Artikel ini berisi kumpulan soal latihan untuk Penilaian Akhir Semester (PAS) ganjil kelas 9 untuk pelajaran matematika
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Mendekati masa-masa ujian kayak gini, sebagai murid, pasti ada dong perasaan deg-degan. Walaupun udah belajar setiap hari, tapi tetap aja, yang namanya kata “ujian” bikin kita khawatir. Ujian sekolah, ujian SIM, ujian ujianan soire soire sampia pusiang. Apalagi kamu anak kelas 9 yang sebentar lagi bakalan naik jenjang ke SMA. Oleh karena itu, kita butuh yang namanya latihan. Paling tidak, dengan latihan kita bisa mengukur bagian mana dari materi yang udah kita kuasai atau belum. Setelahnya, tinggal kita tingkatin deh materi yang belum kita pahamin.
Berikut adalah kumpulan soal latihan untuk Penilaian Akhir Semester (PAS) yang bisa kamu coba:
1) Topik: Bilangan Berpangkat
Subtopik: Pengertian bilangan berpangkat
Perkalian 3 X 3 X 3 X 3 X 3 jika dituliskan dalam bentuk pangkat menjadi….
A. 3-5
B. 5-3
C. 35
D. 53
Jawaban: C
Pembahasan
Dalam bentuk pangkat, yaitu:
3 X 3 X 3 X 3 X 3 = 35
2) Topik: Bilangan Berpangkat – Eksponen
Subtopik: Sifat bilangan berpangkat I
Sebuah kubus memiliki sisi 4k satuan. Perbandingan luas permukaan dan volume kubus tersebut adalah….
A. 1 : 2k
B. 2 : k
C. 2 : 3k
D. 3 : 2k
Jawaban: D
Pembahasan:
Sisi kubus (s) = 4k
Luas permukaan kubus (L) = 6s2
Volume Kubus (V) = s3
Maka,
L= 6s2 = 6(4k)2= 6 (42k2)=96k2
V = s3 = (4k)3= 64k3
LV = 96k2/64k3 = 3/2k
Jadi, perbandingan luas permukaan dan volume kubus tersebut adalah 3 : 2k
3) Topik: Bilangan Berpangkat – Eksponen
Subtopik: Persamaan bilangan berpangkat I
Nilai x yang memenuhi persamaan adalah …
A. 9
B. 12
C. 18
D. 36
Jawaban: C
Pembahasan:
Ingat bahwa am x an = am + n, (am)n = am x n, am/an = am-n maka
Jadi, nilai x yang memenuhi persamaan tersebut adalah 18.
4) Topik: Bentuk Akar
Subtopik: Penjumlahan dan pengurangan bentuk akar
Hasil dari 6√2 +4√8 – 3√32 adalah …
A. 2√2
B. 3√2
C. 5√2
D. 7√2
Jawaban: A
Pembahasan:
Jadi, hasil dari 6√2 +4√8 – 3√32 adalah 2√2
.
5) Topik: Bentuk Akar
Subtopik: Pembagian bentuk akar
Hasil dari √1350 ÷ √3 adalah….
A. 5√2
B. 5√3
C. 15√2
D. 15√3
Jawaban: C
Pembahasan:
6) Topik: Bentuk Akar
Subtopik: Rasional bentuk akar
Bentuk sederhana dari adalah…
A. 2(√6+2√3+2√2-2)
B. 4(√6-2√3+2√2+2)
C. 2(√6-2√3-2√2+2)
D. 4(√6+2√3-2√2-2)
Jawaban: D
Pembahasan:
7) Topik: Logaritma
Subtopik: Sifat Logaritma
Diketahui 2log a =1/2 dan 3log b =1/3. Jika x = a2 dan y = b3, maka xlog y =…
A. 3log12
B. 2log 12
C. 3log 2
D. 2log 3
Jawaban: D
Pembahasan:
Ingat, Bentuk umum logaritma!
alog b =x ↔ax =b di mana a,b>0
Maka:
2log a =1/2↔21/2 = a↔a = √2
dan
3log b =1/3 ↔ 31/3 = b ↔ b = 3√3
Karena
x = a2
x = 2√2 = 2
dan
y = b3
y = (3√3)3 = 3
Sehingga:
xlog y = 2log 3
Baca juga: Latihan Penilaian Akhir Semester 2019 Bahasa Indonesia Kelas 10
8) Topik: Logaritma
Subtopik: Persamaan logaritma
Jika persamaan x log 3 + x log (3x-6) = 2 memiliki akar-akar x1 dan x2 dengan x1 > x2, maka x1 – x2 adalah…
A. 1
B. 2
C. 3
D. 4
Jawaban: C
Pembahasan:
x log 3 + x log (3x-6) = 2
x log (3(3x-6)) = x log x2
x log (9x-18) = x log x2
9x -18 = x2
x2 – 9x + 18 = 0
(x – 6) (x – 3) = 0
x1 = 6 x2 = 3
karena akar-akar x1 dan x2 dengan x1 > x2 maka
x1-x2
= 6-3
= 3
9) Topik: Logaritma
Subtopik: Persamaan logaritma
Nilai x yang memenuhi persamaan (2log x)2 – 5 2log x +6=0 adalah ….
A. x = 4 atau x = 9
B. x = 2 atau x = 8
C. x = 4 atau x = 8
D. x = 2 atau x = 9
Jawaban: C
Pembahasan:
misalkan: 2log x = y
Persamaan tersebut dapat ditulis sebagai:
y2 – 5y + 6 = 0
(y – 2) (y – 3) = 0
y – 2 = 0 | y – 3 = 0
y = 2 | y = 3
2log x = 2 | 2log x = 3
x = 22 | x = 23
x = 4 | x = 8
10) Topik: Persamaan Kuadrat
Subtopik: Faktorisasi pada persamaan kuadrat
Salah satu akar-akar dari persamaan kuadrat 3x2 + 8x – 35 = 0 adalah ….
A. 5
B. 7
C. 5/3
D. 7/3
Jawaban: D
Pembahasan:
3x2 + 8x – 35 = 0 (faktor dari 35 adalah 1 dan 35 atau 5 dan 7), maka:
- (3x – 1) (x + 35) = 0 (-1 dan 105 di jumlahkan menjadi 104 (salah))
- (3x – 7) (x + 5) = 0 (15 dan -7 di jumlahkan menjadi 8 (benar)
Jadi, (3x – 7) (x + 5) = 0
x = 7/3 | dan x = -5
- Jadi, salah satu akar-akar dari persamaan kuadrat 3x2 + 8x – 35 = 0 adalah 7/3
11) Topik: Persamaan Kuadrat
Subtopik: Jumlah, hasil kali, dan selisih akar persamaan kuadrat
Diketahui persamaan 2x2 = – 6x – 8 memiliki penyelesaian p dan q maka nilai dari 1/p2 + 1/q2 adalah ….
A. 1/8
B. 1/16
C. 8
D. 16
Jawaban: B
Pembahasan:
Karena p dan q merupakan penyelesaian, maka ia juga termasuk dari akar-akar persamaan kuadrat 2x2 + 6x + 8 = 0
Ingat kembali rumus:
p + q = – (b/a) = -3
pq = c/a = 4
Sehingga;
12) Topik: Persamaan Kuadrat
Subtopik: Menyusun persamaan kuadrat baru
Persamaan kuadrat 2x2 – 2x + a – 1 = 0 mempunyai dua akar real berlawanan tanda, maka nilai a yang memenuhi adalah ….
A. a > 1.5
B. a < 1.5
C. a > 3
D. a < 3
Jawaban: B
Pembahasan:
Dari persamaan kuadrat 2x2 – 2x + a – 1 = 0 di mana (a = 2, b = -2, c = a-1), maka:
Syarat akar real berlawanan tanda :
x1 . x2 < 1 c/a < 1
(a-1)/2 < 1
a-1 < 2
a < 3 … (1)
b2 – 4ac > 0
(-2)2 – 4 (2) (a-1) > 0
4 – 8a + 8 > 0
12 > 8a
a < 12/8
a < 1.5 … (2)
Dengan mengiris persamaan (1) dan (2), didapat bahwa a < 1.5
13) Topik: Fungsi Kuadrat
Subtopik: Grafik fungsi kuadrat
Berikut ini yang benar mengenai grafik fungsi f(x)=-3x2 – x – 5 adalah…
A. Grafik terbuka ke atas
B. Titik puncak kurva ada di kiri sumbu Y
C. Grafik memotong sumbu X di 2 titik
D. Titik potong dengan sumbu Y ada di atas sumbu X
Jawaban: B
Pembahasan:
a = -3, b = -1, c = -5
D = b2 – 4ac = 1 – 4 (- 3) (- 5) = 1 – 60 = -59
Dari sini, didapat bahwa:
a < 0, maka grafik terbuka ke bawah
a dan b tandanya sama, maka titik puncaknya di kiri sumbu Y
c < 0 maka titik potong dengan sumbu Y ada di bawah sumbu X
D < 0 maka grafik tidak memotong sumbu X
Jadi, opsi yang benar adalah opsi B.
14) Topik: Fungsi Kuadrat
Subtopik: Membuat fungsi kuadrat
Persamaan fungsi kuadrat yang melalui titik puncak (3, 4) dan titik lain di titik (2,3) adalah….
A. f(x) = x2 – 6x + 5
B. f(x) = -x2 + 6x – 5
C. f(x) = x2 – 4x – 5
D. f(x) = -x2 + 4x – 5
Jawaban: B
Pembahasan:
Persamaan grafik fungsi kuadrat yang melalui titik puncak (xp, yp) dan titik lain (x, y) yaitu :
y = a(x – xp)2 + yp
maka persamaan fungsi kuadrat yang melalui titik puncak (3,4) dan titik lain (2,3), yaitu :
3 = a(2 – 3)2 + 4
-1 = a(1) ↔ a = -1
Sehingga persamaan fungsi kuadrat tersebut adalah :
f(x) = -1(x – 3)2 + 4
f(x) = -1(x2 – 6x + 9) + 4
f(x) = -x2 + 6x – 5
15) Topik: Fungsi Kuadrat
Subtopik: Aplikasi fungsi kuadrat
Sebuah roket diluncurkan ke atas yang lintasannya membentuk grafik fungsi kuadrat dengan persamaan h(t) = t2 + 6t + 18. Tinggi maksimum yang dicapai roket tersebut adalah….
A. 8 meter
B. 9 meter
C. 10 meter
D. 11 meter
Jawaban: B
Pembahasan:
16) Topik: Transformasi Geometri
Subtopik: Translasi, refleksi
Sebuah titik A (2,3) ditranslasikan sejauh (a, b), lalu direfleksikan terhadap sumbu -X mempunyai bayangan di titik A’ (4, -4). Nilai dari a + b…
A. 1
B. 2
C. 3
D. 4
Jawaban: C
Pembahasan:
Ingat bahwa translasi sebuah titik, yaitu:
diperoleh:
2 + a = 4a = 4 – 2a = 2
dan
-(3 + b) = -43 + b = 4b = 4 – 3b = 1
Jadi, nilai
a + b
= 2 + 1
= 3
17) Topik: Transformasi Geometri
Subtopik: Rotasi
Titik (3, -7) dirotasi 90o searah jarum jam dengan pusat rotasi adalah (1, 5), maka bayangan titik tersebut adalah…
A. (-11, 4)
B. (-11, 1)
C. (-11, 3)
D. (11, -2)
Jawaban: C
Pembahasan:
Pertama, translasikan dulu pusatnya ke (0, 0) yaitu (-1, -5).
Titiknya harus ditranslasikan dengan arah yang sama, sehingga titik setelah di translasikan adalah ( 3 + (- 1), -7+ (- 5) ) = (2, -12)
Bayangan titik setelah di rotasi 90o searah jarum jam adalah (y, -x). Maka bayangan titiknya adalah (12, -2).
Setelah itu kembalikan ke titik asal (-12 + 1, -2 + 5) = (-11, 3)
18) Topik : Transformasi Geometri
Subtopik : Rotasi, Dilatasi
Titik A (a, b) dirotasikan berlawanan arah jarum jam dengan pusat O (0, 0) sejauh 90o dan dilanjutkan dengan dilatasi dengan pusat O (0, 0) dan faktor skala 2 yang menghasilkan bayangan A” (6, 4). Koordinat titik A adalah ….
A. (3, -2)
B. (-2, 3)
C. (2, -3)
D. (-3, 2)
Jawaban: C
Pembahasan:
Ingat bahwa rotasi terhadap pusat O(0, 0) berlawanan arah jarum jam sejauh 90o, yaitu:
A (x, y) R(O, 90°) → A’ (-y, x)
dan
Dilatasi terhadap pusat O(0, 0) dengan faktor skala k, yaitu:
A (x, y) D(O, k)→ A’ (kx, ky)
Maka:
A (a, b) R(O, 90°) → A’ (-b, a) D(O,2) →A”(-2b, 2a)
Bayangan yang diperoleh yaitu: A” (6, 4)
Sehingga:
(-2b, 2a) = (6, 4)
diperoleh:
-2b = 6 ↔ b = -3
dan
2a = 4 ↔ a = 2
Jadi, koordinat titik A adalah (2, -3)
19) Topik: Kongruen dan Kesebangunan
Subtopik: Kesebangunan dua bangun
Perhatikan gambar di bawah ini!
Gambar trapesium ABCD dengan PQ//AB. Jika diketahui DP = 5 cm, AP = 3 cm dan CQ = 7,5 cm, maka panjang QB = …
A. 4,5 cm
B. 7,5 cm
C. 9 cm
D. 12 cm
Jawaban: A
Pembahasan:
20) Topik: Kongruen dan Kesebangunan
Subtopik: Segitiga sebangun
Perhatikan gambar berikut!
Luas trapesium ABED adalah….
A. 1875/8 cm2
B. 1875/16 cm2
C. 1875/32 cm2
D. 1875/64 cm2
Jawaban: A
Pembahasan:
Dengan kesebangunan segitiga ABD dan segitiga DAE akan diperoleh:
Nah, dari kedua puluh soal untuk latihan Penilaian Akhir Semester (PAS) matematika kelas 9 ini, mana yang belum kamu kuasai? Coba, latihan lagi sebelum menyesal. Kalau kamu ingin memahami konsepnya lagi, tonton aja materinya di ruangbelajar!
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<h1 class="content-title">
Latihan Soal Penilaian Akhir Semester 2019 Matematika Kelas 9 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/kresnoadi" class="">Kresnoadi</a> </p>
<p class="content-info"><span>November 20, 2019 • </span> <span>8 minutes read</span></p>
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<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/latihan%20soal%20pas%20matematika%20kelas%209.png" alt="latihan soal pas matematika kelas 9" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p><em>Artikel ini berisi kumpulan soal latihan untuk Penilaian Akhir Semester (PAS) ganjil kelas 9 untuk pelajaran matematika</em></p>
<p><span id="more-7534"></span></p>
<p style="text-align: center;"><em>—</em></p>
<p style="text-align: justify;">Mendekati masa-masa ujian kayak gini, sebagai murid, pasti ada dong perasaan deg-degan. Walaupun udah belajar setiap hari, tapi tetap aja, yang namanya kata “ujian” bikin kita khawatir. Ujian sekolah, ujian SIM, ujian ujianan soire soire sampia pusiang. Apalagi kamu anak kelas 9 yang sebentar lagi bakalan naik jenjang ke SMA. Oleh karena itu, kita butuh yang namanya latihan. Paling tidak, dengan latihan kita bisa mengukur bagian mana dari materi yang udah kita kuasai atau belum. Setelahnya, tinggal kita tingkatin deh materi yang belum kita pahamin.</p>
<p style="text-align: justify;">Berikut adalah kumpulan soal latihan untuk Penilaian Akhir Semester (PAS) yang bisa kamu coba:</p>
<p style="text-align: justify;"> </p>
<p><span style="background-color: #ffff04;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika.png" alt="separator - latihan soal matematika" width="820" style="width: 820px; display: block; margin: 0px auto;"></span></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>1) Topik: Bilangan Berpangkat</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Pengertian bilangan berpangkat</strong></p>
<p style="text-align: justify;"> </p>
<p>Perkalian 3 X 3 X 3 X 3 X 3 jika dituliskan dalam bentuk pangkat menjadi….<br />A. 3<sup>-5</sup><br />B. 5<sup>-3</sup><br />C. 3<sup>5</sup><br />D. 5<sup>3</sup></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>Jawaban: C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan</strong></p>
<p style="text-align: justify;">Dalam bentuk pangkat, yaitu:</p>
<p style="text-align: justify;">3 X 3 X 3 X 3 X 3 = 3<sup>5</sup></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika.png" alt="separator - latihan soal matematika" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><strong>2) Topik: Bilangan Berpangkat – Eksponen</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Sifat bilangan berpangkat I</strong></p>
<p style="text-align: justify;"> </p>
<p>Sebuah kubus memiliki sisi 4k satuan. Perbandingan luas permukaan dan volume kubus tersebut adalah….</p>
<p>A. 1 : 2k<br />B. 2 : k<br />C. 2 : 3k<br />D. 3 : 2k</p>
<p> </p>
<p style="text-align: justify;"><strong>Jawaban: D</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Sisi kubus (s) = 4k</p>
<p style="text-align: justify;">Luas permukaan kubus (L) = 6s<sup>2</sup></p>
<p style="text-align: justify;">Volume Kubus (V) = s<sup>3</sup></p>
<p style="text-align: justify;">Maka,</p>
<div style="text-align: justify;">
<p>L= 6s<sup>2 </sup>= 6(4k)<sup>2</sup>= 6 (42k<sup>2</sup>)=96k2</p>
<p>V = s<sup>3 </sup>= (4k)<sup>3</sup>= 64k<sup>3</sup></p>
<p>LV = 96k<sup>2</sup>/64k<sup>3 </sup>= 3/2k</div>
<p style="text-align: justify;"> </p>
<p>Jadi, perbandingan luas permukaan dan volume kubus tersebut adalah 3 : 2k</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika.png" alt="separator - latihan soal matematika" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><strong>3) Topik: Bilangan Berpangkat – Eksponen</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Persamaan bilangan berpangkat I</strong></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><span style="background-color: transparent;">Nilai x yang memenuhi persamaan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/contoh%20soal%20bilangan%20berpangkat.jpg" alt="contoh soal bilangan berpangkat" width="150" style="width: 150px;"> </span>adalah …</p>
<p style="text-align: justify;"><span style="background-color: transparent;">A. 9<br /></span><span style="background-color: transparent;">B. 12<br /></span><span style="background-color: transparent;">C. 18<br /></span><span style="background-color: transparent;">D. 36</span></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>Jawaban: C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Ingat bahwa a<sup>m</sup> x a<sup>n</sup><strong> = </strong>am + n<strong>, </strong><strong>(</strong>a<sup>m</sup><strong>)</strong><sup>n</sup><strong> = </strong>a<sup>m x n</sup><strong>, </strong>a<sup>m</sup>/a<sup>n</sup> = a<sup>m-n </sup>maka</p>
<div style="text-align: justify;"> </div>
<div style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-550.png" alt="latihan soal bilangan berpangkat"></div>
<div style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-551.png"></div>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;">Jadi, nilai x yang memenuhi persamaan tersebut adalah 18.</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika.png" alt="separator - latihan soal matematika" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><strong>4) Topik: Bentuk Akar</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Penjumlahan dan pengurangan bentuk akar</strong></p>
<p style="text-align: justify;"> </p>
<p>Hasil dari 6√2 +4√8 – 3√32 <span style="text-align: justify; background-color: transparent;">adalah …</span></p>
<p><span style="text-align: justify; background-color: transparent;">A. 2√2<br />B. 3√2<br />C. 5√2<br />D. 7√2</span></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>Jawaban: A</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<div style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-552.png" width="300" style="width: 300px;"></div>
<p style="text-align: justify;"> </p>
<p>Jadi, hasil dari 6√2 +4√8 – 3√32 <span style="text-align: justify; background-color: transparent;">adalah 2√2</span></p>
<p><em>. <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika.png" alt="separator - latihan soal matematika" width="820" style="width: 820px; display: block; margin: 0px auto;"></em></p>
<p style="text-align: justify;"><strong>5) Topik: Bentuk Akar</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Pembagian bentuk akar</strong></p>
<p style="text-align: justify;"> </p>
<p>Hasil dari √1350 ÷ √3 adalah….</p>
<p>A. 5√2<br />B. 5√3<br />C. 15√2<br />D. 15√3</p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>Jawaban: C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;"> </p>
<div style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-553.png" width="175" style="width: 175px;"></div>
<p style="text-align: justify;"> </p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika.png" alt="separator - latihan soal matematika" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><strong>6) Topik: Bentuk Akar</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Rasional bentuk akar</strong></p>
<p style="text-align: justify;"> </p>
<p>Bentuk sederhana dari <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-557.png" width="75" style="width: 75px;"> adalah…</p>
<p>A. 2(√6+2√3+2√2-2)<br />B. 4(√6-2√3+2√2+2)<br />C. 2(√6-2√3-2√2+2)<br />D. 4(√6+2√3-2√2-2)</p>
<p> </p>
<p style="text-align: justify;"><strong>Jawaban: D</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-558.png" width="250" style="width: 250px;"></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika.png" alt="separator - latihan soal matematika" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><strong>7) Topik: Logaritma</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Sifat Logaritma</strong></p>
<p style="text-align: justify;"> </p>
<p>Diketahui <sup>2</sup>log a =1/2 dan <sup>3</sup>log b =1/3. Jika x = a<sup>2</sup> dan y = b<sup>3</sup>, maka <sup>x</sup>log y =…</p>
<p>A. <sup>3</sup>log12<br />B. <sup>2</sup>log 12<br />C. <sup>3</sup>log 2<br />D. <sup>2</sup>log 3</p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>Jawaban: D</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Ingat, Bentuk umum logaritma!</p>
<div style="text-align: justify;"><sup>a</sup>log b =x ↔a<sup>x</sup> =b di mana a,b>0</div>
<div style="text-align: justify;"> </div>
<p style="text-align: justify;">Maka:</p>
<p style="text-align: justify;"><sup>2</sup>log a =1/2↔2<sup>1/2 </sup>= a↔a = √2</p>
<p style="text-align: justify;">dan</p>
<p style="text-align: justify;"><sup> 3</sup>log b =1/3 ↔ 3<sup>1/3 </sup>= b ↔ b = <sup>3</sup>√3 </p>
<p style="text-align: justify;">Karena</p>
<div style="text-align: justify;">
<p> x = a<sup>2</sup></p>
</div>
<p style="text-align: justify;">x = <sup>2</sup>√2 = 2 </p>
<p style="text-align: justify;">dan</p>
<p style="text-align: justify;">y = b<sup>3</sup></p>
<p style="text-align: justify;">y = (<sup>3</sup>√3)<sup>3</sup> = 3</p>
<p style="text-align: justify;">Sehingga:</p>
<p style="text-align: justify;"><sup>x</sup>log y = <sup>2</sup>log 3</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><strong>Baca juga: <a href="/latihan-soal-pas-bahasa-indonesia-kelas-10-tahun-2019" rel="noopener" target="_blank">Latihan Penilaian Akhir Semester 2019 Bahasa Indonesia Kelas 10</a> </strong></p>
<p style="text-align: justify;"><strong>8) Topik: Logaritma</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Persamaan logaritma</strong></p>
<p style="text-align: justify;"> </p>
<p>Jika persamaan <sup>x</sup> log 3 + <sup>x</sup> log (3x-6) = 2 memiliki akar-akar x<sub>1</sub> dan x<sub>2</sub> dengan x<sub>1</sub> > x<sub>2</sub>, maka x<sub>1</sub> – x<sub>2</sub> adalah…</p>
<p> </p>
<p>A. 1<br />B. 2<br />C. 3<br />D. 4</p>
<p></p>
<p style="text-align: justify;"><strong>Jawaban: C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p> <sup>x</sup> log 3 + <sup>x</sup> log (3x-6) = 2</p>
<p> <sup>x</sup> log (3(3x-6)) = <sup>x</sup> log x<sup>2</sup></p>
<p> <sup>x</sup> log (9x-18) = <sup>x</sup> log x<sup>2</sup></p>
<p>9x -18 = x<sup>2</sup></p>
<p>x<sup>2 </sup>– 9x + 18 = 0</p>
<p>(x – 6) (x – 3) = 0</p>
<p>x<sub>1</sub> = 6 x<sub>2</sub> = 3</p>
<div style="text-align: justify;"> </div>
<p style="text-align: justify;">karena akar-akar x<sub>1</sub> dan x<sub>2</sub> dengan x<sub>1</sub> > x<sub>2</sub> maka</p>
<p style="text-align: justify;">x<sub>1</sub>-x<sub>2</sub></p>
<p style="text-align: justify;">= 6-3</p>
<p style="text-align: justify;">= 3</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><strong>9) Topik: Logaritma</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Persamaan logaritma</strong></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><span style="background-color: transparent;">Nilai x yang memenuhi persamaan (<sup>2</sup>log x)<sup>2 </sup>– 5 <sup>2</sup>log x +6=0 </span>adalah ….</p>
<p style="text-align: justify;">A. x = 4 atau x = 9<br /><span style="background-color: transparent;">B. x = 2 atau x = 8<br /></span><span style="background-color: transparent;">C. x = 4 atau x = 8<br /></span><span style="background-color: transparent;">D. x = 2 atau x = 9</span></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>Jawaban: C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">misalkan: <sup>2</sup>log x = y</p>
<p style="text-align: justify;">Persamaan tersebut dapat ditulis sebagai:</p>
<div style="text-align: justify;">
<p>y<sup>2</sup> – 5y + 6 = 0</p>
<p>(y – 2) (y – 3) = 0</p>
<p>y – 2 = 0 | y – 3 = 0</p>
<p>y = 2 | y = 3</p>
<p><sup>2</sup>log x = 2 | <sup>2</sup>log x = 3</p>
<p>x = 2<sup>2</sup> | x = 2<sup>3</sup></p>
<p>x = 4 | x = 8</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
</div>
<p style="text-align: justify;"><strong>10) Topik: Persamaan Kuadrat</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Faktorisasi pada persamaan kuadrat</strong></p>
<p style="text-align: justify;"> </p>
<p>Salah satu akar-akar dari persamaan kuadrat 3x<sup>2</sup> + 8x – 35 = 0 <span style="text-align: justify; background-color: transparent;">adalah ….</span></p>
<p>A. 5<br /><span style="background-color: transparent;">B. 7<br />C. 5/3</span><br />D. 7/3</p>
<p></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>Jawaban: D</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;">3x<sup>2</sup> + 8x – 35 = 0 (faktor dari 35 adalah 1 dan 35 atau 5 dan 7), maka:</p>
<ul style="text-align: justify;">
<li>(3x – 1) (x + 35) = 0 (-1 dan 105 di jumlahkan menjadi 104 (salah))</li>
<li>(3x – 7) (x + 5) = 0 (15 dan -7 di jumlahkan menjadi 8 (benar)</li>
</ul>
<p>Jadi, (3x – 7) (x + 5) = 0</p>
<p style="text-align: justify;">x = 7/3 | dan x = -5</p>
<div style="text-align: justify;"> </div>
<ul style="text-align: justify;">
<li>Jadi, salah satu akar-akar dari persamaan kuadrat 3x<sup>2</sup> + 8x – 35 = 0 adalah 7/3</li>
</ul>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><strong>11) Topik: Persamaan Kuadrat</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Jumlah, hasil kali, dan selisih akar persamaan kuadrat</strong></p>
<p> </p>
<p>Diketahui persamaan 2x<sup>2</sup> = – 6x – 8 memiliki penyelesaian <em>p</em> <em>dan</em> <em>q </em>maka nilai dari 1/p<sup>2</sup> + 1/q<sup>2</sup> adalah ….</p>
<p>A. 1/8<br />B. 1/16<br />C. 8<br />D. 16</p>
<p> </p>
<p> </p>
<p style="text-align: justify;"><strong>Jawaban: B</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Karena p dan q merupakan penyelesaian, maka ia juga termasuk dari akar-akar persamaan kuadrat 2x<sup>2</sup> + 6x + 8 = 0</p>
<p style="text-align: justify;"><strong>Ingat kembali rumus:</strong></p>
<p style="text-align: justify;">p + q = – (b/a) = -3</p>
<p style="text-align: justify;">pq = c/a = 4</p>
<p style="text-align: justify;">Sehingga;</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-562.png"></p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="820" style="width: 820px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;"><strong>12) Topik: Persamaan Kuadrat</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Menyusun persamaan kuadrat baru</strong></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><span style="background-color: transparent;">Persamaan kuadrat 2x<sup>2 </sup>– 2x + a – 1 = 0 </span>mempunyai dua akar real berlawanan tanda, maka nilai <em>a</em> yang memenuhi adalah ….</p>
<p style="text-align: justify;">A. a > 1.5<br />B. a < 1.5<br />C. a > 3<br />D. a < 3</p>
<p></p>
<p style="text-align: justify;"><strong>Jawaban: B</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Dari persamaan kuadrat <span style="background-color: transparent;">2x<sup>2 </sup>– 2x + a – 1 = 0 </span>di mana (a = 2, b = -2, c = a-1), maka:</p>
<p style="text-align: justify;">Syarat akar real berlawanan tanda :</p>
<ul style="text-align: justify;">
<li>x<sub>1</sub>x<sub>2</sub> < 1</li>
</ul>
<p>x<sub>1</sub> . x<sub>2</sub> < 1 c/a < 1</p>
<p>(a-1)/2 < 1</p>
<p>a-1 < 2</p>
<p>a < 3 … (1)</p>
<p style="text-align: justify;"> </p>
<ul style="text-align: justify;">
<li>D >0</li>
</ul>
<p>b<sup>2</sup> – 4ac > 0</p>
<p>(-2)<sup>2</sup> – 4 (2) (a-1) > 0</p>
<p>4 – 8a + 8 > 0</p>
<p>12 > 8a</p>
<p>a < 12/8</p>
<p>a < 1.5 … (2)</p>
<p>Dengan mengiris persamaan (1) dan (2), didapat bahwa a < 1.5</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="820" style="width: 820px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;"><strong>13) Topik: Fungsi Kuadrat</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Grafik fungsi kuadrat</strong></p>
<p> </p>
<p>Berikut ini yang benar mengenai grafik fungsi f(x)=-3x<sup>2 </sup>– x – 5 adalah…</p>
<p><span style="background-color: transparent;">A. Grafik terbuka ke atas<br /></span><span style="background-color: transparent;">B. Titik puncak kurva ada di kiri sumbu Y<br /></span><span style="background-color: transparent;">C. Grafik memotong sumbu X di 2 titik<br /></span><span style="background-color: transparent;">D. Titik potong dengan sumbu Y ada di atas sumbu X</span></p>
<p> </p>
<p> </p>
<p style="text-align: justify;"><strong>Jawaban: B</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;"> </p>
<div style="text-align: justify;">
<p>a = -3, b = -1, c = -5</p>
<p><span style="background-color: transparent;">D = b<sup>2</sup> – 4ac = 1 – 4 (- 3) (- 5) = 1 – 60 = -59</span></p>
</div>
<p style="text-align: justify;">Dari sini, didapat bahwa:</p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;">a < 0, maka grafik terbuka ke bawah<br />a dan b tandanya sama, maka titik puncaknya di kiri sumbu Y<br />c < 0 maka titik potong dengan sumbu Y ada di bawah sumbu X<br />D < 0 maka grafik tidak memotong sumbu X</p>
<p style="text-align: justify;">Jadi, opsi yang benar adalah opsi B.</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><strong>14) Topik: Fungsi Kuadrat</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Membuat fungsi kuadrat</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">Persamaan fungsi kuadrat yang melalui titik puncak (3, 4) dan titik lain di titik (2,3) adalah….</span></p>
<p style="text-align: justify;"><span style="background-color: transparent;">A. </span><span style="background-color: transparent;">f(x) = x<sup>2</sup> – 6x + 5<br />B. </span><span style="background-color: transparent;">f(x) = -x<sup>2</sup> + 6x – 5<br /></span><span style="background-color: transparent;">C. f(x) = x<sup>2</sup> – 4x – 5<br /></span><span style="background-color: transparent;">D. f(x) = -x<sup>2</sup> + 4x – 5</span></p>
<p style="text-align: justify;"><strong>Jawaban: B</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p>Persamaan grafik fungsi kuadrat yang melalui titik puncak (x<sub>p</sub>, y<sub>p</sub>) dan titik lain (x, y) yaitu :</p>
<p>y = a(x – x<sub>p</sub>)<sup>2</sup> + y<sub>p</sub></p>
<p>maka persamaan fungsi kuadrat yang melalui titik puncak (3,4) dan titik lain (2,3), yaitu :</p>
<p>3 = a(2 – 3)<sup>2</sup> + 4</p>
<p>-1 = a(1) ↔ a = -1</p>
<p>Sehingga persamaan fungsi kuadrat tersebut adalah :</p>
<p>f(x) = -1(x – 3)<sup>2</sup> + 4</p>
<p>f(x) = -1(x<sup>2</sup> – 6x + 9) + 4</p>
<p style="text-align: justify;">f(x) = -x<sup>2</sup> + 6x – 5</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="820" style="width: 820px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;"><strong>15) Topik: Fungsi Kuadrat</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Aplikasi fungsi kuadrat</strong></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><span style="background-color: transparent;">Sebuah roket diluncurkan ke atas yang lintasannya membentuk grafik fungsi kuadrat dengan persamaan h(t) = t<sup>2</sup> + 6t + 18</span>. Tinggi maksimum yang dicapai roket tersebut adalah….</p>
<p style="text-align: justify;"><span style="background-color: transparent;">A. 8 meter<br /></span><span style="background-color: transparent;">B. 9 meter<br /></span><span style="background-color: transparent;">C. 10 meter<br /></span><span style="background-color: transparent;">D. </span><span style="background-color: transparent;">11 meter</span></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>Jawaban: B</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-563.png"></p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="820" style="width: 820px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;"><strong>16) Topik: Transformasi Geometri</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Translasi, refleksi</strong></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><span style="background-color: transparent;">Sebuah titik <em>A</em> (2,3) </span>ditranslasikan sejauh (a, b), lalu direfleksikan terhadap sumbu -X mempunyai bayangan di titik A’ (4, -4). Nilai dari a + b…</p>
<p style="text-align: justify;"><span style="background-color: transparent;">A. 1<br /></span><span style="background-color: transparent;">B. 2<br /></span><span style="background-color: transparent;">C. 3<br /></span><span style="background-color: transparent;">D. 4</span></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>Jawaban: C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Ingat bahwa translasi sebuah titik, yaitu:</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-564.png" width="375" style="width: 375px;"></p>
<p style="text-align: justify;">diperoleh:</p>
<p style="text-align: justify;">2 + a = 4a = 4 – 2a = 2</p>
<p style="text-align: justify;">dan</p>
<p style="text-align: justify;">-(3 + b) = -43 + b = 4b = 4 – 3b = 1</p>
<p style="text-align: justify;">Jadi, nilai</p>
<p style="text-align: justify;">a + b</p>
<div style="text-align: justify;">= 2 + 1</div>
<div style="text-align: justify;">= 3</div>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><strong>17) Topik: Transformasi Geometri</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Rotasi</strong></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><span style="background-color: transparent;">Titik (3, -7) </span>dirotasi 90<sup>o </sup>searah jarum jam dengan pusat rotasi adalah (1, 5), maka bayangan titik tersebut adalah…</p>
<p style="text-align: justify;">A. <span style="background-color: transparent;">(-11, 4)<br /></span><span style="background-color: transparent;">B. (-11, 1)<br /></span><span style="background-color: transparent;">C. (-11, 3)<br /></span>D. (11, -2)</p>
<p></p>
<p style="text-align: justify;"><strong>Jawaban: C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Pertama, translasikan dulu pusatnya ke (0, 0) yaitu (-1, -5).</p>
<p style="text-align: justify;">Titiknya harus ditranslasikan dengan arah yang sama, sehingga titik setelah di translasikan adalah ( 3 + (- 1), -7+ (- 5) ) = <strong>(2, -12)</strong></p>
<p style="text-align: justify;">Bayangan titik setelah di rotasi 90<sup>o </sup>searah jarum jam adalah (y, -x). Maka bayangan titiknya adalah <strong>(12, -2).</strong></p>
<p style="text-align: justify;">Setelah itu kembalikan ke titik asal (-12 + 1, -2 + 5) = <strong>(-11, 3)</strong></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="3418" style="width: 3418px;"></p>
<p style="text-align: justify;"><strong>18) Topik : Transformasi Geometri</strong></p>
<p style="text-align: justify;"><strong>Subtopik : Rotasi, Dilatasi</strong></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><span style="background-color: transparent;">Titik A (a, b) dirotasikan berlawanan arah jarum jam dengan pusat O (0, 0) </span>sejauh 90<sup>o</sup> dan dilanjutkan dengan dilatasi dengan pusat O (0, 0) dan faktor skala 2 yang menghasilkan bayangan A” (6, 4). Koordinat titik A adalah ….</p>
<p style="text-align: justify;">A. <span style="background-color: transparent;">(3, -2)<br /></span><span style="background-color: transparent;">B. (-2, 3)<br /></span><span style="background-color: transparent;">C. (2, -3)<br /></span>D. (-3, 2)</p>
<p></p>
<p style="text-align: justify;"><strong>Jawaban: C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Ingat bahwa rotasi terhadap pusat O(0, 0) berlawanan arah jarum jam sejauh 90<sup>o</sup>, yaitu:</p>
<p style="text-align: justify;">A (x, y) R(O, 90°) → A’ (-y, x)</p>
<p style="text-align: justify;">dan</p>
<p style="text-align: justify;">Dilatasi terhadap pusat O(0, 0) dengan faktor skala k, yaitu:</p>
<p style="text-align: justify;">A (x, y) D(O, k)→ A’ (kx, ky)</p>
<p style="text-align: justify;">Maka:</p>
<p style="text-align: justify;">A (a, b) R(O, 90°) → A’ (-b, a) D(O,2) →A”(-2b, 2a)</p>
<p style="text-align: justify;">Bayangan yang diperoleh yaitu: A” (6, 4)</p>
<p style="text-align: justify;">Sehingga:</p>
<p style="text-align: justify;">(-2b, 2a) = (6, 4)</p>
<p style="text-align: justify;">diperoleh:</p>
<p style="text-align: justify;">-2b = 6 ↔ b = -3</p>
<p style="text-align: justify;">dan</p>
<p style="text-align: justify;">2a = 4 ↔ a = 2</p>
<p style="text-align: justify;">Jadi, koordinat titik A adalah (2, -3)</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><strong>19) Topik: Kongruen dan Kesebangunan</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Kesebangunan dua bangun</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">Perhatikan gambar di bawah ini!</span></p>
<p style="text-align: justify;"> </p>
<div style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Paket%202%20PAS%20Ganjil%20Matematika%20SMP%20Kelas%20IX-1.jpeg" alt="12"></div>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;">Gambar trapesium ABCD dengan PQ//AB. Jika diketahui DP = 5 cm, AP = 3 cm dan CQ = 7,5 cm, maka panjang QB = …</p>
<p style="text-align: justify;"><span style="background-color: transparent;">A. 4,5 cm<br /></span><span style="background-color: transparent;">B. 7,5 cm<br /></span><span style="background-color: transparent;">C. 9 cm<br /></span>D. 12 cm</p>
<p></p>
<p style="text-align: justify;"><strong>Jawaban: A</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-565.png"></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/separator%20-%20latihan%20soal%20matematika-1.png" alt="separator - latihan soal matematika-1" width="820" style="width: 820px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><strong>20) Topik: Kongruen dan Kesebangunan</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Segitiga sebangun</strong></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><span style="background-color: transparent;">Perhatikan gambar berikut!</span></p>
<p style="text-align: justify;"> </p>
<div style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Paket%202%20PAS%20Ganjil%20Matematika%20SMP%20Kelas%20IX-1.png" alt=""></div>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;">Luas trapesium ABED adalah….</p>
<p style="text-align: justify;"><span style="background-color: transparent;">A. 1875/8 cm<sup>2</sup><br />B. 1875/16 cm<sup>2</sup><br />C. 1875/32 cm<sup>2</sup><br />D. 1875/64 cm<sup>2</sup></span></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>Jawaban: A</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;"> </p>
<div style="text-align: justify;"><img decoding="async" src="https://docs.google.com/a/ruangguru.com/drawings/d/s0znC7YxfYSphqCuEC13jmw/image?parent=11kjcdLdl1hQIKj-ZnboC1mhWIJRGDnd4PLAIuTxbUYU&rev=1&h=171&w=335&ac=1" alt=""></div>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;">Dengan kesebangunan segitiga ABD dan segitiga DAE akan diperoleh:</p>
<div style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-566.png"></div>
<p style="text-align: justify;">Nah, dari kedua puluh soal untuk latihan Penilaian Akhir Semester (PAS) matematika kelas 9 ini, mana yang belum kamu kuasai? Coba, latihan lagi sebelum menyesal. Kalau kamu ingin memahami konsepnya lagi, tonton aja materinya di <a href="https://ruangguru.onelink.me/blPk/eaff0eb9" rel="noopener" target="_blank"><strong>ruangbelajar!</strong></a></p>
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<li><a href="https://www.ruangguru.com/cicilan">Cicilan Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/promo">Promo Ruangguru</a></li>
<li><a href="https://ticketing.ruangguru.com/help?request_type_id=459" target="_blank">Vulnerability Report</a></li>
<li><a href="https://www.ruangguru.com/bantuan#layanan">Layanan Pengaduan</a></li>
<li><a href="https://www.ruangguru.com/terms-conditions">Syarat & Ketentuan</a></li>
<li><a href="https://www.ruangguru.com/privacy-policy">Kebijakan Privasi</a></li>
<li><a href="https://www.ruangguru.com/about-us">Tentang Kami</a></li>
<li><a href="https://www.ruangguru.com/contact-us">Kontak Kami</a></li>
<li><a href="https://www.ruangguru.com/press">Press Kit</a></li>
<li><a href="https://www.ruangguru.com/bantuan">Bantuan</a></li>
<li><a href="https://career.ruangguru.com/">Karier</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Lainnya</p>
<ul type="none">
<li><a href="https://www.brainacademy.id/" target="_blank">Brain Academy</a></li>
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<li><a href="https://skillacademy.com/" target="_blank">Skill Academy</a></li>
<li><a href="https://www.ruangkerja.id/" target="_blank">Ruangkerja</a></li>
<li><a href="https://www.schoters.com/id/" target="_blank">Schoters</a></li>
<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
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<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
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</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
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</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
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</picture>
</a>
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<picture>
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</picture>
</a>
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</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>