✨ Math 41 Quiz Time! ✨

End Behavior & Trigonometry — Learn, Practice, Master! 🎯

Welcome, Math Star! 🌟

This quiz covers two important topics from Math 41.
Read the concepts first, then pick any questions you want to practice!

📈 Polynomial Degree 🔢 Leading Coefficient ➡️ End Behavior 🔵 Unit Circle 📐 sin / cos / tan 🎯 Even & Odd Functions
📊 Topic 1: Polynomial Basics — Degree & Leading Coefficient

A polynomial is an expression with terms like \(ax^n\). The key features are:

🔑 Degree = the highest exponent in the polynomial.
🔑 Leading coefficient = the number in front of the highest-degree term.
🔑 Even degree → both ends go the same direction.
🔑 Odd degree → ends go opposite directions.
📝 Example: \( f(x) = 3x^5 - 6x^2 - 10 \)

• Degree = 5 (highest power is 5) → Odd

• Leading coefficient = 3 (positive)

• End behavior: As \(x \to -\infty\), \(y \to -\infty\)  |  As \(x \to +\infty\), \(y \to +\infty\)

✅ Think: odd degree + positive LC → falls left, rises right!
➡️ Topic 2: End Behavior Rules
Even degree, Positive LC: \(y \to +\infty\) on both sides ↑ ↑
Even degree, Negative LC: \(y \to -\infty\) on both sides ↓ ↓
Odd degree, Positive LC: left ↓, right ↑
Odd degree, Negative LC: left ↑, right ↓
📝 Example: \( g(x) = 15x + 4x^3 - 7x^7 \)

Rewrite in standard form: \( g(x) = -7x^7 + 4x^3 + 15x \)

• Degree = 7 (odd)  •  Leading coefficient = −7 (negative)

• Odd + Negative: As \(x \to -\infty\), \(y \to +\infty\); As \(x \to +\infty\), \(y \to -\infty\)

✅ Odd + negative LC → rises left, falls right!
🔵 Topic 3: Unit Circle & Trig Values

A point \((x, y)\) on the unit circle at angle \(\theta\) gives:

🔑 \(\cos\theta = x\) (the x-coordinate)
🔑 \(\sin\theta = y\) (the y-coordinate)
🔑 \(\tan\theta = \dfrac{y}{x} = \dfrac{\sin\theta}{\cos\theta}\)
📝 Example: Point \(\left(\dfrac{4}{7},\, \dfrac{\sqrt{33}}{7}\right)\) on the unit circle

• \(\sin\theta = \dfrac{\sqrt{33}}{7}\)

• \(\cos\theta = \dfrac{4}{7}\)

• \(\tan\theta = \dfrac{\sqrt{33}/7}{4/7} = \dfrac{\sqrt{33}}{4}\)

✅ Just read (cos, sin) from the (x, y) coordinate!
Choose Your Questions! 🎯
Select the questions you want to practice, then press Start!
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