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Diffstat (limited to 'lessons/matematika')
| -rw-r--r-- | lessons/matematika/index.html | 2 | ||||
| -rw-r--r-- | lessons/matematika/pangkat-akar/akar.html | 112 | ||||
| -rw-r--r-- | lessons/matematika/pangkat-akar/latihan.html | 152 | ||||
| -rw-r--r-- | lessons/matematika/pangkat-akar/pangkat.html | 34 |
4 files changed, 296 insertions, 4 deletions
diff --git a/lessons/matematika/index.html b/lessons/matematika/index.html index 5fcdabc..7033a61 100644 --- a/lessons/matematika/index.html +++ b/lessons/matematika/index.html @@ -42,6 +42,8 @@ <section> <h1 id="bab1">Chapter 1 - Bentuk Pangkat dan Akar</h1> <p><a href="pangkat-akar/pangkat.html" class="link">Materi 1: Exponent</a></p> + <p><a href="pangkat-akar/akar.html" class="link">Materi 2: Root</a></p> + <p><a href="pangkat-akar/latihan.html" class="link">Latihan 1</a></p> </section> </div> diff --git a/lessons/matematika/pangkat-akar/akar.html b/lessons/matematika/pangkat-akar/akar.html new file mode 100644 index 0000000..b519d5e --- /dev/null +++ b/lessons/matematika/pangkat-akar/akar.html @@ -0,0 +1,112 @@ +<!DOCTYPE html> +<html lang="en"> + +<head> + <meta charset="UTF-8"> + <meta http-equiv="X-UA-Compatible" content="IE=edge"> + <meta name="viewport" content="width=device-width, initial-scale=1.0"> + <link rel="stylesheet" href="/style.css"> + <link rel="icon" href="/assets/images/master.png"> + <title>Al Azhar 9th Grade Lesson Notes</title> + <link rel="apple-touch-icon" sizes="180x180" href="/apple-touch-icon.png"> + <link rel="icon" type="image/png" sizes="32x32" href="/favicon-32x32.png"> + <link rel="icon" type="image/png" sizes="16x16" href="/favicon-16x16.png"> + <link rel="manifest" href="/site.webmanifest"> + <script src="https://kit.fontawesome.com/d279a1f519.js" crossorigin="anonymous"></script> +</head> + +<body> + <a class="fixed-top-btn menu-btn" onclick="toggleNav()" href="javascript:void(0)"><i + class="fa-solid fa-bars"></i></a> + <a href="../" class="fixed-top-btn back-btn" id="backbtn"><i class="fa-solid fa-chevron-left"></i></a> + <div id="console"></div> + <div id="sidebar"> + <a href="/index.html"> + <img src="/assets/images/master.png" alt="" class="sidebar-logo"> + </a> + <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> + <hr class="divider"> + <a href="/about/author.html" class="sidebar-link link">About the Author</a> + <a href="/about/school.html" class="sidebar-link link">About School</a> + <a href="/lessons" class="sidebar-link link">Lessons</a> + + <hr class="divider"> + <div id="toc"> + <h4>Table of Contents</h4> + </div> + </div> + + <div class="banner-container" id="banner"> + <div class="banner-bg" id="img-supplies"></div> + <h1 class="banner-text" id="banner-txt">Bentuk Pangkat dan Akar: Root</h1> + </div> + + <div id="main"> + <section> + <h1 id="definition">Definition</h1> + Root is the inverse of exponent. For example;<br> + <ul> + <li>4<sup>2</sup> = 16, <b>so <span class="root">16</span> = 4</b></li> + <li>5<sup>2</sup> = 25, <b>so <span class="root">25</span> = 5</b></li> + <li>10<sup>2</sup> = 100, <b>so <span class="root">100</span> = 10</b></li> + </ul> + + <h1 id="simplification">Simplifying Square Roots</h1> + You can simplify a root by factoring the root number another number that is rational. Or in other words, divide the root number by the perfect squares. For example; + <ul> + <li> + <strong>Simplify <span class="root">60</span></strong><br> + <span class="root">60</span> = <span class="root">4 × 15</span> = 2<span class="root">15</span><br> + </li> + <li> + <strong>Simplify <span class="root">48</span></strong><br> + <span class="root">48</span> = <span class="root">16 × 3</span> = 4<span class="root">3</span><br> + </li> + <li> + <strong>Simplify <span class="root">125</span></strong><br> + <span class="root">125</span> = <span class="root">25 × 5</span> = 5<span class="root">5</span><br> + </li> + </ul> + + <h1 id="root-operations">Root Operations</h1> + <h2 id="root-operations--addition">Addition</h2> + Roots with coefficient can be added with another coefficient that have the same roots. <br> + <strong>a<span class="root">c</span> + b<span class="root">c</span> = (a + b)<span class="root">c</span></strong> + <ul> + <li>3<span class="root">2</span> + 4<span class="root">2</span> = (3 + 4)<span class="root">2</span> = <strong>7<span class="root">2</span></strong></li> + <li><span class="root">5</span> + 3<span class="root">5</span> = (1 + 3)<span class="root">5</span> = <strong>4<span class="root">5</span></strong></li> + </ul> + <h2 id="root-operations--subtraction">Subtraction</h2> + Roots with coefficient can be subtracted with another coefficient that have the same roots. <br> + <strong>a<span class="root">c</span> - b<span class="root">c</span> = (a - b)<span class="root">c</span></strong> + <ul> + <li>7<span class="root">3</span> - 4<span class="root">3</span> = (7 - 4)<span class="root">3</span> = <strong>3<span class="root">2</span></strong></li> + <li>10<span class="root">6</span> - 5<span class="root">6</span> = (10 - 5)<span class="root">6</span> = <strong>5<span class="root">6</span></strong></li> + </ul> + <h2 id="root-operations--multiplication">Multiplication</h2> + Roots can be multiplied with any other roots. If the root is the same as the other multiplied root, the root can be deleted (if you want to be faster). <br> + <strong>a<span class="root">c</span> × b<span class="root">d</span> = (a × b)<span class="root">c × d</span></strong> + <ul> + <li><span class="root">2</span> × <span class="root">5</span> = <strong><span class="root">10</span></strong></li> + <li>3<span class="root">2</span> × 4<span class="root">3</span> = (3 × 4)<span class="root">2 × 3</span> = <strong>12<span class="root">6</span></strong></li> + <li>2<span class="root">5</span> × 3<span class="root">5</span> = (2 × 3)(5) = 6(5) = <strong>30</strong></li> + </ul> + <h2 id="root-operations--division">Division</h2> + Roots can be divided with any other roots. <br> + <strong>a<span class="root">c</span> ÷ b<span class="root">d</span> = (a ÷ b)<span class="root">c ÷ d</span></strong> + <ul> + <li> + <span class="root">12</span> ÷ <span class="root">3</span> = <strong><span class="root">2</span></strong> + </li> + <li> + 8<span class="root">6</span> ÷ 4<span class="root">3</span> = (8 ÷ 4)<span class="root">6 ÷ 3</span> = <strong>2<span class="root">2</span></strong> + </li> + </ul> + </section> + </div> + + <script src="/scripts/toc.js"></script> + <script src="/scripts/sidebar.js"></script> +</body> + +</html>
\ No newline at end of file diff --git a/lessons/matematika/pangkat-akar/latihan.html b/lessons/matematika/pangkat-akar/latihan.html new file mode 100644 index 0000000..4aa75e7 --- /dev/null +++ b/lessons/matematika/pangkat-akar/latihan.html @@ -0,0 +1,152 @@ +<!DOCTYPE html> +<html lang="en"> + +<head> + <meta charset="UTF-8"> + <meta http-equiv="X-UA-Compatible" content="IE=edge"> + <meta name="viewport" content="width=device-width, initial-scale=1.0"> + <link rel="stylesheet" href="/style.css"> + <link rel="icon" href="/assets/images/master.png"> + <title>Al Azhar 9th Grade Lesson Notes</title> + <link rel="apple-touch-icon" sizes="180x180" href="/apple-touch-icon.png"> + <link rel="icon" type="image/png" sizes="32x32" href="/favicon-32x32.png"> + <link rel="icon" type="image/png" sizes="16x16" href="/favicon-16x16.png"> + <link rel="manifest" href="/site.webmanifest"> + <script src="https://kit.fontawesome.com/d279a1f519.js" crossorigin="anonymous"></script> +</head> + +<body> + <a class="fixed-top-btn menu-btn" onclick="toggleNav()" href="javascript:void(0)"><i + class="fa-solid fa-bars"></i></a> + <a href="../" class="fixed-top-btn back-btn" id="backbtn"><i class="fa-solid fa-chevron-left"></i></a> + <div id="console"></div> + <div id="sidebar"> + <a href="/index.html"> + <img src="/assets/images/master.png" alt="" class="sidebar-logo"> + </a> + <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> + <hr class="divider"> + <a href="/about/author.html" class="sidebar-link link">About the Author</a> + <a href="/about/school.html" class="sidebar-link link">About School</a> + <a href="/lessons" class="sidebar-link link">Lessons</a> + + <hr class="divider"> + <div id="toc"> + <h4>Table of Contents</h4> + </div> + </div> + + <div class="banner-container" id="banner"> + <div class="banner-bg" id="img-supplies"></div> + <h1 class="banner-text" id="banner-txt">Bentuk Pangkat dan Akar: Latihan</h1> + </div> + + <div id="main"> + <section> + <h1 id="questions">Pertanyaan</h1> + <ol> + <h2 id="questions--pangkat">Pangkat</h1> + <li style="margin-top: 10px;">8p<sup>2</sup>q × 2pq<sup>3</sup></li> + <li style="margin-top: 10px;">64<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>2</sub></span></sup> + 81<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>3</sub></span></sup></li> + <li style="margin-top: 10px;">2<span class="root">5</span> + 3<span class="root">20</span> - 4<span class="root">5</span></li> + + <h2 id="questions--rasional">Merasionalkan Akar</h2> + <li style="margin-top: 10px;"><span class="frac"><sup>4</sup><span>⁄</span><sub><span class="root">5</span></sub></span></li> + <li style="margin-top: 10px;"><span class="frac"><sup>3<span class="root">5</span></sup><span>⁄</span><sub>2<span class="root">3</span></sup></sub></span></li> + <li style="margin-top: 10px;"><span class="frac"><sup>5</sup><span>⁄</span><sub><span class="root">3</span> - <span class="root">2</span></sub></span></li> + <li style="margin-top: 10px;"><span class="frac"><sup><span class="root">5</span> - <span class="root">7</span></sup><span>⁄</span><sub><span class="root">5</span> - <span class="root">2</span></sub></span></li> + + <h2 id="question--operasi-pangkat">Operasi Pangkat</h2> + <li style="margin-top: 10px;">(8p<sup>2</sup>3)<sup>3</sup> ÷ 2pq</li> + <li style="margin-top: 10px;"><span class="frac"><sup>(a<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>3</sub></span></sup>b<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>3</sub></span></sup>)<sup>6</sup></sup><span>⁄</span><sub>(a<sup><span class="frac"><sup>2</sup><span>⁄</span><sub>3</sub></span></sup>b<sup><span class="frac"><sup>4</sup><span>⁄</span><sub>3</sub></span></sup>)<sup>9</sup></sup></sub></span></li> + + <h2 id="question--persamaan-pangkat">Persamaan Pangkat</h2> + <li style="margin-top: 10px;">2<sup>x + 8</sup> = 64</li> + <li style="margin-top: 10px;">16<sup>2x + 3</sup> = 32</li> + </ol> + <h1 id="jawaban">Jawaban</h1> + <ol> + <li style="margin-top: 10px;">16p<sup>3</sup>q<sup>4</sup></li> + <li style="margin-top: 10px;"> + 64<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>2</sub></span></sup> + 81<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>3</sub></span></sup><br> + = <span class="root">64</span> + <sup>3</sup><span class="root">81</span><br> + = 8 + <sup>3</sup><span class="root">81</span> + </li> + <li style="margin-top: 10px;"> + 2<span class="root">5</span> + 3<span class="root">20</span> - 4<span class="root">5</span><br> + = 6<span class="root">5</span> + 3<span class="root">20</span><br> + = 6<span class="root">5</span> + 3<span class="root">4 × 5</span><br> + = 6<span class="root">5</span> + 3<span class="root">2<sup>2</sup> × 5</span><br> + = 6<span class="root">5</span> + 3 × 2<span class="root">5</span><br> + = 6<span class="root">5</span> + 6<span class="root">5</span><br> + = <strong>12<span class="root">5</span></strong><br> + </li> + <li style="margin-top: 10px;"> + <span class="frac"><sup>4</sup><span>⁄</span><sub><span class="root">5</span></sub></span><br> + = <span class="frac"><sup>4</sup><span>⁄</span><sub><span class="root">5</span></sub></span> × <span class="frac"><sup><span class="root">5</span></sup><span>⁄</span><sub><span class="root">5</span></sub></span> = <strong><span class="frac"><sup>4<span class="root">5</span></sup><span>⁄</span><sub>5</sub></span></strong> + </li> + <li style="margin-top: 10px;"> + <span class="frac"><sup>3<span class="root">5</span></sup><span>⁄</span><sub>2<span class="root">3</span></sup></sub></span><br> + = <span class="frac"><sup>3<span class="root">5</span></sup><span>⁄</span><sub>2<span class="root">3</span></sup></sub></span> × <span class="frac"><sup><span class="root">3</span></sup><span>⁄</span><sub><span class="root">3</span></sup></sub></span><br> + = <span class="frac"><sup><span style="text-decoration: line-through;">3</span><span class="root">15</span></sup><span>⁄</span><sub>2 × <span style="text-decoration: line-through;">3</span></sup></sub></span><br> + = <strong><span class="frac"><sup><span class="root">15</span></sup><span>⁄</span><sub>2</sup></sub></span></strong> + </li> + <li style="margin-top: 10px;"> + <span class="frac"><sup>5</sup><span>⁄</span><sub><span class="root">3</span> - <span class="root">2</span></sub></span><br> + = <span class="frac"><sup>5</sup><span>⁄</span><sub><span class="root">3</span> - <span class="root">2</span></sub></span> × <span class="frac"><sup><span class="root">3</span> + <span class="root">2</span></sup><span>⁄</span><sub><span class="root">3</span> + <span class="root">2</span></sub></span><br> + = <span class="frac"><sup>5(<span class="root">3</span> + <span class="root">2</span>)</sup><span>⁄</span><sub>(<span class="root">3</span>)<sup>2</sup> - (<span class="root">2</span>)<sup>2</sup></sub></span><br> + = <span class="frac"><sup>5(<span class="root">3</span> + <span class="root">2</span>)</sup><span>⁄</span><sub>3 - 2</sub></span> = <span class="frac"><sup>5(<span class="root">3</span> + <span class="root">2</span>)</sup><span>⁄</span><sub>1</sub></span><br> + = <strong>5(<span class="root">3</span> + <span class="root">2</span>)</strong> + </li> + <li style="margin-top: 10px;"> + <span class="frac"><sup><span class="root">5</span> - <span class="root">7</span></sup><span>⁄</span><sub><span class="root">5</span> - <span class="root">2</span></sub></span><br> + = <span class="frac"><sup><span class="root">5</span> - <span class="root">7</span></sup><span>⁄</span><sub><span class="root">5</span> - <span class="root">2</span></sub></span> × <span class="frac"><sup><span class="root">5</span> + <span class="root">2</span></sup><span>⁄</span><sub><span class="root">5</span> + <span class="root">2</span></sub></span><br> + = <span class="frac"><sup>(<span class="root">5</span> - <span class="root">7</span>) × (<span class="root">5</span> + <span class="root">2</span>)</sup><span>⁄</span><sub>(<span class="root">5</span>)<sup>2</sup> - (<span class="root">2</span>)<sup>2</sup></sub></span><br> + = <span class="frac"><sup>5 + <span class="root">10</span> - <span class="root">35</span> - <span class="root">14</span></sup><span>⁄</span><sub>5 - 2</sub></span> = <strong><span class="frac"><sup>5 + <span class="root">10</span> - <span class="root">35</span> - <span class="root">14</span></sup><span>⁄</span><sub>3</sub></span></strong> + </li> + <li style="margin-top: 10px;"> + (8p<sup>2</sup>3)<sup>3</sup> ÷ 2pq <br> + = (24p<sup>2</sup>)<sup>3</sup> ÷ 2pq <br> + = 24<sup>3</sup> p<sup>6</sup> ÷ 2pq <br> + = <strong>6912p<sup>5</sup> ÷ q</strong> + </li> + <li style="margin-top: 10px;"> + = <span class="frac"><sup>(a<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>3</sub></span></sup>b<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>3</sub></span></sup>)<sup>6</sup></sup><span>⁄</span><sub>(a<sup><span class="frac"><sup>2</sup><span>⁄</span><sub>3</sub></span></sup>b<sup><span class="frac"><sup>4</sup><span>⁄</span><sub>3</sub></span></sup>)<sup>9</sup></sup></sub></span><br> + = <span class="frac"> + <sup>(a<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>3</sub></span></sup>)<sup>6</sup> (b<sup><span class="frac"><sup>1</sup><span>⁄</span><sub>3</sub></span></sup>)<sup>6</sup></sup> + <span>⁄</span> + <sub>(a<sup><span class="frac"><sup>2</sup><span>⁄</span><sub>3</sub></span></sup>)<sup>9</sup> (b<sup><span class="frac"><sup>4</sup><span>⁄</span><sub>3</sub></span></sup>)<sup>9</sup></sub> + </span><br> + = <span class="frac"> + <sup>a<sup>2</sup> b<sup>2</sup></sup> + <span>⁄</span> + <sub>a<sup>6</sup> ba<sup>12</sup></sub> + </span><br> + = <strong>a<sup>-4</sup> b<sup>-10</sup></strong> + </li> + <li style="margin-top: 10px;"> + 2<sup>x + 8</sup> = 64 <br> + = <span style="text-decoration: line-through;">2</span><sup>x + 8</sup> = <span style="text-decoration: line-through;">2</span><sup>6</sup><br> + = x + 8 = 6 <br> + = x = 6 - 8 <br> + = <strong>x = -2</strong> + </li> + <li style="margin-top: 10px;"> + 16<sup>2x + 3</sup> = 32 <br> + = (2<sup>4</sup>)<sup>2x + 3</sup> = 2<sup>6</sup><br> + = <span style="text-decoration: line-through;">2</span><sup>8x + 12</sup> = <span style="text-decoration: line-through;">2</span><sup>6</sup> <br> + = 8x + 12 = 6 <br> + = 8x = 6 - 12 <br> + = 8x = 6 <br> + = x = <span class="frac"><sup>-6</sup><span>⁄</span><sub>8</sub></span><br> + = <strong>x = -<span class="frac"><sup>3</sup><span>⁄</span><sub>4</sub></span></strong> + </li> + </ol> + </section> + </div> + + <script src="/scripts/toc.js"></script> + <script src="/scripts/sidebar.js"></script> +</body> + +</html>
\ No newline at end of file diff --git a/lessons/matematika/pangkat-akar/pangkat.html b/lessons/matematika/pangkat-akar/pangkat.html index f3af1a2..efba6e1 100644 --- a/lessons/matematika/pangkat-akar/pangkat.html +++ b/lessons/matematika/pangkat-akar/pangkat.html @@ -53,10 +53,20 @@ <h1 id="exponent-operations">Exponent Operations</h1> <h2 id="exponent-operations--multiplication">Multiplication</h2> a<sup>x</sup> × b<sup>y</sup> = (a × b)<sup>x + y</sup> + <ul> + <li>10<sup>4</sup> × 2<sup>2</sup> = (10 × 2)<sup>4 + 2</sup> = <strong>20<sup>6</sup></strong></li> + </ul> <h2 id="exponent-operations--division">Division</h2> a<sup>x</sup> ÷ b<sup>y</sup> = (a ÷ b)<sup>x - y</sup> + <ul> + <li>10<sup>3</sup> ÷ 2<sup>4</sup> = (10 ÷ 2)<sup>4 - 2</sup> = <strong>5<sup>2</sup></strong></li> + </ul> <h2 id="exponent-operations--exponent">Exponent</h2> - a<sup>x<sup>y</sup></sup> = a<sup>x × y</sup> + (a<sup>x</sup>)<sup>y</sup> = a<sup>x × y</sup> + <ul> + <li>(2<sup>2</sup>)<sup>3</sup> = 2<sup>2 × 3</sup> <strong>= 2<sup>6</sup> = 64</li> + + </ul> <h1 id="zero-exponent">Zero Exponent</h1> <p>a<sup>0</sup> = 1</p> @@ -79,14 +89,30 @@ <h1 id="fractional-exponent">Fractional Exponent</h1> <img src="/assets/images/math/fractional_exponent.svg" alt=""> <p>x <sup><span class="frac"><sup>y</sup><span>⁄</span><sub>z</sub></span></sup> = - <sup>z</sup><span>√(x</span><sup style="font-size: small;">y</sup><span>)</span></p> + <sup>z</sup><span><span class="root">x</span><sup style="font-size: small;">y</sup><span></span></span></p> <h2 id="fractional-exponent--examples">Examples</h2> <ul> <li>5 <sup><span class="frac"><sup>1</sup><span>⁄</span><sub>2</sub></span></sup> = - <sup>2</sup><span>√5</span></li> + <sup>2</sup><span><span class="root">5</span></span></li> <li>7 <sup><span class="frac"><sup>2</sup><span>⁄</span><sub>3</sub></span></sup> = - <sup>3</sup><span>√(5<sup>2</sup>)</span></li> + <sup>3</sup><span><span class="root">5<sup>2</sup></span></span></li> </ul> + <h1 id="exponential-equation">Exponential Equation</h1> + <ol> + <li>2<sup>x + 5</sup> = 64<br> + = <span style="text-decoration: line-through;">2</span><sup>x + 5</sup> = <span style="text-decoration: line-through;">2</span><sup>6</sup> <sub>↖ ubah ke bentuk 2 berpangkat (2<sup>x</sup>)</sub><br> + = x + 5 = 6<br> + = x = <strong>1</strong> + </li> + <li>16<sup>x + 2</sup> = 32<br> + = (2<sup>4</sup>)<sup>x + 2</sup> = 2<sup>5</sup><br> + = <span style="text-decoration: line-through;">2</span><sup>4x + 8</sup> = <span style="text-decoration: line-through;">2</span><sup>5</sup><br> + = 4x + 8 = 5<br> + = 4x = 5 - 8<br> + = 4x = -3<br> + = x = <span class="frac"><sup>-3</sup><span>⁄</span><sub>4</sub></span> = <strong>-<span class="frac"><sup>3</sup><span>⁄</span><sub>4</sub></span></strong> + </li> + </ol> </section> </div> |