Mathematics Study Guide
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## **1. Algebra & Functions**
Algebra is the foundation of most mathematics. It involves solving equations, working with
variables, and understanding relationships between quantities.
### Key Concepts:
* Variables and constants
* Expressions and equations
* Functions and graphs
* Domain and range
* Function transformations
### Important Formulas:
* Linear:
**y = mx + b**
* Slope:
**m = (y₂ - y₁) / (x₂ - x₁)**
* Quadratic:
**ax² + bx + c = 0**
* Quadratic Formula:
**x = (-b ± √(b² - 4ac)) / 2a**
* Exponent Rules:
**a^m × a^n = a^(m+n)**
**(a^m)^n = a^(mn)**
**a⁰ = 1**
### Skills to Practice:
* Solving equations and inequalities
* Graphing functions
* Factoring polynomials
* Understanding transformations
---
## **2. Trigonometry**
, Trigonometry studies relationships between angles and sides of triangles.
### Key Concepts:
* Right triangles
* Unit circle
* Radians and degrees
* Trigonometric identities
### Important Formulas:
* SOH-CAH-TOA:
**sinθ = opposite/hypotenuse**
**cosθ = adjacent/hypotenuse**
**tanθ = opposite/adjacent**
* Pythagorean Identity:
**sin²θ + cos²θ = 1**
* Tangent Identity:
**tanθ = sinθ / cosθ**
### Unit Circle:
* Important angles: 0°, 30°, 45°, 60°, 90°
* Memorize sine and cosine values
### Skills to Practice:
* Solving triangles
* Using identities
* Graphing trig functions
---
## **3. Calculus I – Limits & Derivatives**
Calculus focuses on change and motion.
### Key Concepts:
* Limits
* Continuity
---
## **1. Algebra & Functions**
Algebra is the foundation of most mathematics. It involves solving equations, working with
variables, and understanding relationships between quantities.
### Key Concepts:
* Variables and constants
* Expressions and equations
* Functions and graphs
* Domain and range
* Function transformations
### Important Formulas:
* Linear:
**y = mx + b**
* Slope:
**m = (y₂ - y₁) / (x₂ - x₁)**
* Quadratic:
**ax² + bx + c = 0**
* Quadratic Formula:
**x = (-b ± √(b² - 4ac)) / 2a**
* Exponent Rules:
**a^m × a^n = a^(m+n)**
**(a^m)^n = a^(mn)**
**a⁰ = 1**
### Skills to Practice:
* Solving equations and inequalities
* Graphing functions
* Factoring polynomials
* Understanding transformations
---
## **2. Trigonometry**
, Trigonometry studies relationships between angles and sides of triangles.
### Key Concepts:
* Right triangles
* Unit circle
* Radians and degrees
* Trigonometric identities
### Important Formulas:
* SOH-CAH-TOA:
**sinθ = opposite/hypotenuse**
**cosθ = adjacent/hypotenuse**
**tanθ = opposite/adjacent**
* Pythagorean Identity:
**sin²θ + cos²θ = 1**
* Tangent Identity:
**tanθ = sinθ / cosθ**
### Unit Circle:
* Important angles: 0°, 30°, 45°, 60°, 90°
* Memorize sine and cosine values
### Skills to Practice:
* Solving triangles
* Using identities
* Graphing trig functions
---
## **3. Calculus I – Limits & Derivatives**
Calculus focuses on change and motion.
### Key Concepts:
* Limits
* Continuity
