Lecture Notes for Patrick Devlin’s Spring 2019 Sections of MA 15300


(these are the notes that I use in my BoilerCast lectures)














After EXAM 6








Lesson 1

Exponents and the Product, Quotient, and Power Rules


Lesson 6

Factoring and GCF


Factor by Grouping and the ac-method


Factoring using Formulas


Factoring Addendum

Lesson 11

Solving Rational Equations


Solving Rational Formulas


Applications of Rational Equations

Lesson 16

Rectangular Coordinate System


Finding Slope Algebraically


Finding Slope Graphically


Finding the Equation of a Line Algebraically


Finding the Equation of a Line Graphically

Lesson 21

Vertical Shifts


Horizontal Shifts


Vertical and Horizontal Stretch and Compression


Notes for LON-CAPA Problems



Lesson 26

Applications of Piecewise Defined Functions

Lesson 31

Logarithmic Functions


Graphs of Logarithmic Functions

Quiz Rules

Lesson 2

Product to a Power and Quotient to a Power Rules for Exponents


Exponent of Zero and Negative Exponents


Lesson 7

Steps for Factoring


Rational Expressions and Simplifying


Multiplying Fractions and Rational Expressions

Lesson 12

Quadratic Equations, the Zero Factor Theorem, and Factoring


Solving Quadratic Equations by Extracting Square Roots


Solving Formulas that are Quadratic Equations

Lesson 17

Parallel Lines


Perpendicular Lines


Graphing Lines using a Chart


Graphing Lines using Intercepts


Graphing Lines using Slope-Intercept Form

Lesson 22

Matching a Transformation to a Graph


Transforming a Point


Domain and Range of a Transformation


Tables for LON-CAPA Problems

(these do NOT need to be printed for class)

Lesson 27

One-to-one Functions


Inverse Functions

Lesson 32

Common Logs and Natural Logs


Graphs of Common and Natural Logs


Finding the Inverse of an Exponential or Logarithmic Function

Quiz 1 Solution

Lesson 3

Radical Notation


Fractional Exponents


Lesson 8

Dividing Fractions and Rational Expressions


Adding and Subtracting Fractions and Rational Expressions

Lesson 13

Solving Quadratic Equations by Completing the Square


Applications of Quadratic Equations (Part1)

Lesson 18

Functions, Function Notation, and the Domain of a Function


Finding Function Values Algebraically (numeric)

Lesson 23

Quadratic Functions and Parabolas


The Vertex of a Quadratic Function


Finding a Quadratic Function Algebraically from Polynomials

Lesson 28

Domain and Range of an Inverse Function


Checking Inverse Functions

Lesson 33

Solving Log Equations (Part1)


Properties of Logarithms and Solving Log Equations (Part2)

Quiz 2 Solution

Lesson 4

Simplifying Radicals


Rationalizing Denominators


Lesson 9

Complex Fractions and Simplifying

Lesson 14

Solving Quadratic Equations using the Quadratic Formula


Applications of Quadratic Equations (Part2)

Lesson 19

Finding Function Values Algebraically (expressions)


Difference Quotients


Graphs of Functions

Lesson 24

Finding a Quadratic Function Algebraically from Information


Finding a Quadratic Function Graphically


Graphing Quadratic Functions

Lesson 29

Exponential Functions


Graphs of Exponential Functions


Interest Compounded n Times Per Year

Lesson 34

Converting Exponential Equations to Log Equations (Part1)


Converting Exponential Equations to Log Equations (Part2)


Solving Exponential Formulas

Quiz 3 Solution

Lesson 5

Polynomials, Adding and Subtracting


Polynomial Multiplication


Polynomial Division


Lesson 10

Equations and Solving Linear Equations


Solving Linear Formulas


Applications of Linear Equations

Lesson 15

Polynomial Equations


Radical Equations


Equations with Fractional Exponents

Lesson 20

Linear Functions

Lesson 25

Piecewise Defined Functions and Function Values


Graphing Piecewise Defined Functions


Information about the Graph of a Piecewise Defined Function

Lesson 30

Natural Exponential Functions and their Graphs


Finding an Exponential Function Algebraically


Interest Compounded Continuously

Lesson 35

Method of Substitution


Applications of Systems of Equations (Part1)

Quiz 4 Solution







Lesson 36

Method of Elimination


Applications of Systems of Equations (Part2)


Quiz 5 Solution







Lesson 37

Direct Variation


Joint Variation


Indirect Variation


Combined Variation


Quiz 6 Solution








Quiz 7 Solution








Quiz 8 Solution








Quiz 9 Solution








Quiz 10 Solution








Quiz 11 Solution








Quiz 12 Solution








Quiz 13 Solution








Quiz 14 Solution








Quiz 15 Solution








Quiz 16 Solution








Quiz 17 Solution








Quiz 18 Solution








Quiz 19 Solution








Quiz 20 Solution








Quiz 21 Solution








Quiz 22 Solution








Quiz 23 Solution








Quiz 24 Solution








Quiz 25 Solution



Email Patrick at pdevlin@purdue.edu