## Lecture Notes

Lecture Notes

... or separate links can be found below to each video in the "Course Materials Organized By Section" portion of the page

## Class Videos

Class Videos

... or separate links can be found below to each video in the "Course Materials Organized By Section" portion of the page

## Homework Assignments

The exact list of problems to be completed in each section can be found at this link:

Due Date --- Homework Number --- Sections Due

Tuesday Sep. 08, 2015 --- Homework #1 --- Sections 1.1-1.6

Tuesday Sep. 15, 2015 --- Homework #2 --- Sections 1.7-1.8, 2.1-2.3

Tuesday Sep. 22, 2015 --- Homework #3 --- Sections 2.4-2.7

Tuesday Sep. 29, 2015 --- Homework #4 --- Sections 3.1

Tuesday Oct. 06, 2015 --- Homework #5 --- Sections 3.2-3.4

Tuesday Oct. 13, 2015 --- Homework #6 --- Sections 3.5, 4.1-4.3

Tuesday Oct. 20, 2015 --- Homework #7 --- Sections 5.1-5.2

Tuesday Oct. 27, 2015 --- Homework #8 --- Sections 5.3 and 5.5

Tuesday Nov. 03, 2015 --- Homework #9 --- Sections 6.1-6.4

Tuesday Nov. 10, 2015 --- Homework #10 --- Sections 6.5-6.6, 7.1-7.2

Tuesday Nov. 17, 2015 --- Homework #11 --- Sections 7.3-7.4, 7.6-7.7

Tuesday Nov. 24, 2015 --- Homework #12 --- Sections 8.1-8.2

Tuesday Dec. 01, 2015 --- Homework #13 --- Sections 8.3-8.4

Tuesday Dec. 08, 2015 --- Homework #14 --- Sections 9.1-9.3

## Course Materials Organized by Section

This course uses the textbook "Introductory Algebra" by Robert Blitzer (6th Edition)

Class 01 - Entire First Class Video. This was the first day of class for a similar course (Math 261 at Monterey Peninsula College in the summer of 2015). This course uses the same textbook and covers the same materials as Math 154. This introduction should help you see what this class will entail. This covers introductions, a course overview, and sections 1.1 and 1.2. We begin to discuss section 1.3 but do not complete the lesson.

Chapter 1 (Introduction to Algebra)

• Section 1.1 - Introduction to Algebra
[Video] - [Notes] - Khan Links [#1] [#2] [#3]
Focuses on evaluation expressions by plugging in a number in place of a variable and correctly applying the order of operations.
• Section 1.2 - Fractions
[Video] - [Notes] - Khan Links [#1]
Focuses on the four main operations with fractions (addition, subtraction, multiplication and division) as well as how to deal with improper fractions and mixed numbers.
• Section 1.3 - Real Numbers
[Video] - [Notes] - Khan Links [#1] [#2] [#3] [#4] [#5] [#6]
Categories of Real Numbers (e.g. rational, natural, whole, integers, etc), comparing real numbers with inequalities (greater than, less than or equal to, etc), and evaluating absolute values
• Section 1.4 - Basic Rules of Algebra
[Video] - [Notes] - Khan Links [#1] [#2] [#3]
Basic terminology of algebra (terms, coefficients, like terms, etc) and how to simplify expressions by combining like terms
• Section 1.5 - Addition of Real Numbers
[Video] - [Notes] - Khan Links [#1]
How to add positive and negative numbers as well as what negative numbers mean
• Section 1.6 - Subtraction of Real Numbers
[Video] - [Notes] - Khan Links [#1]
How to subtract positive and negative numbers
• Section 1.7 - Multiplication & Division of Real Numbers
[Video] - [Notes] - Khan Links [#1]
How to multiply and divide positive and negative numbers
• Section 1.8 - Exponents and Order of Operations
[Video] - [Notes] - Khan Links [#1]
There was no lecture, but instead a quick 5 question quiz where we go over the five problems together on Order of Operations.

Chapter 2 - Solving Linear Equations with One Variable

• Section 2.1 - Addition Property of Equality
[Video] - [Notes] - Khan Links [#1]
Solving linear equations by adding (or subtracting) something to both sides of the equation.
• Section 2.2 - Multiplication Property of Equality
[Video] - [Notes] - Khan Links [#1]
Solving linear equations by multiplying (or dividing) something to both sides of the equation ... and then combining this with section 2.1 to solve multiple step problems.
• Section 2.3 - Solving Linear Equations
[Video] - [Notes] - Khan Links [#1]
Arguably the single most central section in algebra. This section is all about how to solve general linear equations with one variable such as "2(x+3)-5=6x-7"
• Section 2.4 - Formulas
[Video] - [Notes] - Khan Links [#1]
How to solve a formula such as "y=mx+b" for a specific variable such as "solve y=mx+b for x"
• Section 2.5 - Introduction to Problem Solving (word problems)
[Video] - [Notes] - Khan Links [#1] [#2] [#3] [#4]
How to translate sentences into math equations such as "five more than a number is eight" into "x+5=8"
• Section 2.6 - Problem solving in geometry
[Video] - [Notes] - Khan Links [#1]
Using the area and perimeter formulas of rectangles, triangles and circles to solve various problems.
• Section 2.7 - Solving Linear Inequalities
[Video] - [Notes] - Khan Links [#1]
Solving inequalities such as "2x+5>6" and then representing these as an inequality, a graph on a number line, and in interval notation.

Chapter 3 (Graphing Linear Equations with Two Variables)

• Section 3.1 - Introduction to Graphing
[Video] - [Notes] - Khan Links [#1]
How to graph linear equations with two variables using points and tables of values, such as "graph the line 2x+4y=8". Really focuses on what it means to have an equation with two variables in it as well as what a solution to an equation means.
• Section 3.2 - X- and Y-Intercepts
[Video] - [Notes] - Khan Links [#1]
Focuses on x- and y-intercepts. We find the intercepts from graphs first, then find them from the equations of lines, then combine these skills to find the intercepts from an equation and use these points to graph the line.
• Section 3.3 - Slope
[Video] - [Notes] - Khan Links [#1]
Focuses on "slope". We discuss slope in a big picture way as steepness of a line and positive vs negative slopes. We then find the slope of lines from graphs given and follow this by finding the slopes between two points. Also introduced are the ideas of lines being parallel or perpendicular.
• Section 3.4 - Slope-Intercept Form (y=mx+b)
[Video] - [Notes] - Khan Links [#1]
This section focuses on the equation "y=mx+b" and its significance. We practice finding the slope and y-intercept of lines when given the equation in this format. We then practice rearranging equations to be in this form to get the slope and y-intercept. We finally put these together and use our slope and y-intercept to graph the line.
• Section 3.5 - Point-Slope Form (y-y1=m[x-x1])
[Video] - [Notes] - Khan Links [#1]
This section focuses on how to write the equation of a line if you are given some information about the line. We discuss how you could only ever really be given two points or a point and a slope. We then practice using this information to write the equation of lines.

Chapter 4

• Section 4.1 - Introduction to Systems of Linear Equations & Solving by Graphing
[Video] - [Notes] - Khan Links [#1] [#2]
Focuses on the basic idea of a system of equations, such as what a solution looks like and why. It also introduces the viewpoint of a system of equations as two lines on a graph and uses this as our first method to solve the system of equations.
• Section 4.2 - Solving Systems of Equations by Substitution
[Video] - [Notes] - Khan Links [#1]
Focuses on solving the same types of problems as section 4.1 but introduces a second method to solve them. The idea here is that you will solve for a variable, then substitute in this equal value in place of that variable to solve the system.
• Section 4.3 - Solving Systems of Equations by Elimination/Addition
[Video] - [Notes] - Khan Links [#1] [#2]
Focuses on solving the same types of problems as sections 4.1-4.2 but introduces a third method to solve them. The idea here is that you add the two equations together after cleverly rearranging them so that one of the variables cancels out.
• Section 4.4 - Word Problems Involving Systems of Equations
[Video] - [Notes] - Khan Links [#1]
The problems in this section are the same as in sections 4.1-4.3, but the new part is reading a word problem and turning it into a system of equations.

Chapter 5

• Section 5.1 - Adding and Subtracting Polynomials
[Video] - [Notes] - Khan Links [#1] [#2]
Focuses on combining like terms and remembering to distribute the negative sign. Otherwise the section is just addition and subtraction of individual terms.
• Section 5.2 - Multiplying Polynomials
[Video (Part 1)] - [Video (Part 2)] - [Notes] - Khan Links [#1] [#2] [#3]
Focuses on the multiplication of monomials and polynomials as well as exponents. For example, you would see problems like (2x)(7x) and (x+2)(5x-4).
• Section 5.3 - Special Products
[Video]
- [Notes] - Khan Links [#1]
Focuses on identifying two common forms that products come in. Specifically it focuses on the difference of squares "(a+b)(a-b)" and a perfect square of binomials (a+b) squared.
• Section 5.5 - Dividing polynomials by monomials (getting ready to take out the GCF)
[Video] - [Notes] - Khan Links [#1] [#2]
Focuses on ...

Chapter 6

• Section 6.1 - Greatest Common Factor and Factor by Grouping
[Video] - [Notes] - Khan Links [#1] [#2] [#3] [#4] [#5] [#6]
Focuses on finding the greatest common factor of a polynomial. This is always the first step in the factoring process. Once we have figured out the greatest common factor, we factor it out of the polynomial. The second half of this section focuses on the method of "factoring by grouping" which is our general plan to factor any polynomial with four or more terms. This method splits a polynomial up into smaller groups that share common factors. After you take the common factors out of the smaller groups, the remaining binomial is the same in the two groups and can be factored out.
• Section 6.2 - Factoring Trinomials with a Lead Coefficient of 1 ("X-Factor")
[Video] - [Notes] - Khan Links [#1]
Focuses on learning to factor the most common types of polynomials you will see: x^2+5x-6
• Section 6.3 - Factoring Trinomials without a Lead Coefficient of 1 ("Hokey Pokey")
[Video] - [Notes] - Khan Links [#1] - Description of Process [#1]
Focuses on factoring more challenging trinomials (those where the lead coefficient is not 1). There are many strategies to factor these. Most books suggest a form of guess and check. In this lesson I focus on a method I call the "Hokey Pokey". This method is not common, but I find it more useful than the guess and check method (and more enjoyable and elegant as well).
• Section 6.4 - Factoring Special Forms (Difference of Squares)
[Video] - [Notes] - Khan Links [#1] [#2]
Focuses on recognizing a few special/common forms. Specifically, you need to be able to recognize a difference of squares. The key hint is that when faced with a factoring problem, if there are only two terms this is your only plan of action (so far).
• Section 6.5 - General Factoring Strategy
[Video] - [Notes] - Khan Links [#1] [#2]
Focuses on an overall strategy to factor mixed problems. For the remainder of this class you will encounter polynomials in most every lesson, and you will need to decide which factoring method ot use to solve the problem.
• Section 6.6 - Solving Quadratic Equations by Factoring
[Video] - [Notes] - Khan Links [#1]
Focuses on the zero product rule and using this to solve equations by factoring. The basic idea is that you cannot isolate the "x" like you could with a linear equation (chapter 2). Instead you are stuck with this polynomial with so many terms added together. If you factor the polynomial into a product though and the product is equal to zero ... well then you know one of the things being multiplied together MUST be zero. We use this to solve for the values of "x".

Chapter 7

• Section 7.1 - Simplifying Polynomial Fractions
[Video] - [Notes] - Khan Links [#1]
Focuses on how to reduce/simplify a fraction when there are polynomials involved. The main idea is that you can never cancel one term of a polynomial from the top of a fraction with one term of a polynomial on the bottom of a fraction EVER. Instead, you factor the polynomials in the numerator (top) and denominator (bottom) completely. This changes something with many terms into one big product of factors. Now since you have a product (one big term), you can cancel any factor from the top with any identical factor from the bottom.
• Section 7.2 - Multiplying & Dividing Polynomial Fractions
[Video] - [Notes] - Khan Links [#1]
Focuses on how to multiply and divide fractions that contain polynomials. There is not much new from 7.1 and should be thought of as a continued practice. The idea is when multiplying two fractions, since you are just multiplying the tops together and the bottoms together, you can just treat it as a single fraction and reduce anything from the top with anything from the bottom. As far as division goes, the only new step is that you first need to flip the second fraction and change the sign to multiplication. Other than this single step, you are really just simplifying fractions like in section 7.1.
• Section 7.3 - Adding & Subtracting Polynomial Fractions (with the same denominator)
[Video] - [Notes] - Khan Links [#1]
Focuses on how to add and subtract polynomial fractions that already have the same denominator (or denominators that might be off by a negative sign). Really we just add them like normal fractions with numbers in them. We add the numerators (tops) together and keep the common denominator (bottom) the same. Then you simplify like in section 7.1.
• Section 7.4 - Adding & Subtracting of Polynomial Fractions (with different denominators)
[Video] - [Notes] - Khan Links [#1]
Focuses on how to add/subtract two fractions with different denominators when there are polynomials in the numerators and denominators. The big idea of this section is how to find the least common denominator (LCD) and then how to modify each fraction to have this denominator. It is not different from fractions with numbers, as you follow the same steps, the the difficulty is in performing those same steps with polynomials.
• Section 7.6 - Solving Rational Equations (Equations with Polynomial Fractions)
[Video] - [Notes] - Khan Links [#1]
Focuses on how to solve equations that involve fractions with polynomials in them. The strategy is the same as in chapter two when we had equations with numerical fractions. The big trick is to multiply the entire equations by the LCD of all of the fractions. This immediately cancels out all of the fractions and gives you a normal fraction-less equation. Then we use one of our two methods to solve the equation, either the classic method from chapter two for linear equations or our new method from section 6.6 to solve all non-linear (polynomial) equations.
• Section 7.7 - Applications (Word Problems)
[Video] - [Notes] - Khan Links [#1]
Focuses on how to solve rate, time and distance word problems that involve polynomial fractions. There are also a few problems involving similar triangles.

Chapter 8

• Section 8.1 - Roots
[Video] - [Notes] - Khan Links [#1]
Focuses on the basics of radicals (aka roots). In this section the problems can be evaluated such as the square root of 16 is four. The cube root of 27 is 3. You will explore square roots, cube roots, negative signs and common exponents and bases.
• Section 8.2 - Multiplication and Division of Radicals
[Video] - [Notes] - Khan Links (Videos ONLY) [#1] [#2]
Focuses on simplifying radical expressions. We are dealing with a single term in each problem. Each problem will be a product or fraction with square roots. The goal is to simplify each of these as much as possible.
• Section 8.3 - Operations with Radicals
[Video] - [Notes] - Khan Links [#1]
Focuses on combining multiple terms that have radicals. The big idea here is to simplify each term completely and then combine like terms. For example, three root two plus five root two is equal to eight root two (just like we can add 3x + 5x = 8x )
• Section 8.4 - Rationalizing Denominators
[NO VIDEO] - [Notes] - Khan Links (Video ONLY) [#1]
Focuses on simplifying fractions that have a radical (aka root) in the denominator. The reason we do this is so that it is clear whether or not we have like terms that can be combined. There are two possible ways in which we rationalize the denominator. If there is just one radical term in the denominator, we multiply the top and the bottom by that radical term. If there are two radical terms in the denominator, we multiply the top and bottom of the fraction by the conjugate of that binomial.
• Section 8.5 - Radical Equations ( ----- NOT COVERED THIS SEMESTER ----- )
[NO VIDEO] - [Notes] - Khan Links [#1]
Focuses on solving equations where the variable is under a radical (aka root). This is done by isolation the radical on one side of the equation and then squaring both sides of the equation. Beware of false solutions though, so always plug in your final answers to see if they are actual solutions to the equation.

Chapter 9

• Section 9.1 - Solving Quadratic Equations by the Square Root Property
[Video] - [Notes] - Khan Links [#1]
Focuses on solving quadratic equations (equations with an "x squared" term in them). The method in this section is for solving problems where there is no middle term with an "x to the one power". If this is the case, you can actually isolate the "x squared" on one side and the number on the other side. You can then solve the equation by taking the square root of both sides.
• Section 9.2 - Solving Quadratic Equations by Completing the Square
[Video] - [Notes] - Khan Links [#1]
Builds on section 9.1. We extend section 9.1 and see that we can use the same method to solve problems when there is a middle term. We just need to make the polynomial a perfect square by adding or subtracting from both sides to get the right constant term. Then by taking the square root of both sides you can solve the equation (as in 9.1).
• Section 9.3 - The Quadratic Formula
[Video] - [Notes] - Khan Links [#1]
We develop and then use the Quadratic Formula. This formula allows us to solve any quadratic equation (an equation with an "x squared" term) by just plugging the coefficients into a formula. This is VERY useful and is how we solve all quadratic formulas that cannot be factored nicely.

## Course Calendar

Listed below are the book sections assigned each class period. Homework is due every Tuesday. Instructions on how to complete homework assignments, as well as the grading policy can be found in the class syllabus. The exact problems to complete in each section can be found above in the "Homework Assignments ..." link.

1st Class (Tuesday September 1, 2015)

• General introductions
• Section 1.1 - Introduction to Algebra: Variables & Mathematical Models
• Section 1.2 - Fractions in Algebra

2nd Class (Thursday September 3, 2015)

• Section 1.3 - The Real Numbers
• Section 1.4 - Basic Rules of Algebra
• Section 1.5 - Addition of Real Numbers
• Section 1.6 - Subtraction of Real Numbers

3rd Class (Tuesday September 8, 2015) --- First Homework Collected (Sections 1.1-1.6)

• Section 1.7 - Multiplication and Division of Real Numbers
• Section 1.8 - Exponents and Order of Operations
• Section 2.1 - Solving One Step Linear Equations with Addition and Subtraction (a.k.a. The Addition Property of Equality)
• This is the last week to drop the class without receiving a permanent "W" mark on your transcript, as would happen if you drop the class at a later date.

4th Class (Thursday September 10, 2015)

• Section 2.2 - Solving One Step Linear Equations with Multiplication and Division (a.k.a. The Multiplication Property of Equality)
• Section 2.3 - Solving Multiple Step Linear Equations (a.k.a. Solving Linear Equations)
• This is the last week to drop the class without receiving a permanent "W" mark on your transcript, as would happen if you drop the class at a later date.

5th Class (Tuesday September 15, 2015) --- Second Homework Collected (Sections 1.7-1.8, 2.1-2.4)

• Section 2.4 - Formulas and Percents
• Section 2.5 - An Introduction to Problem Solving (a.k.a. Word Problems)
• Section 2.6 - Problem Solving in Geometry
• Short Review for Test #1 (Wednesday)

6th Class (Thursday September 17, 2015)

• Visit the computer lab (Sign up for Khan Academy and start using it)
• Section 2.7 - Solving Linear Inequalities

7th Class (Tuesday September 22, 2015) --- Third Homework Collected (Sections 2.4-2.7)

• Sections 3.1 - Graphing Linear Equations in Two Variables (not on test #1)
• Review for Test #1 (Thursday) - Covering Chapters 1 and 2

8th Class (Thursday September 24, 2015)

• Test #1 - Covering all of Chapter 1 and Chapter 2. This is the first of four tests (not including the final which is the fifth overall test). You may use a scientific calculator on the test, but not a graphing calculator or cell phone. The test will be for the first 90 minutes of class and then after this we will have a lesson for the remaining 80 minutes of class.
• Section 3.1 - (continued)
• Section 3.2 - Lines and Intercepts

9th Class (Tuesday September 29, 2015) --- Fourth Homework Collected (Section 3.1)

• Section 3.2 - (continued)
• Section 3.3 - Slope

10th Class (Thursday October 1, 2015)

• MDTP Testing (This is a pre-assessment of algebra skills. You will take the same test at the end of the course. It does not affect your grade but shows me and Khan Academy what you learned)
• Section 3.4 - Slope-Intercept Form

11th Class (Tuesday October 6, 2015) --- Fifth Homework Collected (Sections 3.2-3.4)

• Section 3.5 - Point-Slope Form
• Section 4.1 - Solving Systems of Linear Equations by Graphing

12th Class (Thursday October 8, 2015)

• Section 4.2 - Solving Systems of Linear Equations by Substitution
• Section 4.3 - Solving Systems of Linear Equations by Addition (aka Elimination)

13th Class (Tuesday October 13, 2015) --- Sixth Homework Collected (Sections 3.5, 4.1-4.3)

• Section 5.1 - Adding and Subtracting Polynomials (not on test #2)
• Section 5.2 (Part 1) - Multiplying Polynomials (Part 1 - only multiplying monomials by polynomials)

14th Class (Thursday October 15, 2015)

• Section 5.2 (Part 2) - Multiplying Polynomials (Part 2 - multiplying polynomials by polynomials)
• Section 5.3 as well?
• Test #2 Review (covering chapters 3 and 4) - Test on Tuesday
• Important note - the most recent practice test(s) do not include sections 4.2-4.4. Be sure to practice problems from these sections before the test. These problems are on older versions of the test.

15th Class (Tuesday October 20, 2015) --- Seventh Homework Collected (Sections 5.1-5.2)

• Test #2 - Covering Chapter 3 and Chapter 4
• Section 5.3 (continued?) - Special products - For example, perfect squares or difference of squares
• Section 5.5 - Dividing polynomials by monomials

16th Class (Thursday October 22, 2015)

--- No class --- Class is canceled due to me having parent teacher conferences in Mountain View.

17th Class (Tuesday October 27, 2015) --- Eighth Homework Collected (Sections 5.3 and 5.5)

• Section 6.1 - Factoring out the Greatest Common Factor and Factor by groupings
• Section 6.2 - Factoring trinomials with a leading coefficient of 1

18th Class (Thursday October 29, 2015)

• Section 6.4 - Factoring special forms (perfect square trinomials and the difference of squares)

19th Class (Tuesday November 3, 2015) --- Ninth Homework Collected (Sections 6.1-6.4)

• Section 6.5 - General factoring strategy
• Section 6.6 - Solving quadratic equations by factoring

20th Class (Thursday November 5, 2015)

• Section 7.1 - Simplifying polynomial fractions
• Section 7.2 - Multiplying and dividing polynomial fractions

21st Class (Tuesday November 10, 2015) --- Tenth Homework Collected (Sections 6.5-6.6,7.1-7.2)

• Section 7.3 - Adding and subtracting polynomial fractions with the same denominator
• Section 7.4 - Adding and subtracting of polynomial fractions with different denominators

22nd Class (Thursday November 12, 2015)

• Section 7.6 - Solving Rational Equations (a.k.a. equations with polynomial fractions)
• Section 7.7 - Applications (a.k.a. word problems with equations involving polynomial fractions)

23rd Class (Tuesday November 17, 2015) --- Eleventh Homework Collected (Sections 7.3-7.4, 7.6-7.7)

• Section 8.1 - Roots
• Test #3 Review - Covering Chapters 5, 6, and 7
• Important Note - This is the last week to drop this course with a "W". After this week, you will earn a letter grade whether or not you drop the course.

24th Class (Thursday November 19, 2015)

• Test #3 - Covering Chapter 5, Chapter 6 and Chapter 7 (more information below)
• Section 8.2 - Multiplication and Division of Radicals
• Important Note - This is the last week to drop this course with a "W". After this week, you will earn a letter grade whether or not you drop the course.

25th Class (Tuesday November 24, 2015) --- Twelfth Homework Collected (Sections 8.1-8.2)

• Section 8.3 - Operations with Radicals
• Section 8.4 - Rationalizing Denominators

26th Class (Tuesday December 1, 2015) --- Thirteenth Homework Collected (Sections 8.3-8.4)

• Section 9.1 - Solving Quadratic Equations by the Square Root Property
• Section 9.2 - Solving Quadratic Equations by Completing the Square

27th Class (Thursday December 3, 2015)

• Section 9.3 - The Quadratic Formula
• Test #4 Review

28th Class (Tuesday December 8, 2015) --- Fourteenth Homework Collected (Sections 9.1-9.3)

• Test #4 - Covering Chapter 8 and chapter 9 (not including section 8.5)
• Final Exam Review

29th Class (Thursday December 10, 2015)

• Test #4 returned to you
• Final Exam Review

30th Class (Tuesday December 15, 2015)

• Final Exam

Sections Skipped this semester (different from previous semesters)

• Section 4.4 - Problem Solving Using Systems of Equations (aka Word Problems)
• Section 8.5 - Radical Equations