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| author | altaf-creator <athaalaa@gmail.com> | 2023-09-25 20:18:57 +0700 |
|---|---|---|
| committer | altaf-creator <athaalaa@gmail.com> | 2023-09-25 20:18:57 +0700 |
| commit | 18670260285d25b14921a89fae60089da334c921 (patch) | |
| tree | dbd0d0a17a7704e963504744e21a273b9c374b3b /lessons/matematika | |
| parent | 7420ea9926c6cca698efa670d837a1cd753c4931 (diff) | |
Unlocked website, added rationalising roots
Diffstat (limited to 'lessons/matematika')
| -rw-r--r-- | lessons/matematika/index.html | 70 | ||||
| -rw-r--r-- | lessons/matematika/locked.html | 58 | ||||
| -rw-r--r-- | lessons/matematika/pangkat-akar/akar.html | 170 | ||||
| -rw-r--r-- | lessons/matematika/pangkat-akar/latihan.html | 167 | ||||
| -rw-r--r-- | lessons/matematika/pangkat-akar/pangkat.html | 139 | ||||
| -rw-r--r-- | lessons/matematika/pangkat-akar/scientific.html | 69 | ||||
| -rw-r--r-- | lessons/matematika/quadratic-equation/finding-suitable.html | 117 | ||||
| -rw-r--r-- | lessons/matematika/quadratic-equation/index.html | 277 | ||||
| -rw-r--r-- | lessons/matematika/quadratic-function/index.html | 75 |
9 files changed, 1142 insertions, 0 deletions
diff --git a/lessons/matematika/index.html b/lessons/matematika/index.html new file mode 100644 index 0000000..4c800ec --- /dev/null +++ b/lessons/matematika/index.html @@ -0,0 +1,70 @@ +<!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.svg"> + <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> + <div class="fixed-top-btn-container" id="topbtn"> + <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"><i class="fa-solid fa-chevron-left"></i></a> + </div> + <div id="console"></div> + <div id="sidebar"> + <div> + <a href="/index.html"> + <img src="/assets/images/master.svg" alt="" class="sidebar-logo"> + </a> + + <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> + </div> + + <div> + <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> + + <div class="banner-container" id="banner"> + <div class="banner-bg" id="img-supplies"></div> + <div class="gradient-bg"></div> + <div class="banner-text-container"> + <h1 class="banner-text" id="banner-txt">Matematika</h1> + <h3 class="banner-text" id="banner-txt">Hidayatullah, S.Pd.</h3> + </div> + </div> + + <div id="main"> + <section> + <h1 id="bab1">Chapter 1 - Bentuk Pangkat dan Akar</h1> + <p><a href="pangkat-akar/pangkat.html" class="link">Lesson 1: Exponent</a></p> + <p><a href="pangkat-akar/akar.html" class="link">Lesson 2: Root</a></p> + <p><a href="pangkat-akar/latihan.html" class="link">Exercise 1</a></p> + <p><a href="pangkat-akar/scientific.html" class="link">Lesson 3: Exponents Extended - Scientific Form of Decimals</a></p> + <h1 id="bab2">Chapter 2 - Quadratic Equation</h1> + <p><a href="quadratic-equation/" class="link">Main Lesson: Quadratic Equation - The Introduction</a></p> + <h1 id="bab3">Chapter 3 - Quadratic Function (no it's not equation)</h1> + <p><a href="quadratic-function/" class="link">Main Lesson: Quadratic Function - The Introduction</a></p> + </section> + </div> + + <script src="/scripts/toc.js"></script> + <script src="/scripts/sidebar.js"></script> +</body> +</html> diff --git a/lessons/matematika/locked.html b/lessons/matematika/locked.html new file mode 100644 index 0000000..c6384ec --- /dev/null +++ b/lessons/matematika/locked.html @@ -0,0 +1,58 @@ +<!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.svg"> + <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> + <div class="fixed-top-btn-container" id="topbtn"> + <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"><i class="fa-solid fa-chevron-left"></i></a> + </div> + <div id="console"></div> + <div id="sidebar"> + <div> + <a href="/index.html"> + <img src="/assets/images/master.svg" alt="" class="sidebar-logo"> + </a> + + <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> + </div> + + <div> + <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> + + <div class="banner-container" id="banner"> + <div class="banner-bg" id="img-supplies"></div> + <h1 class="banner-text" id="banner-txt">Matematika</h1> + </div> + + <div id="main"> + <section> + <p style="text-align: center; width: 100%;"><i class="fa-solid fa-file-circle-question"></i> This lesson is locked.</p> + </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/akar.html b/lessons/matematika/pangkat-akar/akar.html new file mode 100644 index 0000000..1bacf4c --- /dev/null +++ b/lessons/matematika/pangkat-akar/akar.html @@ -0,0 +1,170 @@ +<!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.svg"> + <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> + <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.css" + integrity="sha384-pRsDYiLLocCzWnUN/YEr9TBTTaZOUi5x8adKfqi6Qt44lDaFkoP++x1j2ohSMtdf" crossorigin="anonymous"> + <script src="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.js" + integrity="sha384-tMzugJpfLv7v0f+KXzNMqNCC6sVzLMM3sCnZDgzy0lcO/0h3sAkEBg/URFcV0JpE" + crossorigin="anonymous"></script> +</head> + +<body> + <div class="fixed-top-btn-container" id="topbtn"> + <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"><i class="fa-solid fa-chevron-left"></i></a> + </div> + <div id="console"></div> + <div id="sidebar"> + <div> + <a href="/index.html"> + <img src="/assets/images/master.svg" alt="" class="sidebar-logo"> + </a> + + <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> + </div> + + <div> + <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> + + <div class="banner-container" id="banner"> + <div class="banner-bg" id="img-supplies"></div> + <div class="gradient-bg"></div> + <div class="banner-text-container"> + <h1 class="banner-text" id="banner-txt">Root</h1> + <h3 class="banner-text" id="banner-txt">Chapter 1</h3> + </div> + </div> + + <div class="chip-container" id="chip-container"> + <div class="chip"><span>✅ Verified</span></div> + </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="sroot">16</span> = 4</b></li> + <li>5<sup>2</sup> = 25, <b>so <span class="sroot">25</span> = 5</b></li> + <li>10<sup>2</sup> = 100, <b>so <span class="sroot">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="sroot">60</span></strong><br> + <span class="sroot">60</span> = <span class="sroot">4 × 15</span> = 2<span class="sroot">15</span><br> + </li> + <li> + <strong>Simplify <span class="sroot">48</span></strong><br> + <span class="sroot">48</span> = <span class="sroot">16 × 3</span> = 4<span class="sroot">3</span><br> + </li> + <li> + <strong>Simplify <span class="sroot">125</span></strong><br> + <span class="sroot">125</span> = <span class="sroot">25 × 5</span> = 5<span class="sroot">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="sroot">c</span> + b<span class="sroot">c</span> = (a + b)<span class="sroot">c</span></strong> + <ul> + <li>3<span class="sroot">2</span> + 4<span class="sroot">2</span> = (3 + 4)<span class="sroot">2</span> = <strong>7<span class="sroot">2</span></strong></li> + <li><span class="sroot">5</span> + 3<span class="sroot">5</span> = (1 + 3)<span class="sroot">5</span> = <strong>4<span class="sroot">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="sroot">c</span> - b<span class="sroot">c</span> = (a - b)<span class="sroot">c</span></strong> + <ul> + <li>7<span class="sroot">3</span> - 4<span class="sroot">3</span> = (7 - 4)<span class="sroot">3</span> = <strong>3<span class="sroot">2</span></strong></li> + <li>10<span class="sroot">6</span> - 5<span class="sroot">6</span> = (10 - 5)<span class="sroot">6</span> = <strong>5<span class="sroot">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="sroot">c</span> × b<span class="sroot">d</span> = (a × b)<span class="sroot">c × d</span></strong> + <ul> + <li><span class="sroot">2</span> × <span class="sroot">5</span> = <strong><span class="sroot">10</span></strong></li> + <li>3<span class="sroot">2</span> × 4<span class="sroot">3</span> = (3 × 4)<span class="sroot">2 × 3</span> = <strong>12<span class="sroot">6</span></strong></li> + <li>2<span class="sroot">5</span> × 3<span class="sroot">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="sroot">c</span> ÷ b<span class="sroot">d</span> = (a ÷ b)<span class="sroot">c ÷ d</span></strong> + <ul> + <li> + 8<span class="sroot">6</span> ÷ 4<span class="sroot">3</span> = (8 ÷ 4)<span class="sroot">6 ÷ 3</span> = <strong>2<span class="sroot">2</span></strong> + </li> + </ul> + + <h2 id="rationalising">Rationalising Roots</h2> + <p>We can rationalise or simplify a fraction with a root denominator. To rationalise a root, multiply the fraction with a fraction of opposite roots. For example:</p> + <p><b>Example 1:</b></p> + <span id="id1"></span> + <script defer> + var element = document.getElementById("id1"); + katex.render(String.raw`\dfrac{3}{\sqrt{5}}\\ + = \dfrac{3}{\sqrt{5}} \times \dfrac{\sqrt{5}}{\sqrt{5}}\\ + = \dfrac{3\sqrt{5}}{5} + `, element, { + throwOnError: false + }); + </script> + <p><b>Example 2:</b></p> + <span id="id2"></span> + <script defer> + var element = document.getElementById("id2"); + katex.render(String.raw`\dfrac{2}{3\sqrt{6}}\\ + = \dfrac{2}{3\sqrt{6}} \times \dfrac{\sqrt{6}}{\sqrt{6}}\\ + = \dfrac{2\sqrt{6}}{3 \cdot 6}\\ + = \dfrac{2\sqrt{6}}{18}\\ + = \dfrac{1}{9}\sqrt{6} + `, element, { + throwOnError: false + }); + </script> + <p><b>Example 3:</b></p> + <span id="id3"></span> + <script defer> + var element = document.getElementById("id3"); + katex.render(String.raw`\dfrac{8}{3 + \sqrt{7}}\\ + = \dfrac{8}{3 + \sqrt{7}} \times \dfrac{3 - \sqrt{7}}{3 - \sqrt{7}}\\ + = \dfrac{8(3 \cdot \sqrt{7})}{(3 \cdot \sqrt{7})(3 \cdot \sqrt{7})}\\ + = \dfrac{8(3 \cdot \sqrt{7})}{9 - 3\sqrt{7} + 3\sqrt{7} - 7}\\ + = \dfrac{8(3 \cdot \sqrt{7})}{9 - 7}\\ + = \dfrac{8(3 \cdot \sqrt{7})}{2} + `, element, { + throwOnError: false + }); + </script> + </section> + </div> + + <script src="/scripts/toc.js"></script> + <script src="/scripts/sidebar.js"></script> +</body> + +</html> diff --git a/lessons/matematika/pangkat-akar/latihan.html b/lessons/matematika/pangkat-akar/latihan.html new file mode 100644 index 0000000..6bdae1d --- /dev/null +++ b/lessons/matematika/pangkat-akar/latihan.html @@ -0,0 +1,167 @@ +<!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.svg"> + <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> + <div class="fixed-top-btn-container" id="topbtn"> + <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"><i class="fa-solid fa-chevron-left"></i></a> + </div> + <div id="console"></div> + <div id="sidebar"> + <div> + <a href="/index.html"> + <img src="/assets/images/master.svg" alt="" class="sidebar-logo"> + </a> + + <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> + </div> + + <div> + <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> + + <div class="banner-container" id="banner"> + <div class="banner-bg" id="img-supplies"></div> + <div class="gradient-bg"></div> + <div class="banner-text-container"> + <h1 class="banner-text" id="banner-txt">Exercise</h1> + <h3 class="banner-text" id="banner-txt">Chapter 1</h3> + </div> + </div> + + <div class="chip-container" id="chip-container"> + <div class="chip"><span>❓ Unchecked</span></div> + </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="sroot">5</span> + 3<span class="sroot">20</span> - 4<span class="sroot">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="sroot">5</span></sub></span></li> + <li style="margin-top: 10px;"><span class="frac"><sup>3<span class="sroot">5</span></sup><span>⁄</span><sub>2<span class="sroot">3</span></sup></sub></span></li> + <li style="margin-top: 10px;"><span class="frac"><sup>5</sup><span>⁄</span><sub><span class="sroot">3</span> - <span class="sroot">2</span></sub></span></li> + <li style="margin-top: 10px;"><span class="frac"><sup><span class="sroot">5</span> - <span class="sroot">7</span></sup><span>⁄</span><sub><span class="sroot">5</span> - <span class="sroot">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="sroot">64</span> + <sup>3</sup><span class="sroot">81</span><br> + = 8 + <sup>3</sup><span class="sroot">81</span> + </li> + <li style="margin-top: 10px;"> + 2<span class="sroot">5</span> + 3<span class="sroot">20</span> - 4<span class="sroot">5</span><br> + = 6<span class="sroot">5</span> + 3<span class="sroot">20</span><br> + = 6<span class="sroot">5</span> + 3<span class="sroot">4 × 5</span><br> + = 6<span class="sroot">5</span> + 3<span class="sroot">2<sup>2</sup> × 5</span><br> + = 6<span class="sroot">5</span> + 3 × 2<span class="sroot">5</span><br> + = 6<span class="sroot">5</span> + 6<span class="sroot">5</span><br> + = <strong>12<span class="sroot">5</span></strong><br> + </li> + <li style="margin-top: 10px;"> + <span class="frac"><sup>4</sup><span>⁄</span><sub><span class="sroot">5</span></sub></span><br> + = <span class="frac"><sup>4</sup><span>⁄</span><sub><span class="sroot">5</span></sub></span> × <span class="frac"><sup><span class="sroot">5</span></sup><span>⁄</span><sub><span class="sroot">5</span></sub></span> = <strong><span class="frac"><sup>4<span class="sroot">5</span></sup><span>⁄</span><sub>5</sub></span></strong> + </li> + <li style="margin-top: 10px;"> + <span class="frac"><sup>3<span class="sroot">5</span></sup><span>⁄</span><sub>2<span class="sroot">3</span></sup></sub></span><br> + = <span class="frac"><sup>3<span class="sroot">5</span></sup><span>⁄</span><sub>2<span class="sroot">3</span></sup></sub></span> × <span class="frac"><sup><span class="sroot">3</span></sup><span>⁄</span><sub><span class="sroot">3</span></sup></sub></span><br> + = <span class="frac"><sup><span style="text-decoration: line-through;">3</span><span class="sroot">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="sroot">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="sroot">3</span> - <span class="sroot">2</span></sub></span><br> + = <span class="frac"><sup>5</sup><span>⁄</span><sub><span class="sroot">3</span> - <span class="sroot">2</span></sub></span> × <span class="frac"><sup><span class="sroot">3</span> + <span class="sroot">2</span></sup><span>⁄</span><sub><span class="sroot">3</span> + <span class="sroot">2</span></sub></span><br> + = <span class="frac"><sup>5(<span class="sroot">3</span> + <span class="sroot">2</span>)</sup><span>⁄</span><sub>(<span class="sroot">3</span>)<sup>2</sup> - (<span class="sroot">2</span>)<sup>2</sup></sub></span><br> + = <span class="frac"><sup>5(<span class="sroot">3</span> + <span class="sroot">2</span>)</sup><span>⁄</span><sub>3 - 2</sub></span> = <span class="frac"><sup>5(<span class="sroot">3</span> + <span class="sroot">2</span>)</sup><span>⁄</span><sub>1</sub></span><br> + = <strong>5(<span class="sroot">3</span> + <span class="sroot">2</span>)</strong> + </li> + <li style="margin-top: 10px;"> + <span class="frac"><sup><span class="sroot">5</span> - <span class="sroot">7</span></sup><span>⁄</span><sub><span class="sroot">5</span> - <span class="sroot">2</span></sub></span><br> + = <span class="frac"><sup><span class="sroot">5</span> - <span class="sroot">7</span></sup><span>⁄</span><sub><span class="sroot">5</span> - <span class="sroot">2</span></sub></span> × <span class="frac"><sup><span class="sroot">5</span> + <span class="sroot">2</span></sup><span>⁄</span><sub><span class="sroot">5</span> + <span class="sroot">2</span></sub></span><br> + = <span class="frac"><sup>(<span class="sroot">5</span> - <span class="sroot">7</span>) × (<span class="sroot">5</span> + <span class="sroot">2</span>)</sup><span>⁄</span><sub>(<span class="sroot">5</span>)<sup>2</sup> - (<span class="sroot">2</span>)<sup>2</sup></sub></span><br> + = <span class="frac"><sup>5 + <span class="sroot">10</span> - <span class="sroot">35</span> - <span class="sroot">14</span></sup><span>⁄</span><sub>5 - 2</sub></span> = <strong><span class="frac"><sup>5 + <span class="sroot">10</span> - <span class="sroot">35</span> - <span class="sroot">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> b<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 new file mode 100644 index 0000000..e8362dd --- /dev/null +++ b/lessons/matematika/pangkat-akar/pangkat.html @@ -0,0 +1,139 @@ +<!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.svg"> + <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 defer src="https://kit.fontawesome.com/d279a1f519.js" crossorigin="anonymous"></script> +</head> + +<body> + <div class="fixed-top-btn-container" id="topbtn"> + <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"><i class="fa-solid fa-chevron-left"></i></a> + </div> + <div id="console"></div> + <div id="sidebar"> + <div> + <a href="/index.html"> + <img src="/assets/images/master.svg" alt="" class="sidebar-logo"> + </a> + + <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> + </div> + + <div> + <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> + + <div class="banner-container" id="banner"> + <div class="banner-bg" id="img-supplies"></div> + <div class="gradient-bg"></div> + <div class="banner-text-container"> + <h1 class="banner-text" id="banner-txt">Exponents</h1> + <h3 class="banner-text" id="banner-txt">Chapter 1</h3> + </div> + </div> + + <div class="chip-container" id="chip-container"> + <div class="chip"><span>✅ Verified</span></div> + </div> + + <div id="main"> + <section> + <h1 id="exponent">Exponents</h1> + x<sup>n</sup> = x<sub>1</sub> × x<sub>2</sub> × ... × x<sub>n</sub> + <h2 id="exponent--examples">Examples</h2> + <ul> + <li>2<sup>5</sup> = 2 × 2 × 2 × 2 × 2 = 32</li> + <li>5<sup>7</sup> = 5 × 5 × 5 × 5 × 5 × 5 × 5 = 78.125</li> + </ul> + <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>)<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></strong> + </ul> + + <h1 id="zero-exponent">Zero Exponent</h1> + <p>a<sup>0</sup> = 1</p> + <h2 id="zero-exponent--examples">Examples</h2> + <ul> + <li>5<sup>0</sup> = 1</li> + <li>7<sup>0</sup> = 1</li> + <li>100<sup>0</sup> = 1</li> + <li>28,67<sup>0</sup> = 1</li> + </ul> + <h1 id="one-exponent">One Exponent</h1> + <p>a<sup>1</sup> = a</p> + <h2 id="one-exponent--examples">Examples</h2> + <ul> + <li>5<sup>1</sup> = 5</li> + <li>7<sup>1</sup> = 7</li> + <li>100<sup>1</sup> = 100</li> + <li>28,67<sup>1</sup> = 28,67</li> + </ul> + <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><span class="sroot">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><span class="sroot">5</span></span></li> + <li>7 <sup><span class="frac"><sup>2</sup><span>⁄</span><sub>3</sub></span></sup> = + <sup>3</sup><span><span class="sroot">7<sup>2</sup></span></span></li> + </ul> + <p><strong>Small Note:</strong> 2</sup><span class="sroot">x</span> or <span class="sroot">x</span> menans square root. The 2 before root should be removed. The 2 is only present for easier purposes.<br>3</sup><span><span class="sroot">x</span> means cubic root.</p> + + <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> + + <script src="/scripts/toc.js"></script> + <script src="/scripts/sidebar.js"></script> +</body> + +</html> diff --git a/lessons/matematika/pangkat-akar/scientific.html b/lessons/matematika/pangkat-akar/scientific.html new file mode 100644 index 0000000..9394f6e --- /dev/null +++ b/lessons/matematika/pangkat-akar/scientific.html @@ -0,0 +1,69 @@ +<!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.svg"> + <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> + <div class="fixed-top-btn-container" id="topbtn"> + <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"><i class="fa-solid fa-chevron-left"></i></a> + </div> + <div id="console"></div> + <div id="sidebar"> + <div> + <a href="/index.html"> + <img src="/assets/images/master.svg" alt="" class="sidebar-logo"> + </a> + + <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> + </div> + + <div> + <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> + + <div class="banner-container" id="banner"> + <div class="banner-bg" id="img-supplies"></div> + <div class="gradient-bg"></div> + <div class="banner-text-container"> + <h1 class="banner-text" id="banner-txt">Standard Form (decimals)</h1> + <h3 class="banner-text" id="banner-txt">Chapter 1</h3> + </div> + </div> + + <div class="chip-container" id="chip-container"> + <div class="chip"><span>🔍 Unfinished</span></div> + </div> + + <div id="main"> + <section> + + </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/quadratic-equation/finding-suitable.html b/lessons/matematika/quadratic-equation/finding-suitable.html new file mode 100644 index 0000000..9e13f01 --- /dev/null +++ b/lessons/matematika/quadratic-equation/finding-suitable.html @@ -0,0 +1,117 @@ +<!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.svg"> + <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> + <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.css" + integrity="sha384-pRsDYiLLocCzWnUN/YEr9TBTTaZOUi5x8adKfqi6Qt44lDaFkoP++x1j2ohSMtdf" crossorigin="anonymous"> + <script src="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.js" + integrity="sha384-tMzugJpfLv7v0f+KXzNMqNCC6sVzLMM3sCnZDgzy0lcO/0h3sAkEBg/URFcV0JpE" + crossorigin="anonymous"></script> +</head> + +<body> + <div class="fixed-top-btn-container" id="topbtn"> + <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"><i class="fa-solid fa-chevron-left"></i></a> + </div> + <div id="console"></div> + <div id="sidebar"> + <div> + <a href="/index.html"> + <img src="/assets/images/master.svg" alt="" class="sidebar-logo"> + </a> + + <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> + </div> + + <div> + <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> + + <div class="banner-container" id="banner"> + <div class="banner-bg" id="img-supplies"></div> + <div class="gradient-bg"></div> + <div class="banner-text-container"> + <h1 class="banner-text" id="banner-txt">Quadratic Equation: Finding the suitable factor</h1> + <h3 class="banner-text" id="banner-txt">Chapter 2 sub-page</h3> + </div> + </div> + + <div class="chip-container" id="chip-container"> + <div class="chip" title="Beware of mistakes. Please report to me (Altaf) if you caught a mistake here."><span>❓ Unchecked by Professionals</span></div> + </div> + + <div id="main"> + <section> + <p><strong><a href="/lessons/matematika/quadratic-equation/" class="link">← Go back to Main Lesson</a></strong></p> + Firstly, lets use this equation. <br> + <span id="m1"></span><br> + <h1 id="steps">Step-by-step</h1> + <ol> + <li>Find the factors of <span class="math-font">c</span>, which in this equation, <span class="math-font">c = </span><span class="math-font-main">30</span>.</li> + <li>The factors of 30 are: + <ul> + <li>1, 30</li> + <li>2, 15</li> + <li>3, 10</li> + <li>5, 6</li> + </ul> + </li> + <li>Lets define that the first and second factors are <span class="math-font">y<sub>1, 2</sub></span>. To find the suitable factors for the equation, you need to check if; + <ul> + <li><span id="m2"></span>, and</li> + <li><span id="m3"></span></li> + </ul> + </li> + <li>Check for each of the factors. We end up with 5 and 6. <br> <span id="m4"></span></li> + <li>So, the answer is <strong><span class="math-font-main">5 & 6</span></strong></li> + </ol> + <p><strong><a href="/lessons/matematika/quadratic-equation/" class="link">← Go back to Main Lesson</a></strong></p> + <script defer> + var element1 = document.getElementById("m1"); + var element2 = document.getElementById("m2"); + var element3 = document.getElementById("m3"); + var element4 = document.getElementById("m4"); + + katex.render(String.raw`x^2 + 11x + 30 = 0`, element1, { + throwOnError: false + }); + katex.render(String.raw`y_1 + y_2 = b`, element2, { + throwOnError: false + }); + katex.render(String.raw`y_1 \times y_2 = c`, element3, { + throwOnError: false + }); + katex.render(String.raw`5 \times 6 = 30\\5 + 6 = 11`, element4, { + throwOnError: false + }); + </script> + </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/quadratic-equation/index.html b/lessons/matematika/quadratic-equation/index.html new file mode 100644 index 0000000..288d0d9 --- /dev/null +++ b/lessons/matematika/quadratic-equation/index.html @@ -0,0 +1,277 @@ +<!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.svg"> + <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> + <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.css" + integrity="sha384-pRsDYiLLocCzWnUN/YEr9TBTTaZOUi5x8adKfqi6Qt44lDaFkoP++x1j2ohSMtdf" crossorigin="anonymous"> + <script src="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.js" + integrity="sha384-tMzugJpfLv7v0f+KXzNMqNCC6sVzLMM3sCnZDgzy0lcO/0h3sAkEBg/URFcV0JpE" + crossorigin="anonymous"></script> +</head> + +<body> + <div class="fixed-top-btn-container" id="topbtn"> + <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"><i class="fa-solid fa-chevron-left"></i></a> + </div> + <div id="console"></div> + <div id="sidebar"> + <div> + <a href="/index.html"> + <img src="/assets/images/master.svg" alt="" class="sidebar-logo"> + </a> + + <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> + </div> + + <div> + <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> + + <div class="banner-container" id="banner"> + <div class="banner-bg" id="img-supplies"></div> + <div class="gradient-bg"></div> + <div class="banner-text-container"> + <h1 class="banner-text" id="banner-txt">Quadratic Equation: The Introduction</h1> + <h3 class="banner-text" id="banner-txt">Chapter 2</h3> + </div> + </div> + + <div class="chip-container" id="chip-container"> + <div class="chip" title="Beware of mistakes. Please report to me (Altaf) if you caught a mistake here."><span>❓ Unchecked by Professionals</span></div> + </div> + + <div id="main"> + <section> + <h1 id="introduction">Introduction</h1> + In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x + represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.<sup>[<a + href="#reference-1" class="link-compact">1</a>]</sup> + <h2 id="introduction--formula">Formula / Format</h2> + <span class="math-font">ax<sup>2</sup> + bx + c = 0</span> + <p> + <span class="math-font">a, b, c</span> = known numbers, where a ≠ 0 <br> + <span class="math-font">x</span> = the unknown, or the root + </p> + <h2 id="introduction--exercise">Exercises</h2> + <h3>Finding the roots with factorisation.</h3> + <ol> + <li> + <span id="q1.1.1"></span> + <p> + <hr> + <span>To find the answer, we need to find the factors of c that is suitable for b and c. <a href="finding-suitable.html" class="link">What and how do I find the suitable factors?</a></span><br> + <span>The suitable factor for the equation are <b>2 and -3</b>. </span><br> + <span>Then, insert each numbers to this formula: <span id="q1.1.2"></span>, where <span + class="math-font">y</span> is the factor.</span><br><br> + <span id="q1.1.3"></span><br><span id="q1.1.31"></span><br> + <hr> + <strong>So, the answer is <span id="q1.1.4"></span></strong> + </p> + <script defer> + var element1 = document.getElementById("q1.1.1"); + var element2 = document.getElementById("q1.1.2"); + var element3 = document.getElementById("q1.1.3"); + var element31 = document.getElementById("q1.1.31"); + var element4 = document.getElementById("q1.1.4"); + + katex.render(String.raw`x^2 - 1x - 6 = 0`, element1, { + throwOnError: false + }); + katex.render(String.raw`x + y`, element2, { + throwOnError: false + }); + katex.render(String.raw` + \begin{aligned} + x + 2 &= 0\\ + x &= -2\\ + \end{aligned} + `, element3, { + throwOnError: true + }); katex.render(String.raw` + \begin{aligned} + x - 3 &= 0\\ + x &= 3 + \end{aligned} + `, element31, { + throwOnError: true + }); + katex.render(String.raw`x = \{-2, 3\}`, element4, { + throwOnError: false + }); + </script> + </li> + <li> + <p> + <span id="q1.2.1"></span><br> + <span><strong>Factors:</strong> <span class="math-font">2, 4</span></span><br> + <hr> + <span id="q1.2.2"></span><br> + <span id="q1.2.3"></span><br> + <hr> + <span id="q1.2.4"></span><br> + </p> + <script defer> + var element1 = document.getElementById("q1.2.1"); + var element2 = document.getElementById("q1.2.2"); + var element3 = document.getElementById("q1.2.3"); + var element4 = document.getElementById("q1.2.4"); + + katex.render(String.raw`x^2 + 6x + 8 = 0`, element1, { + throwOnError: false + }); + katex.render(String.raw` + \begin{aligned} + x + 2 &= 0\\ + x &= -2\\ + \end{aligned} + `, element2, { + throwOnError: true + }); katex.render(String.raw` + \begin{aligned} + x + 4 &= 0\\ + x &= 4 + \end{aligned} + `, element3, { + throwOnError: true + }); + katex.render(String.raw`x = \{-2, -4\}`, element4, { + throwOnError: false + }); + </script> + </li> + </ol> + <h1 id="relation-algebra">Relation between Quadratic Equation and Algebraic Expressions</h1> + <p>This is an algebraic expression → <span id="m0"></span>. You can turn that into a quadratic equation.</p> + <span id="m1"></span> + <script> + const m0 = document.getElementById("m0"); + const m1 = document.getElementById("m1"); + + katex.render(String.raw`(x + 5)(x + 7)`, m0, { + throwOnError: false + }); + katex.render(String.raw` + \begin{aligned} + (x + 5)(x + 7) &= x^2 + 5x + 7x + 35&\\ + &= x^2 + 12x + 35&\larr\textnormal{quadratic equation 😱😱} + \end{aligned} + `, m1, { + throwOnError: true + }); + </script> + <h1 id="all-about-roots">Quadratic Equation's Root Operations</h1> + <h2 id="finding-qe">Finding Quadratic Equation with Roots</h2> + <p>You can use the formula below to find a Quadratic Equation with 2 roots.</p> + <span id="m2"></span><span>, where <span class=math-font>x<sub>1, 2</sub></span> are the roots.</span><br> + <p> + <strong>Example:</strong><br><br> + <span id="m3"></span> + </p> + <script> + const m2 = document.getElementById("m2"); + const m3 = document.getElementById("m3"); + + katex.render(String.raw`(x - x_1)(x - x_2) = 0`, m2, { + throwOnError: false + }); + katex.render(String.raw` + \begin{aligned} + (x - x_1)(x - x_2) &= 0\\ + (x - (-3))(x - 4) &= 0\\ + (x + 3))(x - 4) &= 0\\ + x^2 - 4x + 3x - 12 &= 0\\ + x^2 - x - 12 &= 0 + \end{aligned} + `, m3, { + throwOnError: true + }); + </script> + <h2 id="operations">Quadratic Root's Mathematical Operations</h2> + <h3 id="operations--formulas">Formulas</h3> + <p id="m4"></p> + <p id="m5"></p> + <h3 id="operations--examples">Examples</h3> + <ol> + <li> + <p>Diketahui persamaan kuadrat <span id="q1"></span>, memiliki akar-akar persamaan kuadrat <span class="math-font">x<sub>1</sub></span> dan <span class="math-font">x<sub>2</sub></span>. Jika <span class="math-font">x<sub>1</sub> < x<sub>2</sub></span>, maka tentukan: + <ol type="a"> + <li><span class="math-font">x<sub>1</sub> + x<sub>2</sub></span></li> + <li><span class="math-font">x<sub>1</sub> × x<sub>2</sub></span></li> + </ol> + </p> + <hr> + <ol type="a"> + <li><span id="a1"></span></li> + <li><span id="a2"></span></li> + </ol> + </li> + </ol> + <script> + const m4 = document.getElementById("m4"); + const m5 = document.getElementById("m5"); + const q1 = document.getElementById("q1"); + const a1 = document.getElementById("a1"); + const a2 = document.getElementById("a2"); + + katex.render(String.raw`x_1 + x_2 = \dfrac{-b}{a}`, m4, { + throwOnError: false + }); + katex.render(String.raw`x_1 \times x_2 = \dfrac{c}{a}`, m5, { + throwOnError: false + }); + katex.render(String.raw`2x^2 + 7x + 3 = 0`, q1, { + throwOnError: false + }); + katex.render(String.raw` + \begin{aligned} + x_1 + x_2 &= \dfrac{-b}{a}\\ + &= \dfrac{-7}{2}\\ + \end{aligned} + `, a1, { + throwOnError: true + }); + katex.render(String.raw` + \begin{aligned} + x_1 \times x_2 &= \dfrac{c}{a}\\ + &= \dfrac{3}{2}\\ + \end{aligned} + `, a2, { + throwOnError: true + }); + </script> + <h1>References</h1> + <ol> + <li id="reference-1" tabindex="-1">Quadratic Equation - The English Wikipedia, <a + href="https://en.wikipedia.org/wiki/Quadratic_equation" + class="link">https://en.wikipedia.org/wiki/Quadratic_equation</a></li> + </li> + </section> + </div> + + <script src="/scripts/toc.js"></script> + <script src="/scripts/sidebar.js"></script> +</body> + +</html>
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