LİSE ÖĞRENCİLERİNİN ÜNİVERSİTE SINAVLARINA HAZIRLANMALARI İÇİN GEOMETRİ SORU BANKASI KİTABI HAZIRLAYAN Erol GEDİKLİ Matematik Öğretmeni
SUNUŞ Sevgili öğrenciler! Bu kitap; hazırlandığınız üniversite sınavlarında, geometride önemli bir yardımcınız olacaktır. Kitabınızda; her bölümle ilgili zorluk dereceleri farklı olan pek çok sorular bulacaksınız. Kitabınız; 1. bölümde temel geometrik kavramlar, 2. Bölümde açılar, 3. Bölümde üçgenler, 4. bölümde çokgenler ve dörtgenler, 5. Bölümde çember ve daire, 6. Bölümde analitik geometri, 7. Bölümde düzlemde vektörler, 8. Bölümde geometride dönüşümler, 9. Bölümde uzay geometri, 10. bölümde uzayda vektörler, doğrular ve düzlemler, 11. Bölümde üniversite sınavlarında sorulan geometri soruları olmak üzere toplam 11 bölümden oluşmaktadır. Tüm çalışmalarınızda ve gireceğiniz üniversite sınavlarınızda başarı dileklerimle; sağlıklı ve mutlu günler dilerim. Erol GEDİKLİ Matematik Öğretmeni I
İÇİNDEKİLER KONULAR: SAYFA: 1.BÖLÜM: TEMEL GEOMETRİK KAVRAMLAR ----------------------------------------------------- 1 Test-1 ------------------------------------------------------------------------------------------------------ 1 Test-2 ------------------------------------------------------------------------------------------------------- 3 Test-3 ------------------------------------------------------------------------------------------------- ---- 5 Test-4 ------------------------------------------------------------------------------------------------------ 8 Test-5 ------------------------------------------------------------------------------------------------------ 11 Test-6 ------------------------------------------------------------------------------------------------------- 13 Test-7 ------------------------------------------------------------------------------------------------------ 14 Test-8 ------------------------------------------------------------------------------------------------------- 15 2. BÖLÜM: AÇILAR ---------------------------------------------------------------------------------------- 17 Test-1 ------------------------------------------------------------------------------------------------------ 17 Test-2 ------------------------------------------------------------------------------------------------------- 19 Test-3 ------------------------------------------------------------------------------------------------- ---- 22 Test-4 ------------------------------------------------------------------------------------------------------ 25 Test-5 ------------------------------------------------------------------------------------------------------ 28 Test-6 ------------------------------------------------------------------------------------------------------- 31 Test-7 ------------------------------------------------------------------------------------------------------ 34 Test-8 ------------------------------------------------------------------------------------------------------- 36 Test-9 -------------------------------------------------------------------------------------------------------- 39 Test-10 ------------------------------------------------------------------------------------------------------ 42 Test-11 ------------------------------------------------------------------------------------------------------ 45 3. BÖLÜM: ÜÇGENLER --------------------------------------------------------------------------- 47 3.1. Üçgende Açılar ve açı Kenar Bağıntıları ------------------------------------------------------ 47 Test-1 ------------------------------------------------------------------------------------------------------ 47 Test-2 ------------------------------------------------------------------------------------------------------- 50 Test-3 ------------------------------------------------------------------------------------------------- ---- 53 Test-4 ------------------------------------------------------------------------------------------------------ 56 Test-5 ------------------------------------------------------------------------------------------------------ 59 Test6 ------------------------------------------------------------------------------------------------------- 63 Test-7 ------------------------------------------------------------------------------------------------------ 67 3.2. Üçgende Açıortay, Kenarortay ve Yükseklik Bağıntıları ----------------------------------- 70 Test-1 ------------------------------------------------------------------------------------------------------ 70 Test-2 ------------------------------------------------------------------------------------------------------- 73 Test-3 ------------------------------------------------------------------------------------------------- ---- 76 Test-4 ------------------------------------------------------------------------------------------------------ 79 Test-5 ------------------------------------------------------------------------------------------------------ 82 Test-6 ------------------------------------------------------------------------------------------------------- 85 Test-7 ------------------------------------------------------------------------------------------------------ II 88
Test-8 ------------------------------------------------------------------------------------------------------- 91 Test-9 -------------------------------------------------------------------------------------------------------- 94 3.3. Dik üçgen, İkizkenar Üçgen ve Eşkenar Üçgen ------------------------------------------------- 97 Test-1 ------------------------------------------------------------------------------------------------------ 97 Test-2 ------------------------------------------------------------------------------------------------------- 100 Test-3 ------------------------------------------------------------------------------------------------- ---- 103 Test-4 ------------------------------------------------------------------------------------------------------ 106 Test-5 ------------------------------------------------------------------------------------------------------ 110 Test-6 ------------------------------------------------------------------------------------------------------- 113 Test-7 ------------------------------------------------------------------------------------------------------ 119 Test-8 ------------------------------------------------------------------------------------------------------- 122 Test-9 -------------------------------------------------------------------------------------------------------- 122 3.4. Üçgende Eşlik ve Benzerlik------------------------------------------------------------------------- 124 Test-1 ------------------------------------------------------------------------------------------------------ 124 Test-2 ------------------------------------------------------------------------------------------------------- 127 Test-3 ------------------------------------------------------------------------------------------------- ---- 130 Test-4 ------------------------------------------------------------------------------------------------------ 133 Test-5 ------------------------------------------------------------------------------------------------------ 135 Test6 ------------------------------------------------------------------------------------------------------- 138 Test-7 ------------------------------------------------------------------------------------------------------ 141 Test-8 ------------------------------------------------------------------------------------------------------- 143 Test-9 -------------------------------------------------------------------------------------------------------- 147 Test-10 ------------------------------------------------------------------------------------------------------- 150 3.5.Üçgenlerde Alan ve Alan bağıntıları-------------------------------------------------------------- 153 Test-1 ------------------------------------------------------------------------------------------------------ 153 Test-2 ------------------------------------------------------------------------------------------------------- 156 Test-3 ------------------------------------------------------------------------------------------------- ---- 159 Test-4 ------------------------------------------------------------------------------------------------------ 161 Test-5 ------------------------------------------------------------------------------------------------------ 165 Test-6 ------------------------------------------------------------------------------------------------------- 168 Test-7 ------------------------------------------------------------------------------------------------------ 171 Test-8 ------------------------------------------------------------------------------------------------------- 175 Test-9 -------------------------------------------------------------------------------------------------------- 177 Test-10 ------------------------------------------------------------------------------------------------------- 180 Test-11 -------------------------------------------------------------------------------------------------------- 183 3.6. Üçgenlerde Özel Bağıntılar ------------------------------------------------------------------------- 186 Test-1 ------------------------------------------------------------------------------------------------------ 186 Test-2 ------------------------------------------------------------------------------------------------------- 189 Test-3 ------------------------------------------------------------------------------------------------- ---- 192 Test-4 ------------------------------------------------------------------------------------------------------ 195 Test-5 ------------------------------------------------------------------------------------------------------ 198 III
4. BÖLÜM:ÇOKGENLER VE DÖRTGENLER 201 4.1 Çokgenler ve dörtgenler--------------------------------------------------------------------------- 201 Test-1 ------------------------------------------------------------------------------------------------------ 201 Test-2 ------------------------------------------------------------------------------------------------------- 203 Test-3 ------------------------------------------------------------------------------------------------- ---- 205 Test-4 ------------------------------------------------------------------------------------------------------ 207 4.2. Yamuk------------------------------------------------------------------------------------------------- 209 Test-1 ------------------------------------------------------------------------------------------------------ 209 Test-2 ------------------------------------------------------------------------------------------------------- 212 Test-3 ------------------------------------------------------------------------------------------------- ---- 215 Test-4 ------------------------------------------------------------------------------------------------------ 218 Test-5 ------------------------------------------------------------------------------------------------------ 221 Test-6 ------------------------------------------------------------------------------------------------------- 224 4.3. Paralelkenar ve Eşkenar Dörtgen--------------------------------------------------------------- 227 Test-1 ------------------------------------------------------------------------------------------------------ 227 Test-2 ------------------------------------------------------------------------------------------------------- 230 Test-3 ------------------------------------------------------------------------------------------------- ---- 232 Test-4 ------------------------------------------------------------------------------------------------------ 236 Test-5 ------------------------------------------------------------------------------------------------------ 239 Test-6 ------------------------------------------------------------------------------------------------------- 242 4.4 Dikdörtgen, Kare ve Deltoid------------------------------------------------------------------------ 245 Test-1 ------------------------------------------------------------------------------------------------------ 245 Test-2 ------------------------------------------------------------------------------------------------------- 248 Test-3 ------------------------------------------------------------------------------------------------- ---- 251 Test-4 ------------------------------------------------------------------------------------------------------ 253 Test-5 ------------------------------------------------------------------------------------------------------ 257 Test-6 ------------------------------------------------------------------------------------------------------- 260 Test-7 ------------------------------------------------------------------------------------------------------ 263 Test-8 ------------------------------------------------------------------------------------------------------- 266 Test-9 -------------------------------------------------------------------------------------------------------- 269 5. BÖLÜM: ÇEMBER VE DAİRE-------------------------------------------------------------------------- 272 5.1. Çemberde Yaylar ve Açılar------------------------------------------------------------------------- 272 Test-1 ------------------------------------------------------------------------------------------------------ 272 Test-2 ------------------------------------------------------------------------------------------------------- 275 Test-3 ------------------------------------------------------------------------------------------------- ---- 278 Test-4 ------------------------------------------------------------------------------------------------------ 281 Test-5 ------------------------------------------------------------------------------------------------------ 284 Test-6 ------------------------------------------------------------------------------------------------------- 297 Test-7 ------------------------------------------------------------------------------------------------------ 290 IV
Test-8 ------------------------------------------------------------------------------------------------------- 293 Test-9 -------------------------------------------------------------------------------------------------------- 296 Test-10 ------------------------------------------------------------------------------------------------------- 299 5.2. Çemberde Uzunluk ---------------------------------------------------------------------------------- 302 Test-1 ------------------------------------------------------------------------------------------------------ 302 Test-2 ------------------------------------------------------------------------------------------------------- 305 Test-3 ------------------------------------------------------------------------------------------------- ---- 308 Test-4 ------------------------------------------------------------------------------------------------------ 311 Test-5 ------------------------------------------------------------------------------------------------------ 314 Test-6 ------------------------------------------------------------------------------------------------------- 317 Test-7 ------------------------------------------------------------------------------------------------------ 320 Test-8 ------------------------------------------------------------------------------------------------------- 323 Test-9 -------------------------------------------------------------------------------------------------------- 326 Test-10 ------------------------------------------------------------------------------------------------------- 329 5.3. Daire ve alanlar---------------------------------------------------------------------------------------- 332 Test-1 ------------------------------------------------------------------------------------------------------ 332 Test-2 ------------------------------------------------------------------------------------------------------- 335 Test-3 ------------------------------------------------------------------------------------------------- ---- 338 Test-4 ------------------------------------------------------------------------------------------------------ 341 Test-5 ------------------------------------------------------------------------------------------------------ 344 Test-6 ------------------------------------------------------------------------------------------------------- 347 Test-7 ------------------------------------------------------------------------------------------------------ 350 Test-8 ------------------------------------------------------------------------------------------------------- 353 Test-9 -------------------------------------------------------------------------------------------------------- 356 Test-10 ------------------------------------------------------------------------------------------------------- 359 6. BÖLÜM: ANALİTİK GEOMETRİ------------------------------------------------------------------------ 362 6.1. Doğrunun Analitik İncelenmesi------------------------------------------------------------------- 362 Test-1 ------------------------------------------------------------------------------------------------------ 362 Test-2 ------------------------------------------------------------------------------------------------------- 364 Test-3 ------------------------------------------------------------------------------------------------- ---- 366 Test-4 ------------------------------------------------------------------------------------------------------ 368 Test-5 ------------------------------------------------------------------------------------------------------ 371 Test-6 ------------------------------------------------------------------------------------------------------- 373 Test-7 ------------------------------------------------------------------------------------------------------ 375 Test-8 ------------------------------------------------------------------------------------------------------- 377 Test-9 -------------------------------------------------------------------------------------------------------- 380 Test-10 ------------------------------------------------------------------------------------------------------- 382 V
Test-11 -------------------------------------------------------------------------------------------------------- 384 Test-12 -------------------------------------------------------------------------------------------------------- 387 6.2. Çemberin Analitik İncelenmesi--------------------------------------------------------------------- 390 Test-1 ------------------------------------------------------------------------------------------------------ 390 Test-2 ------------------------------------------------------------------------------------------------------- 392 Test-3 ------------------------------------------------------------------------------------------------- ---- 394 Test-4 ------------------------------------------------------------------------------------------------------ 396 Test-5 ------------------------------------------------------------------------------------------------------ 399 Test-6 ------------------------------------------------------------------------------------------------------- 402 Test-7 ------------------------------------------------------------------------------------------------------ 406 6.3. Elipsin Analitik İncelenmesi---------------------------------------------------------------------- 409 Test-1 ------------------------------------------------------------------------------------------------------ 409 Test-2 ------------------------------------------------------------------------------------------------------- 412 Test-3 ------------------------------------------------------------------------------------------------- ---- 415 Test-4 ------------------------------------------------------------------------------------------------------ 418 Test-5 ------------------------------------------------------------------------------------------------------ 420 6.4. Hiperbolün Analitik İncelenmesi ---------------------------------------------------------------- 422 Test-1 ------------------------------------------------------------------------------------------------------ 422 Test-2 ------------------------------------------------------------------------------------------------------- 424 Test-3 ------------------------------------------------------------------------------------------------- ---- 426 Test-4 ------------------------------------------------------------------------------------------------------ 428 Test-5 ------------------------------------------------------------------------------------------------------ 430 Test-6 ------------------------------------------------------------------------------------------------------- 432 6.5. Parabolün Analitik İncelenmesi------------------------------------------------------------------- 434 Test-1 ------------------------------------------------------------------------------------------------------ 434 Test-2 ------------------------------------------------------------------------------------------------------- 436 Test-3 ------------------------------------------------------------------------------------------------- ---- 438 Test-4 ------------------------------------------------------------------------------------------------------ 440 Test-5 ------------------------------------------------------------------------------------------------------ 442 Test-6 ------------------------------------------------------------------------------------------------------ 444 7. BÖLÜM: DÜZLEMDE VEKTÖRLER----------------------------------------------------------------- 446 Test-1 ------------------------------------------------------------------------------------------------------ 446 Test-2 ------------------------------------------------------------------------------------------------------- 448 Test-3 ------------------------------------------------------------------------------------------------- ---- 452 Test-4 ------------------------------------------------------------------------------------------------------ 454 Test-5 ------------------------------------------------------------------------------------------------------ 457 Test-6 ------------------------------------------------------------------------------------------------------- 460 8. BÖLÜM: GEOMETRİDE DÖNÜŞÜMLER----------------------------------------------------------- 464 Test-1 ------------------------------------------------------------------------------------------------------ 464 Test-2 ------------------------------------------------------------------------------------------------------- 466 Test-3 ------------------------------------------------------------------------------------------------- ---- 469 Test-4 ------------------------------------------------------------------------------------------------------ 471 Test-5 ------------------------------------------------------------------------------------------------------ 473 VI
Test-6 ------------------------------------------------------------------------------------------------------- 475 Test-7 ------------------------------------------------------------------------------------------------------- 477 Test-8 ------------------------------------------------------------------------------------------------------- 479 9. BÖLÜM: UZAY GEOMETRİ------------------------------------------------------------------------------ 484 9.1.Uzay Aksiyomları ve Uzay Teoremleri------------------------------------------------------------- 484 Test-1 ------------------------------------------------------------------------------------------------------ 484 Test-2 ------------------------------------------------------------------------------------------------------- 486 Test-3 ------------------------------------------------------------------------------------------------- ---- 488 Test-4 ------------------------------------------------------------------------------------------------------ 491 Test-5 ------------------------------------------------------------------------------------------------------ 493 Test-6 ------------------------------------------------------------------------------------------------------- 496 9.2. Katı Cisimler------------------------------------------------------------------------------------------ 499 Test-1 ------------------------------------------------------------------------------------------------------ 499 Test-2 ------------------------------------------------------------------------------------------------------- 501 Test-3 ------------------------------------------------------------------------------------------------- ---- 503 Test-4 ------------------------------------------------------------------------------------------------------ 505 Test-5 ------------------------------------------------------------------------------------------------------ 507 Test-6 ------------------------------------------------------------------------------------------------------- 509 Test-7 ------------------------------------------------------------------------------------------------------ 512 Test-8 ------------------------------------------------------------------------------------------------------- 515 Test-9 -------------------------------------------------------------------------------------------------------- 518 Test-10 ------------------------------------------------------------------------------------------------------- 521 Test-11 -------------------------------------------------------------------------------------------------------- 523 Test-12------------------------------------------------------------------------------------------------------ 526 10. BÖLÜM: UZAYDA VEKTÖRLER,DOĞRULAR VE DÜZLEMLER--------------------------------- 528 Test-1 ------------------------------------------------------------------------------------------------------ 528 Test-2 ------------------------------------------------------------------------------------------------------- 530 Test-3 ------------------------------------------------------------------------------------------------- ---- 532 Test-4 ------------------------------------------------------------------------------------------------------ 534 Test-5 ------------------------------------------------------------------------------------------------------ 536 Test-6 ------------------------------------------------------------------------------------------------------ 538 Test-7 ------------------------------------------------------------------------------------------------------ 540 11. BÖLÜM: ÜNİVERSİTE SINAVLARINDA SORULAN GEOMETRİ SORULARI VE CEVAPLARI 542 11.1.1996 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 542 11.2.1997 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 546 11.3.1998 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 550 11.4.1999 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 554 11.5.2000 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 558 11.6.2001 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 562 11.7.2002 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 566 11.8.2003 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 570 11.9.2004 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 574 VII
11.10.2005 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 579 11.11.2006 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 583 11.12.2007 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 587 11.13.2008 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 590 11.14.2009 ÖSS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 594 11.15.2010 LYS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 597 11.16.2011 LYS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 600 11.17.2011 YGS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 607 11.18.2012 YGS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 614 11.19.2012 LYS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 619 11.20.2013 LYS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 626 11.21.2013 YGS de Sorulan Geometri Soru ve Cevapları----------------------------------------- 634 VIII