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Workbook 10

Chapter 1: Exponents

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Objectives

Understand exponents

• Video: Solving exponential equation | Exponential and logarithmic functions | Algebra II | Khan Academy - YouTube
• Video: Solving Exponential Equations - YouTube
• Reference: Exponentiation - Wikipedia

Understand exponent properties

• Video: Solving exponential equations using exponent properties | High School Math | Khan Academy - YouTube
• Reference: Exponent Rules | Laws of Exponents | Exponent Rules Chart

Understand fractional exponents

• Video: Basic fractional exponents | Exponent expressions and equations | Algebra I | Khan Academy - YouTube
• Video: Fractional Exponents - YouTube
• Reference: Fractional Exponents - Rules, Method, Simplification, Examples

Prerequisites

• Understand interest and compound interest from Chapter 2: "Compound Interest" in Workbook 10
• Understand and define a function, and its domains/ranges. Differentiate from relations. Be able to use functions to find their input/outputs. from Chapter 4: "Functions and Their Graphs" in Workbook 05

Chapter 2: Compound Interest

PDF

Objectives

Understand interest and compound interest

• Video: Compound interest introduction | Interest and debt | Finance & Capital Markets | Khan Academy - YouTube
• Video: Introduction to interest | Interest and debt | Finance & Capital Markets | Khan Academy - YouTube
• Video: The rule of 72 for compound interest | Interest and debt | Finance & Capital Markets | Khan Academy - YouTube
• Reference: Compound interest - Wikipedia

Calculate exponential growth and understand exponents

• Video: Exponential growth functions | Exponential and logarithmic functions | Algebra II | Khan Academy - YouTube
• Video: Exponential growth and epidemics - YouTube
• Reference: Exponential growth - Wikipedia
• Reference: Exponential function - Wikipedia

Prerequisites

• Define a spreadsheet from Chapter 2: "Basic Statistics in Spreadsheets" in Workbook 03

Chapter 3: Logarithms

PDF

Objectives

Understand how to use logarithms

• Video: Logarithms - The Easy Way! - YouTube
• Video: Logarithms, Explained - Steve Kelly - YouTube
• Video: Introduction to Logarithms - YouTube
• Reference: Logarithm - Wikipedia

Understand how to use logarithm properties

• Video: Properties of Logarithms - YouTube
• Reference: Logarithm - Wikipedia

Understand natural logs

• Video: Natural Logarithms - YouTube
• Reference: Natural logarithm - Wikipedia

Prerequisites

• Understand exponents from Chapter 1: "Exponents" in Workbook 10
• Understand exponent properties from Chapter 1: "Exponents" in Workbook 10
• Be able to program in python. This holistic overview includes writing lines of code, creating variables, understand basic file structure, up to advanced data structures and simulation libraries. from Chapter 1: "Falling Bodies" in Workbook 07
• Define a spreadsheet from Chapter 2: "Basic Statistics in Spreadsheets" in Workbook 03

Chapter 4: Exponential Decay

PDF

Objectives

Understand and calculate exponential decay

• Video: Introduction to exponential decay - YouTube
• Video: Exponential Decay Functions - YouTube
• Video: Exponential Growth and Decay Word Problems & Functions - Algebra & Precalculus - YouTube
• Video: Graphing exponential growth & decay | Mathematics I | High School Math | Khan Academy - YouTube
• Reference: Exponential decay - Wikipedia

Understand the concept of a half life

• Video: Half Life Chemistry Problems - Nuclear Radioactive Decay Calculations Practice Examples - YouTube
• Video: Nuclear Half Life: Intro and Explanation - YouTube
• Reference: Half-life - Wikipedia

Prerequisites

• Calculate exponential growth and understand exponents from Chapter 2: "Compound Interest" in Workbook 10
• Understand interest and compound interest from Chapter 2: "Compound Interest" in Workbook 10
• Understand exponents from Chapter 1: "Exponents" in Workbook 10
• Understand exponent properties from Chapter 1: "Exponents" in Workbook 10
• Understand fractional exponents from Chapter 1: "Exponents" in Workbook 10
• Define a spreadsheet from Chapter 2: "Basic Statistics in Spreadsheets" in Workbook 03

Chapter 5: Inverse Trigonometric Functions

PDF

Objectives

Understand and calculate all inverse trig functions

• Video: Evaluating Inverse Trigonometric Functions - YouTube
• Video: Evaluate Inverse Trig Functions - Step by Step - YouTube
• Video: Inverse Trigonometric Functions - YouTube
• Video: Inverse trig functions: arcsin | Trigonometry | Khan Academy - YouTube
• Video: Inverse trig functions: arccos | Trigonometry | Khan Academy - YouTube
• Video: Inverse trig functions: arctan | Trigonometry | Khan Academy - YouTube
• Reference: Inverse trigonometric functions - Wikipedia
• Reference: Khan Academy

Know the inverse trig derivatives

• Video: Derivatives of Inverse Trigonometric Functions - YouTube
• Video: Inverse trig functions derivatives - YouTube
• Reference: Inverse trigonometric functions - Wikipedia

Prerequisites

• Understand the relationships with all of the trig functions from Chapter 1: "Trigometric Functions" in Workbook 06
• Identify a right triangle from Chapter 6: "Pythagorean Theorem" in Workbook 04
• Understand the conversion between functions and their inverses. from Chapter 4: "Functions and Their Graphs" in Workbook 05
• Introduction to the sine function and its graph from Chapter 1: "Trigometric Functions" in Workbook 06
• Introduction to the cosine function and its graph from Chapter 1: "Trigometric Functions" in Workbook 06

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