{"id":279274,"date":"2020-01-23T14:47:04","date_gmt":"2020-01-23T07:47:04","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=279274"},"modified":"2021-11-03T18:18:12","modified_gmt":"2021-11-03T11:18:12","slug":"utbk-matematika-dasar-2017","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/masuk-ptn\/sbmptn\/soal-sbmptn\/utbk-matematika-dasar-2017\/","title":{"rendered":"Soal UTBK SBMPTN Matematika Dasar 2017"},"content":{"rendered":"

\"\"<\/p>\n

Hai Quipperian, sudah siapkah kamu menyambut seleksi akbar, SBMPTN? Atau justru kamu masih bingung mencari soal-soal SBMPTN? Bagi kamu yang saat ini masih bingung mencari soal-soal SBMPTN, tampaknya kamu berada di artikel yang tepat, <\/span>nih<\/span><\/em>.\u00a0<\/span><\/p>\n

Kali ini, Quipper Blog akan membahas latihan soal SBMPTN Matematika Dasar TKPA 2017. Kabar baiknya, latihan soal yang disediakan Quipper Blog, lengkap dengan jawaban beserta pembahasannya, <\/span>lho<\/span><\/em>. Semakin penasaran? Yuk, segera kerjakan soalnya!<\/span><\/p>\n

Latihan Soal 1<\/strong><\/h2>\n

\"\"<\/p>\n

    \n
  1. 30<\/span><\/li>\n
  2. 10<\/span><\/li>\n
  3. 60<\/span><\/li>\n
  4. 6<\/span><\/li>\n
  5. 20<\/span><\/li>\n<\/ol>\n

    Jawaban: C<\/strong><\/p>\n

    Pembahasan:<\/strong><\/p>\n

    \"\"<\/p>\n

    Penyelesaian:<\/span><\/p>\n

    Mula-mula, tentukan nilai det(A).<\/span><\/p>\n

    \"\"<\/p>\n

    Gunakan sifat-sifat determinan berikut.<\/span><\/p>\n

    \"\"<\/p>\n

    Berdasarkan dua sifat determinan di atas, diperoleh:<\/span><\/p>\n

    \"\"<\/p>\n

    Jadi, hasil kali semua nilai\u00a0<\/span>a\u00a0<\/span><\/em>yang mungkin adalah\u00a0<\/span>a<\/span><\/em>1<\/span><\/sub>.<\/span>a<\/span><\/em>2 <\/span><\/sub>= 10 (6) = 60.<\/span><\/p>\n

    Latihan Soal 2<\/strong><\/h2>\n

    \"\"<\/p>\n

    Jawaban: D<\/strong><\/p>\n

    Pembahasan:<\/strong><\/p>\n

    Diketahui:<\/span><\/p>\n

    \"\"<\/p>\n

    Ditanya: Himpunan penyelesaian =\u2026?<\/span><\/p>\n

    Penyelesaian:<\/span><\/p>\n

    Oleh karena nilai penyebut pasti positif, maka kedua ruas dikali dengan\u00a0|<\/span>x <\/span><\/em>+ 3|.<\/span><\/p>\n

    \"\"<\/p>\n

    Dengan menggunakan garis bilangan, diperoleh daerah penyelesaiannya adalah sebagai berikut.<\/span><\/p>\n

    \"\"<\/p>\n

    Latihan Soal 3<\/strong><\/h2>\n

    Perhatikan gambar berikut.<\/span><\/p>\n

    \"\"\u00a0<\/span><\/p>\n

    Pada segitiga siku-siku sama kaki\u00a0ABC, sisi\u00a0AB\u00a0dan\u00a0BC\u00a0masing-masing terbagi menjadi tiga bagian yang sama, berturut-turut oleh titik\u00a0K, L\u00a0dan\u00a0M, N. Jika luas\u00a0\u25b3ABC\u00a0adalah\u00a04,5<\/span>x<\/span><\/em>2<\/span><\/sup>\u00a0cm<\/span>2<\/span><\/sup>, luas\u00a0\u25b3KMN\u00a0adalah …\u00a0\u00a0cm<\/span>2<\/span><\/sup>.<\/span><\/p>\n

      \n
    1. 2<\/span>x<\/span><\/em>2<\/span><\/sup>\u00a0cm<\/span>2<\/span><\/sup><\/li>\n
    2. 3<\/span>x<\/span><\/em>2<\/span><\/sup>\u00a0cm<\/span>2<\/span><\/sup><\/li>\n
    3. x<\/span><\/em>2<\/span><\/sup>\u00a0cm<\/span>2<\/span><\/sup><\/li>\n
    4. 1,5<\/span>x<\/span><\/em>2<\/span><\/sup>\u00a0cm<\/span>2<\/span><\/sup><\/li>\n
    5. 0,5<\/span>x<\/span><\/em>2<\/span><\/sup>\u00a0cm<\/span>2<\/span><\/sup><\/li>\n<\/ol>\n

      Jawaban: C<\/strong><\/p>\n

      Pembahasan:<\/strong><\/p>\n

      Diketahui: <\/span>Pada segitiga siku-siku sama kaki\u00a0ABC, sisi\u00a0AB\u00a0dan\u00a0BC\u00a0masing-masing terbagi menjadi tiga bagian yang sama, berturut-turut oleh titik\u00a0K, L\u00a0dan\u00a0M, N. Jika luas\u00a0\u25b3ABC\u00a0adalah\u00a04,5<\/span>x<\/span><\/em>2<\/span><\/sup>\u00a0cm<\/span>2<\/span><\/sup>.<\/span><\/p>\n

      Ditanya: Luas\u00a0\u25b3KMN =\u2026?<\/span><\/p>\n

      Penyelesaian:<\/span><\/p>\n

      Oleh karena luas\u00a0\u25b3ABC\u00a0adalah\u00a04,5<\/span>x<\/span><\/em>2<\/span><\/sup>\u00a0cm<\/span>2<\/span><\/sup>, maka:<\/span><\/p>\n

      \"\"<\/p>\n

      Oleh karena panjang sisi\u00a0AB\u00a0dan\u00a0BC\u00a0masing-masing dibagi tiga sama panjang, maka:<\/span><\/p>\n

      \"\"<\/p>\n

      Dengan demikian, diperoleh:<\/span><\/p>\n

      \"\"<\/p>\n

      Jadi, luas <\/span>\u25b3KMN adalah <\/span>x<\/span><\/em>2<\/span><\/sup> cm<\/span>2<\/span><\/sup>.<\/span><\/p>\n

      Latihan Soal 4<\/strong><\/h2>\n

      Tiga puluh data mempunyai rata-rata\u00a0<\/span>p<\/span><\/em>. Jika rata-rata\u00a020%\u00a0data di antaranya adalah\u00a0<\/span>p<\/span><\/em> + 0,1, 40%\u00a0lainnya adalah\u00a0<\/span>p<\/span><\/em> \u2013 0,1,\u00a010%\u00a0lainnya lagi adalah\u00a0<\/span>p<\/span><\/em> \u2013 0,5,\u00a0dan rata-rata\u00a030%\u00a0data sisanya adalah\u00a0<\/span>p<\/span><\/em> + <\/span>q<\/span><\/em>, nilai\u00a0<\/span>q<\/span><\/em>\u00a0= \u2026<\/span><\/p>\n

      \"\"<\/p>\n

      Jawaban: C<\/strong><\/p>\n

      Pembahasan:<\/strong><\/p>\n

      Diketahui:<\/span><\/p>\n

      \"\"<\/p>\n

      Ditanya: Nilai <\/span>q<\/span><\/em> =\u2026?<\/span><\/p>\n

      Penyelesaian:<\/span><\/p>\n

      Gunakan rumus rata-rata gabungan.<\/span><\/p>\n

      \"\"<\/p>\n

      Latihan Soal 5<\/strong><\/h2>\n

      Seseorang memiliki suatu peternakan ayam yang cukup besar. Rata-rata banyaknya telur ayam per bulan yang dihasilkan peternakan itu adalah\u00a0(40 \u2013 0,0025<\/span>x<\/span><\/em>)\u00a0butir, dengan\u00a0<\/span>x<\/span><\/em>\u00a0menyatakan banyak ayam betina yang ada di peternakan tersebut.\u00a0<\/span><\/p>\n

      Pada beberapa bulan terakhir, wabah penyakit melanda ayam-ayam di peternakan, sehingga rata-rata banyaknya telur yang dihasilkan berkurang sebanyak\u00a020%\u00a0dari biasanya. Total maksimum telur ayam yang dihasilkan saat terjadi wabah penyakit pada bulan tersebut adalah … butir.<\/span><\/p>\n

        \n
      1. 8.000<\/span><\/li>\n
      2. 160.000<\/span><\/li>\n
      3. 16.000<\/span><\/li>\n
      4. 256.000<\/span><\/li>\n
      5. 128.000<\/span><\/li>\n<\/ol>\n

        Jawaban: E<\/strong><\/p>\n

        Pembahasan:<\/strong><\/p>\n

        Diketahui:<\/span><\/p>\n

          \n
        • Banyaknya ayam = <\/span>x<\/span><\/em>.<\/span><\/li>\n
        • Rata-rata banyaknya telur ayam per bulan = 40 \u2013 0,0025<\/span>x<\/span><\/em>.<\/span><\/li>\n<\/ul>\n

          Ditanya: <\/span>Total maksimum telur ayam yang dihasilkan saat terjadi wabah penyakit pada bulan tersebut =\u2026?<\/span><\/p>\n

          Penyelesaian:<\/span><\/p>\n

          Oleh karena rata-rata banyaknya telur yang dihasilkan berkurang sebanyak\u00a020%\u00a0saat terjadi wabah penyakit, maka rata-rata banyak telur ayam menjadi:<\/span><\/p>\n

          \"\"<\/p>\n

          Misalkan total telur ayam yang dihasilkan saat terjadi wabah penyakit adalah\u00a0<\/span>f<\/span><\/em>(<\/span>x<\/span><\/em>). Ini berarti:<\/span><\/p>\n

          f<\/span><\/em>(<\/span>x<\/span><\/em>)\u00a0= rata-rata banyaknya telur ayam saat terjadi wabah penyakit\u00a0\u00d7\u00a0banyak ayam<\/span>
          \n<\/span>\u21d4 <\/span>f<\/span><\/em>(<\/span>x<\/span><\/em>) = (32 \u2212 0,002<\/span>x<\/span><\/em>)<\/span>x<\/span><\/em> = 32<\/span>x<\/span><\/em> \u2212 0,002<\/span>x<\/span><\/em>2<\/span><\/sup><\/p>\n

          Oleh karena koefisien\u00a0<\/span>x<\/span><\/em>2<\/span><\/sup>\u00a0bernilai negatif\u00a0(<\/span>a<\/span><\/em> = \u22120,002 < 0), maka fungsi kuadrat\u00a0<\/span>f<\/span><\/em>(<\/span>x<\/span><\/em>)\u00a0hanya memiliki nilai maksimum\u00a0(<\/span>f<\/span><\/em>\u2033(<\/span>x<\/span><\/em>) = 2<\/span>a<\/span><\/em> = \u22120,004 < 0). Agar total telur ayam yang dihasilkan maksimum, maka\u00a0<\/span>f<\/span><\/em>\u2032(<\/span>x<\/span><\/em>)=0.<\/span><\/p>\n

          \"\"<\/p>\n

          Dengan mensubstitusikan\u00a0<\/span>x<\/span><\/em> = 8.000\u00a0ke\u00a0<\/span>f<\/span><\/em>(<\/span>x<\/span><\/em>), diperoleh:<\/span><\/p>\n

          \"\"<\/p>\n

          Jadi, total maksimum telur ayam yang dihasilkan saat terjadi wabah penyakit pada bulan tersebut adalah\u00a0128.000\u00a0butir.<\/span><\/p>\n

          Latihan Soal 6<\/strong><\/h2>\n

          \"\"\u00a0<\/span><\/p>\n

          Jawaban: D<\/strong><\/p>\n

          Pembahasan:<\/strong><\/p>\n

          Diketahui: Bentuk integral.<\/span><\/p>\n

          Ditanya:<\/span><\/p>\n

          \"\"\u00a0<\/span><\/p>\n

          Penyelesaian:<\/span><\/p>\n

          Ubah dahulu bentuk pembilang pada integran menggunakan sifat berikut.<\/span><\/p>\n

          \"\"<\/p>\n

          Ini berarti:<\/span><\/p>\n

          \"\"<\/p>\n

          Latihan Soal 7<\/strong><\/h2>\n

          Perbandingan suku ke-5\u00a0terhadap suku ke-2\u00a0suatu barisan geometri adalah\u00a0127. Jika jumlah suku ke-2\u00a0dan suku ke-4\u00a0adalah\u00a090, jumlah suku ke-3\u00a0dan suku ke-4\u00a0barisan tersebut adalah…<\/span><\/p>\n

            \n
          1. 32<\/span><\/li>\n
          2. 34<\/span><\/li>\n
          3. 35<\/span><\/li>\n
          4. 33<\/span><\/li>\n
          5. 36<\/span><\/li>\n<\/ol>\n

            Jawaban: E<\/strong><\/p>\n

            Pembahasan:<\/strong><\/p>\n

            Diketahui:<\/span><\/p>\n

              \n
            • Perbandingan suku ke-5\u00a0terhadap suku ke-2\u00a0suatu barisan geometri adalah\u00a0127.<\/span><\/li>\n
            • Jumlah suku ke-2\u00a0dan suku ke-4\u00a0adalah\u00a090.<\/span><\/li>\n<\/ul>\n

              Ditanya: Jumlah suku ke-3\u00a0dan suku ke-4\u00a0barisan tersebut =\u2026?<\/span><\/p>\n

              Penyelesaian:<\/span><\/p>\n

              \"\"<\/p>\n

              Diketahui jumlah suku ke-2\u00a0dan ke-4\u00a0adalah\u00a090. Ini berarti:<\/span><\/p>\n

              \"\"<\/p>\n

              Dengan demikian, suku ke-3\u00a0dan ke-4\u00a0adalah sebagai berikut.<\/span><\/p>\n

              \"\"<\/p>\n

              Jadi, jumlah suku ke-3\u00a0dan suku ke-4\u00a0adalah\u00a0<\/span>U<\/span><\/em>3<\/span><\/em><\/sub> + <\/span>U<\/span><\/em>4<\/span><\/em><\/sub> = 27 + 9 = 36.<\/span><\/p>\n

              Bagaimana Quipperian, apakah kamu sudah mulai paham mengerjakan latihan soal SBMPTN Matematika Dasar TKPA 2017 di atas? Agar pemahamanmu semakin terasah, sering-seringlah mengerjakan latihan soal. Ingat, selangkah lagi kamu akan memasuki PTN impian.\u00a0<\/span><\/p>\n

              Untuk mendukung kesuksesanmu masuk PTN, Quipper Video hadir dengan Paket Intensif UTBK SBMPTN 2020. Semua kebutuhan sudah tersedia di dalamnya, mulai dari materi persiapan, materi pemantapan, latihan soal, bank soal, hingga pembahasan lengkapnya. Jadi, tunggu apalagi. Yuk, gabung Quipper Video sekarang!<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

              Hai Quipperian, sudah siapkah kamu menyambut seleksi akbar, SBMPTN? Atau justru kamu masih bingung mencari soal-soal SBMPTN? Bagi kamu yang saat ini masih bingung…<\/p>\n","protected":false},"author":99400369,"featured_media":279308,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[679385273,679385209],"tags":[],"ppma_author":[679386827],"class_list":["post-279274","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sbmptn","category-soal-sbmptn"],"acf":[],"yoast_head":"\nSoal UTBK SBMPTN Matematika Dasar 2017 - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Quipperian, jangan bingung! 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