzun kenar\u0131n\u0131n uzunlu\u011fu 30 cm\u2019dir. land\u0131\u011f\u0131nda elde edilen cebirsel ifadenin \u00e7arpanla- r\u0131na ayr\u0131lm\u0131\u015f h\u00e2li a\u015fa\u011f\u0131dakilerden hangisidir? 5x2-20 x-2 A) (2x \u2013 4)\u00b7(2x \u2013 4) B) (2x \u2013 4)\u00b7(2x + 4) C) (x \u2013 4)\u00b7(x \u2013 4) D) (x + 4)\u00b7(x + 4) Buna g\u00f6re bu kartonun k\u0131sa kenar\u0131n\u0131n uzunlu\u011fu 13. Alanlar\u0131 fark\u0131 40 cm2 olan iki karesel b\u00f6lgenin kenar ka\u00e7 santimetredir? uzunluklar\u0131 s\u0131ras\u0131yla a ve b\u2019dir. A) 1 B) 2 C) 3 D) 4 a + b = 8 cm oldu\u011funa g\u00f6re a \u2013 b ka\u00e7 santimet- redir? 10. Bir mimar bir kenar\u0131 6x metre olan kare \u015feklindeki A) 5 B) 4 C) 3 D) 2 arsada, her birinin kenar uzunlu\u011fu 7 metre olan belli say\u0131da karesel b\u00f6lge belirlemi\u015ftir. 14. Arsada geri kalan b\u00f6lgenin alan\u0131 36x2 \u2013 441 ol- 512 - 492 du\u011funa g\u00f6re belirlenen karesel b\u00f6lgelerin say\u0131s\u0131 ka\u00e7t\u0131r? 512 - 2\u00b751\u00b749 + 492 A) 9 B) 8 C) 7 D) 6 i\u015fleminin sonucu ka\u00e7t\u0131r? A) 10 B) 50 C) 100 D) 200 11. (3x2+18x+27)dm Bir ad\u0131m uzunlu\u011fu (x + 3) dm olan bir ki\u015fi yukar\u0131- 15. x= 1881 oldu\u011funa g\u00f6re x\u00b7^x - 4h + 4 i\u015fleminin da verilen yolu ka\u00e7 ad\u0131mda bitirir? sonucu ka\u00e7t\u0131r? A) 3x + 3 B) 3x + 9 C) x + 3 D) x + 9 A) 1879 B) 1880 C) 1882 D) 1883 8. S\u0131n\u0131f 213","Ba\u015far\u0131yorum \u00d6zde\u015flikler ve \u00c7arpanlara Ay\u0131rma Test 49 1. Yanda \u015eekil 1\u2019de uzunlu\u011fu verilen mumun g\u00f6r\u00fcn\u00fcm\u00fc yanmaya ba\u015flad\u0131ktan 20 dakika sonra \u015eekil 2\u2019deki gibi oluyor. Bu mumun \u015eekil 2 her 10 dakika sonunda e\u015fit miktarda k\u0131sald\u0131\u011f\u0131 biliniyor. Buna g\u00f6re \u015eekil 2\u2019deki g\u00f6r\u00fcn\u00fcm\u00fcnden 1 bu\u00e7uk saat sonra(3a-b) cm (12x2+28x) cm mumun santimetre cinsinden uzunlu\u011funu g\u00f6steren cebirsel (12x2+24x) cm ifadenin \u00e7arpanlar\u0131na ayr\u0131lm\u0131\u015f h\u00e2li a\u015fa\u011f\u0131dakilerden hangisi- dir? A) 6x (2x + 1) B) 6 (2x + 1) \u015eekil 1 C) 3x (4x + 1) D) 3 (2x + 1) 2. Kenar uzunluklar\u0131 verilen dikd\u00f6rtgen bi\u00e7imindeki karton kesikli \u00e7izgiler boyunca kesilerek d\u00f6rt e\u015f par\u00e7aya ayr\u0131l\u0131yor. Ard\u0131ndan bu par\u00e7alar kenarlar\u0131 \u00e7ak\u0131\u015facak bi\u00e7imde yerle\u015ftirilerek a\u015fa\u011f\u0131daki \u015fekil olu\u015fturuluyor. (4a+8b) cm Buna g\u00f6re olu\u015fan \u015feklin i\u00e7 b\u00f6lgesinde kalan k\u0131sm\u0131n alan\u0131n\u0131 santimetrekare cinsinden veren cebirsel ifade a\u015fa\u011f\u0131dakilerden hangisidir? A) 16a2 + 8ab + b2 B) 4a2 \u2013 6ab + 9b2 C) 4a2 - 12ab + 9b2 D) 16a2 \u2013 8ab + b2 3. Bir bilgisayar oyununda para birimi olarak \u201cMon\u201d kullan\u0131lmaktad\u0131r. Bu oyundaki mon para birimine ait para \u00e7e\u015fitle- rinden birer tanesi a\u015fa\u011f\u0131da verilmi\u015ftir. 16x2+24x+9 100x2-y2 4x2\u20137xy+6 -2x2y+6y2x Bu para \u00e7e\u015fitlerinin de\u011ferleri \u015fu \u015fekilde tan\u0131mlanm\u0131\u015ft\u0131r: \u201cTam kare \u00f6zde\u015fli\u011fi belirten cebirsel ifadeler 100 mon, iki kare fark\u0131 \u00f6zde\u015fli\u011fi belirten cebirsel ifadeler 150 mon, di\u011fer cebirsel ifadeler ise katsay\u0131lar toplam\u0131 kadar mon de- \u011ferine sahiptir.\u201d Buna g\u00f6re bu bilgisayar oyununda 877 mon de\u011ferinde bir \u00fcr\u00fcn almak isteyen ki\u015fi bu paralardan en az ka\u00e7 tanesi ile bu \u00fcr\u00fcn\u00fc hi\u00e7 para \u00fcst\u00fc almadan sat\u0131n alabilir? A) 10 B) 12 C) 13 D) 15 214 8. S\u0131n\u0131f","Test \u00d6zde\u015flikler ve \u00c7arpanlara Ay\u0131rma Ba\u015far\u0131yorum 49 4. A\u015fa\u011f\u0131da g\u00f6sterilen kare bi\u00e7imindeki k\u00e2\u011f\u0131t s\u0131ras\u0131yla oklar y\u00f6n\u00fcnde \u015feklideki gibi kendi \u00fczerine katlan\u0131yor. 4a a a a ab aaaa a ab Son durumda olu\u015fan \u015fekilden dik kenar uzunluklar\u0131 b br olan ikizkenar dik \u00fc\u00e7gen bi\u00e7iminde bir par\u00e7a kesilerek at\u0131- l\u0131yor. Bu k\u00e2\u011f\u0131t tekrar a\u00e7\u0131ld\u0131\u011f\u0131nda bir y\u00fcz\u00fcn\u00fcn alan\u0131n\u0131 birimkare cinsinden veren cebirsel ifade a\u015fa\u011f\u0131dakilerden hangisidir? A) 16a2 \u2013 b2 B) 8 (a2 - b2) C) 16a2 - 4b2 D) 16a2 - 16b2 5. A\u015fa\u011f\u0131da daire bi\u00e7imindeki bir tepsinin \u00fczerinde bulunan dikd\u00f6rtgen \u015feklinde \u00f6zde\u015f iki tabak verilmi\u015ftir. 5x+2y 4x+y Tabaklardan birinin kenar uzunluklar\u0131 \u015fekildeki gibi olup iki taba\u011f\u0131n toplam \u00e7evre uzunlu\u011fu tepsinin \u00e7evre uzunlu- \u011funa e\u015fittir. Buna g\u00f6re bu tepsinin \u00fcst y\u00fcz\u00fcn\u00fcn alan\u0131n\u0131 veren cebirsel ifade a\u015fa\u011f\u0131dakilerden hangisidir? (\u220f yerine 3 al\u0131n\u0131z.) A) 108x2 + 36xy + 18y2 B) 108x2 + 72xy + 12y2 C) 72x2 + 18xy + 9y2 D)54x2 + 18xy + 9y2 8. S\u0131n\u0131f 215","Ba\u015far\u0131yorum \u00d6zde\u015flikler ve \u00c7arpanlara Ay\u0131rma Test 50 1. Kare \u015feklindeki bir k\u00e2\u011f\u0131d\u0131n bir y\u00fcz\u00fc a\u015fa\u011f\u0131daki gibi dikd\u00f6rtgensel ve karesel b\u00f6lgelere ayr\u0131lm\u0131\u015ft\u0131r. Ayn\u0131 renklerle g\u00f6sterilen b\u00f6lgeler e\u015f ve pembe karesel b\u00f6lgelerden her birinin bir y\u00fcz\u00fcn\u00fcn alan\u0131 9x2 santimetreka- redir. Buna g\u00f6re ba\u015flang\u0131\u00e7ta verilen kare \u015feklindeki k\u00e2\u011f\u0131d\u0131n \u00e7evresinin uzunlu\u011funu santimetre cinsinden veren cebirsel ifade a\u015fa\u011f\u0131dakilerden hangisidir? A) 36x B) 48x C) 60x D) 72x 2. A\u015fa\u011f\u0131da d\u00fcz bir rafa kare dik prizma \u015feklindeki \u00f6zde\u015f ya\u011f tenekeleri e\u015fit aral\u0131klarla dizilmi\u015ftir. 10 Adet (6x+8) cm Ya\u011f (x2+20) cm (x2+20) cm Ya\u011f Ya\u011f Ya\u011f Tenekelerin g\u00f6r\u00fcnen y\u00fczlerinin alanlar\u0131 36x2 - 64 cm2 olup en soldaki ve en sa\u011fdaki tenekelerin raf\u0131n kenarlar\u0131yla aralar\u0131nda bo\u015fluk bulunmamaktad\u0131r. Buna g\u00f6re raf\u0131n santimetre cinsinden uzunlu\u011fu a\u015fa\u011f\u0131dakilerden hangisi ile \u00f6zde\u015ftir? A) 9x2 + 60x + 100 B) 9x2 + 30x + 25 C) 36x2 + 120x + 100 D) 36x2 + 30x + 25 216 8. S\u0131n\u0131f","Test \u00d6zde\u015flikler ve \u00c7arpanlara Ay\u0131rma Ba\u015far\u0131yorum 50 3. A\u015fa\u011f\u0131da kare bi\u00e7imindeki pembe ve dikd\u00f6rtgen bi\u00e7imindeki mavi ile ye\u015fil kartonlar\u0131n birer kenarlar\u0131n\u0131n \u00e7ak\u0131\u015ft\u0131r\u0131lma- s\u0131yla olu\u015fan \u015fekil g\u00f6sterilmi\u015ftir. (9x2+30x+25) br2 (9x2-25) br2 (2x+3) br (x-4) br 2 br Etiket Pembe ve mavi kartonlar\u0131n birer y\u00fczlerinin alanlar\u0131 \u00fczerlerine yaz\u0131lm\u0131\u015f olup ye\u015fil kartonun bir k\u00f6\u015fesine yap\u0131\u015ft\u0131r\u0131lan etiketin bu kartonun kenarlar\u0131na uzakl\u0131klar\u0131 \u015fekildeki gibidir. Buna g\u00f6re bu etiketin santimetrekare cinsinden bir y\u00fcz\u00fcn\u00fcn alan\u0131n\u0131 veren cebirsel ifade a\u015fa\u011f\u0131dakilerden hangisidir? A) 16x2 - 4 B) 16x2 \u2013 1 C) 4x2 \u2013 4 D) 4x2 - 1 4. A\u015fa\u011f\u0131da dikd\u00f6rtgen \u015feklindeki \u00fc\u00e7 levhan\u0131n birer y\u00fczlerinin alanlar\u0131 verilmi\u015ftir. 18a+24 12a-16 36a2-96a+64 Bu levhalardan birer kenar uzunlu\u011fu birbirine e\u015fit olan iki tanesi al\u0131narak e\u015fit kenarlar\u0131 \u00e7ak\u0131\u015facak \u015fekilde bir zemine \u00fcst \u00fcste yerle\u015ftiriliyor. Buna g\u00f6re sonra durumda olu\u015fan \u015feklin santimetre cinsinden uzunlu\u011funun \u00e7arpanlar\u0131na ayr\u0131lm\u0131\u015f h\u00e2li a\u015fa- \u011f\u0131dakilerden hangisi olabilir? A) 6(a +1) B) 6(a \u2013 1) C) 3(a + 2) D) 3(a \u2013 2) 8. S\u0131n\u0131f 217","4 \u00dcN\u0130TE DO\u011eRUSAL DENKLEMLER 8. SINIF VE E\u015e\u0130TS\u0130ZL\u0130KLER Do\u011frusal Denklemler E\u015fitsizlikler Kazan\u0131mlar; Birinci dereceden bir bilinmeyenli denklemleri \u00e7\u00f6zer. M.8.2.2.1 M.8.2.2.2 Koordinat sistemini \u00f6zellikleriyle tan\u0131r ve s\u0131ral\u0131 ikilileri M.8.2.2.3 g\u00f6sterir. M.8.2.2.4 Aralar\u0131nda do\u011frusal ili\u015fki bulunan iki de\u011fi\u015fkenden M.8.2.2.5 birinin di\u011ferine ba\u011fl\u0131 olarak nas\u0131l de\u011fi\u015fti\u011fini tablo ve M.8.2.2.6 denklem ile ifade eder. M.8.2.3.1 Do\u011frusal denklemlerin gra\ufb01\u011fini \u00e7izer. M.8.2.3.2 M.8.2.3.3 Do\u011frusal ili\u015fki i\u00e7eren ger\u00e7ek hayat durumlar\u0131na ait denklem, tablo ve gra\ufb01\u011fi olu\u015fturur ve yorumlar. Do\u011frunun e\u011fimini modellerle a\u00e7\u0131klar, do\u011frusal denklemleri ve gra\ufb01klerini e\u011fimle ili\u015fkilendirir. Birinci dereceden bir bilinmeyenli e\u015fitsizlik i\u00e7eren g\u00fcnl\u00fck hayat durumlar\u0131na uygun matematik c\u00fcmleleri yazar. Birinci dereceden bir bilinmeyenli e\u015fitsizlikleri say\u0131 do\u011frusunda g\u00f6sterir. Birinci dereceden bir bilinmeyenli e\u015fitsizlikleri \u00e7\u00f6zer.","\u00dcN\u0130TE NOTLANDIRMA \u00dcN\u0130TE \u00d6NCEL\u0130KLER\u0130M \u00dcN\u0130TEDEK\u0130 MOOD NOTLARIM F\u0130K\u0130RLER\u0130M FORM\u00dcLLER","Birinci Dereceden Bir Bilinmeyenli Denklemler \u0130\u00e7inde bilinmeyen bulunan ve bu bilinmeyenin baz\u0131 de\u011fer ya da de\u011ferleri i\u00e7in do\u011fru olan e\u015fitliklere denklem denir. Bu de\u011ferleri bulma i\u015flemine denklem \u00e7\u00f6zme denir. \u0130\u00e7inde bir bilinmeyen bulunan ve bilinmeyenin kuvveti 1 olan denklemlere birinci dereceden bir bilinmeyenli denklemler denir. a, b birer ger\u00e7ek say\u0131 ve x bilinmeyen olmak \u00fczere bu denklemler ax + b = 0 bi\u00e7iminde g\u00f6sterilir. Denklemler \u00e7\u00f6z\u00fcl\u00fcrken; \u2022 E\u015fitli\u011fin her iki taraf\u0131na ayn\u0131 say\u0131 eklenebilir ya da her iki taraf\u0131ndan ayn\u0131 say\u0131 \u00e7\u0131kar\u0131labilir. \u2022 E\u015fitli\u011fin her iki taraf\u0131 s\u0131f\u0131rdan farkl\u0131 bir say\u0131 ile \u00e7arp\u0131labilir ya da s\u0131f\u0131rdan farkl\u0131 bir say\u0131ya b\u00f6l\u00fcnebilir. \u2022 Denklemlerin \u00e7\u00f6z\u00fcm\u00fcnde ayr\u0131ca, e\u015fitli\u011fin bir taraf\u0131nda bilinenler, di\u011fer taraf\u0131nda bilinmeyenler olacak bi\u00e7imde her iki tarafa ayn\u0131 i\u015flemlerin uygulanmas\u0131 kullan\u0131labilir. \u00d6rnek: \u2022 3x \u2013 4 = x + 10 \u2022 5\u00b7(x + 1) = 2\u00b7(2x + 4) 3x \u2013 x = 10 + 4 5x + 5 = 4x + 8 5x \u2013 4x = 8 \u2013 5 2x = 14 x=3 x=7 54 \u00e7) 2\u00b7(4x \u2013 15) = 3\u00b7(x + 5) 1. A\u015fa\u011f\u0131daki denklemleri sa\u011flayan x de\u011ferlerini bu- lunuz. a) x + 8 = 13 d) 7 + 5\u00b7(x \u2013 1) = 11 + 2x b) 2x \u2013 7 = x \u2013 10 e) \u20134(x \u2013 1) + 72 = 0 c) 3x \u2013 12 = 5x \u2013 5 220 8. S\u0131n\u0131f","Rasyonel Denklemler Katsay\u0131lar\u0131 rasyonel ifade olan denklemlerde \u00e7\u00f6z\u00fcm yap\u0131l\u0131rken payda e\u015fitleme, geni\u015fletme, sadele\u015ftirme veya i\u00e7ler d\u0131\u015flar \u00e7arp\u0131m\u0131ndan yararlan\u0131labilir. Bu denklemler rasyonel denklem olarak adland\u0131r\u0131l\u0131r. Rasyonel denklemlerde bilinmeyenin de\u011ferinin payday\u0131 s\u0131f\u0131r yapmamas\u0131 gerekir. Bulunan de\u011fer payday\u0131 s\u0131f\u0131r yap\u0131- yorsa, bu de\u011fer denklemin \u00e7\u00f6z\u00fcm\u00fc olarak al\u0131namaz. \u00d6rnek: A\u015fa\u011f\u0131daki denklemlerde x\u2019in de\u011ferlerini bulal\u0131m. \u2022 3x = 15 (\u0130\u00e7ler d\u0131\u015flar \u00e7arp\u0131m\u0131 yapal\u0131m.) \u2022 x-2 =4 (\u0130\u00e7ler d\u0131\u015flar \u00e7arp\u0131m\u0131 yapal\u0131m.) 4 5 3x = 15 ( 3x\u00b71 = 15\u00b74 x-2 = 4 ( 1\u00b7(x \u2013 2) = 4\u00b75 4 1 5 1 3x = 60 x \u2013 2 = 20 x = 20 x = 22 \u2022 x + x = 12 (Payda e\u015fitleyelim.) \u2022 2x - 1 1 - x 1 (Payda e\u015fitleyelim.) 3 6 += 3 22 x + x = 12 ( 2x + x = 12 2x - 1 1 - x 1 4x - 2 3 - 3x 1 3 6 6 6 + 2 =2( + = 3 6 6 2 ^2h 3x 12 = ^2h ^3h x+1 1 = 61 62 3x = 72 2x = 6 \u2013 2 x = 24 2x = 4 x=2 55 1. A\u015fa\u011f\u0131daki e\u015fitliklerde x\u2019in kesinlikle alamayaca\u011f\u0131 \u00e7) x-3 = 1 de\u011ferleri bulunuz. 4x - 12 4 a) a =6 x+4 -2^x - 5h d) 10 - 2x = 1 b) a =-2 x-3 c) a =-1 e) 8 = a 3x - 6 x+4 x-1 8. S\u0131n\u0131f 221","Rasyonel Denklemler 2. A\u015fa\u011f\u0131daki denklemleri sa\u011flayan x\u2019in de\u011ferlerini bulunuz. a) x =6 e) x + x - x =x-1 3 4 3 12 b) x+1 =-3 f) x + 1 = 11 5 3 4 12 c) - 3x g) x + x-1 =3 +9 = 0 23 2 \u00e7) x+x = 15 1-x 2+x 24 \u011f) - 7 = 6 x 3x 5 d) + 18 = h) 8 \u00b7^x + 7h = 15 2 4 222 8. S\u0131n\u0131f","Rasyonel Denklemler x 3x 9 m) x-1 x-2 x-3 \u0131) - =- 2 - 5 =4- 10 5 10 2 i) 2\u00b7^x + 2h =x+5 n) x-1 + x-2 =1+ x-1 3 2 6 3 j) x+1 x = 16 o) x+1 = 0, 5 + x+2 43 x 5x \u00f6) 1 = 3 k) 8 - 6 = 6 2x x+5 l) x-1 +5= 2x - 2 p) 3 = 2 4 3 2x + 1 x+2 8. S\u0131n\u0131f 223","Rasyonel Denklemler r) 1 =1- 1 \u00fc) 1 - 2 + 7 = 12 3x 2x x x x s) 1 -2= 1 v) 1 \u00b7^x - 1h - 3 \u00b7^x - 1h = 0 4x 3x 3 4 13 =4 y) 1 3 \u015f) - 2 \u00b7^x - 1h + 2 \u00b7^x + 1h = 5 x+1 x+1 t) 5 = 3 -1 z) 0, 4 = 0, 5 2-x x-2 0, 2\u00b7x x + 0, 5 u) 2x - 11 = 9 + 3 q) 10 = 5 x - 10 x - 10 2 0, 2 + x x + 0, 1 224 8. S\u0131n\u0131f","Rasyonel Denklemler 1 d) Hangi say\u0131n\u0131n 9 fazlas\u0131n\u0131n 3 \u2019\u00fc \u20135\u2019tir? 3. A\u015fa\u011f\u0131daki problemlerin \u00e7\u00f6z\u00fcm\u00fcn\u00fc veren denk- lemleri kurunuz. a) Bir say\u0131, kendisinin 3 eksi\u011finin 2 kat\u0131na e\u015fit oldu- \u011funa g\u00f6re bu say\u0131 ka\u00e7t\u0131r? b) Toplam 27 \u00f6\u011frenci olan bir s\u0131n\u0131fta k\u0131z \u00f6\u011frencile- e) Bir say\u0131 ile bu say\u0131n\u0131n yar\u0131s\u0131n\u0131n toplam\u0131 36 oldu- rin say\u0131s\u0131 erkek \u00f6\u011frencilerin say\u0131s\u0131ndan 3 fazla- \u011funa g\u00f6re bu say\u0131 ka\u00e7t\u0131r? d\u0131r. Buna g\u00f6re s\u0131n\u0131ftaki erkek \u00f6\u011frenci say\u0131s\u0131 ka\u00e7t\u0131r? c) 50 TL paras\u0131 olan Canan paras\u0131n\u0131n bir k\u0131sm\u0131 ile f) Bir merdivenin basamaklar\u0131 iki\u015fer iki\u015fer \u00e7\u0131k\u0131ld\u0131- defter ald\u0131ktan sonra, defter i\u00e7in harcad\u0131\u011f\u0131 para- \u011f\u0131nda 20 ad\u0131m at\u0131lmaktad\u0131r. n\u0131n 2 TL fazlas\u0131 ile kalem al\u0131yor. Buna g\u00f6re bu merdiven ka\u00e7 basamakl\u0131d\u0131r? Canan\u2019\u0131n geriye defter i\u00e7in harcad\u0131\u011f\u0131 kadar para- s\u0131 kal\u0131yor. Buna g\u00f6re Canan\u2019\u0131n ka\u00e7 liras\u0131 kalm\u0131\u015ft\u0131r? \u00e7) 30 ki\u015filik bir s\u0131n\u0131ftaki \u00f6\u011frenciler s\u0131ralar\u0131n yar\u0131s\u0131na g) 1 \u2019\u00fc ile 1 iki\u015ferli, di\u011fer yar\u0131s\u0131na \u00fc\u00e7erli oturdu\u011funda ayakta 4 5 \u2019inin fark\u0131 10 olan say\u0131 ka\u00e7t\u0131r? \u00f6\u011frenci kalmad\u0131\u011f\u0131na g\u00f6re bu s\u0131n\u0131fta ka\u00e7 s\u0131ra var- d\u0131r? 8. S\u0131n\u0131f 225","4. A\u015fa\u011f\u0131daki problemleri \u00e7\u00f6z\u00fcn\u00fcz. Rasyonel Denklemler d) a) 1 Hangi say\u0131n\u0131n 3 \u2019\u00fcn\u00fcn 5 fazlas\u0131 ayn\u0131 say\u0131n\u0131n ya- r\u0131s\u0131na e\u015fittir? b) Bir say\u0131n\u0131n 1 eksi\u011fi, ayn\u0131 say\u0131n\u0131n 3 Yukar\u0131daki e\u015f b\u00f6lmeli su kab\u0131na 3 L daha su ek- 4 \u2019\u00fcn\u00fcn 12 faz- lenince kab\u0131n yar\u0131s\u0131 dolmu\u015ftur. las\u0131na e\u015fittir. Buna g\u00f6re kap tamamen doldu\u011funda ka\u00e7 litre su al\u0131r? Buna g\u00f6re bu say\u0131 ka\u00e7t\u0131r? c) 2 e) 1 Bir s\u0131n\u0131ftaki \u00f6\u011frencilerin 3 \u2019\u00fc matematik s\u0131nav\u0131n- Bir araba yolun \u00f6nce 6 \u2019s\u0131n\u0131 sonra ise kalan yo- 2 lun 5 \u2019ini gidiyor. dan ba\u015far\u0131l\u0131 olurken 8 \u00f6\u011frenci ba\u015far\u0131s\u0131z olmu\u015f- tur. Bu araba toplam 100 km yol gitti\u011fine g\u00f6re gitmesi Buna g\u00f6re s\u0131n\u0131ftaki \u00f6\u011frenci say\u0131s\u0131 ka\u00e7t\u0131r? gereken ka\u00e7 kilometre yolu kalm\u0131\u015ft\u0131r? \u00e7) Ece paras\u0131n\u0131n 3 f) Ard\u0131\u015f\u0131k \u00fc\u00e7 \u00e7ift say\u0131n\u0131n toplam\u0131n\u0131n yar\u0131s\u0131 9 oldu\u011fu- 5 \u2019ini harcad\u0131\u011f\u0131nda paras\u0131 12 TL na g\u00f6re bu say\u0131 ka\u00e7t\u0131r? azald\u0131\u011f\u0131na g\u00f6re Ece\u2019nin ba\u015flang\u0131\u00e7ta ka\u00e7 liras\u0131 vard\u0131r? 226 8. S\u0131n\u0131f","g) Rasyonel Denklemler \u0131) 5a 2a-1 24 2 TL Yukar\u0131daki e\u015fkenar \u00fc\u00e7gen ile karenin \u00e7evre Yukar\u0131da sat\u0131\u015f fiyat\u0131 verilen not defteri, al\u0131\u015f fiya- uzunluklar\u0131 e\u015fittir. 3 Buna g\u00f6re karenin bir kenar\u0131 ka\u00e7 birimdir? t\u0131n\u0131n 5 kat\u0131 fazlas\u0131na sat\u0131lmaktad\u0131r. Buna g\u00f6re not defterinin al\u0131\u015f fiyat\u0131 ka\u00e7 lirad\u0131r? \u011f) 1 \u2019i ile 1 2 5 \u2019inin toplam\u0131 28 olan say\u0131 ka\u00e7t\u0131r? i) A\u00e7\u0131l\u0131\u015f \u00fccreti 7,25 TL olan bir taksi i\u00e7in gidilen her kilometre ba\u015f\u0131na 3,5 TL \u00f6denmektedir. Bu taksiyle belirli bir yolu giden Ender bu yol i\u00e7in 66,75 TL \u00f6deme yapt\u0131\u011f\u0131na g\u00f6re yol ka\u00e7 kilomet- redir? h) Yunus, bir kitab\u0131 her g\u00fcn bir \u00f6nceki g\u00fcnden 6 j) 2 sayfa fazla okuyarak 4 g\u00fcnde bitiriyor. Bir terzi elindeki kuma\u015f\u0131n \u00f6nce 5 \u2019ini, sonra ka- 7 Yunus, 3. g\u00fcn\u00fcn sonunda kitab\u0131n 10 \u2019unu oku- 3 du\u011funa g\u00f6re bu kitap ka\u00e7 sayfad\u0131r? lan\u0131n 4 \u2019\u00fcn\u00fc sat\u0131yor ve elinde 12 m kuma\u015f kal\u0131- yor. Buna g\u00f6re terzinin elindeki kuma\u015f ka\u00e7 metredir? 8. S\u0131n\u0131f 227","Uyguluyorum Birinci Dereceden Bir Bilinmeyenli Denklemler Test 51 1. 5. 1 = 3 x - x =2 x-5 x-5 45 denklemini sa\u011flayan x de\u011feri ka\u00e7t\u0131r? denklemini sa\u011flayan x de\u011feri ka\u00e7t\u0131r? A) 10 B) 20 C) 30 D) 40 A) 1 B) 0 C) \u20131 D) Yoktur 6. 2. a 1 x br x br + =2 2 2 63 denklemini sa\u011flayan a de\u011feri ka\u00e7t\u0131r? x br 2 A) 20 B) 15 C) 10 D) 5 Yukar\u0131daki e\u015fkenar \u00fc\u00e7genin \u00e7evre uzunlu\u011fu 24 br oldu\u011funa g\u00f6re x ka\u00e7t\u0131r? A) 20 B) 18 C) 16 D) 14 3. 7. 2-x x +3= x -1 32 3+ =4 2 denklemini sa\u011flayan x ka\u00e7t\u0131r? A) \u20131 B) 0 C) 1 D) 2 denklemini sa\u011flayan x de\u011feri ka\u00e7t\u0131r? A) 24 B) 18 C) 12 D) 6 4. x x 8. 1 + 1 + a = 1 + a 100 10 a3 a6 + = 1, 21 denklemini sa\u011flayan x de\u011feri ka\u00e7t\u0131r? denklemini sa\u011flayan a de\u011feri ka\u00e7t\u0131r? A) 9 B) 11 C) 13 D) 15 A) 1 B) 3 C) \u20134 D) \u20136 228 8. S\u0131n\u0131f","Test Birinci Dereceden Bir Bilinmeyenli Denklemler Uyguluyorum 51 9. 13. Uzunlu\u011fu a cm olan bir \u00e7ubuk, bir ucundan 2 x+2 =3+ x-3 5 \u2019i ka- 32 dar kesilirse \u00e7ubu\u011fun orta noktas\u0131 10 cm kayacakt\u0131r. denklemini sa\u011flayan x de\u011feri ka\u00e7t\u0131r? Buna g\u00f6re \u00e7ubu\u011fun santimetre cinsinden uzun- lu\u011funu veren denklem a\u015fa\u011f\u0131dakilerden hangisi- A) \u201310 B) \u20135 C) 0 D) 1 dir? 2a a - 2a A) a = 5 - 10 B) 5 = a - 10 2 2 2 a- 2a a - 2a C) a - 5 = 10 D) 5 = a + 10 2 2 22 10. 3 \u00b7^x - 6h - 6 = x 2 4 denklemini sa\u011flayan x de\u011feri ka\u00e7t\u0131r? 14. \u0130ki ki\u015filik ve \u00fc\u00e7 ki\u015filik banklar\u0131n bulundu\u011fu bir parkta, \u00fc\u00e7 ki\u015filik banklar\u0131n say\u0131s\u0131, iki ki\u015filik banklar\u0131n say\u0131s\u0131- A) 12 B) 18 C) 24 D) 30 3 n\u0131n 4 \u2019\u00fcne e\u015fittir. Bu banklara ayn\u0131 anda en fazla 170 ki\u015fi oturabil- di\u011fine g\u00f6re parktaki toplam bank say\u0131s\u0131 ka\u00e7t\u0131r? A) 90 B) 80 C) 70 D) 60 11. Bir otob\u00fcsteki erkeklerin say\u0131s\u0131 kad\u0131nlar\u0131n say\u0131s\u0131n\u0131n yar\u0131s\u0131d\u0131r. Otob\u00fcsten 10 evli \u00e7ift inince erkeklerin sa- y\u0131s\u0131 kad\u0131nlar\u0131n say\u0131s\u0131n\u0131n 1 \u2019\u00fcne e\u015fit oluyor. 15. A\u015fa\u011f\u0131da Erhan ve Beril\u2019in toplam paras\u0131 g\u00f6sterilmi\u015f- 4 tir. Buna g\u00f6re otob\u00fcste ba\u015flang\u0131\u00e7taki yolcu say\u0131s\u0131 ka\u00e7t\u0131r? A) 15 B) 30 C) 45 D) 60 12. Murat, ilk g\u00fcn paras\u0131n\u0131n \u00e7eyre\u011fini harcad\u0131ktan sonra, 43 her g\u00fcn bir \u00f6nceki g\u00fcne g\u00f6re 5 TL az harcayarak t\u00fcm Erhan\u2019\u0131n paras\u0131n\u0131n 5 \u2019i, Beril\u2019in paras\u0131n\u0131n 4 \u2019\u00fcne paras\u0131n\u0131 5 g\u00fcnde bitiriyor. e\u015fit oldu\u011funa g\u00f6re Beril\u2019in paras\u0131 ka\u00e7 lirad\u0131r? A) 40 B) 44 C) 48 D) 52 Buna g\u00f6re Murat, son g\u00fcn ka\u00e7 lira harcam\u0131\u015ft\u0131r? A) 20 B) 30 C) 40 D) 50 8. S\u0131n\u0131f 229","Ba\u015far\u0131yorum Birinci Dereceden Bir Bilinmeyenli Denklemler Test 52 1. Esma Han\u0131m \u00f6zde\u015f k\u00e2seleri bir mutfak raf\u0131na iki farkl\u0131 \u015fekilde yerle\u015ftirdi\u011finde en \u00fcstteki k\u00e2selerin raf\u0131n \u00fcst k\u0131sm\u0131na uzakl\u0131klar\u0131 a\u015fa\u011f\u0131daki gibi olmu\u015ftur. 24 cm 39 cm 9 4 adet adet Buna g\u00f6re Esma Han\u0131m bu rafa yerle\u015ftirilebilecek en fazla say\u0131da k\u00e2seyi yerle\u015ftirdi\u011finde en \u00fcstteki k\u00e2senin raf\u0131n \u00fcst k\u0131sm\u0131na uzakl\u0131\u011f\u0131 ka\u00e7 santimetre olur? A) 0 B) 1 C) 2 D) 3 2. A\u015fa\u011f\u0131da iki farkl\u0131 ma\u011fazada kampanyal\u0131 olarak sat\u0131\u015fa sunulan ve kampanyas\u0131z fiyat\u0131 ayn\u0131 olan iki tablet g\u00f6steril- mi\u015ftir. 1.Ma\u011faza 2.Ma\u011faza %30 indirim %20 indirim ve ve 400 TL hediye \u00e7eki 750 TL hediye \u00e7eki Bir m\u00fc\u015fteri hediye \u00e7eklerini de ald\u0131\u011f\u0131nda 2. ma\u011fazan\u0131n \u00fccreti 100 TL daha avantajl\u0131 olmaktad\u0131r. Buna g\u00f6re tabletin kampanyas\u0131z sat\u0131\u015f fiyat\u0131 ka\u00e7 lirad\u0131r? A) 4000 B) 3500 C) 3000 D) 2500 230 8. S\u0131n\u0131f","Test Birinci Dereceden Bir Bilinmeyenli Denklemler Ba\u015far\u0131yorum 52 3. Dikd\u00f6rtgen bi\u00e7imindeki bir havlu do\u011frusal bir ask\u0131ya havlunun k\u0131sa kenarlar\u0131 ask\u0131ya paralel olacak \u015fekilde as\u0131l\u0131yor. Havlunun y\u00fczlerinin \u00fcst \u00fcste gelmeyen k\u0131sm\u0131n\u0131n uzunlu\u011fu, havlu \u015eekil 1\u2019deki gibi as\u0131ld\u0131\u011f\u0131nda 4 cm; \u015eekil 2\u2019deki gibi as\u0131ld\u0131\u011f\u0131nda ise 10 cm oluyor. 4 cm 10 cm \u015eekil 1 \u015eekil 2 6 Havlunun \u015eekil 1\u2019de g\u00f6r\u00fcnen \u00f6n k\u0131sm\u0131n\u0131n alan\u0131n\u0131n \u015eekil 2\u2019de g\u00f6r\u00fcnen \u00f6n k\u0131sm\u0131n\u0131n alan\u0131na oran\u0131 5 \u2019dir. Buna g\u00f6re havlunun uzun kenar\u0131 ka\u00e7 santimetredir? A) 28 B) 36 C) 40 D) 52 4. Bir dijital terazi, kefelerine konulan cisimlerin kilogram cinsinden k\u00fctleleri fark\u0131n\u0131 ekran\u0131nda g\u00f6stermektedir. A\u015fa\u011f\u0131da \u015eekil 1\u2019de bu terazinin g\u00f6r\u00fcn\u00fcm\u00fc verilmi\u015ftir. 3 kg 2 kg \u015eekil 1 \u015eekil 2 4 Terazinin sol kefesine buradaki cismin k\u00fctlesinin 5 \u2019i kadar, sa\u011f kefesine ise buradaki cismin k\u00fctlesi kadar k\u00fctleye sahip birer cisim daha koyuldu\u011funda g\u00f6r\u00fcn\u00fcm \u015eekil 2\u2019deki gibi olmu\u015ftur. Buna g\u00f6re ba\u015flang\u0131\u00e7ta terazinin sol kefesinde bulunan cismin k\u00fctlesi ka\u00e7 kilogramd\u0131r? A) 10 B) 15 C) 20 D) 25 8. S\u0131n\u0131f 231","Ba\u015far\u0131yorum Birinci Dereceden Bir Bilinmeyenli Denklemler Test 52 5. Bir tiyatroda oyuncular\u0131n sahneye \u00e7\u0131kabilmesi i\u00e7in haz\u0131rlanan \u00f6zde\u015f be\u015f basamakl\u0131 ta\u015f\u0131nabilir merdivenin baz\u0131 uzunluklar\u0131 a\u015fa\u011f\u0131da verilmi\u015ftir. 2m 3m Bu merdivenin her bir basama\u011f\u0131n\u0131n yan y\u00fcz\u00fc zemine dik iken, \u00fcst y\u00fcz\u00fc zemine paraleldir. Merdivenin basamakla- r\u0131n\u0131n tamam\u0131 dikd\u00f6rtgen \u015feklindeki k\u0131rm\u0131z\u0131 bir hal\u0131 ile hal\u0131 hi\u00e7bir taraftan sarkmayacak bi\u00e7imde \u015fekildeki gibi kaplan- m\u0131\u015ft\u0131r. Bu hal\u0131n\u0131n alan\u0131 20 m2 oldu\u011funa g\u00f6re \u00e7evresi ka\u00e7 metredir? A) 16 B) 17 C) 18 D) 19 6. Videolar\u0131 izlerken i\u00e7eriklerinden hi\u00e7bir \u015fey kaybetmeden video izleme h\u0131z\u0131n\u0131 art\u0131r\u0131p azaltabiliriz. Video ilk a\u00e7\u0131ld\u0131\u011f\u0131nda h\u0131z se\u00e7ene\u011fi yava\u015f h\u0131zdad\u0131r. Tablo: Video \u0130zleme H\u0131z Se\u00e7enekleri 0,5x \u00c7ok Yava\u015f 0,75x Yava\u015f 1,0x Normal 1,25x H\u0131zl\u0131 1,5x Daha H\u0131zl\u0131 2,0x \u00c7ok H\u0131zl\u0131 H\u0131z se\u00e7ene\u011fi ile videonun izlenme s\u00fcresi aras\u0131nda ters orant\u0131 vard\u0131r. \u00d6rne\u011fin, \u00e7ok yava\u015f h\u0131z se\u00e7ene\u011fi ile 10 dakika- da izlenen video, normal h\u0131z se\u00e7ene\u011fi ile 5 dakikada izlenmektedir. 11 Ahmet bir filmin 3 \u2019\u00fcn\u00fc yava\u015f, 3 \u2019\u00fcn\u00fc h\u0131zl\u0131, kalan\u0131 ise daha h\u0131zl\u0131 se\u00e7enekleri ile 126 dakikada izlemi\u015ftir. Buna g\u00f6re Ahmet bu filmi sadece h\u0131zl\u0131 se\u00e7ene\u011fi ile izlemi\u015f olsayd\u0131 ka\u00e7 dakikada izlerdi? A) 90 B) 108 C) 120 D) 135 232 8. S\u0131n\u0131f","Test Birinci Dereceden Bir Bilinmeyenli Denklemler Ba\u015far\u0131yorum 52 7. A\u015fa\u011f\u0131da derece k\u00fcrs\u00fcn\u00fcne \u00e7\u0131kan \u00fc\u00e7 \u00f6\u011frencinin k\u00fcrs\u00fcn\u00fcn \u00fczerindeki durumlar\u0131 g\u00f6sterilmi\u015ftir. Bu\u011fra An\u0131l Cenk 1 2 3 4x cm K\u00fcrs\u00fclerden 3 numaral\u0131 olan\u0131n y\u00fcksekli\u011fi verilirken di\u011fer ikisinin y\u00fcksekli\u011fi s\u0131ras\u0131yla bir \u00f6ncekinden 10\u2019ar cm daha fazlad\u0131r. Ayr\u0131ca 1 ve 2 numaral\u0131 k\u00fcrs\u00fclerin santimetre cinsinden y\u00fckseklikleri toplam\u0131 Cenk\u2019in boyuna, 1 numaral\u0131 k\u00fcrs\u00fcn\u00fcn 70 cm fazlas\u0131 ise An\u0131l\u2019\u0131n boyuna e\u015fittir. K\u00fcrs\u00fcn\u00fcn \u00fczerindeki \u00f6\u011frencilerin \u00fc\u00e7\u00fc de ayn\u0131 hizada oldu\u011funa g\u00f6re en uzun olan \u00f6\u011frenci ile en k\u0131sa olan \u00f6\u011frencinin boylar\u0131 toplam\u0131 ka\u00e7 metredir? (1 m = 100 cm) A) 3,4 B) 3,5 C) 3,6 D) 3,7 8. A\u015fa\u011f\u0131da g\u00f6sterilen renkleri d\u0131\u015f\u0131nda \u00f6zde\u015f dikd\u00f6rtgen \u015feklindeki lego par\u00e7alar\u0131ndan bir tanesinin uzun kenar\u0131n\u0131n 3 uzunlu\u011fu k\u0131sa kenar\u0131n\u0131n uzunlu\u011funun 4 \u2019\u00fcnden 5 cm fazlad\u0131r. Bu lego par\u00e7alar\u0131n\u0131n belirli k\u0131s\u0131mlar\u0131n\u0131n \u00e7ak\u0131\u015ft\u0131r\u0131lma- s\u0131yla a\u015fa\u011f\u0131daki gibi iki farkl\u0131 karesel b\u00f6lge olu\u015fturuluyor. \u015eekil 1 \u015eekil 2 1. \u015feklin i\u00e7 k\u0131sm\u0131n\u0131n \u00e7evresi 44 cm oldu\u011funa g\u00f6re 2. \u015feklin i\u00e7 k\u0131sm\u0131n\u0131n alan\u0131 ka\u00e7 santimetrekaredir? A) 36 B) 25 C) 16 D) 9 8. S\u0131n\u0131f 233","Koordinat Sistemi \u0130ki say\u0131 do\u011frusunun O noktas\u0131nda birbirleriyle dik kesi\u015fmesiyle olu\u015fan sisteme koordinat sistemi denir. Say\u0131 do\u011frular\u0131n\u0131n kesi\u015fim noktas\u0131na ba\u015flang\u0131\u00e7 noktas\u0131 (orijin), yatay say\u0131 do\u011frusuna x ekseni, dikey say\u0131 do\u011fru- suna y ekseni denir. y ekseni \u2022 Bu sistemde bir noktan\u0131n yeri belirtilirken, A(x,y) nokta- s\u0131ndaki s\u0131ral\u0131 ikiliden birincisi x ekseninden, ikincisi y ekse- 4 I.B\u00f6lge ninden se\u00e7ilir. 3 (+,+) II.B\u00f6lge 2 Orijin (0,0) \u00d6rnek: y koordinat\u0131 (-,+) 1 x koordinat\u0131 A(\u20131,2) A(\u20131,2) -4 -3 -2 -1 O 1 2 3 4 x ekseni \u2022 Koordinat sistemi eksenler taraf\u0131ndan 4 b\u00f6lgeye ayr\u0131l\u0131r. Bu -1 b\u00f6lgelerin isimleri ve b\u00f6lgelerden se\u00e7ilebilecek s\u0131ral\u0131 ikililerin i\u015faretleri \u015fekildeki gibidir. III.B\u00f6lge -2 IV.B\u00f6lge (-,-) (+,-) -3 -4 56 NOT: x koordinat\u0131 0 olan noktalar (0,y) y ekse- ni \u00fczerinde; y koordinat\u0131 0 olan noktalar (x,0) x 1. A\u015fa\u011f\u0131da \u00fc\u00e7 bloklu bir sitenin giri\u015f kap\u0131s\u0131nda bulunan ekseni \u00fczerindedir. tu\u015f ekran\u0131 g\u00f6sterilmi\u015ftir. 2. A\u015fa\u011f\u0131daki noktalar\u0131n koordinat sistemindeki b\u00f6l- Kap\u0131 1 2 3 4 5 6 7 8 gelerini yaz\u0131n\u0131z. a) (\u20132,4) \u2020 .................. b) (1,5) \u2020 .................. Bina c) (3,\u20133) \u2020 .................. \u00e7) (0,4) \u2020 ................. A d) (\u20131,\u20134) \u2020 ................ e) (\u20135,1) \u2020 ................ B C Buna g\u00f6re a\u015fa\u011f\u0131da bina blok ad\u0131 ve kap\u0131 numa- ras\u0131 verilen ki\u015filerin isimlerini tu\u015f ekran\u0131 \u00fczerine yaz\u0131n\u0131z. Elif \u2020 A7 Fulya \u2020 C3 G\u00f6khan \u2020 B8 Hale \u2020 A1 f) (6,0) \u2020 .................... g) (\u20132,\u20131) \u2020 .............. I\u015f\u0131l \u2020 C7 \u0130nan \u2020 B2 \u011f) (0,\u20131) \u2020 ................... h) (4,2) \u2020 ................. 234 8. S\u0131n\u0131f","Koordinat Sistemi y 6 3. A\u015fa\u011f\u0131da verilen noktalar\u0131n yerlerini yandaki koordinat 5 sistemi \u00fczerinde g\u00f6steriniz. 4 \u2022 A(2,1); B(\u20133,2); C(\u20131,\u20134) 3 2 \u2022 D(4,0); E(0,\u20135); F(\u20132,5) 1 \u2022 G(\u20133,\u20133); H(\u20131,6); I(5,5) -6 -5 -4 -3 -2 -1-O1 1 23456 x -2 -3 -4 -5 \u20136 6. A\u015fa\u011f\u0131da verilen birimkareli zeminde K(\u20131,\u20133) ise di\u011fer noktalar\u0131n koordinatlar\u0131n\u0131 bulunuz. NOT: A(x,y) noktas\u0131n\u0131n birim cinsinden x ekse- L M nine uzakl\u0131\u011f\u0131 |y|, y eksenine uzakl\u0131\u011f\u0131 |x| kadar- N P d\u0131r. \u00d6rnek: A(3,\u20135) noktas\u0131n\u0131n x eksenine 5, y eksenine K uzakl\u0131\u011f\u0131 3 br\u2019dir. 4. A\u015fa\u011f\u0131daki noktalar\u0131n eksenlere uzakl\u0131klar\u0131n\u0131 bu- lunuz. x eksenine y eksenine uzakl\u0131k uzakl\u0131k a) (\u20133,4) \u2020 7. U\u00e7 noktalar\u0131 E(\u20135,2) ve F(4,2) olan EF do\u011fru par- b) (\u20131,\u20133) \u2020 \u00e7as\u0131n\u0131n uzunlu\u011funu bulunuz. c) (2,\u20135) \u2020 \u00e7) (4,0) \u2020 d) (0,\u20136) \u2020 e) (5,2) \u2020 5. A(m\u20134, n+7) noktas\u0131 orijin oldu\u011funa g\u00f6re, 8. Koordinat sisteminde k\u00f6\u015fe noktalar\u0131 A(\u20133,\u20133), B(4,\u20133), C(4,2) ve D(\u20133,2) olan ABCD dikd\u00f6rtgeni- B(\u2013m, \u2013n) noktas\u0131n\u0131n ka\u00e7\u0131nc\u0131 b\u00f6lgede oldu\u011funu bulunuz. nin \u00e7evre uzunlu\u011funu bulunuz. 8. S\u0131n\u0131f 235","Uyguluyorum Koordinat Sistemi Test 53 1. 4. y y AB x 4 3A O 2 D 1 C -4 -3 -2 -1 O x -1 -2 1234 -3 -4 Yukar\u0131da koordinat sisteminde hangi noktan\u0131n x Yukar\u0131daki koordinat sisteminde A noktas\u0131n\u0131n 4 koordinat\u0131 pozitif, y koordinat\u0131 negatiftir? br solunda bulunan B noktas\u0131n\u0131n koordinatlar\u0131 A) A B) B C) C D) D a\u015fa\u011f\u0131dakilerden hangisidir? 2. y A) B(\u20133,3) B) B(\u20132,3) C) B(1,\u20132) D) B(1,\u20133) KL O x M 5. M(\u20136,\u201310) noktas\u0131n\u0131n y eksenine uzakl\u0131\u011f\u0131 ka\u00e7 bi- N rimdir? A) 6 B) 8 C) 10 D) 12 Yukar\u0131da koordinat sisteminde hangi noktan\u0131n koordinatlar\u0131 yanl\u0131\u015f verilmi\u015ftir? A) K(\u20132,3) B) L(3,5) 6. Koordinat sisteminin 3. b\u00f6lgesinde bulunan bir nok- C) M(\u20133,\u20131) D) N(1,\u20133) tan\u0131n x eksenine uzakl\u0131\u011f\u0131 7 br\u2019dir. 3. A\u015fa\u011f\u0131daki noktalardan hangisi koordinat siste- Buna g\u00f6re bu nokta a\u015fa\u011f\u0131dakilerden hangisi ola- minde y ekseni \u00fczerinde bulunur? bilir? A) (0,0) B) (6,0) C) (1,\u20134) D) (\u20131,\u20131) A) (5,7) B) (7,\u20131) C) (\u20137,\u20133) D) (\u20132,\u20137) 236 8. S\u0131n\u0131f","Test Koordinat Sistemi Uyguluyorum 53 7. U\u00e7 noktalar\u0131 P(2,5) ve R(8,5) olan PR do\u011fru par- 10. Koordinat sisteminde K(\u20131,2), L(4,2), M(2,\u20133), \u00e7as\u0131n\u0131n orta noktas\u0131n\u0131n koordinatlar\u0131 a\u015fa\u011f\u0131daki- N(\u20133,\u20133) noktalar\u0131n\u0131n birle\u015ftirilmesiyle olu\u015fan lerden hangisidir? d\u00f6rtgen a\u015fa\u011f\u0131dakilerden hangisidir? A) (3,5) B) (4,5) C) (5,5) D) (6,5) A) E\u015fkenar d\u00f6rtgen B) Dikd\u00f6rtgen C) Yamuk D) Paralelkenar 8. y 2 A 11. K\u00f6\u015fe noktalar\u0131, A(3,7), B(1,2) ve C(5,2) olan ABC x \u00fc\u00e7geninin alan\u0131 ka\u00e7 birimkaredir? -3 O 4 A) 16 B) 14 C) 12 D) 10 B -4 Yukar\u0131daki koordinat sisteminde A noktas\u0131n\u0131n 12. A\u015fa\u011f\u0131daki kareli zemin \u00fczerindeki koordinat siste- x koordinat\u0131, B noktas\u0131n\u0131n y koordinat\u0131ndan ka\u00e7 minde k\u00f6\u015fe noktalar\u0131ndan bir tanesi verilen karenin fazlad\u0131r? alan\u0131 16\u2019d\u0131r. A) 8 B) 7 C) 6 D) 5 y 9. A\u015fa\u011f\u0131daki birimkareli zemin \u00fczerinde verilen koordi- nat sisteminde bir dikd\u00f6rtgene ait k\u00f6\u015fegen g\u00f6steril- mi\u015ftir. y x x O O Buna g\u00f6re bu dikd\u00f6rtgenin k\u00f6\u015fe noktalar\u0131ndan Buna g\u00f6re bu karenin herhangi bir k\u00f6\u015fesinin x ve biri a\u015fa\u011f\u0131dakilerden hangisi olabilir? y koordinatlar\u0131n\u0131n toplam\u0131 en az ka\u00e7t\u0131r? A) (\u20133,\u20131) B) (\u20131,3) C) (3,1) D) (1,3) A) \u201313 B) \u201311 C) \u20139 D) \u20137 8. S\u0131n\u0131f 237","Ba\u015far\u0131yorum Koordinat Sistemi Test 54 1 ve 2. sorular\u0131 a\u015fa\u011f\u0131daki bilgilere g\u00f6re cevaplay\u0131n\u0131z. A\u015fa\u011f\u0131da bir tiyatro salonuna ait koltuklar\u0131n koordinat sistemi \u00fczerindeki modeli g\u00f6sterilmi\u015ftir. Bu salonda biletlerin fiyatlar\u0131, koltuklar\u0131n koordinat sisteminde bulunduklar\u0131 b\u00f6lgelere ve koltuklar\u0131n renklerine g\u00f6re de\u011fi\u015fmektedir. y 4 3 2 1 -5 -4 -3 -2 -1 O 1 2 3 45 x -1 -2 -3 -4 A\u015fa\u011f\u0131daki tabloda b\u00f6lgelerdeki k\u0131rm\u0131z\u0131 koltuklar\u0131n bilet fiyatlar\u0131 g\u00f6sterilmi\u015ftir. Tablo: B\u00f6lgelere G\u00f6re K\u0131rm\u0131z\u0131 Koltuklar\u0131n Bilet Fiyatlar\u0131 B\u00f6lge 1. 2. 3. 4. Bilet Fiyat\u0131 (TL) 40 50 60 70 Ayr\u0131ca her b\u00f6lgede mavi koltuklar\u0131n bilet fiyat\u0131, k\u0131rm\u0131z\u0131 koltuklar\u0131n fiyat\u0131n\u0131n 2 kat\u0131ndan 15 TL daha azd\u0131r. 1. Buna g\u00f6re yukar\u0131da gri renk ile i\u015faretlenmi\u015f koltuk i\u00e7in al\u0131nan bilet ka\u00e7 lirad\u0131r? A) 65 B) 85 C) 105 D) 115 2. A\u015fa\u011f\u0131daki noktalardan hangisindeki koltu\u011fun bilet fiyat\u0131 en fazlad\u0131r? A) (4, -4) B) (2, 1) C) (-5, 3) D) (-3, -1) 238 8. S\u0131n\u0131f","Test Koordinat Sistemi Ba\u015far\u0131yorum 54 3. A\u015fa\u011f\u0131da bir radar\u0131n ve A yerle\u015fim yerinin bulundu\u011fu noktalar\u0131n g\u00f6sterildi\u011fi koordinat sistemi verilmi\u015ftir. y -5 1 A Radar O x -2 4 Bu alanda radar\u0131n konumu sabit kalacak ve orijin olacak bi\u00e7imde yeniden koordinat sistemi \u00e7iziliyor. Buna g\u00f6re yeni koordinat sisteminde A yerle\u015fim yerine ait noktan\u0131n x ve y koordinatlar\u0131n\u0131n toplam\u0131 ka\u00e7t\u0131r? A) 12 B)11 C) 10 D) 9 4. A\u015fa\u011f\u0131da kareli zemin \u00fczerine yerle\u015ftirilmi\u015f koordinat sisteminde farkl\u0131 renklerden olu\u015fan bir hedef tahtas\u0131 g\u00f6steril- mi\u015ftir. y Tablo: B\u00f6lgelerin Renklerine G\u00f6re Puanlar\u0131 Mavi 25 Mor 50 O x Ye\u015fil 75 Turuncu 100 Bu hedef tahtas\u0131na yap\u0131lan ba\u015far\u0131l\u0131 at\u0131\u015flar\u0131n renklerine g\u00f6re puanlar\u0131 ise tabloda g\u00f6sterilmi\u015ftir. Hedef tahtas\u0131na birer ba\u015far\u0131l\u0131 at\u0131\u015f yapan d\u00f6rt \u00f6\u011frencinin att\u0131klar\u0131 noktalar\u0131n koordinatlar\u0131 a\u015fa\u011f\u0131daki gibidir. \u2022 (-9, 4) (5, 6) (-3, -1) (1, -1) Buna g\u00f6re a\u015fa\u011f\u0131dakilerden hangisi bu \u00f6\u011frencilerden herhangi birinin ald\u0131\u011f\u0131 puan olamaz? A) 25 B) 50 C) 75 D) 100 8. S\u0131n\u0131f 239","Do\u011frusal \u0130li\u015fkiler a ve b ger\u00e7ek say\u0131lar, x ve y de\u011fi\u015fken olmak \u00fczere y = ax + b \u015feklindeki denklemlere do\u011frusal denklem denir. Bu denklemlerde x ve y de\u011fi\u015fkenleri aras\u0131nda do\u011frusal ili\u015fki vard\u0131r. \u00d6rnek: Emel her g\u00fcn matematik dersinden 30 soru \u00e7\u00f6zmektedir. Ge\u00e7en zamana (x) g\u00f6re, Emel\u2019in mate- matik dersinden \u00e7\u00f6zd\u00fc\u011f\u00fc toplam soru say\u0131s\u0131 (y) aras\u0131ndaki do\u011frusal ili\u015fkiyi tablo ve denklem ile g\u00f6sterelim. Zaman (g\u00fcn) (x) 123 ... x Ba\u011f\u0131ms\u0131z Soru Say\u0131s\u0131 (y) 30 60 90 ... 30\u00b7x de\u011fi\u015fken \u0130li\u015fki 1\u2019in 30 kat\u0131 2\u2019nin 30 kat\u0131 3\u2019\u00fcn 30 kat\u0131 ... x\u2019in 30 kat\u0131 Ba\u011f\u0131ml\u0131 de\u011fi\u015fken Tabloya g\u00f6re x ile y aras\u0131ndaki ili\u015fkiyi ifade eden denklem y = 30x\u2019tir. \u00d6rnek: A\u015fa\u011f\u0131daki tabloda aralar\u0131nda do\u011frusal ili\u015fki bulunan a ve b de\u011fi\u015fkenlerinin ili\u015fkisini belirten denk- lemi yazal\u0131m. a 1 2 3 4 5 a\u2019n\u0131n 5 kat\u0131n\u0131n 3 fazlas\u0131 b\u2019ye e\u015fit oldu\u011fu i\u00e7in b 8 13 18 23 28 ili\u015fkiyi belirten denklem: b = 5a + 3\u2019t\u00fcr. !!! y = ax + b denkleminde x\u2019e verilen de\u011ferlere ba\u011fl\u0131 olarak y farkl\u0131 de\u011ferler ald\u0131\u011f\u0131 i\u00e7in x ba\u011f\u0131ms\u0131z, y ba\u011f\u0131ml\u0131 de- \u011fi\u015fkendir. 57 c) x0123 \u00e7) y 5 9 13 17 1. A\u015fa\u011f\u0131da tablolarda verilen de\u011fi\u015fkenler aras\u0131nda do\u011frusal ili\u015fki var ise \u00f6n\u00fcndeki kutucu\u011fa \ufffd i\u015fareti x \u20131 0 1 2 koyunuz. Do\u011frusal ili\u015fki olanlar\u0131n denklemini yaz\u0131n\u0131z. y \u20132 1 4 8 a) x 1 2 3 4 y 10 12 16 22 b) x 2 3 4 5 d) x 3 5 8 9 y 4 7 10 13 y 7 11 17 19 240 8. S\u0131n\u0131f","Do\u011frusal \u0130li\u015fkiler 2. Bir f\u0131r\u0131nda ekme\u011fin tanesi 4 TL\u2019ye sat\u0131lmaktad\u0131r. Sa- 4. t\u0131lan ekmek say\u0131s\u0131 (x) ile elde edilen para (y) aras\u0131n- daki do\u011frusal ili\u015fkiye g\u00f6re tabloyu doldurup ba\u011f\u0131ml\u0131 3000 L ve ba\u011f\u0131ms\u0131z de\u011fi\u015fkenleri bulunuz. Yukar\u0131daki depodan bir muslukla saatte 200 L su Ekmek Say\u0131s\u0131 Para (TL) \u0130li\u015fki ak\u0131t\u0131lmaktad\u0131r. (x) (y) Buna g\u00f6re; a) Ge\u00e7en zamana (x) g\u00f6re depoda kalan su mikta- 1 r\u0131n\u0131 (y) g\u00f6steren denklemi yaz\u0131n\u0131z. 2 3 x Denklem :............................................. Ba\u011f\u0131ml\u0131 de\u011fi\u015fken :............................................. Ba\u011f\u0131ms\u0131z de\u011fi\u015fken :............................................. b) 6. saat sonunda depoda ka\u00e7 litre su kal\u0131r? 3. Dikildi\u011finde boyu 25 cm olan fidan her ay 5 cm uza- maktad\u0131r. Ge\u00e7en zaman (x) ile fidan\u0131n boyu (y) ara- s\u0131ndaki do\u011frusal ili\u015fkiye g\u00f6re tabloyu doldurup ba- \u011f\u0131ml\u0131 ve ba\u011f\u0131ms\u0131z de\u011fi\u015fkenleri bulunuz. Zaman (ay) Boy (cm) \u0130li\u015fki c) Ka\u00e7\u0131nc\u0131 saat sonunda depoda 600 L su kal\u0131r? 1 2 3 x 5. Denklemi a = 2b olan iki de\u011fi\u015fkene g\u00f6re a\u015fa\u011f\u0131- 3 Denklem :............................................. daki tabloyu doldurunuz. Ba\u011f\u0131ml\u0131 de\u011fi\u015fken :............................................. a \u201318 12 48 Ba\u011f\u0131ms\u0131z de\u011fi\u015fken :............................................. b15 8. S\u0131n\u0131f 241","Uyguluyorum Do\u011frusal \u0130li\u015fkiler Test 55 1. A\u015fa\u011f\u0131da verilen tablolardaki de\u011fi\u015fkenlerin hangi- 4. Bir fabrikada 1 kg sal\u00e7a yapmak i\u00e7in 5 kg biber kulla- sinin aras\u0131nda do\u011frusal ili\u015fki vard\u0131r? n\u0131lmaktad\u0131r. Sal\u00e7a yapmak i\u00e7in kullan\u0131lan biber mik- tar\u0131 (I) de\u011fi\u015fken, elde edilen sal\u00e7a miktar\u0131 ise A) x y B) x y II de\u011fi\u015fkendir. 14 13 Buna g\u00f6re bo\u015f b\u0131rak\u0131lan yerlere a\u015fa\u011f\u0131dakilerden hangisi gelmelidir? 26 26 3 10 39 I. II. A) Ba\u011f\u0131ms\u0131z Ba\u011f\u0131ml\u0131 4 14 4 12 B) Ba\u011f\u0131ms\u0131z Ba\u011f\u0131ms\u0131z C) Ba\u011f\u0131ml\u0131 Ba\u011f\u0131ms\u0131z C) x y D) x y D) Ba\u011f\u0131ml\u0131 Ba\u011f\u0131ml\u0131 1 10 1 2 2 8 2 5 3 6 3 8 4 2 4 10 2. \u20132 \u20131 0 1 5. y + 2 = 3x denklemine g\u00f6re x ve y de\u011fi\u015fkenlerine a ait de\u011ferleri g\u00f6steren tablo a\u015fa\u011f\u0131dakilerden han- gisi olabilir? b \u20136 \u20132 2 6 A) x y B) x y 3 5 3 7 Tablodaki a ve b de\u011fi\u015fkenleri aras\u0131ndaki do\u011f- rusal ili\u015fkiyi g\u00f6steren denklem a\u015fa\u011f\u0131dakilerden 46 49 hangisidir? 57 5 12 A) b = 4a + 2 B) b = 2a + 4 C) a = 4b + 2 D) a = 2b + 4 3. x ile y de\u011fi\u015fkenleri aras\u0131ndaki do\u011frusal ili\u015fki x = y C) x y D) x y denklemiyle veriliyor. 2 1 1 3 \u20131 2 4 4 1 3 7 5 4 Buna g\u00f6re x = 10 i\u00e7in y ka\u00e7 olur? A) 20 B) 15 C) 10 D) 5 242 8. S\u0131n\u0131f","Test Do\u011frusal \u0130li\u015fkiler Uyguluyorum 55 9, 10, 11 ve 12. sorular\u0131 a\u015fa\u011f\u0131daki bilgilere g\u00f6re 6. A\u015fa\u011f\u0131daki tabloda g\u00fcn say\u0131s\u0131 ile bir kitaptan okunan cevaplay\u0131n\u0131z. sayfa say\u0131s\u0131 aras\u0131nda do\u011frusal ili\u015fki vard\u0131r. G\u00fcn Say\u0131s\u0131 1. 2. 3. 4. A\u015fa\u011f\u0131daki tabloda bir taksi ile gidilen yola g\u00f6re \u00f6de- necek \u00fccret g\u00f6sterilmi\u015ftir. Okunan 21 36 51 66 Sayfa Say\u0131s\u0131 Buna g\u00f6re 12. g\u00fcn\u00fcn sonunda kitaptan ka\u00e7 sayfa Gidilen Yol 1 4 5 8 okunmu\u015f olur? (km) (x) A) 156 B) 171 C) 186 D) 201 \u00dccret 15 39 47 71 (TL) (y) 9. Buna g\u00f6re bu taksinin a\u00e7\u0131l\u0131\u015f \u00fccreti ka\u00e7 lirad\u0131r? A) 5 B) 6 C) 7 D) 8 7. A\u015fa\u011f\u0131daki tabloda a ve b de\u011fi\u015fkenleri aras\u0131nda do\u011f- rusal ili\u015fki vard\u0131r. a 1 4 7\ufffd 10. Bu taksi ile 13 km yol giden bir m\u00fc\u015fteri ka\u00e7 TL \u00f6der? b 3 \ufffd 27 35 A) 102 B) 111 C) 119 D) 127 Buna g\u00f6re \ufffd + \ufffd i\u015fleminin sonucu ka\u00e7t\u0131r? A) 27 B) 26 C) 25 D) 24 11. Gitti\u011fi yol i\u00e7in 87 TL \u00f6deme yapan birisi ka\u00e7 km yol gitmi\u015ftir? A) 12 B) 11 C) 10 D) 8 8. x ve y de\u011fi\u015fkenleri aras\u0131ndaki do\u011frusal ili\u015fkiyi g\u00f6ste- 12. Gidilen yol (x) ile \u00fccret (y) aras\u0131ndaki ili\u015fkiyi belir- ren denklem 2y \u2013 3x = 5\u2019tir. ten denklem a\u015fa\u011f\u0131dakilerden hangisidir? Buna g\u00f6re a\u015fa\u011f\u0131dakilerden hangisi bu denkleme A) y \u2013 8x \u2013 7 = 0 B) y \u2013 7x \u2013 8 = 0 ait olan s\u0131ral\u0131 ikili olabilir? C) y \u2013 8x + 7 = 0 D) y \u2013 7x + 8 = 0 A) (4,5) B) (3,7) C) (2,8) D) (5,9) 8. S\u0131n\u0131f 243","Do\u011frusal Denklemlerin Grafi\u011fi Eksenlere Paralel Do\u011frular\u0131n Grafi\u011fi \u2022 a ger\u00e7ek say\u0131 olmak \u00fczere x = a \u015feklindeki do\u011f- \u2022 b ger\u00e7ek say\u0131 olmak \u00fczere y = b \u015feklindeki do\u011f- rusal denklemlerin grafikleri x eksenini a noktas\u0131nda rusal denklemlerin grafikleri y eksenini b noktas\u0131nda dik keser ve y eksenine paraleldir. dik keser ve x eksenine paraleldir. \u00d6rnek: x = 4 ve x = \u20132 do\u011frular\u0131n\u0131n grafik- \u00d6rnek: y = 2 ve y = \u20133 do\u011frular\u0131n\u0131n grafik- leri a\u015fa\u011f\u0131da verilmi\u015ftir. leri a\u015fa\u011f\u0131da verilmi\u015ftir. y x=-2 x=4 y -2 O x 2 y=2 4 O x -3 y=-3 58 3. A\u015fa\u011f\u0131daki koordinat sisteminde x + 4 = 0, 2y = 6 ve 3y \u2013 3 = 0 do\u011frular\u0131n\u0131n grafiklerini \u00e7iziniz. 1. A\u015fa\u011f\u0131daki koordinat sisteminde x = 3, x = \u20131 ve y = 5 do\u011frular\u0131n\u0131n grafiklerini \u00e7iziniz. y y x x O O 2. Koordinat sisteminde x = 2, y = 3 ve eksenler ara- NOT: x = 0 do\u011frusu y ekseni, y = 0 do\u011frusu x s\u0131nda kalan b\u00f6lgenin \u00e7evresi ka\u00e7 birimdir? eksenidir. 244 8. S\u0131n\u0131f","Orijinden Ge\u00e7en Do\u011frular\u0131n Denklemleri a bir ger\u00e7ek say\u0131 olmak \u00fczere y = ax \u015feklindeki do\u011frusal denklemlerin grafi\u011fi orijinden ge\u00e7er. y = ax denkleminde a\u2019ya 0\u2019dan farkl\u0131 de\u011ferler verilerek kar\u015f\u0131l\u0131k geldi\u011fi y de\u011feri ile birlikte (x,y) s\u0131ral\u0131 ikilileri elde edilir. Bu s\u0131ral\u0131 ikililerin bulunduklar\u0131 noktalar orijin ile birle\u015ftirilerek do\u011frunun grafi\u011fi \u00e7izilir. !!! y = ax denkleminde a = 0 olursa y de\u011feri de 0 olur ve (0,0) noktas\u0131 elde edilir. Bu da do\u011frunun denkleminin ori- jinden ge\u00e7ti\u011fini g\u00f6sterir. \u00d6rnek: y = 2x do\u011frusunun grafi\u011fini \u00e7izelim. y x\u2019e farkl\u0131 de\u011ferler vererek y de\u011ferlerini buluyoruz. y=2x 2 (1,2) x = 0 ise, y = 2x \u2020 y = 2\u00b70 = 0 (0,0) -1 x = 1 ise, y = 2x \u2020 y = 2\u00b71 = 2 (1,2) 1 x x = \u20131 ise, y = 2x \u2020 y = 2\u00b7(\u20131) = \u20132 (\u20131,\u20132) (-1,-2) -2 (0,0), (1,2) ve (\u20131,\u20132) noktalar\u0131n\u0131 yandaki koordinat sisteminde bulup birle\u015ftirerek do\u011fruyu elde edelim. 59 2. A\u015fa\u011f\u0131da verilen denklemlere ait do\u011frular\u0131 \u00e7iziniz. 1. A\u015fa\u011f\u0131daki denklemlere ait do\u011frunun grafi\u011fi ori- a) y = x jinden ge\u00e7iyorsa \u00f6n\u00fcndeki kutucu\u011fa \u201c\ufffd\u201d i\u015fareti koyunuz. y a) x = 4 b) y = \u20132 Ox c) y = \u2013x \u00e7) x \u2013 4y + 2 = 0 d) y = 2x + 1 e) x = 0 f) y \u2013 3x = 0 g) y= x 3 NOT: Sabit terimi 0 (s\u0131f\u0131r) olan do\u011frular orijin- NOT: \u0130ki noktadan sadece bir do\u011fru ge\u00e7ti\u011fi i\u00e7in den ge\u00e7er. bir denkleme ait do\u011frunun grafi\u011fi \u00e7izilirken iki tane s\u0131ral\u0131 ikili bulunmas\u0131 yeterlidir. 8. S\u0131n\u0131f 245","Orijinden Ge\u00e7en Do\u011frular\u0131n Denklemleri b) y = \u20132x d) y = x 4 y y O x Ox c) x + 3y = 0 y O x e) x = 2 ve y = 2x denklemlerine ait do\u011frular\u0131 \u00e7izerek kesi\u015fim noktas\u0131n\u0131 bulunuz. \u00e7) 2x \u2013 3y = 0 y f) y = \u20136 ve 2y = \u20133x denklemlerine ait do\u011frular\u0131 \u00e7izerek kesi\u015fim noktas\u0131n\u0131 bulunuz. O x 246 8. S\u0131n\u0131f","Eksenleri Kesen (Orijinden Ge\u00e7meyen) Do\u011frular\u0131n Denklemleri a ve b s\u0131f\u0131rdan farkl\u0131 ger\u00e7ek say\u0131lar olmak \u00fczere y = ax + b \u015feklindeki do\u011frusal denklemlerin grafikleri orijinden ge\u00e7- meden x ve y eksenlerini birer noktada keser. y = ax + b denkleminde x\u2019in 0 de\u011feri i\u00e7in y de\u011feri, y\u2019nin 0 de\u011feri i\u00e7in x de\u011feri bulunarak 2 tane s\u0131ral\u0131 ikili elde edile- bilir. Bu s\u0131ral\u0131 ikililerin kar\u015f\u0131l\u0131k geldikleri noktalar i\u015faretlenerek bu noktalardan ge\u00e7en bir do\u011fru \u00e7izilir. \u00d6rnek: y = x + 4 do\u011frusunun grafi\u011fini \u00e7izelim. y x = 0 ise, y = 0 + 4 \u2020 y = 4 olur. (0,4) 4 3 y = 0 ise, 0 = x + 4 \u2020 x = \u20134 olur. (\u20134,0) 2 1 x \u20134 \u20133 \u20132 \u20131 O y=x+4 60 2. A\u015fa\u011f\u0131da verilen denklemlere ait do\u011frular\u0131n grafi- \u011fini \u00e7iziniz. 1. A\u015fa\u011f\u0131da denklemleri verilen do\u011frular\u0131n grafi\u011fi eksenleri kesiyorsa \u00f6n\u00fcndeki kutucu\u011fa \u201c\ufffd\u201d i\u015fa- a) y = x \u2013 3 reti koyunuz. y a) y = x + 5 b) x = \u20133 c) y = 3x \u00e7) x + 2y \u2013 8 = 0 Ox d) y \u2013 2x = 1 e) y- x +1 = 0 f) x + y = 0 2 g) y x- 4 =0 NOT: Sabit terimi 0 (s\u0131f\u0131r) olmayan do\u011frular NOT: y = ax + b x\u2019e 0 de\u011ferini verdi\u011fimizde y orijinden ge\u00e7meden eksenleri keser. eksenini, y\u2019ye 0 de\u011feri verdi\u011fimizde x eksenini kesti\u011fi noktay\u0131 buluruz. 8. S\u0131n\u0131f 247","b) y = 2x \u2013 4 Eksenleri Kesen (Orijinden Ge\u00e7meyen) Do\u011frular\u0131n Denklemleri d) y + 2x = 2 yy Ox Ox c) y \u2013 3 = x e) y + 5 = 2x y y O x O x \u00e7) 2x + 3y = 6 f) x + y =1 3 4 y y O x O x 248 8. S\u0131n\u0131f","Eksenleri Kesen (Orijinden Ge\u00e7meyen) Do\u011frular\u0131n Denklemleri 3. y = 2 ve 2x + 3y = 6 do\u011frular\u0131n\u0131n kesi\u015fim noktas\u0131n\u0131 6. 3x \u2013 4y = 12 do\u011frusu ile eksenler aras\u0131nda kalan bulunuz. b\u00f6lgenin alan\u0131n\u0131 birimkare cinsinden bulunuz. 4. y= 2 x + 1 do\u011frusunun grafi\u011fini \u00e7izerek bu do\u011f- 3 runun koordinat sisteminin hangi noktalar\u0131ndan ge\u00e7ti\u011fini bulunuz. y 7. x = 0, y = 5 ve y = 2x + 10 do\u011frular\u0131 aras\u0131nda kalan b\u00f6lgenin birimkare cinsinden alan\u0131n\u0131 bulunuz. Ox 5. 2x \u2013 7y = 14 do\u011frusunun x ve y eksenlerini kesti\u011fi 8. y = 0, x = 6 \u2013 y ve y = 6 + x do\u011frular\u0131 aras\u0131nda ka- noktalar\u0131n koordinatlar\u0131 toplam\u0131n\u0131 bulunuz. lan b\u00f6lgenin alan\u0131n\u0131 bulunuz. 8. S\u0131n\u0131f 249"]