{"id":16432,"date":"2016-02-02T11:09:09","date_gmt":"2016-02-02T04:09:09","guid":{"rendered":"https:\/\/video.quipper.com\/id\/blog\/?p=16432"},"modified":"2016-02-02T11:09:09","modified_gmt":"2016-02-02T04:09:09","slug":"simak-pembahasan-soal-matematika-dasar-sbmptn","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/masuk-ptn\/sbmptn\/matematika-sbmptn\/simak-pembahasan-soal-matematika-dasar-sbmptn\/","title":{"rendered":"Simak Pembahasan Soal Matematika Dasar SBMPTN"},"content":{"rendered":"

\"Pembahasan<\/a><\/p>\n

Bagi kamu yang akan mengikuti tes SBMPTN, apapun pilihan bidangmu, baik IPA maupun IPS, kamu pasti akan diuji TKPA yang berisi ujian TPA, Matematika Dasar, Bahasa Inggris dan Bahasa Indonesia. Maka dari itu, penting sekali untuk dapat mengerjakan TKPA dengan baik. Nah, untuk menunjang proses belajarmu, kamu bisa belajar pembahasan soal-soal Matematika Dasar yang akan disajikan berikut ini. Simak baik-baik yaa.<\/p>\n

\u00a01. Jika <\/strong><\/span><\/i>p<\/i>log a = 2 dan <\/i>q<\/i>log 8p = 2, maka <\/i>2p<\/i>log pq<\/i>2<\/i>\/a =<\/i><\/strong><\/p>\n

a.\u00a03 <\/span>2<\/span>log2p<\/span><\/p>\n

b.\u00a02<\/span>log 2p<\/span><\/p>\n

c.\u00a03\/ <\/span>2<\/span>log 2p:<\/span><\/p>\n

d.\u00a01\u00a0\/<\/span>2<\/span>log 2p<\/span><\/p>\n

e.\u00a03\/ <\/span>2<\/span>log p<\/span><\/p>\n

Jawabannya<\/span> C<\/b><\/p>\n

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

Perhatikan bentuk lain logaritma berikut<\/span><\/p>\n

p<\/span>log a = 2 <\/span>\u00e0<\/span> a = p<\/span>2<\/span><\/p>\n

q<\/span>log 8p = 2 <\/span>\u00e0<\/span> 8p = q<\/span>2<\/span> \u00e0<\/span> q<\/span>2<\/span> = 8p<\/span><\/p>\n

Kemudian dengan mensubstitusi a dan q2 diperoleh<\/span><\/p>\n

2p<\/span>log pq<\/span>2<\/span>\/a = <\/span>2p<\/span>log p.8p\/p<\/span>2<\/span> = <\/span>2p<\/span>log8 = <\/span>2p<\/span>log 2<\/span>3<\/span> = 3 <\/span>2p<\/span>log 2 = 3\/<\/span>2<\/span>log 2p<\/span><\/p>\n

\u00a02. Jika 2a + 1 < 0 dan grafik y = x<\/strong><\/i>2<\/i> \u2013 4ax + a bersinggungan dengan grafik y = 2x<\/i>2<\/i> + 2x, maka a<\/i>2<\/i> + 1 = \u2026<\/i><\/strong><\/p>\n

\"Images<\/a><\/p>\n

Jawabannya <\/span>C<\/b><\/p>\n

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

\"rumus\"<\/a><\/p>\n

Kedua bersinggungan, maka determinan dari f(x) = y<\/span>2<\/span> \u2013 y<\/span>1<\/span> sama dengan nol.<\/span><\/p>\n

y<\/span>2<\/span> = y<\/span>1<\/span><\/p>\n

2x<\/span>2<\/span> + 2x = x<\/span>2<\/span> \u2013 4ax + a<\/span><\/p>\n

x<\/span>2<\/span> + (2 + 4a)x \u2013 a = 0<\/span><\/p>\n

Sehingga A = 1, B = 2 + 4a, C = -a<\/span><\/p>\n

\"rumus<\/a><\/p>\n

Sehingga a2 + 1 = (-1)<\/span>2<\/span> + 1 = 1 + 1 = 2<\/span><\/p>\n

4 Hal Wajib untuk Persiapan Satu Bulan Sebelum SBMPTN<\/a><\/h3>\n

\u00a03. Jika titik (x,y) memenuhi x<\/strong><\/span><\/i>2<\/i> \u2264 y \u2264 x + 6, maka nilai maksimum x+y adalah\u2026<\/i><\/strong><\/p>\n

a. 5<\/span><\/p>\n

b. 6<\/span><\/p>\n

c. 7<\/span><\/p>\n

d. 9<\/span><\/p>\n

e. 12<\/span><\/p>\n

Jawabannya <\/span>E<\/b><\/p>\n

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

Perhatikan bahwa x<\/span>2<\/span> \u2264 y \u2264 x + 6, sehingga dapat ditulis:<\/span><\/p>\n

x<\/span>2<\/span>\u2264 x + 6<\/span><\/p>\n

x<\/span>2<\/span> \u2013 x \u2013 6 \u2264 0<\/span><\/p>\n

(x + 2)(x \u2013 3) \u2264 0<\/span><\/p>\n

-2 \u2264 x \u2264 3<\/span><\/p>\n

Sehingga diperoleh bahwa nilai x akan ebrada pada interval tersebut dan maksimum nilai x adalah 3, kemudian perhatikan<\/span><\/p>\n

x<\/span>2<\/span> \u2264 y \u2264 x + 6<\/span><\/p>\n

x + x<\/span>2<\/span> \u2264 x + y \u2264 x + x + 6<\/span><\/p>\n

x + x<\/span>2<\/span> \u2264 x + y \u2264 2x + 6<\/span><\/p>\n

Dari pernyataan di atas diperoleh bahwa nilai maksimum dari x + y adalah 2x + 6, karena nilai maksimum x adalah 3, maka maksimum dari x + y adalah 2x + 6 = 2(3) + 6 = 12<\/span><\/p>\n

\u00a04. Suku tengah suatu barisan aritmatika adalah 23. Jika suku terakhirnya 43 dan suku ketiganya 13, maka banyak suku barisan ini adalah\u2026<\/strong><\/span><\/i><\/p>\n

a. 5<\/span><\/p>\n

b. 7<\/span><\/p>\n

c. 9<\/span><\/p>\n

d. 11<\/span><\/p>\n

e. 13<\/span><\/p>\n

Jawabannya<\/span> C<\/b><\/p>\n

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

Dari soal diperoleh<\/span><\/p>\n

U<\/span>T<\/span> = 23<\/span><\/p>\n

Un = 43<\/span><\/p>\n

U<\/span>3<\/span> = 13<\/span><\/p>\n

\"rumus<\/a><\/p>\n

Dengan menggunakan rumus Un diperoleh:<\/span><\/p>\n

Un = U<\/span>1<\/span> + (n \u2013 1)b<\/span><\/p>\n

43 = 3 + (n \u2013 1)5<\/span><\/p>\n

43 = 3 + 5n \u2013 5<\/span><\/p>\n

5n = 45<\/span><\/p>\n

n = 9<\/span><\/p>\n

Maka banyak sukunya adalah 9<\/span><\/p>\n

\u00a05. SMA X memiliki 6 kelas dengan banyak siswa pada setiap kelas adalah 16 pria dan 16 wanita. Jika untuk kepengurusan OSIS dipilih satu orang dari setiap kelas, maka peluang 2 orang wanita yang menjadi pengurus OSIS adalah\u2026<\/strong><\/span><\/i><\/p>\n

\"rumus<\/a><\/p>\n

Jawabannya <\/span>B<\/b><\/p>\n

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

n(s) = <\/span>2<\/span>C<\/span>1<\/span> x <\/span>2<\/span>C<\/span>1<\/span> x <\/span>2<\/span>C<\/span>1<\/span> x <\/span>2<\/span>C<\/span>1<\/span> x <\/span>2<\/span>C<\/span>1<\/span> x <\/span>2<\/span>C<\/span>1<\/span> = 2 x 2 x 2 x 2 x 2 x 2 = 64<\/span><\/p>\n

\"rumus<\/a><\/p>\n

\"rumus<\/a><\/p>\n

Substitusi x = 0 ke persamaan di atas, diperoleh:<\/span><\/p>\n

g\u2019(0) = -3. (2f(0) \u2013 1)<\/span>-4<\/span>. 2f\u2019(0)<\/span><\/p>\n

g\u2019(0) = -3. (2(1) \u2013 1)<\/span>-4<\/span>. 2(2)<\/span><\/p>\n

g\u2019(0) = -3. (2\u2013 1)<\/span>-4<\/span>. 4<\/span><\/p>\n

g\u2019(0) = -3. (1)<\/span>-4<\/span>. 4<\/span><\/p>\n

g\u2019(0) = -3. 1. 4<\/span><\/p>\n

g\u2019(0) = -12<\/span><\/p>\n

\n

 <\/p>\n

Gimana Quipperian? Pembahasannya sudah cukup jelas kan? Soal-soal Matematika Dasar SBMPTN tidak sulit kan? Yuk, belajar lebih rajin lagi dan berlatih lebih banyak soal.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Bagi kamu yang akan mengikuti tes SBMPTN, apapun pilihan bidangmu, baik IPA maupun IPS, kamu pasti akan diuji TKPA yang berisi ujian TPA, Matematika…<\/p>\n","protected":false},"author":156446345,"featured_media":17072,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[253044991],"tags":[],"ppma_author":[679386822],"class_list":["post-16432","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika-sbmptn"],"acf":[],"yoast_head":"\nSimak Pembahasan Soal Matematika Dasar SBMPTN<\/title>\n<meta name=\"description\" content=\"Apapun pilihan bidangmu, 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