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<main role="main">
<!-- 1. Solving Equations -->
<section id="solving">
<h2>1. Solving Equations <span class="time">Timestamps: 43:20 · 54:33</span></h2>
<div class="muted">Removing decimals — multiply by a power of 10</div>
<div class="formula">Example:
0.4x + 1.2 = 2 Multiply by 10 → 4x + 12 = 20 Solve → 4x = 8 → x = 2
<div style="margin-top:8px;" class="muted">Quadratic formula (use when ax²+bx+c=0)</div>
<div class="formula">x = (-b ± √(b² - 4ac)) / (2a)</div>
<div class="example">
Example: Solve 2x² - 4x - 6 = 0 a=2, b=-4, c=-6 x = [4 ± √(16 + 48)] / 4 = [4 ± √64] / 4 = [4 ± 8] / 4 x = 3 or x = -1
<div class="rule"></div>
<!-- 2. Factoring & Multiplying Polynomials -->
<section id="polynomials">
<h2>2. Factoring & Multiplying Polynomials <span class="time">Timestamps: 05:07 · 05:59 · 08:31</span></h2>
<div class="muted">Polynomial types:</div>
<ul>
<li><strong>Monomial</strong> — single term (e.g., 5x²)</li>
<li><strong>Binomial</strong> — two terms (e.g., x + 3)</li>
<li><strong>Trinomial</strong> — three terms (e.g., x² + 5x + 6)</li>
</ul>
<div class="muted">Monomial × Trinomial</div>
<div class="formula">3x (x² + 4x + 5) = 3x³ + 12x² + 15x</div>
<div class="muted">Binomial × Binomial — FOIL</div>
<div class="formula">
(x + 3)(x + 4) ⟶ F: x·x = x² O: x·4 = 4x I: 3·x = 3x L: 3·4 = 12 Result: x² + 7x + 12
<div class="rule"></div>
<!-- 3. Exponents -->
<section id="exponents">
<h2>3. Properties of Exponents <span class="time">Timestamps: 13:16 · 14:04 · 16:15</span></h2>
<div class="muted">Key rules</div>
<div class="formula">
Multiplication: a^m · a^n = a^(m+n) e.g., x^3 · x^5 = x^8 Division: a^m / a^n = a^(m-n) e.g., x^7 / x^2 = x^5 Zero exponent: a^0 = 1 (a ≠ 0) e.g., 5^0 = 1 Negative: a^(-n) = 1 / a^n e.g., x^-3 = 1/x^3
<div class="example"><strong>Quick visualization:</strong> Multiplying x² by x³ is like combining two groups of powers → x^(2+3) = x^5.</div>
</section>
<div class="rule"></div>
<!-- 4. Graphing Linear Equations -->
<section id="graphing">
<h2>4. Graphing Linear Equations <span class="time">Timestamps: 01:02:51 · 01:05:25</span></h2>
<div class="muted">Slope-intercept form</div>
<div class="formula">y = mx + b
m = slope (rise / run) b = y-intercept (point where line crosses the y-axis)
<div class="example">
Given y = 2x + 1 → slope = 2, y-intercept = (0,1) Plot (0,1). From there, rise 2, run 1 to get next point (1,3).
<div style="margin-top:8px;" class="muted">Standard form (use intercepts)</div>
<div class="formula">Ax + By = C
x-intercept: set y = 0 → solve for x y-intercept: set x = 0 → solve for y
<div class="example">
2x + 3y = 6 x-intercept: y=0 → 2x=6 → x=3 → (3,0) y-intercept: x=0 → 3y=6 → y=2 → (0,2)
<div class="rule"></div>
<!-- 5. Writing the Equation of a Line -->
<section id="lines">
<h2>5. Writing the Equation of a Line <span class="time">Timestamps: 01:06:53 · 01:09:18 · 01:12:30</span></h2>
<div class="muted">Point-Slope form</div>
<div class="formula">y - y₁ = m(x - x₁)</div>
<div class="example">
Point (2,3), m = 4: y - 3 = 4(x - 2) → y = 4x - 8 + 3 → y = 4x - 5
<div style="margin-top:8px;" class="muted">Two points → find slope</div>
<div class="formula">m = (y₂ - y₁) / (x₂ - x₁)</div>
<div class="example">
Points (1,2) & (3,6): m = (6 - 2) / (3 - 1) = 4/2 = 2 Use point-slope: y - 2 = 2(x - 1) → y = 2x
<div style="margin-top:8px;" class="muted">Parallel & perpendicular</div>
<ul>
<li>Parallel lines → same slope</li>
<li>Perpendicular lines → slope is negative reciprocal (m₂ = -1/m₁)</li>
</ul>
<div class="example">
Line parallel to y = 3x + 1 through (2,4): y - 4 = 3(x - 2) → y = 3x - 2 Line perpendicular to y = (1/2)x + 1 through (0,0): slope = -2 → y = -2x
</main>
<aside aria-labelledby="quick">
<h3 id="quick" style="margin-top:0">Quick Links & Tips</h3>
<p class="small">Timestamps are from the video you shared. If you want to cram fast tonight, focus these first:</p>
<ul>
<li><strong>Multiply polynomials & exponents:</strong> 05:07–16:15</li>
<li><strong>Linear equations & graphing:</strong> 43:20, 01:02:51, 01:06:53</li>
</ul>
<div style="margin-top:10px">
<a class="btn" href="https://www.youtube.com/watch?v=grnP3mduZkM" target="_blank" rel="noopener">Open Video</a>
</div>
<div style="margin-top:12px;" class="small">
<strong>Print tip:</strong> Use your browser's print dialog, or press <span class="kbd">Ctrl/Cmd + P</span>. The right column will be hidden for a compact printout.
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<div>Ready for 9th Grade ✅</div>
<div class="small">Save this file as <span class="kbd">algebra_cheatsheet.html</span></div>
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