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<a href="https://www.blogger.com/blogger.g?blogID=6961009262266450709" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><span style="background-color: white;"><b>Ujian Nasional Matematika Kelas XII SMK TA 2015/2016</b></span></div>
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<span style="background-color: white; font-family: inherit;">01.    Jumlah n suku pertama deret aritmatika adalah Sn = 2n<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>– 6n. Beda deret itu adalah</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     -4                               (D)      6</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      3                                 (E)       8</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      4</span></div>
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<span style="background-color: white; font-family: inherit;">02.    Un suku ke n barisan aritmatika.</span></div>
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<span style="background-color: white; font-family: inherit;">          Jika matriks A =  dan U<sub class="yiv5687647192">6</sub><span class="yiv5687647192"> </span>= 18 ;         U<sub class="yiv5687647192">10</sub><span class="yiv5687647192"> </span>= 30 maka  determinan matriks A adalah</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     -30                             (D)      12      </span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      -18                             (E)       18</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      -12</span></div>
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<span style="background-color: white; font-family: inherit;">03.    Log a + log (ab) + log (ab<sup class="yiv5687647192" id="yiv5687647192yui_3_16_0_1_1410717517625_3519">2</sup>) + log (ab<sup class="yiv5687647192">3</sup>) + …. adalah deret aritmetika. Jumlah 6 suku pertama deret itu.</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     6 log a + 15 log ab</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      6 log a + 12 log ab</span></div>
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<span style="background-color: white; font-family: inherit;">         (C)    6 log a + 18 log ab</span></div>
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<span style="background-color: white; font-family: inherit;">(D)    7 log a + 15 log ab</span></div>
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<span style="background-color: white; font-family: inherit;">(E)      7 log a + 12 log ab</span></div>
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<span style="background-color: white; font-family: inherit;">04.    Jumlah n suku pertama deret aritmetika         Sn = 2n<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>– n. Jumlah n suku berikutnya adalah</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     4n<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>– 2n                   (D)      2n<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>– 2n</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      6n<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>– 2n                   (E)       6n<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>– n</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      4n<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>+ 2n</span></div>
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<span style="background-color: white; font-family: inherit;">05.    Jumlah n suku pertama deret aritmetika            Sn = (pn + 5) (2n – q) + 5q.</span></div>
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<span style="background-color: white; font-family: inherit;">          Jika suku pertama 15 dan bedanya 4, nilai dari  p + q  sama dengan</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     2                                 (D)      -1</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      1                                 (E)       -2</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      0</span></div>
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<span style="background-color: white; font-family: inherit;">06.    Jumlah 5 buah bilangan yang membentuk barisan aritmetika adalah 75. Jika hasil kali bilangan terkecil dan terbesar adalah 161, maka selisih bilangan terbesar dengan yang terkecil sama dengan </span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     14                              (D)      20</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      15                              (E)       30</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      16</span></div>
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<span style="background-color: white; font-family: inherit;">07.    Seorang karyawan menabung dengan teratur setiap bulan. Uang yang ditabungnya setiap bulan dengan bulan sebelumnya selisih yang sama. Apabila jumlah seluruh tabungannya dalam 12 bulan pertama adalah Rp.152.000 dan dalam 20 bulan  pertama Rp. 480.000 maka besar uang yang ditabungkan di bulan ke 10 adalah</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     Rp. 23.000               (D)      Rp. 97.000       </span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      Rp. 27.000               (E)       Rp. 28.000</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      Rp. 64.000</span></div>
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<span style="background-color: white; font-family: inherit;">08.    Suku ke-n barisan aritmetika adalah               Un = 6n + 4. Diantara tiap dua sukunya disisipkan dua suku yang baru, sehingga terbentuk deret aritmerika baru. Jumlah n suku pertama deret baru adalah</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     Sn = n<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>+ 9n            (D)      Sn = n<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>– 6n</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      Sn = n<sup class="yiv5687647192">2<span class="yiv5687647192"> </span></sup>– 9n             (E)       Sn = n<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>+ 6n</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      Sn = n<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>+ 8n</span></div>
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<span style="background-color: white; font-family: inherit;">09.    Jumlah bilangan-bilangan antara 1 dan 150 yang habis dibagi 4 tetapi tidak habis di bagi 7 adalah </span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     2382                          (D)      2412</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      2392                          (E)       2422</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      2402</span></div>
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<span style="background-color: white; font-family: inherit;">10.       Tiga buah bilangan membentuk deret aritmetika. Jika suku ke dua dikurangi 2 dan suku ke tiga ditambah 2, maka diperoleh deret geometri. Jika suku pertama deret semula di tambah dengan 5 maka ia menjadi setengah dari suku ke tiga. Jumlah deret aritmetika semula adalah</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     42                              (D)      48</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      44                              (E)       50</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      46</span></div>
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<span style="background-color: white; font-family: inherit;">11.    Untuk k > 0 bilangan (k – 2) , (k – 6) dan          (2k + 3) membentuk tiga suku pertama deret geometri. Jumlah n suku pertama deret tersebut adalah</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     ¼ (1 – (-3)<sup class="yiv5687647192">n</sup>)            </span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      - ½ (3<sup class="yiv5687647192">n</sup><span class="yiv5687647192"> </span>– 1)</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      - ¼ (1 – 3<sup class="yiv5687647192">n</sup>)</span></div>
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<span style="background-color: white; font-family: inherit;">(D)        - ½(1 – (3)<sup class="yiv5687647192">n</sup>)</span></div>
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<span style="background-color: white; font-family: inherit;">(E)      ¼ (1 – (3)<sup class="yiv5687647192">n</sup>)</span></div>
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<span style="background-color: white; font-family: inherit;">12. akar persamaan kuadrat</span></div>
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<span style="background-color: white; font-family: inherit;">          x<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>–(2k + 4)x + (3k + 4) = 0. Ke dua akar itu bilangan bulat dengan k konstan.</span></div>
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<span style="background-color: white; font-family: inherit;">          Jika merupakan tiga suku pertama deret geometri maka suku ke n deret itu</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)      -1                               (D)      1 +(-1)<sup class="yiv5687647192">n</sup>             </span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      2(-1)<sup class="yiv5687647192">n</sup>                        (E)       1 – 1(-1)<sup class="yiv5687647192">n</sup>          </span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      -(-1)<sup class="yiv5687647192">n</sup></span></div>
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<span style="background-color: white; font-family: inherit;">13.    Diketahui deret geometri dengan suku ke enam 162 jumlah logaritma suku ke dua,     ke tiga, ke empat, dan ke lima sama dengan     4log 2  +  4log 3, maka rasionya adalah</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     1/2                             (D)      3</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      1/4                             (E)       2</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      1/3</span></div>
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<span style="background-color: white; font-family: inherit;">14.    Tiga buah bilangan positif membentuk barisan geometri dengan rasio > 1. Jika suku tengahnya ditambah 4 maka terbentuk barisan aritmetika yang jumlahnya 30. Hasil kali ke tiga bilangan semula adalah…</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     64                              (D)      343</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      125                            (E)       1000  </span></div>
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<span style="background-color: white; font-family: inherit;">(C)         216                           </span></div>
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<span style="background-color: white; font-family: inherit;">15.    Diketahui A = 2 dan</span></div>
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<span style="background-color: white; font-family: inherit;">          B = 1 + 9(0,1) + 9(0,1)<sup class="yiv5687647192">2<span class="yiv5687647192"> </span></sup>+ 9(0,1)<sup class="yiv5687647192">3</sup><span class="yiv5687647192"> </span>+ … + 9(0,1)<sup class="yiv5687647192">6784</sup></span></div>
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<span style="background-color: white; font-family: inherit;">          Pernyataan yang benar adalah</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     A < B                         (D)      A = B</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      A > B                         (E)       A = ½ B</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      a = 0,9 B</span></div>
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<span style="background-color: white; font-family: inherit;">16.    Diketahui barisan tak hingga</span></div>
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<span style="background-color: white; font-family: inherit;">         Jika t = p/3 maka hasil kali semua suku barisan itu adalah</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     0                                 (D)      1/2</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      1/16                           (E)      </span></div>
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<span style="background-color: white; font-family: inherit;">          (C </span></div>
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<span style="background-color: white; font-family: inherit;">17.    Deret geometri</span></div>
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<span style="background-color: white; font-family: inherit;">          1 + cos 2x  + cos<sup class="yiv5687647192">2</sup>2x  +  cos<sup class="yiv5687647192">3</sup>2x + … konvergen ke A dan deret geometri 1 – tan<sup class="yiv5687647192">2</sup>x  +  tan<sup class="yiv5687647192">4</sup>x  –   …..</span></div>
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<span style="background-color: white; font-family: inherit;">          konvergen ke B,  maka nilai  2AB =</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     tan<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>x untuk semua x real</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      tan<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>x untuk |x| < p/4</span></div>
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<span style="background-color: white; font-family: inherit;">(C)         cot<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>x untuk x semua x real</span></div>
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<span style="background-color: white; font-family: inherit;">(D)        cot<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>x untuk 0 < x < p/2</span></div>
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<span style="background-color: white; font-family: inherit;">(E)      cot<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>x untuk 0 < x < p/4</span></div>
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<span style="background-color: white; font-family: inherit;">18.    Jumlah deret</span></div>
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<span style="background-color: white; font-family: inherit;">          S = 1 + log cos x +  log<sup class="yiv5687647192">2</sup>cos x + …mempunyai <img class="yiv5687647192" height="39" style="border: 0px;" width="83" /></span></div>
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<b class="yiv5687647192"><span style="background-color: white; font-family: inherit;">27</span></b></div>
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<span style="background-color: white; font-family: inherit;"> apabila</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     ½ < s < 1                  (D)      s > ½  </span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      ½ < s < 2                  (E)       s > 1</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      s < ½</span></div>
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<span style="background-color: white; font-family: inherit;">19.    Perhatikan lingkaran-lingkaran yang berpusat pada garis y = x yang menyinggung sumbu-sumbu x dan y. lingkaran pertama berpusat di (5 , 5), lingkaran ke dua berpusat di <img class="yiv5687647192" height="45" style="border: 0px;" width="34" /> lingkaran ke tiga bepusat di <img class="yiv5687647192" height="45" style="border: 0px;" width="36" /> dan seterusnya. Jumlah luas semua lingkaran tersebut sama dengan</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     100/3 p satuan luas        </span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      37,5 p satuan luas           </span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102842" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      40 p satuan luas</span></div>
<div class="yiv5687647192" id="yiv5687647192yui_3_16_0_1_1410717517625_3496" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (D)     42,5 p satuan luas</span></div>
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<span style="background-color: white; font-family: inherit;">          (E)      50 p satuan luas</span></div>
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<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
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<span style="background-color: white; font-family: inherit;">20.    Jumlah suku deret geometri tak berhingga adalah 7. sedangkan jumlah suku-suku yang bernomor genap adalah 3, maka suku pertama deret tersebut adalah </span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     3/7                             (D)      7/4</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      3/4                             (E)       7/3</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      4/3</span></div>
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<span style="background-color: white; font-family: inherit;">21.    Sebuah bola tennis jatuh dari ketinggian 5 m dan memantul kembali dengan ketinggian 2/3 kali tinggi sebelumnya. Pantulan berlangsung  terus menerus hingga bola berhenti, maka panjang seluruh lintasan bola adalah </span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     15 m                         (D)      30 m</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      20 m                         (E)       35 m</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      25 m</span></div>
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<span style="background-color: white; font-family: inherit;">22.    Jika  1 + 3 + 5 + 7 + . . . + U<sub class="yiv5687647192">k</sub><span class="yiv5687647192"> </span>= 121, maka nilai dari U<sub class="yiv5687647192">2k</sub><span class="yiv5687647192"> </span>+ U<sub class="yiv5687647192">2k+1<span class="yiv5687647192"> </span></sub>+ . . . + U<sub class="yiv5687647192">3k</sub><span class="yiv5687647192"> </span>= </span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     583                            (D)      648</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      600                            (E)       798</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      636</span></div>
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<span style="background-color: white; font-family: inherit;">24.    Jika A, B, dan C merupakan sudut – sudut suatu segitiga yang membentuk deret aritmatika,    maka cos(A + C) – cosB =</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     0                                 (D)      - 1      </span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      1                                 (E)       - Ö3</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      Ö3</span></div>
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<span style="background-color: white; font-family: inherit;">25.    Antara bilangan x dan y disisipkan 5 bilangan sehingga ketujuh bilangan tersebut membentuk barisan aritmatika. Jika jumlah bilangan yang disisipkan sebesar 45,</span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102846" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          Maka nilai    x + y =</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     16                              (D)      24</span></div>
<div class="yiv5687647192" id="yiv5687647192yui_3_16_0_1_1410717517625_3495" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (B)      18                              (E)       28</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      20</span></div>
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<span style="background-color: white; font-family: inherit;">26.    Diketahui jumlah tiga suku pertama deret aritmatika adalah – 18 dan jumlah tiga suku terakhir sama dengan 36. Jika jumlah semua suku deret tersebut adalah 27, maka banyaknya suku deret aritmatika sama dengan</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     8                                 (D)      12</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      9                                 (E)       15</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      10</span></div>
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<span style="background-color: white; font-family: inherit;">27.    Jumlah semua suku suatu deret geometri yang konvergen adalah dua kali suku pertamanya sedangkan jumlah pangkat tiga setiap suku – sukunya adalah 64/7, maka suku ketiga deret tersebut adalah</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     1/2                             (D)      1/16</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      1/4                             (E)       1/32</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      1/8</span></div>
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<span style="background-color: white; font-family: inherit;">28.    Kurva y = x<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>– nx + 1 memotong sumbu x di  titik (a , 0) dan (b , 0) serta memotong sumbu y di titik (0 , c). Jika susunan bilangan a , b , dan c membentuk barisan aritmatika. maka barisan tersebut akan membentuk deret geometri jika suku ketiga ditambah</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     9/2                             (D)      - 9/8</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      9/4                             (E)       - 9/4</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      9/8</span></div>
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<span style="background-color: white; font-family: inherit;">29.    Suatu deret geometri konvergen, suku kedua dan suku kelima berbanding sebagai 8 : 1.</span></div>
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<span style="background-color: white; font-family: inherit;">          Jika diketahui jumlah dua suku pertama 9, maka jumlah tak hingga deret tersebut adalah</span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102851" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     6                                 (D)      24      </span></div>
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<span style="background-color: white; font-family: inherit;">          (B)      12                              (E)       32</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)      18</span></div>
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<span style="background-color: white; font-family: inherit;">30.    Sebuah deret geometri tak hingga konvergen dengan jumlah 6. Jika suku pertama deret ini a, maka</span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     - 6 < a < 0                 (D)      - 12 < a < 0</span></div>
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<span style="background-color: white; font-family: inherit;">          (B)        0 < a < 6                 (E)       -  12 < a < 12</span></div>
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<span style="background-color: white; font-family: inherit;">          (C)        0 < a < 12</span></div>
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<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
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<span style="background-color: white; font-family: inherit;">31.    Besar suku ke p dari suatu deret geometri adalah 2p. Sedangkan suku ke 2p adalah p. Jumlah p suku pertama adalah </span></div>
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<span style="background-color: white; font-family: inherit;">          (A)     <img class="yiv5687647192" height="43" style="border: 0px;" width="39" />                      (D)      <img class="yiv5687647192" height="25" style="border: 0px;" width="40" /></span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102855" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (B)      <img class="yiv5687647192" height="46" style="border: 0px;" width="39" />                      (E)       <img class="yiv5687647192" height="25" style="border: 0px;" width="40" /></span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102857" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      <img class="yiv5687647192" height="43" style="border: 0px;" width="42" /></span></div>
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<span style="background-color: white; font-family: inherit;">32.    Untuk r > 0, dan  jumlah 6n suku pertam deret geometri tak hingga adalah sembilan kali jumlan 3n suku pertama deret tersebut. Maka nilai n yang memenuhi adalah   </span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)    <span class="yiv5687647192"> </span><sup class="yiv5687647192">r<span class="yiv5687647192"> </span></sup>log 2                       (D)     <span class="yiv5687647192"> </span><sup class="yiv5687647192">2r<span class="yiv5687647192"> </span></sup>log 4              </span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (B)     <span class="yiv5687647192"> </span><sup class="yiv5687647192">r<span class="yiv5687647192"> </span></sup>log 4                       (E)      <span class="yiv5687647192"> </span><sup class="yiv5687647192">2r<span class="yiv5687647192"> </span></sup>log 8</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)     <span class="yiv5687647192"> </span><sup class="yiv5687647192">r<span class="yiv5687647192"> </span></sup>log 8</span></div>
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<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102859" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">33.    2r + s , 6r + s , 14r +  s adalah tiga suku berturut – turut dari barisan geometri dan r adalah rasio. Barisan geometri tersebut akan membentuk barisan aritmatika jika suku kedua ditambah dengan</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     2                                 (D)      8</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (B)      4                                 (E)       10</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      6</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">         </span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">34.    Apabila susunan bilangan berikut,</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">         <span class="yiv5687647192"> </span><sup class="yiv5687647192">2</sup>log x + 4  , <span class="yiv5687647192"> </span><sup class="yiv5687647192">2</sup>log x  ,  2, …</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          membentuk barisan geometri, maka jumlah tak hingga barisan tersebut adalah</span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102861" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     16                              (D)      8</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (B)      14                              (E)       6</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      12</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">35.    U<sub class="yiv5687647192">n</sub><span class="yiv5687647192"> </span>menyatakan suku ke n deret geometri.  Jika U<sub class="yiv5687647192">1</sub><span class="yiv5687647192"> </span>+ U<sub class="yiv5687647192">3</sub><span class="yiv5687647192"> </span>= 18 dan U<sub class="yiv5687647192">2</sub><span class="yiv5687647192"> </span>+ U<sub class="yiv5687647192">4<span class="yiv5687647192"> </span></sub>= 12.       </span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          Maka   U<sub class="yiv5687647192">5</sub><span class="yiv5687647192"> </span>=</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     16/13                        (D)      38/13</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (B)      28/13                        (E)       44/13</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      32/13</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">36.    Untuk n ® ¥ , maka penyelesaian pertidak-samaan berikut</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          1 < (<sup class="yiv5687647192">x</sup>log2) + (<sup class="yiv5687647192">x</sup>log2)<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>+ . . . + (<sup class="yiv5687647192">x</sup>log2)<sup class="yiv5687647192">n</sup><span class="yiv5687647192"> </span>< 3</span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102863" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          adalah</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     2<sup class="yiv5687647192">1/3 <span class="yiv5687647192"> </span></sup><  x  <  2           (D)      2<sup class="yiv5687647192">1/3<span class="yiv5687647192"> </span></sup>< x < 4</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (B)      1  <  x  <  2<sup class="yiv5687647192">1/3</sup>          (E)       2 < x < 4</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      2<sup class="yiv5687647192">1/3</sup>  <  x  <  2<sup class="yiv5687647192">4/3</sup></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<div class="yiv5687647192" id="yiv5687647192yui_3_16_0_1_1410717517625_3492" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">37.    Tiga bilangan a , b dan c membentuk deret aritmatika dengan beda 2. Jika <img class="yiv5687647192" height="29" style="border: 0px;" width="55" />, maka <img class="yiv5687647192" height="28" style="border: 0px;" width="39" /></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     35                              (D)      15</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (B)      28                              (E)       12</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      21</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">38.    Sebuah buku terdiri dari 60 halaman, dimulai halaman 1. Jika 2 lembar yang berurutan dari buku tersebut di sobek, ternyata jumlah halaman buku yang tersisa 1780, maka selisih kuadrat halaman terkecil dan yang terbesar yang tersobek adalah</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     21                              (D)      75</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (B)      48                              (E)       84</span></div>
<div class="yiv5687647192" id="yiv5687647192yui_3_16_0_1_1410717517625_3491" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      69</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">39.    Jumlah sampai tak hingga dari deret konvergen</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (<sup class="yiv5687647192">16</sup>log x) + (<sup class="yiv5687647192">16</sup>logx)<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>+ (<sup class="yiv5687647192">16</sup>logx)<sup class="yiv5687647192">3</sup><span class="yiv5687647192"> </span>+ . . . +  =  S</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          y = log (1 - | S – 2 | ) ada nilainya untuk</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     2  <  x  <  4               (D)      4  <  x  <  8       </span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (B)      2  <  x  <  6               (E)       4  <  x  <  6</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      2  <  x  <  8</span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102865" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">40.    Akar-akar persamaan</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          2<sup class="yiv5687647192">8x – 8</sup><span class="yiv5687647192"> </span>– 40.2<sup class="yiv5687647192">4x – 8</sup><span class="yiv5687647192"> </span>+ 1 = 0</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          adalah suku pertama dan suku kedua sebuah deret geometri tak hingga yang konvergen.</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          Jumlah deret tersebut adalah</span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102866" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     25/16                        (D)      25/4</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (B)      25/12                        (E)       25/2</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      25/8</span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102868" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<table border="0" cellpadding="0" cellspacing="0" class="yiv5687647192" style="margin: 0px; padding: 0px; text-align: justify; width: 768px;"><tbody class="yiv5687647192" style="width: 768px;">
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<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
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<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
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<b class="yiv5687647192"><i class="yiv5687647192"><span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></i></b></div>
</td></tr>
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<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">40.    Jika a =           </span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          maka untuk 0  <  x  <  p/2, deret</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          1  + <span class="yiv5687647192"> </span><sup class="yiv5687647192">a</sup>log sin x +<span class="yiv5687647192"> </span><sup class="yiv5687647192">a</sup>log<sup class="yiv5687647192">2</sup>sinx +<span class="yiv5687647192"> </span><sup class="yiv5687647192">a</sup>log<sup class="yiv5687647192">3</sup>sinx + …</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          konvergen hanya pada selang</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     p/6  <  x  <  p/2       </span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (B)      p/6  <  x  <  p/4</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      p/4  <  x  <  p/3       </span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (D)     p/4  <  x  <  p/2</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (E)      p/3  <  x  <  p/2</span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102870" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">41.    Diketahui a dan b adalah akar-akar persamaan x<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>– 2x + k = 0 dan</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          a – 5/2 , a + b , a + 5 merupakan bariasan geometri dengan suku – suku positif.</span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102872" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          Nilai k adalah</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     2                                 (B)       - 3</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      3                                 (D)      - 2</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (E)      6</span></div>
<div class="yiv5687647192" id="yiv5687647192yui_3_16_0_1_1410717517625_3490" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">42.    Jika x , y , z membentuk barisan geometri,</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          maka <img class="yiv5687647192" height="35" style="border: 0px;" width="108" /></span></div>
<div class="yiv5687647192" id="yiv5687647192yui_3_16_0_1_1410717517625_3489" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     1/x                             (B)       1</span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102874" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      1/y                             (D)      2</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (E)      1/2</span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102876" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
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<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
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<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
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<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
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<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<table border="0" cellpadding="0" cellspacing="0" class="yiv5687647192" style="margin: 0px; padding: 0px; text-align: justify; width: 768px;"><tbody class="yiv5687647192" style="width: 768px;">
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<b class="yiv5687647192"><span style="background-color: white; font-family: inherit;">                                                                    </span></b></div>
</td></tr>
</tbody></table>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
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<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">43.    Jika suku pertama deret geometri <img class="yiv5687647192" height="24" style="border: 0px;" width="28" /> dengan m > 0 sedangkan suku ke 5 adalah m<sup class="yiv5687647192">2</sup>, maka suku ke 21 adalah</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (A)     <img class="yiv5687647192" height="25" style="border: 0px;" width="52" />                  (B)       <img class="yiv5687647192" height="25" style="border: 0px;" width="49" /></span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102878" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (C)      <img class="yiv5687647192" height="27" style="border: 0px;" width="52" />                  (D)      <img class="yiv5687647192" height="25" style="border: 0px;" width="33" /></span></div>
<div class="yiv5687647192" id="yui_3_16_0_1_1411020391613_102880" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">          (E)      <img class="yiv5687647192" height="25" style="border: 0px;" width="49" /></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">44.       Suatu deret geometri dengan suku ke-5 dan suku ke-8 berturut-turut adalah x<sup class="yiv5687647192">3</sup><span class="yiv5687647192"> </span>dan x<sup class="yiv5687647192">4</sup>Öx, maka jumlah enam suku pertama deret itu adalah</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">            (A)       (Öx – 1) (x<sup class="yiv5687647192">3</sup><span class="yiv5687647192"> </span>+ x<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>+ x)   </span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">            (B)       (Öx – 1) (x<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>+ x + 1)</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">            (C)       (Öx + 1) (x<sup class="yiv5687647192">3</sup><span class="yiv5687647192"> </span>+ x<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>+ x)   </span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">            (D)       (x<sup class="yiv5687647192">3</sup><span class="yiv5687647192"> </span>+ x<sup class="yiv5687647192">2</sup><span class="yiv5687647192"> </span>+ x)</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;">            (E)       (Öx + 1)</span></div>
<div class="yiv5687647192" style="text-align: justify;">
<span style="background-color: white; font-family: inherit;"><br class="yiv5687647192" /></span></div>
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<span style="background-color: white; font-family: inherit;">45.       Pada gambar dibawah ini, D A<sub class="yiv5687647192">1</sub>OB<sub class="yiv5687647192">1</sub><span class="yiv5687647192"> </span>sama kaki dengan sudut puncak O = 90<sup class="yiv5687647192">0</sup><span class="yiv5687647192"> </span>dan OA<sub class="yiv5687647192">2</sub><span class="yiv5687647192"> </span>garis tinggi, DA<sub class="yiv5687647192">2</sub>OB<sub class="yiv5687647192">2</sub><span class="yiv5687647192"> </span>sama kaki dengan sudut puncak O = 90<sup class="yiv5687647192">0</sup><span class="yiv5687647192"> </span>dan OA<sub class="yiv5687647192">3</sub><span class="yiv5687647192"> </span>garis tinggi, DA<sub class="yiv5687647192">3</sub>OB<sub class="yiv5687647192">3</sub><span class="yiv5687647192"> </span>sama kaki dengan sudut puncak       O = 90<sup class="yiv5687647192">0</sup><span class="yiv5687647192"> </span>dan OA<sub class="yiv5687647192">4</sub><span class="yiv5687647192"> </span>garis tinggi dan demikian seterusnya. Jika OA<sub class="yiv5687647192">1</sub><span class="yiv5687647192"> </span>= 500Ö2, sisi miring dalam segitiga ke n lebih kecil dari 100, untuk</span></div>
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<span style="background-color: white; font-family: inherit;">            (A)       n  >  logÖ2  </span></div>
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<span style="background-color: white; font-family: inherit;">            (B)        n  >  logÖ2 + 1           </span></div>
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<span style="background-color: white; font-family: inherit;">            (C)        n  >  2 / log 2              </span></div>
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<span style="background-color: white; font-family: inherit;">            (D)       n  >  (2 / log 2) + 1</span></div>
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<span style="background-color: white; font-family: inherit;">            (E)        n sembarang</span></div>
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Ujian Nasional Matematika Kelas XII SMK TA 2015/2016 01. Jumlah n suku pertama deret aritmatika adalah Sn = 2n 2 – 6n. Beda deret ...