Soal dan Pembahasan UNBK 2019 SMK Kelompok TKP You are reading Tutorial from Thủ Thuật Blogspot Jangan lupa membaca artikel tentang bisnis di > <a href="http://www.mediabisnis.co.id/" rel="dofollow"><b>Informasi bisnis terbaik 2020</b></a>.<br/><br/><div dir="ltr" style="text-align: left;" trbidi="on"> <span class="fullpost"> </span><br /> <div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgybQ0kI9fopPpgls_J0J_affr9sMksjdwmF2h1gT6030svyZJ2LmA5hMaUHmOYUSa5oQU-_Y-KzPpFt-OgCA3LrUNwgOU0lEI0IGGFu3I-GRUV3A1f4JunktscX2dpn843U_UsTmLeDK0/s1600/Isian+Singkat+%2528FILEminimizer%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="683" data-original-width="1186" height="368" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgybQ0kI9fopPpgls_J0J_affr9sMksjdwmF2h1gT6030svyZJ2LmA5hMaUHmOYUSa5oQU-_Y-KzPpFt-OgCA3LrUNwgOU0lEI0IGGFu3I-GRUV3A1f4JunktscX2dpn843U_UsTmLeDK0/s640/Isian+Singkat+%2528FILEminimizer%2529.jpg" width="640" /></a></div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;">Soal dan Pembahasan Isian Singkat Ujian Nasional Berbasis Komputer (UNBK) Tahun 2019 SMK kelompok TKP (Teknologi, Kesehatan dan Pertanian)</span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;">Ujian Nasional Berbasis Komputer (UNBK) Tahun 2019 sudah selesai diselenggarakan. Untuk Sekolah Menengah Kejuruan (SMK) penyelenggaraan Ujian Nasional lebih dulu dari SMA/MA dan juga SMP yaitu tanggal 25 sampai 28 Maret 2019 dan Ujian Susulannya tanggal 15 dan 16 Arpil 2019.</span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;">Khusus untuk mata pelajaran matematika, berdasarkan informasi dari beberapa peserta ujian, soal tahun ini lebih sulit dari soal UN tahun lalu. Berikut ini kami akan membahas 4 soal isian singkat UNBK 2019 SMK kelompok Teknologi, Kesehatan dan Pertanian yang kami peroleh dari beberapa siswa peserta UN 2019 berdasarkan ingatan mereka dan bekas coretan kertas buram saat mereka melaksanakan ujian.</span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;">Soal isian singkat UNBK terdiri dari 4 butir soal. Materi yang diujikan pada isian singkat UNBK 2019 Matematika SMK Kelompok TKP terdiri dari:</span></div> <div style="text-align: justify;"> <ul> <li><span style="font-family: "georgia" , "times new roman" , serif;">Deret Geometri</span></li> <li><span style="font-family: "georgia" , "times new roman" , serif;">Dimensi Tiga / Bangun Ruang</span></li> <li><span style="font-family: "georgia" , "times new roman" , serif;">Kombinasi</span></li> <li><span style="font-family: "georgia" , "times new roman" , serif;">Fungsi Kuadrat</span></li> </ul> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><b><span style="color: red;">Update! </span><a href=" " target="_blank">soal Matematika UNBK 2019 download di sini <i class="fa fa-external-link"></i> </a></b></span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Berikut ini soal dan pembahasan isian singkat UNBK 2019 SMK Kelompok TKP:</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: orange; font-family: "georgia" , "times new roman" , serif; font-size: large;"><b>Soal 1 (Deret Geometri)</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: blue; font-family: "georgia" , "times new roman" , serif;">Diketahui dua bilangan yaitu 4 dan 2.916. Diantara dua bilangan tersebut disisipkan 5 bilangan sehingga bersama bilangan tersebut membentuk deret geometri. Jumlah deret geometri yang terbentuk tersebut adalah ....</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><b>Pembahasan:</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">rasio dari dua buah bilangan sebelum disisipkan 5 bilangan baru (rasio dari 4 dan 2.916) adalah $\displaystyle r_1=\frac{2.916}{4}=729$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Misal $r_2$ adalah rasio barisan bilangan baru setelah disisipkan $n$ buah bilangan, maka:</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div style="text-align: center;"> <span style="font-family: "georgia" , "times new roman" , serif;">$\displaystyle r_2=\sqrt[n+1]{r_1}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Dengan menggunakan formula di atas, maka barisan bilangan yang terbentuk setelah mensisipkan 5 buah bilangan diantara 4 dan 2.916 adalah:</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">$\begin{align*}r&=\sqrt[5+1]{729}\\&=\sqrt[6]{729}\\&=3\end{align*}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Karena $r>1$ maka untuk menentukan jumlah $n$ suku pertama kita gunakan formula $\displaystyle S_n=\frac{a(r^n-1)}{r-1}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Jadi, jumlah barisan tersebut (jumlah 7 suku pertama) dengan suku pertama $a=4$ dan $r=3$ adalah:</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">$\begin{align*}S_7&=\frac{4(3^7-1)}{3-1}\\&=\frac{4(2.187-1)}{2}\\&=2(2.186)\\&=4.372\end{align*}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: orange; font-family: "georgia" , "times new roman" , serif; font-size: large;"><b>Soal 2 (Bangun Ruang)</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: blue; font-family: "georgia" , "times new roman" , serif;">Perhatikan gambar kubus $ABCD.EFGH$ di bawah ini</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjN-PU9em8EmT_NROhzF6VQ-yLzkskaBxmM83Rs3_6wAR1lzfA0fBbPcdkZlY8H-YIW81S-Cgn2abd2T5LbBfCP5ncWxKCE6UtmD18sKnXYKkHonQsOJ6i23qP4IckdO3TCyhQr8Wuicbk/s1600/Kubus.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: "georgia" , "times new roman" , serif;"><img border="0" data-original-height="327" data-original-width="316" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjN-PU9em8EmT_NROhzF6VQ-yLzkskaBxmM83Rs3_6wAR1lzfA0fBbPcdkZlY8H-YIW81S-Cgn2abd2T5LbBfCP5ncWxKCE6UtmD18sKnXYKkHonQsOJ6i23qP4IckdO3TCyhQr8Wuicbk/s320/Kubus.png" width="309" /></span></a></div> <div class="separator" style="clear: both; text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div class="separator" style="clear: both; text-align: justify;"> <span style="color: blue; font-family: "georgia" , "times new roman" , serif;">Jika panjang rusuk kubus adalah $6\sqrt{5}$ cm dan titik $P$ adalah titik tengah $GH$. Jarak titik $D$ ke garis $CP$ adalah ... cm</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><b>Pembahasan:</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Perhatikan gambar di bawah ini:</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRKoclRe3ewsP6yTB6DnhYXh3-bxanILetROidw-t1AA8MjcbatLY-JtXY0P9MLcYO3q1SRXM9nKwzR1gmMG2VkCNmSs7GtYsHOHGgJBTtJi6ymPRYSz5gGMZzWDjkQSJ173apWqtXQjU/s1600/Kubus+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="334" data-original-width="325" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRKoclRe3ewsP6yTB6DnhYXh3-bxanILetROidw-t1AA8MjcbatLY-JtXY0P9MLcYO3q1SRXM9nKwzR1gmMG2VkCNmSs7GtYsHOHGgJBTtJi6ymPRYSz5gGMZzWDjkQSJ173apWqtXQjU/s320/Kubus+2.png" width="311" /></a></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Titik $P$ terletak di tengah garis $GH$ sehingga </span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">$\begin{align*}GP=PH&=\frac{1}{2}\times GH\\&=\frac{1}{2}\times 6\sqrt{5}\\&=3\sqrt{5}\end{align*}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <br /></div> <div> $\begin{align*}CP&=\sqrt{CG^2+GP^2}\\&=\sqrt{(6\sqrt{5})^2+(3\sqrt{5})^2}\\&=\sqrt{180+45}\\&=\sqrt{225}\\&=15\end{align*}$</div> <div> <br /></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">$PQ=GC=6\sqrt{5}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Perhatikan segitiga $DCP$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">$\begin{align*}DR\times PC&=DC\times PQ\\DR&=\frac{DC\times PQ}{PC}\\&=\frac{6\sqrt{5}\times 6\sqrt{5}}{15}\\&=\frac{180}{15}\\&=12\end{align*}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Jadi, jarak dari titik $D$ ke garis $PC$ adalah 12 cm</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: orange; font-family: "georgia" , "times new roman" , serif; font-size: large;"><b>Soal 3 (Kombinasi)</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: blue; font-family: "georgia" , "times new roman" , serif;">Di dalam keranjang berisi 20 butir telur dan 2 butir diantaranya busuk. Ibu mengambil 3 butir telur dari keranjang tersebut secara acak. Banyak cara pengambilan jika terambil paling sedikit 2 telur yang baik adalah ....</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><b>Pembahasan:</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Di dalam keranjang berisi 18 telur baik dan 2 telur busuk. Jika ibu mengambil 3 telur, kemungkinan mendapat paling sedikit 2 telur baik adalah ibu mendapat </span><span style="font-family: "georgia" , "times new roman" , serif;">2 baik dan 1 busuk atau ketiganya telur baik, dengan kombinasi kita peroleh:</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">$\begin{align*} C_2^{18}\times C_1^2+C_3^{18}&=153\times 2+816\\&=1122\end{align*}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Jadi banyak cara pengambilan adalah 1.122 cara</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: orange; font-family: "georgia" , "times new roman" , serif; font-size: large;"><b>Soal 4 (Fungsi Kuadrat/Aplikasi Turunan)</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: blue; font-family: "georgia" , "times new roman" , serif;">Suatu pekerjaan dapat diselesaikan dalam $x$ hari dengan biaya $f(x)=x^2-4x+5$ dalam ratusan ribu rupiah. Banyak hari yang diperlukan agar biaya yang dikeluarkan minimum adalah .... hari.</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><b>Pembahasan:</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Soal ini dapat kita selesaikan dengan menggunkan rumus titik balik fungsi kuadrat atau bisa juga dengan menggunkan turunan.</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><b>Cara 1:</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Titik balik/puncak suatu fungsi kuadrat $f(x)=ax^2+bx+c$ adalah $\left(-\frac{b}{2a},-\frac{D}{4a}\right)$ dengan $D=b^2-4ac$</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">Karena pada soal di atas yang ditanyakan hanya nilai $x$-nya saja, maka kita hanya tinggal mencari absis dari titik balik fungsi $f(x)=x^2-4x+5$ yaitu $x=-\frac{-4}{2(1)}=2$</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;"><b>Cara 2:</b></span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">Nilai maksimum/minimum suatu fungsi dapat kita cari dengan menggunakan turunan pertama.</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">$\begin{align*}f'(x)&=0\\2x-4&=0\\2x&=4\\x=2\end{align*}$</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">Jadi, agar biaya yang dikeluarkan minimum, diperlukan waktu 2 hari.</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">Demikianlah pembahasan soal isian singkat UNBK 2019 SMK Kelompok TKP.</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">Semoga bermanfaat.</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">Lihat video pembahasannya <a href="https://youtu.be/GbridPYrcDs" target="_blank"><b>di sini <i class="fa fa-external-link"></i></b></a></span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <br /> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;">Silakan gabung di Fans Page Facebook, Channel Telegram untuk memperoleh update terbaru, dan Subscribe Channel YouTube IndoINT untuk memperoleh video pembelajaran matematika secara gratis, untuk mengikuti tautan klik pada tombol di bawah ini:</span></div> <div class="separator" style="clear: both; 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Soal dan Pembahasan UNBK 2019 SMK Kelompok TKP You are reading Tutorial from Thủ Thuật Blogspot Jangan lupa membaca artikel tentang bisnis di > <a href="http://www.mediabisnis.co.id/" rel="dofollow"><b>Informasi bisnis terbaik 2020</b></a>.<br/><br/><div dir="ltr" style="text-align: left;" trbidi="on"> <span class="fullpost"> </span><br /> <div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgybQ0kI9fopPpgls_J0J_affr9sMksjdwmF2h1gT6030svyZJ2LmA5hMaUHmOYUSa5oQU-_Y-KzPpFt-OgCA3LrUNwgOU0lEI0IGGFu3I-GRUV3A1f4JunktscX2dpn843U_UsTmLeDK0/s1600/Isian+Singkat+%2528FILEminimizer%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="683" data-original-width="1186" height="368" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgybQ0kI9fopPpgls_J0J_affr9sMksjdwmF2h1gT6030svyZJ2LmA5hMaUHmOYUSa5oQU-_Y-KzPpFt-OgCA3LrUNwgOU0lEI0IGGFu3I-GRUV3A1f4JunktscX2dpn843U_UsTmLeDK0/s640/Isian+Singkat+%2528FILEminimizer%2529.jpg" width="640" /></a></div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;">Soal dan Pembahasan Isian Singkat Ujian Nasional Berbasis Komputer (UNBK) Tahun 2019 SMK kelompok TKP (Teknologi, Kesehatan dan Pertanian)</span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;">Ujian Nasional Berbasis Komputer (UNBK) Tahun 2019 sudah selesai diselenggarakan. Untuk Sekolah Menengah Kejuruan (SMK) penyelenggaraan Ujian Nasional lebih dulu dari SMA/MA dan juga SMP yaitu tanggal 25 sampai 28 Maret 2019 dan Ujian Susulannya tanggal 15 dan 16 Arpil 2019.</span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;">Khusus untuk mata pelajaran matematika, berdasarkan informasi dari beberapa peserta ujian, soal tahun ini lebih sulit dari soal UN tahun lalu. Berikut ini kami akan membahas 4 soal isian singkat UNBK 2019 SMK kelompok Teknologi, Kesehatan dan Pertanian yang kami peroleh dari beberapa siswa peserta UN 2019 berdasarkan ingatan mereka dan bekas coretan kertas buram saat mereka melaksanakan ujian.</span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;">Soal isian singkat UNBK terdiri dari 4 butir soal. Materi yang diujikan pada isian singkat UNBK 2019 Matematika SMK Kelompok TKP terdiri dari:</span></div> <div style="text-align: justify;"> <ul> <li><span style="font-family: "georgia" , "times new roman" , serif;">Deret Geometri</span></li> <li><span style="font-family: "georgia" , "times new roman" , serif;">Dimensi Tiga / Bangun Ruang</span></li> <li><span style="font-family: "georgia" , "times new roman" , serif;">Kombinasi</span></li> <li><span style="font-family: "georgia" , "times new roman" , serif;">Fungsi Kuadrat</span></li> </ul> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><b><span style="color: red;">Update! </span><a href=" " target="_blank">soal Matematika UNBK 2019 download di sini <i class="fa fa-external-link"></i> </a></b></span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Berikut ini soal dan pembahasan isian singkat UNBK 2019 SMK Kelompok TKP:</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: orange; font-family: "georgia" , "times new roman" , serif; font-size: large;"><b>Soal 1 (Deret Geometri)</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: blue; font-family: "georgia" , "times new roman" , serif;">Diketahui dua bilangan yaitu 4 dan 2.916. Diantara dua bilangan tersebut disisipkan 5 bilangan sehingga bersama bilangan tersebut membentuk deret geometri. Jumlah deret geometri yang terbentuk tersebut adalah ....</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><b>Pembahasan:</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">rasio dari dua buah bilangan sebelum disisipkan 5 bilangan baru (rasio dari 4 dan 2.916) adalah $\displaystyle r_1=\frac{2.916}{4}=729$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Misal $r_2$ adalah rasio barisan bilangan baru setelah disisipkan $n$ buah bilangan, maka:</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div style="text-align: center;"> <span style="font-family: "georgia" , "times new roman" , serif;">$\displaystyle r_2=\sqrt[n+1]{r_1}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Dengan menggunakan formula di atas, maka barisan bilangan yang terbentuk setelah mensisipkan 5 buah bilangan diantara 4 dan 2.916 adalah:</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">$\begin{align*}r&=\sqrt[5+1]{729}\\&=\sqrt[6]{729}\\&=3\end{align*}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Karena $r>1$ maka untuk menentukan jumlah $n$ suku pertama kita gunakan formula $\displaystyle S_n=\frac{a(r^n-1)}{r-1}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Jadi, jumlah barisan tersebut (jumlah 7 suku pertama) dengan suku pertama $a=4$ dan $r=3$ adalah:</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">$\begin{align*}S_7&=\frac{4(3^7-1)}{3-1}\\&=\frac{4(2.187-1)}{2}\\&=2(2.186)\\&=4.372\end{align*}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: orange; font-family: "georgia" , "times new roman" , serif; font-size: large;"><b>Soal 2 (Bangun Ruang)</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: blue; font-family: "georgia" , "times new roman" , serif;">Perhatikan gambar kubus $ABCD.EFGH$ di bawah ini</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjN-PU9em8EmT_NROhzF6VQ-yLzkskaBxmM83Rs3_6wAR1lzfA0fBbPcdkZlY8H-YIW81S-Cgn2abd2T5LbBfCP5ncWxKCE6UtmD18sKnXYKkHonQsOJ6i23qP4IckdO3TCyhQr8Wuicbk/s1600/Kubus.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: "georgia" , "times new roman" , serif;"><img border="0" data-original-height="327" data-original-width="316" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjN-PU9em8EmT_NROhzF6VQ-yLzkskaBxmM83Rs3_6wAR1lzfA0fBbPcdkZlY8H-YIW81S-Cgn2abd2T5LbBfCP5ncWxKCE6UtmD18sKnXYKkHonQsOJ6i23qP4IckdO3TCyhQr8Wuicbk/s320/Kubus.png" width="309" /></span></a></div> <div class="separator" style="clear: both; text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div class="separator" style="clear: both; text-align: justify;"> <span style="color: blue; font-family: "georgia" , "times new roman" , serif;">Jika panjang rusuk kubus adalah $6\sqrt{5}$ cm dan titik $P$ adalah titik tengah $GH$. Jarak titik $D$ ke garis $CP$ adalah ... cm</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><b>Pembahasan:</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Perhatikan gambar di bawah ini:</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRKoclRe3ewsP6yTB6DnhYXh3-bxanILetROidw-t1AA8MjcbatLY-JtXY0P9MLcYO3q1SRXM9nKwzR1gmMG2VkCNmSs7GtYsHOHGgJBTtJi6ymPRYSz5gGMZzWDjkQSJ173apWqtXQjU/s1600/Kubus+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="334" data-original-width="325" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRKoclRe3ewsP6yTB6DnhYXh3-bxanILetROidw-t1AA8MjcbatLY-JtXY0P9MLcYO3q1SRXM9nKwzR1gmMG2VkCNmSs7GtYsHOHGgJBTtJi6ymPRYSz5gGMZzWDjkQSJ173apWqtXQjU/s320/Kubus+2.png" width="311" /></a></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Titik $P$ terletak di tengah garis $GH$ sehingga </span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">$\begin{align*}GP=PH&=\frac{1}{2}\times GH\\&=\frac{1}{2}\times 6\sqrt{5}\\&=3\sqrt{5}\end{align*}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <br /></div> <div> $\begin{align*}CP&=\sqrt{CG^2+GP^2}\\&=\sqrt{(6\sqrt{5})^2+(3\sqrt{5})^2}\\&=\sqrt{180+45}\\&=\sqrt{225}\\&=15\end{align*}$</div> <div> <br /></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">$PQ=GC=6\sqrt{5}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Perhatikan segitiga $DCP$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">$\begin{align*}DR\times PC&=DC\times PQ\\DR&=\frac{DC\times PQ}{PC}\\&=\frac{6\sqrt{5}\times 6\sqrt{5}}{15}\\&=\frac{180}{15}\\&=12\end{align*}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Jadi, jarak dari titik $D$ ke garis $PC$ adalah 12 cm</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: orange; font-family: "georgia" , "times new roman" , serif; font-size: large;"><b>Soal 3 (Kombinasi)</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: blue; font-family: "georgia" , "times new roman" , serif;">Di dalam keranjang berisi 20 butir telur dan 2 butir diantaranya busuk. Ibu mengambil 3 butir telur dari keranjang tersebut secara acak. Banyak cara pengambilan jika terambil paling sedikit 2 telur yang baik adalah ....</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><b>Pembahasan:</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Di dalam keranjang berisi 18 telur baik dan 2 telur busuk. Jika ibu mengambil 3 telur, kemungkinan mendapat paling sedikit 2 telur baik adalah ibu mendapat </span><span style="font-family: "georgia" , "times new roman" , serif;">2 baik dan 1 busuk atau ketiganya telur baik, dengan kombinasi kita peroleh:</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">$\begin{align*} C_2^{18}\times C_1^2+C_3^{18}&=153\times 2+816\\&=1122\end{align*}$</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Jadi banyak cara pengambilan adalah 1.122 cara</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: orange; font-family: "georgia" , "times new roman" , serif; font-size: large;"><b>Soal 4 (Fungsi Kuadrat/Aplikasi Turunan)</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="color: blue; font-family: "georgia" , "times new roman" , serif;">Suatu pekerjaan dapat diselesaikan dalam $x$ hari dengan biaya $f(x)=x^2-4x+5$ dalam ratusan ribu rupiah. Banyak hari yang diperlukan agar biaya yang dikeluarkan minimum adalah .... hari.</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><b>Pembahasan:</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Soal ini dapat kita selesaikan dengan menggunkan rumus titik balik fungsi kuadrat atau bisa juga dengan menggunkan turunan.</span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><b>Cara 1:</b></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></div> <div> <span style="font-family: "georgia" , "times new roman" , serif;">Titik balik/puncak suatu fungsi kuadrat $f(x)=ax^2+bx+c$ adalah $\left(-\frac{b}{2a},-\frac{D}{4a}\right)$ dengan $D=b^2-4ac$</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">Karena pada soal di atas yang ditanyakan hanya nilai $x$-nya saja, maka kita hanya tinggal mencari absis dari titik balik fungsi $f(x)=x^2-4x+5$ yaitu $x=-\frac{-4}{2(1)}=2$</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;"><b>Cara 2:</b></span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">Nilai maksimum/minimum suatu fungsi dapat kita cari dengan menggunakan turunan pertama.</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">$\begin{align*}f'(x)&=0\\2x-4&=0\\2x&=4\\x=2\end{align*}$</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">Jadi, agar biaya yang dikeluarkan minimum, diperlukan waktu 2 hari.</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">Demikianlah pembahasan soal isian singkat UNBK 2019 SMK Kelompok TKP.</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">Semoga bermanfaat.</span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <span style="font-family: "georgia" , "times new roman" , serif;">Lihat video pembahasannya <a href="https://youtu.be/GbridPYrcDs" target="_blank"><b>di sini <i class="fa fa-external-link"></i></b></a></span><br /> <span style="font-family: "georgia" , "times new roman" , serif;"><br /></span> <br /> <div style="text-align: justify;"> <span style="font-family: "georgia" , "times new roman" , serif;">Silakan gabung di Fans Page Facebook, Channel Telegram untuk memperoleh update terbaru, dan Subscribe Channel YouTube IndoINT untuk memperoleh video pembelajaran matematika secara gratis, untuk mengikuti tautan klik pada tombol di bawah ini:</span></div> <div class="separator" style="clear: both; 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font-family: "times new roman"; text-align: center;"> <b><span style="color: orange; font-family: "georgia" , "times new roman" , serif; font-size: large;"><br /></span></b></div> <div class="separator" style="clear: both; font-family: "times new roman"; text-align: center;"> <b><span style="color: orange; font-family: "georgia" , "times new roman" , serif; font-size: large;">IndoINT Telegram Channel:</span></b></div> <div class="separator" style="clear: both; font-family: "times new roman"; text-align: center;"> <b><span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></b></div> <div class="separator" style="clear: both; font-family: "times new roman"; text-align: center;"> <b><span style="font-family: "georgia" , "times new roman" , serif;">@banksoalmatematika</span></b></div> <span style="font-family: "georgia" , "times new roman" , serif;"></span><br /> <div style="font-family: "Times New Roman"; text-align: left;"> <span style="font-family: "georgia" , "times new roman" , serif;"><span style="font-family: "georgia" , "times new roman" , serif;"></span></span></div> <div style="font-family: "Times New Roman";"> </div> <br /> <div class="separator" style="-webkit-text-stroke-width: 0px; 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