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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>The SAT Study Guide</title>
<link href="https://cdn.jsdelivr.net/npm/remixicon@4.6.0/fonts/remixicon.css" rel="stylesheet"/>
<link rel="icon" type="image/x-icon" href="icon.ico">
<style>
:root {
--bg: #fff;
--text: #111;
--muted: #666;
--card: #f6f6f6;
--border: #e6e6e6
}
.good-viz {
margin-top: 12px;
display: flex;
justify-content: center;
}
.good-viz svg {
width: 140px;
height: auto;
}
.good-viz text {
font-size: 8px;
fill: #666;
}
.good-viz line,
.good-viz path {
vector-effect: non-scaling-stroke;
}
* {
box-sizing: border-box;
margin: 0;
padding: 0;
font-family: -apple-system,BlinkMacSystemFont,"Segoe UI",Roboto,Arial,sans-serif
}
.good-card {
display: flex;
flex-direction: column;
gap: 10px;
}
.good-card-title {
font-size: 1.1rem;
font-weight: 700;
text-align: left;
padding-left: 4px;
}
.good-card-content {
background: #fff;
border: 1px solid var(--border);
border-radius: 10px;
padding: 16px;
}
.section {
display: flex;
flex-direction: column;
text-align: center;
gap: 20px;
margin: 20px 0px;
}
.section-item {
background: var(--card);
border: 1px solid var(--border);
border-radius: 14px;
padding: 18px;
}
body {
background: var(--bg);
color: var(--text);
}
/* HEADER */
header {
text-align: center;
padding: 40px 20px 20px;
}
header h1 {
font-size: 2.5rem
}
header p {
color: var(--muted);
margin-top: 8px;
}
/* TOGGLE BUTTON */
/* FLOATING CALCULATOR BUTTON */
.chevron {
display: inline-block;
transition: transform 0.25s ease;
transform-origin: center;
line-height: 1;
height: 16px;
}
.formula-header.active .chevron {
transform: rotate(180deg);
}
.calc-toggle {
position: fixed;
bottom: 20px;
right: 20px;
z-index: 1000;
padding: 12px 16px;
border: 1px solid var(--border);
background: #fff;
border-radius: 999px;
cursor: pointer;
box-shadow: 0 4px 12px rgba(0,0,0,0.08);
}
.calc-toggle i {
font-size: 1rem;
}
.calc-toggle:hover {
background: #f5f5f5;
}
/* CATEGORY BUTTONS */
.categories {
display: flex;
gap: 10px;
justify-content: center;
flex-wrap: wrap;
padding: 20px;
}
.example {
position: relative;
}
.cat-btn {
position: relative;
overflow: hidden;
border: 1px solid var(--border);
background: #fff;
padding: 8px 14px;
border-radius: 999px;
cursor: pointer;
font-size: 16px;
transition: color 0.35s ease;
z-index: 1;
}
.cat-btn span,
.cat-btn i {
position: relative;
z-index: 2;
}
.cat-btn::before {
content: "";
position: absolute;
inset: -150%;
background: #111;
transform: translate(-100%, -100%) rotate(135deg);
transition: transform 3s cubic-bezier(.22,1,.36,1);
z-index: 1;
}
.cat-btn:hover::before {
transform: translate(0%, 0%) rotate(135deg);
transition-duration: 0.8s;
}
.cat-btn:hover {
color: white;
}
.cat-btn.active {
background: #111;
color: #fff;
}
.cat-btn.active::before {
display: none;
}
/* MAIN LAYOUT */
.layout {
display: flex;
width: 100%;
min-height: calc(100vh - 90px);
justify-content: center;
transition: justify-content 0.6s ease;
}
/* LEFT SIDE (CARDS) */
.container {
width: 100%;
max-width: 1100px;
padding: 0 20px;
transition: transform 0.6s ease;
will-change: transform;
}
.layout.calc-active .container {
transform: translateX(max(-220px, calc(-100vw + 100%)));
}
.grid {
column-width: 300px;
column-gap: 20px;
}
.card {
background: var(--card);
border: 1px solid var(--border);
border-radius: 14px;
padding: 18px;
break-inside: avoid;
margin-bottom: 20px;
}
.card h2 {
margin-bottom: 20px;
line-height: 0.7;
}
/* FORMULAS */
.formula {
background: #fff;
border: 1px solid var(--border);
border-radius: 10px;
margin-top: 8px;
overflow: hidden;
}
.formula-header {
padding: 12px;
display: flex;
justify-content: space-between;
cursor: pointer;
font-family: monospace;
align-items: center;
}
.formula-header:hover {
background: #fafafa;
}
.formula-content {
max-height: 0;
overflow: hidden;
transition: max-height 0.3s ease;
}
.formula-inner {
padding: 12px;
border-top: 1px solid var(--border);
}
.formula-inner p {
color: var(--muted);
margin: 6px 0 10px;
}
/* FRACTIONS */
.frac {
display: inline-block;
text-align: center;
font-size: 0.95em;
}
.frac .top {
display: block;
border-bottom: 1px solid #111;
padding: 0 3px;
}
.frac .bottom {
display: block;
padding: 0 3px;
}
/* ANSWERS */
.reveal-btn {
margin-top: 8px;
padding: 4px 8px;
font-size: .75rem;
border: 1px solid var(--border);
border-radius: 6px;
background: white;
cursor: pointer;
}
.answer {
position: absolute;
bottom: 0px;
right: 0px;
display: none;
}
.calc-panel {
position: fixed;
right: 0;
top: 0;
height: 100vh;
width: 420px;
margin-right: 20px;
transform: translateX(100%);
opacity: 0;
border-left: 1px solid var(--border);
transition: transform 0.6s ease, opacity 0.3s ease;
background: white;
z-index: 999;
}
.calc-panel iframe {
width: 100%;
height: 100vh;
border: none;
}
@media (max-width: 457px) {
.calc-panel {
margin-top: 272px;
}
}
.layout.calc-active .calc-panel {
transform: translateX(0);
opacity: 1;
}
.container, .calc-panel {
will-change: flex, max-width;
}
.grid {
align-items: start;
}
.layout.calc-active .calc-panel {
width: 420px;
opacity: 1;
}
@media (max-width: 457px) {
.layout.calc-active .calc-panel {
width: 100%;
margin-right: 0px;
}
}
/* SCROLLBAR HIDE */
::-webkit-scrollbar {
width: 0;
height: 0;
}
* {
scrollbar-width: none;
-ms-overflow-style: none;
}
</style>
</head>
<body>
<header>
<img src="bigicon.png" width="100" height="100" style="margin-bottom: 20px;"/>
<h1>The SAT Study Guide</h1>
<p>Focused math formulas — Organized by topic — Love from FreeCoderExperience</p>
<p>SAT® is a trademark registered and owned by the College Board®, which is not affiliated with and does not endorse this product or site.</p>
<button class="calc-toggle" onclick="toggleCalc()">
<i class="ri-calculator-line"></i>
<span>Enable Calculator</span>
</button>
</header>
<div class="categories">
<button class="cat-btn active" onclick="filterCat('all',this)">
<i class="ri-apps-line"></i>
<span>All</span>
</button>
<button class="cat-btn" onclick="filterCat('algebra',this)">
<i class="ri-function-line"></i>
<span>Algebra</span>
</button>
<button class="cat-btn" onclick="filterCat('geometry',this)">
<i class="ri-ruler-line"></i>
<span>Geometry</span>
</button>
<button class="cat-btn" onclick="filterCat('trig',this)">
<i class="ri-compass-3-line"></i>
<span>Trigonometry</span>
</button>
<button class="cat-btn" onclick="filterCat('stats',this)">
<i class="ri-bar-chart-line"></i>
<span>Statistics</span>
</button>
</div>
<!-- MAIN SPLIT LAYOUT -->
<div class="layout" id="layout">
<!-- LEFT: CARDS AREA -->
<div class="container">
<div class="grid">
<!-- ALGEBRA -->
<div class="card" data-cat="algebra">
<h2>Linear Equations</h2>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>y = mx + b</span><i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Slope-intercept form. m is slope and b is y-intercept.</p>
<div class="example">
Line: y = 4x + 7. What is the y-intercept?
<br>
<button class="reveal-btn" onclick="revealAnswer(this)">Show Answer</button>
<div class="answer"><strong>Answer:</strong> 7</div>
</div>
</div>
</div>
</div>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>m = <span class="frac"><span class="top">y₂ - y₁</span><span class="bottom">x₂ - x₁</span></span></span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Finds slope between two points.</p>
<div class="example">
(2,3) and (6,11). Find slope.
<br>
<button class="reveal-btn" onclick="revealAnswer(this)">Show Answer</button>
<div class="answer"><strong>Answer:</strong> 2</div>
</div>
</div>
</div>
</div>
</div>
<!-- QUADRATICS -->
<div class="card" data-cat="algebra">
<h2>Quadratics</h2>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>x = <span class="frac"><span class="top">-b ± √(b² - 4ac)</span><span class="bottom">2a</span></span></span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Used to solve quadratic equations.</p>
<div class="example">
Solve x² − 5x + 6 = 0
<br>
<button class="reveal-btn" onclick="revealAnswer(this)">Show Answer</button>
<div class="answer"><strong>Answer:</strong> x = 2 and x = 3</div>
</div>
</div>
</div>
</div>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>b² − 4ac</span><i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>
Discriminant determines the number of real solutions.
<br><br>
b² - 4ac < 0 → No real solutions
<br>
b² - 4ac = 0 → One real solution
<br>
b² - 4ac > 0 → Two real solutions
</p>
<div class="example">
For x² − 6x + 9 = 0
<br>
<button class="reveal-btn" onclick="revealAnswer(this)">Show Answer</button>
<div class="answer"><strong>Answer:</strong> 0</div>
</div>
</div>
</div>
</div>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>Vertex: x = <span class="frac"><span class="top">-b</span><span class="bottom">2a</span></span></span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Finds the x-coordinate of a parabola’s vertex.</p>
<div class="example">
f(x) = x² − 4x + 3
<br>
<button class="reveal-btn" onclick="revealAnswer(this)">Show Answer</button>
<div class="answer">
<strong>Answer:</strong> x = 2, y = -1 → Vertex (2, -1)
</div>
</div>
</div>
</div>
</div>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>Sum of Solutions = -b/a</span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>For ax² + bx + c = 0, the sum of all solutions is -b/a.</p>
<div class="example">
x² - 5x + 6 = 0
<br>
<button class="reveal-btn" onclick="revealAnswer(this)">Show Answer</button>
<div class="answer">
<strong>Answer:</strong> 5
</div>
</div>
</div>
</div>
</div>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>Product of Solutions = c/a</span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>For ax² + bx + c = 0, the product of all solutions is c/a.</p>
<div class="example">
x² - 5x + 6 = 0
<br>
<button class="reveal-btn" onclick="revealAnswer(this)">Show Answer</button>
<div class="answer">
<strong>Answer:</strong> 6
</div>
</div>
</div>
</div>
</div>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>f(a)=0 ⇒ (x-a) is a factor</span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Factor Theorem. If f(a)=0, then (x-a) is a factor of the polynomial.</p>
<div class="example">
f(x)=x²-9. Is (x-3) a factor?
<br>
<button class="reveal-btn" onclick="revealAnswer(this)">Show Answer</button>
<div class="answer">
<strong>Answer:</strong> Yes, because f(3)=0
</div>
</div>
</div>
</div>
</div>
</div>
<!-- GEOMETRY -->
<div class="card" data-cat="geometry">
<h2>Triangles</h2>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>Area = <span class="frac"><span class="top">1</span><span class="bottom">2</span></span>bh</span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Area of a triangle.</p>
<div class="example">
Base 8, height 6.
<br>
<button class="reveal-btn" onclick="revealAnswer(this)">Show Answer</button>
<div class="answer"><strong>Answer:</strong> 24</div>
</div>
</div>
</div>
</div>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>a² + b² = c²</span><i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Pythagorean theorem.</p>
<div class="example">
Sides 5 and 12.
<br>
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<div class="answer"><strong>Answer:</strong> 13</div>
</div>
</div>
</div>
</div>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>a - b < c < a + b</span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Triangle Inequality Theorem. c is the unknown side length and a ≥ b.</p>
<div class="example">
Sides 8 and 5. Possible values of c?
<br>
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<div class="answer">
<strong>Answer:</strong> 3 < c < 13
</div>
</div>
</div>
</div>
</div>
</div>
<div class="card" data-cat="geometry">
<h2>Coordinate Geometry</h2>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>
M = <span class="frac">
<span class="top">(x₁ + x₂, y₁ + y₂)</span>
<span class="bottom">2</span>
</span>
</span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Finds the point exactly halfway between two coordinates.</p>
<div class="example">
(2, 4) and (8, 10)
<br><br>
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<div class="answer">
<strong>Answer:</strong> (5, 7)
</div>
</div>
</div>
</div>
</div>
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>d = √((x₂ − x₁)² + (y₂ − y₁)²)</span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Finds the distance between two points on a coordinate plane.</p>
<div class="example">
(1, 2) and (4, 6)
<br><br>
<button class="reveal-btn" onclick="revealAnswer(this)">Show Answer</button>
<div class="answer">
<strong>Answer:</strong> 5
</div>
</div>
</div>
</div>
</div>
</div>
<!-- 3D SHAPES / VOLUMES -->
<div class="card" data-cat="geometry">
<h2>3D Shapes (Volumes)</h2>
<!-- Rectangular Prism -->
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>V = lwh</span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Volume of a rectangular prism (box).</p>
<div class="example">
l = 4, w = 3, h = 2
<br>
<button class="reveal-btn" onclick="revealAnswer(this)">Show Answer</button>
<div class="answer"><strong>Answer:</strong> 24</div>
</div>
</div>
</div>
</div>
<!-- Cylinder -->
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>V = πr²h</span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Volume of a cylinder.</p>
<div class="example">
r = 3, h = 5
<br>
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<div class="answer"><strong>Answer:</strong> 45π</div>
</div>
</div>
</div>
</div>
<!-- Cone -->
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>V = <span class="frac"><span class="top">1</span><span class="bottom">3</span></span>πr²h</span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Volume of a cone.</p>
<div class="example">
r = 2, h = 9
<br>
<button class="reveal-btn" onclick="revealAnswer(this)">Show Answer</button>
<div class="answer"><strong>Answer:</strong> 12π</div>
</div>
</div>
</div>
</div>
<!-- Sphere -->
<div class="formula">
<div class="formula-header" onclick="toggleFormula(this)">
<span>V = <span class="frac"><span class="top">4</span><span class="bottom">3</span></span>πr³</span>
<i class="ri-arrow-down-s-line chevron"></i>
</div>
<div class="formula-content">
<div class="formula-inner">
<p>Volume of a sphere.</p>