feat(lessons): add lessons from client db
This commit is contained in:
shafin-r
473
src/pages/student/lessons/RationalRadicalLesson.tsx
Normal file
473
src/pages/student/lessons/RationalRadicalLesson.tsx
Normal file
@ -0,0 +1,473 @@
|
||||
import React, { useRef, useState, useEffect } from "react";
|
||||
import { ArrowDown, Check, BookOpen, Target, Grid } from "lucide-react";
|
||||
import RationalExplorer from "../../../components/lessons/RationalExplorer";
|
||||
import RadicalSolutionWidget from "../../../components/lessons/RadicalSolutionWidget";
|
||||
import Quiz from "../../../components/lessons/Quiz";
|
||||
import { ADV_RATIONAL_QUIZ } from "../../../utils/constants";
|
||||
import { Frac } from "../../../components/Math";
|
||||
|
||||
interface LessonProps {
|
||||
onFinish?: () => void;
|
||||
}
|
||||
|
||||
const RationalRadicalLesson: React.FC<LessonProps> = ({ onFinish }) => {
|
||||
const [activeSection, setActiveSection] = useState(0);
|
||||
const sectionsRef = useRef<(HTMLElement | null)[]>([]);
|
||||
|
||||
const scrollToSection = (index: number) => {
|
||||
setActiveSection(index);
|
||||
sectionsRef.current[index]?.scrollIntoView({
|
||||
behavior: "smooth",
|
||||
block: "start",
|
||||
});
|
||||
};
|
||||
|
||||
useEffect(() => {
|
||||
const observer = new IntersectionObserver(
|
||||
(entries) => {
|
||||
entries.forEach((entry) => {
|
||||
if (entry.isIntersecting) {
|
||||
const index = sectionsRef.current.indexOf(
|
||||
entry.target as HTMLElement,
|
||||
);
|
||||
if (index !== -1) setActiveSection(index);
|
||||
}
|
||||
});
|
||||
},
|
||||
{ rootMargin: "-20% 0px -60% 0px" },
|
||||
);
|
||||
sectionsRef.current.forEach((section) => {
|
||||
if (section) observer.observe(section);
|
||||
});
|
||||
return () => observer.disconnect();
|
||||
}, []);
|
||||
|
||||
const SectionMarker = ({
|
||||
index,
|
||||
title,
|
||||
icon: Icon,
|
||||
}: {
|
||||
index: number;
|
||||
title: string;
|
||||
icon: any;
|
||||
}) => {
|
||||
const isActive = activeSection === index;
|
||||
const isPast = activeSection > index;
|
||||
return (
|
||||
<button
|
||||
onClick={() => scrollToSection(index)}
|
||||
className={`flex items-center gap-3 p-3 w-full rounded-lg transition-all ${isActive ? "bg-white shadow-md border border-violet-100" : "hover:bg-slate-100"}`}
|
||||
>
|
||||
<div
|
||||
className={`w-8 h-8 rounded-full flex items-center justify-center shrink-0 ${isActive ? "bg-violet-600 text-white" : isPast ? "bg-violet-400 text-white" : "bg-slate-200 text-slate-500"}`}
|
||||
>
|
||||
{isPast ? (
|
||||
<Check className="w-4 h-4" />
|
||||
) : (
|
||||
<Icon className="w-4 h-4" />
|
||||
)}
|
||||
</div>
|
||||
<div className="text-left">
|
||||
<p
|
||||
className={`text-sm font-bold ${isActive ? "text-violet-900" : "text-slate-600"}`}
|
||||
>
|
||||
{title}
|
||||
</p>
|
||||
</div>
|
||||
</button>
|
||||
);
|
||||
};
|
||||
|
||||
return (
|
||||
<div className="flex flex-col lg:flex-row min-h-screen">
|
||||
<aside className="w-full lg:w-64 lg:fixed lg:top-20 lg:bottom-0 lg:overflow-y-auto p-4 border-r border-slate-200 bg-slate-50 z-0 hidden lg:block">
|
||||
<nav className="space-y-2">
|
||||
<SectionMarker index={0} title="Rational Functions" icon={Grid} />
|
||||
<SectionMarker index={1} title="Radical Equations" icon={Target} />
|
||||
<SectionMarker index={2} title="Practice" icon={BookOpen} />
|
||||
</nav>
|
||||
</aside>
|
||||
|
||||
<div className="flex-1 lg:ml-64 p-6 md:p-12 max-w-4xl mx-auto">
|
||||
{/* Section 1: Rational Functions */}
|
||||
<section
|
||||
ref={(el) => {
|
||||
sectionsRef.current[0] = el;
|
||||
}}
|
||||
className="min-h-screen flex flex-col justify-center mb-24 pt-20 lg:pt-0"
|
||||
>
|
||||
<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
|
||||
Rational Functions & Discontinuities
|
||||
</h2>
|
||||
<div className="prose prose-slate text-lg text-slate-600 mb-8">
|
||||
<p>
|
||||
A <strong>rational function</strong> is any function of the form
|
||||
f(x) = P(x) ÷ Q(x), where both P and Q are polynomials. Wherever
|
||||
Q(x) = 0, the function is undefined — creating a{" "}
|
||||
<strong>discontinuity</strong>. There are two types of
|
||||
discontinuities: holes and vertical asymptotes.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
{/* Holes vs Vertical Asymptotes */}
|
||||
<div className="bg-violet-50 border border-violet-200 rounded-2xl p-6 mb-8 space-y-5">
|
||||
<h3 className="text-lg font-bold text-violet-900">
|
||||
Holes vs. Vertical Asymptotes
|
||||
</h3>
|
||||
|
||||
<div className="bg-violet-100 rounded-xl p-4 text-sm">
|
||||
<p className="font-bold text-violet-900 mb-1">
|
||||
Key Step: Always Factor Both Numerator and Denominator First
|
||||
</p>
|
||||
<p className="text-slate-700">
|
||||
Once factored, look at the denominator's zeros. If a zero also
|
||||
cancels with the numerator → <strong>hole</strong>. If it does
|
||||
not cancel → <strong>vertical asymptote</strong>.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div className="grid grid-cols-1 md:grid-cols-2 gap-4">
|
||||
<div className="bg-white rounded-xl p-5 border border-violet-100">
|
||||
<div className="text-center mb-3">
|
||||
<span className="inline-block bg-amber-100 text-amber-800 font-bold px-3 py-1 rounded-full text-sm">
|
||||
Hole (Removable Discontinuity)
|
||||
</span>
|
||||
</div>
|
||||
<p className="text-slate-600 text-sm mb-2">
|
||||
Occurs when a factor in the denominator{" "}
|
||||
<strong>also cancels</strong> with a factor in the numerator.
|
||||
The function is undefined at that x-value, but there's no
|
||||
asymptote.
|
||||
</p>
|
||||
<div className="bg-amber-50 rounded-lg p-3 font-mono text-sm">
|
||||
<p className="text-slate-600">
|
||||
f(x) = <Frac n="(x − 2)(x + 3)" d="(x − 2)(x − 1)" />
|
||||
</p>
|
||||
<p className="text-slate-600">
|
||||
After canceling: f(x) = <Frac n="x + 3" d="x − 1" />
|
||||
</p>
|
||||
<p className="text-amber-700 font-bold">
|
||||
Hole at x = 2 (canceled factor)
|
||||
</p>
|
||||
<p className="text-violet-700 font-bold">
|
||||
V. asymptote at x = 1 (remains)
|
||||
</p>
|
||||
</div>
|
||||
<p className="text-slate-500 text-xs mt-2">
|
||||
To find the y-coordinate of the hole: plug x = 2 into the
|
||||
simplified function: f(2) = (2 + 3) ÷ (2 − 1) = 5. Hole is at
|
||||
(2, 5).
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div className="bg-white rounded-xl p-5 border border-violet-100">
|
||||
<div className="text-center mb-3">
|
||||
<span className="inline-block bg-red-100 text-red-800 font-bold px-3 py-1 rounded-full text-sm">
|
||||
Vertical Asymptote
|
||||
</span>
|
||||
</div>
|
||||
<p className="text-slate-600 text-sm mb-2">
|
||||
Occurs when a denominator factor does{" "}
|
||||
<strong>NOT cancel</strong>. The function approaches ±∞ near
|
||||
that x-value. The graph has a vertical line it never crosses.
|
||||
</p>
|
||||
<div className="bg-red-50 rounded-lg p-3 font-mono text-sm">
|
||||
<p className="text-slate-600">
|
||||
f(x) = <Frac n="x + 1" d="(x − 3)(x + 2)" />
|
||||
</p>
|
||||
<p className="text-slate-600">No factors cancel.</p>
|
||||
<p className="text-red-700 font-bold">
|
||||
V. asymptotes at x = 3 and x = −2
|
||||
</p>
|
||||
</div>
|
||||
<p className="text-slate-500 text-xs mt-2">
|
||||
The denominator has zeros at x = 3 and x = −2. Neither cancels
|
||||
with the numerator, so both are vertical asymptotes.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
{/* Horizontal Asymptotes */}
|
||||
<div className="bg-white rounded-xl p-5 border border-violet-100">
|
||||
<p className="font-bold text-violet-800 mb-3">
|
||||
Horizontal Asymptotes — End Behavior of Rational Functions
|
||||
</p>
|
||||
<p className="text-slate-600 text-sm mb-3">
|
||||
Compare the degree of the numerator (n) to the degree of the
|
||||
denominator (d):
|
||||
</p>
|
||||
<div className="overflow-x-auto">
|
||||
<table className="w-full text-sm border-collapse">
|
||||
<thead>
|
||||
<tr className="bg-violet-100 text-violet-900">
|
||||
<th className="p-2 text-left font-bold">Condition</th>
|
||||
<th className="p-2 text-left font-bold">
|
||||
Horizontal Asymptote
|
||||
</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody className="text-slate-600">
|
||||
<tr className="border-b border-violet-50">
|
||||
<td className="p-2 font-semibold">
|
||||
n < d (numerator degree lower)
|
||||
</td>
|
||||
<td className="p-2">y = 0</td>
|
||||
</tr>
|
||||
<tr className="border-b border-violet-50 bg-violet-50">
|
||||
<td className="p-2 font-semibold">n = d (same degree)</td>
|
||||
<td className="p-2">
|
||||
y ={" "}
|
||||
<Frac
|
||||
n="leading coefficient of top"
|
||||
d="leading coefficient of bottom"
|
||||
/>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td className="p-2 font-semibold">
|
||||
n > d (numerator degree higher)
|
||||
</td>
|
||||
<td className="p-2">
|
||||
No horizontal asymptote (oblique asymptote instead)
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
</div>
|
||||
<div className="mt-3 bg-violet-50 rounded-lg p-3 text-sm font-mono">
|
||||
<p className="text-slate-600">
|
||||
f(x) = <Frac n="3x²" d="x² − 4" />: n = d = 2 → H.A. at y ={" "}
|
||||
<Frac n="3" d="1" /> ={" "}
|
||||
<strong className="text-violet-700">3</strong>
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<RationalExplorer />
|
||||
<button
|
||||
onClick={() => scrollToSection(1)}
|
||||
className="mt-12 group flex items-center text-violet-600 font-bold hover:text-violet-800 transition-colors"
|
||||
>
|
||||
Next: Radical Equations{" "}
|
||||
<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
|
||||
</button>
|
||||
</section>
|
||||
|
||||
{/* Section 2: Radical Equations */}
|
||||
<section
|
||||
ref={(el) => {
|
||||
sectionsRef.current[1] = el;
|
||||
}}
|
||||
className="min-h-screen flex flex-col justify-center mb-24"
|
||||
>
|
||||
<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
|
||||
Radical Equations & Extraneous Solutions
|
||||
</h2>
|
||||
<div className="prose prose-slate text-lg text-slate-600 mb-8">
|
||||
<p>
|
||||
A <strong>radical equation</strong> has the variable under a
|
||||
square root (or other radical). The key strategy is to isolate the
|
||||
radical and then raise both sides to the appropriate power to
|
||||
eliminate it. This process can introduce{" "}
|
||||
<strong>extraneous solutions</strong> — values that satisfy the
|
||||
transformed equation but not the original. You{" "}
|
||||
<strong>must always check</strong> your answers in the original
|
||||
equation.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div className="bg-violet-50 border border-violet-200 rounded-2xl p-6 mb-8 space-y-5">
|
||||
<h3 className="text-lg font-bold text-violet-900">
|
||||
Solving Radical Equations: Step-by-Step
|
||||
</h3>
|
||||
|
||||
<div className="bg-white rounded-xl p-5 border border-violet-100">
|
||||
<p className="font-bold text-violet-800 mb-3">General Process</p>
|
||||
<div className="space-y-2">
|
||||
{[
|
||||
{
|
||||
step: "1",
|
||||
text: "Isolate the radical on one side of the equation.",
|
||||
},
|
||||
{
|
||||
step: "2",
|
||||
text: "Square both sides (for square roots) or cube both sides (for cube roots).",
|
||||
},
|
||||
{
|
||||
step: "3",
|
||||
text: "Solve the resulting equation (may be linear or quadratic).",
|
||||
},
|
||||
{
|
||||
step: "4",
|
||||
text: "CHECK all solutions in the ORIGINAL equation. Reject any that make the original false.",
|
||||
},
|
||||
].map((item) => (
|
||||
<div key={item.step} className="flex gap-3 items-start">
|
||||
<div className="w-6 h-6 bg-violet-600 text-white rounded-full flex items-center justify-center font-bold text-xs shrink-0">
|
||||
{item.step}
|
||||
</div>
|
||||
<p className="text-slate-600 text-sm">{item.text}</p>
|
||||
</div>
|
||||
))}
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div className="grid grid-cols-1 md:grid-cols-2 gap-4">
|
||||
<div className="bg-white rounded-xl p-5 border border-violet-100">
|
||||
<p className="font-bold text-green-700 mb-3">
|
||||
Example 1 — No Extraneous Solution
|
||||
</p>
|
||||
<div className="font-mono text-sm space-y-1 text-slate-600">
|
||||
<p>√(x + 3) = 5</p>
|
||||
<p>Square both sides:</p>
|
||||
<p>x + 3 = 25</p>
|
||||
<p>x = 22</p>
|
||||
<p className="text-slate-500 mt-1">
|
||||
Check: √(22 + 3) = √25 = 5 ✓
|
||||
</p>
|
||||
<p className="text-green-700 font-bold">x = 22 ✓ (valid)</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div className="bg-white rounded-xl p-5 border border-violet-100">
|
||||
<p className="font-bold text-red-700 mb-3">
|
||||
Example 2 — Extraneous Solution Found!
|
||||
</p>
|
||||
<div className="font-mono text-sm space-y-1 text-slate-600">
|
||||
<p>√(2x + 1) = x − 1</p>
|
||||
<p>Square both sides:</p>
|
||||
<p>2x + 1 = x² − 2x + 1</p>
|
||||
<p>0 = x² − 4x → x(x − 4) = 0</p>
|
||||
<p>x = 0 or x = 4</p>
|
||||
<p className="text-slate-500 mt-1">
|
||||
Check x = 0: √1 = 0 − 1 → 1 ≠ −1 ✗
|
||||
</p>
|
||||
<p className="text-slate-500">
|
||||
Check x = 4: √9 = 4 − 1 → 3 = 3 ✓
|
||||
</p>
|
||||
<p className="text-red-700 font-bold">
|
||||
x = 0 is extraneous! Only x = 4.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
{/* Why Extraneous Solutions Occur */}
|
||||
<div className="bg-violet-100 rounded-xl p-4 text-sm">
|
||||
<p className="font-bold text-violet-900 mb-1">
|
||||
Why Do Extraneous Solutions Appear?
|
||||
</p>
|
||||
<p className="text-slate-700">
|
||||
Squaring both sides is not a reversible step — if you square a
|
||||
negative number, it becomes positive. For example, if the
|
||||
original equation has √x = A, then A must be non-negative (a
|
||||
square root can never give a negative output). But squaring
|
||||
produces solutions for both A and −A. Any solution that would
|
||||
require the radical to equal a negative number is extraneous.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
{/* Rational Exponents */}
|
||||
<div className="bg-white rounded-xl p-5 border border-violet-100">
|
||||
<p className="font-bold text-violet-800 mb-3">
|
||||
Rational Exponents: Connecting Radicals and Powers
|
||||
</p>
|
||||
<div className="bg-violet-50 rounded-lg p-3 text-center mb-3">
|
||||
<p className="font-mono text-violet-800 font-bold text-lg">
|
||||
x<sup>m/n</sup> = (<sup>n</sup>√x)<sup>m</sup> = <sup>n</sup>
|
||||
√(x<sup>m</sup>)
|
||||
</p>
|
||||
</div>
|
||||
<div className="grid grid-cols-1 sm:grid-cols-3 gap-3 text-sm">
|
||||
<div className="bg-violet-50 rounded-lg p-3 text-center">
|
||||
<p className="font-mono text-violet-700 font-bold">
|
||||
x<sup>1/2</sup> = √x
|
||||
</p>
|
||||
<p className="text-slate-500 text-xs mt-1">
|
||||
Exponent ½ = square root
|
||||
</p>
|
||||
</div>
|
||||
<div className="bg-violet-50 rounded-lg p-3 text-center">
|
||||
<p className="font-mono text-violet-700 font-bold">
|
||||
x<sup>1/3</sup> = <sup>3</sup>√x
|
||||
</p>
|
||||
<p className="text-slate-500 text-xs mt-1">
|
||||
Exponent ⅓ = cube root
|
||||
</p>
|
||||
</div>
|
||||
<div className="bg-violet-50 rounded-lg p-3 text-center">
|
||||
<p className="font-mono text-violet-700 font-bold">
|
||||
x<sup>2/3</sup> = (<sup>3</sup>√x)²
|
||||
</p>
|
||||
<p className="text-slate-500 text-xs mt-1">
|
||||
Numerator = power, denominator = root
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<div className="mt-3 bg-violet-50 rounded-lg p-3 font-mono text-sm">
|
||||
<p className="text-slate-600">
|
||||
Solve: x<sup>2/3</sup> = 4
|
||||
</p>
|
||||
<p className="text-slate-600">
|
||||
Raise both sides to power 3/2: x = 4<sup>3/2</sup> = (√4)³ =
|
||||
2³ = <strong className="text-violet-700">8</strong>
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div className="bg-red-50 border border-red-200 rounded-xl p-4 text-sm">
|
||||
<p className="font-bold text-red-800 mb-1">
|
||||
SAT Trap: The Domain of Radical Functions
|
||||
</p>
|
||||
<p className="text-slate-700">
|
||||
For even roots (square root, fourth root, etc.), the expression
|
||||
under the radical must be <strong>≥ 0</strong>. The SAT may test
|
||||
this by asking for the domain of f(x) = √(2x − 6). Set 2x − 6 ≥
|
||||
0 → x ≥ 3. The domain is x ≥ 3.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<RadicalSolutionWidget />
|
||||
|
||||
<button
|
||||
onClick={() => scrollToSection(2)}
|
||||
className="mt-12 group flex items-center text-violet-600 font-bold hover:text-violet-800 transition-colors"
|
||||
>
|
||||
Next: Practice Quiz{" "}
|
||||
<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
|
||||
</button>
|
||||
</section>
|
||||
|
||||
{/* Section 3: Quiz */}
|
||||
<section
|
||||
ref={(el) => {
|
||||
sectionsRef.current[2] = el;
|
||||
}}
|
||||
className="min-h-screen flex flex-col justify-center"
|
||||
>
|
||||
<h2 className="text-4xl font-extrabold text-slate-900 mb-8">
|
||||
Practice Time
|
||||
</h2>
|
||||
{ADV_RATIONAL_QUIZ.map((quiz, idx) => (
|
||||
<div key={quiz.id} className="mb-12">
|
||||
<Quiz data={quiz} />
|
||||
</div>
|
||||
))}
|
||||
<div className="p-8 bg-violet-900 rounded-2xl text-white text-center mt-12">
|
||||
<h3 className="text-2xl font-bold mb-4">Topic Mastered!</h3>
|
||||
<button
|
||||
onClick={onFinish}
|
||||
className="px-6 py-3 bg-white text-violet-900 font-bold rounded-full hover:bg-violet-50 transition-colors"
|
||||
>
|
||||
Finish Lesson ✓
|
||||
</button>
|
||||
</div>
|
||||
</section>
|
||||
</div>
|
||||
</div>
|
||||
);
|
||||
};
|
||||
|
||||
export default RationalRadicalLesson;
|
||||
Reference in New Issue
Block a user