Summary Complete College Math Notes: Calculus, Algebra, Trigonometry & More

📘 Ultimate College Math Study Guide
Table of Contents
1.​ Algebra
2.​ Functions and Graphs
3.​ Trigonometry
4.​ Pre-Calculus
5.​ Calculus
6.​ Key Formulas & Cheat Sheet
7.​ Practice Questions & Answers
8.​ Study Tips & Strategies




1. Algebra
1.1 Basic Concepts

●​ Variables and constants: Symbols representing numbers.
●​ Expressions: Combination of variables, numbers, and operations.
●​ Equations: Statements that two expressions are equal.

Example: Solve for x:​
2x + 5 = 13​
Solution:​
2x = 13 − 5 → 2x = 8 → x = 4




1.2 Factoring

●​ Factoring quadratics: a² + 5a + 6 = (a + 2)(a + 3)
●​ Difference of squares: a² − b² = (a − b)(a + b)
●​ Factoring by grouping: ab + ac + bd + bc = (a + b)(c + d)

Practice Problem: Factor x² − 9

, 1.3 Solving Equations

●​ Linear equations: ax + b = c
●​ Quadratic equations: ax² + bx + c = 0 → use factoring or quadratic formula

Quadratic formula:​
x = [−b ± √(b² − 4ac)] / 2a

Practice Problem: Solve x² − 5x + 6 = 0




2. Functions and Graphs
2.1 Functions

●​ Definition: A relation where each input has exactly one output.
●​ Notation: f(x), g(x), h(x)

Example: f(x) = 2x + 3

●​ f(2) = 2(2) + 3 = 7




2.2 Graphs

●​ Linear function: y = mx + b → slope = m, y-intercept = b
●​ Quadratic function: y = ax² + bx + c → parabola shape
●​ Exponential function: y = a·b^x → growth/decay

Practice Problem: Graph y = x² − 4x + 3




3. Trigonometry
3.1 Basic Ratios

●​ sin(θ) = opposite / hypotenuse
●​ cos(θ) = adjacent / hypotenuse
●​ tan(θ) = opposite / adjacent

Practice Problem: Find sin(30°), cos(60°), tan(45°)