Kurzius Math Notes

Table of Contents

• AP Calculus
  • P Preparation for Calculus
  • 1 Limits and Their Properties
  • 2 Differentiation
  • Cheat Sheets
• Algebra II and Trigonometry Honors
  • 1 Linear Functions and Systems
  • 2 Quadratic Functions and Equations
• Probability and Statistics
  • 1 Displaying a single quantitative variable
  • 2 Analyzing a single quantitative variable

AP Calculus

P Preparation for Calculus

• P.1 Graphs and Models
• P.2 Linear Model and Rates of Change
• P.3 Functions and Their Graphs
• P.4 Inverse Functions
• P.5 Exponential and Logarithmic Functions

1 Limits and Their Properties

• 1.1 A Preview of Calculus
• 1.2 Finding Limits Graphically and Numerically
• 1.3 Evaluating Limits Analytically
• 1.4 Continuity and One-Sided Limits
• 1.5 Infinite Limits
• 1.6 Limits at Infinity

2 Differentiation

• 2.1 The Derivative and the Tangent Line Problem
• 2.2 Basic Differentiation Rules and Rates of Change
• 2.3 Product and Quotient Rules and Higher-Order Derivatives
• 2.4 The Chain Rule
• 2.5 Implicit Differentiation
• 2.6 Derivatives of Inverse Functions
• 2.7 Related Rates

Cheat Sheets

• Differentiation cheat sheet
• Integration cheat sheet

Algebra II and Trigonometry Honors

1 Linear Functions and Systems

• 1.1 Key Features of Functions
• 1.2 Transformation of Functions
• 1.3 Piecewise-Defined Functions
• 1.4 Arithmetic Sequences and Series
• 1.5 Solving Equations and Inequalities By Graphing
• 1.6 Linear Systems
• 1.7 Solving Linear Systems Using Matrices

2 Quadratic Functions and Equations

• 2.1 Vertex Form of a Quadratic Formula
• 2.2 Standard Form of a Quadratic Formula
• 2.3 Factored Form of a Quadratic Function
• 2.4 Complex Numbers and Operations
• 2.5 Completing the Square
• 2.6 The Quadratic Formula
• 2.7 Linear-Quadratic Systems

Probability and Statistics

Old notes

1 Displaying a single quantitative variable

• Mean and median in data displays
• Interquartile range
• Box and whisker plots

2 Analyzing a single quantitative variable

• Standard deviation
• Comparing distributions
• Percentiles and z-scores
• Normal distributions and the empirical rule
• Normal distribution calculations