Algebra for College-bound 11th Graders

Teacher: Richard
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Section 0: Course Introduction

0 Welcome to Algebra for College-Bound 11th Graders 03:19

A brief introduction to this course.

Basic Algebra Review

-1 Basic Algebra Review 11:02

A list of critical basic algebra vocabulary and processes that need to be mastered before beginning this course.

Section 1: Introduction to Set Theory

1 Lesson 1 – Set Theory 05:13

Numbers that share specific characteristics can be "put" into unique sets. It's not unlike a set of dishes; each dish shares a certain characteristic. It's the same concept with numbers; a set of numbers are a group of numbers that share a common characteristic. 

 

Set Theory

 

 

 

 

2 Lesson 2 - Number Sets 12:35

The main Number Sets that we use today.

 

 

 

 

3 Number Set Worksheet ANSWERS 02:42

Number Set Worksheet ANSWER Videos and ANSWERS

4 Lesson 3 – Symbols Used in Set Theory 02:48

5 Lesson 4 - Set Notation 12:35

Set Notation

There are many ways to represent a set of numbers. Below are the main two types of set notation.

 Set Notation

 

6 Set Notation Worksheet ANSWERS 05:17

Set Notation Worksheet ANSWERS and ANSWER Videos

7 Lesson 5 - Subsets 03:07

Subsets

 

Sets and Subsets

Any set "contained" inside another set is called a subset. Another way to think about a subset is any set which all the elements of a set are contained in another set.

Example:  Let A = {1, 3, 5, 7} and let B = {x|x ∈ N}, then A is a subset of B (all elements of A are contained in B).

We write subsets like this: A ⊆ B  (The set A is a subset of set B.)

A proper subset is a subset that does not contain every element of the original set. So, we can also say that the set A is a proper subset of set B: A ⊂ B.

Example: The set of Natural numbers is a proper subset of the set of Whole numbers because the set of Natural numbers does not contain the number 0.

N ⊂ W (The set of Natural numbers is a proper subset of the set of Whole numbers.)

All sets are also subsets of themselves, but not proper subsets of themselves. 

Example: N ⊆ N (The set of Natural numbers is a subset of itself.)

8 Lesson 6 - Unions and Intersections of Sets 06:57

Unions and intersections

 

9 Unions and Intersections Worksheet ANSWERS 06:05

Unions and Intersections worksheet ANSWER Videos and ANSWERS

 

10 Lesson 7 - Venn Diagrams 10:00

Venn Diagrams

 

Venn Diagrams

 

11 Venn Diagrams Worksheet ANSWERS 04:27

Venn Diagrams Worksheet ANSWER Videos and ANSWERS

12 Section 1: Set Theory Quiz 00:00

Section 1: Set Theory Quiz (Answers under Resources)

 

13 Section 1 - Brain Candy 02:50

Proof that you are what you are not!

Section 2: The Cartesian Plane and Coordinate Geometry

14 Lesson 1 - The Cartesian Plane 03:41

The Cartesian Plane

The Cartesian Plane 

15 Lesson 2 - The Fundamental Graphing Principle 02:16

The Fundamental Graphing Principle

16 Lesson 3 - Vertical and Horizontal Lines on a Graph 01:58

Vertical and Horizontal Lines

17 Vertical and Horizontal Lines Worksheet ANSWERS 02:27

Vertical and Horizontal Lines on a Graph Worksheet ANSWER Videos ANSWERS

18 Lesson 4 - Reflections on a Graph 04:36

Reflections

19 Reflections Worksheet ANSWERS 03:54

Reflections Worksheet ANSWER Videos and ANSWERS

20 Lesson 5 - Intercepts 04:24

Intercepts

21 Intercepts Worksheet ANSWERS 08:21

Intercepts Worksheet Review Video ans answers

22 Lesson 6 - Midpoints 04:14

Midpoints

23 Lesson 7 - Distance Formula 04:10

Distance Formula

24 Midpoint and Distance Worksheet ANSWERS 03:50

Midpoint and Distance between coordinates worksheet ANSWER videos and ANSWERS

25 Lesson 8 - Finding points on a graph with a fixed distance 04:34

Finding points on a graph with a fixed distance

 Fixed point distance

 

26 Lesson 9 - Triangle XYZ is a right triangle. 03:41

 XYZ is a right triangle
 

27 Lesson 10 - Find the third vertex of a 30-60-90 degree triangle 04:34

30-60-90 vertex problem

28 Lesson 11 - Find the fourth point of a square 05:23

Find a point D(x; y) such that the points A(-3; 1), B(4; 0), C(0;-3) and D are the corners of a square.

 

Corner of a square

 

29 Lesson 12 - Area of circle and a triangle 04:56

Circle C passes through the three vertices of triangle T. If the vertices of triangle T are (-1, 2), (1, 6), and (5, 4), then what is the area of cirlce C?


Circle and Triangle

30 Lesson 13 - Right triangle problem no coordinates 04:09

30-60-90 triangle problem no coordinates

31 Coordinate Geometry Worksheet 02:50

The Cartesian Plane and Coordinate Geometry Worksheet

32 Coordinate Geometry Worksheet ANSWERS 14:44

The Cartesian Plane and Coordinate Geometry Worksheet ANSWER videos and ANSWERS

33 Section 2: Cartesian Plane and Coordinate Geometry Quiz 02:03

Section 2: Cartesian Plane and Coordinate Geometry Quiz (Answers under Resources)

34 Section 2 - Brain Candy 01:50

How did the right triangle get its name?

right triangle

Midterm 1

35 PRACTICE Midterm 1 00:00

PRACTICE Midterm 1

36 PRACTICE Midterm 1 ANSWERS 00:00

PRACTICE Midterm 1 ANSWERS

37 Midterm 1 (pdf) 00:00

Midterm 1 (Answers under Resources)

Section 3: Functions (General) and Graphing

38 Lesson 1 - Relations 05:45

Relation or Function?

39 Lesson 2 - Relations Graphing using Set Notation 14:48

Graphing relations

40 Lesson 3 - Set notation in a plane 08:05

Set notation in a plane

41 Relations and Set Notation ANSWERS 16:48

Relation Graphing Worksheet ANSWER Videos and ANSWERS

42 Lesson 3 - Function notation 07:32

Function Notation

43 Lesson 4 - Domains and Ranges of Functions 04:53

Domains and Ranges of functions

44 Domains and Ranges Worksheet ANSWERS 08:12

Domains and Ranges of Functions Worksheet ANSWER Videos and ANSWERS

45 Lesson 5 - Linear Functions: SLOPE 03:46

Linear Functions: SLOPE

46 Lesson 6 - Linear Functions GRAPHING 07:17

You remember the the slope-intercept equation for a straight line? It's our old friend ... y = mx + b

47 Lesson 7 - Linear Equations: SOLVING 04:28

How to algebraically write out a linear equation.

48 Lesson 8 - Linear inequalities: GRAPHING 02:54

How to graph linear inequalities.

49 Linear Functions Worksheet ANSWERS 18:07

Linear Functions Worksheet ANSWERS and ANSWER VIDEOS

50 Lesson 9 - Step-wise Functions (Piece-wise) 10:15

A step-wise function can be thought of as a "multiple" function; which function to use depends on the value of the number (x) being plugged into the step-wise function.

51 Step-wise Functions Worksheet ANSWERS 02:44

Step-wise Functions Worksheet ANSWER Videos and ANSWERS

52 Lesson 11 - Absolute Value Functions 10:25

Absolute value functions are very common in mathematics. They can be tricky!

53 Absolute Value Functions Worksheet ANSWERS 04:51

Absolute Value Functions Worksheet ANSWER Videos and ANSWERS

54 Lesson 11 - Absolute Value Inequalities 07:46

Rules for solving inequalities

55 Lesson 12 - Absolute Value Inequalities GRAPHING 03:25

How to graph an inequality equation.

56 Absolute Value Inequalities Worksheet ANSWERS 16:43

Absolute Value Inequalities Worksheet ANSWER Videos and ANSWERS

57 Section 3: Functions (General) and Graphing Quiz 00:38

Section 3: Functions (General) and Graphing Quiz  (Answers under Resources)

58 Section 3 - Brain Candy 02:47

Section 3 - Brain Candy

Section 4: Quadratic Functions

59 Lesson 1 - Graphing Quadratic Functions 04:15

Graphing quadratic functions

 

 

 

60 Graphing Quadratic Functions Worksheet ANSWERS 06:04

Graphing Quadratic Functions Worksheet ANSWER Videos and ANSWERS

61 Lesson 2 - Graphing Quadratics with x intercepts 04:02

Graphing Quadratic Functions with x intercepts

62 Quadratic Functions with X Intercepts ANSWERS 04:52

Graphing Quadratic Functions with X Intercepts Worksheet ANSWER Videos and ANSWERS

63 Lesson 3 - Imaginary Numbers 03:32

Imaginary numbers with exponents

64 Lesson 4 - Complex Numbers 04:44

Complex numbers

65 Imaginary and Complex Numbers ANSWERS 11:52

Imaginary and Complex Numbers Worksheet ANSWER Videos and ANSWERS

66 Lesson 5 - Quadratics with No X Intercepts 07:52

Parabolas with no x intercepts

67 Quadratics with No X Intercepts Worksheet ANSWERS 02:56

Graphing Quadratic Equations with No X Intercepts Worksheet ANSWER Videos and ANSWERS

68 Lesson 6 - Solving Quadratics by Completing the Square 05:28

Solving Quadratic Equations by Completing the Square

69 Lesson 7 - Solving Quadratics using the Quadratic Formula 09:44

Solving Quadratic Equations using the Quadratic Formula

70 Solving Quadratic Equations Worksheet ANSWERS 08:42

Solving Quadratic Equations Worksheet ANSWER Videos and ANSWERS

71 Lesson 8 - Graphing Quadratic Inequalities 06:13

Graphing Quadratic Inequalities

72 Graphing Quadratic Inequalities ANSWERS 03:37

Graphing Quadratic Inequalities Worksheet ANSWER Videos and ANSWERS

73 Lesson 9 - Minimums and maximums of quadratic functions 12:05

Minimums and maximums of quadratic functions.

74 Lesson 10 - Maximization of quadratics word problems 04:42

Farmer Skippy has 32 linear feet of fencing and he wants to fence in his yard so that it will maximize the area. He decides on a rectangular yard but he only needs three sides because the fourth side will be the wall of his house. Find the dimensions of the sides and the maximum area of the yard.

75 Minimums and Maximums Worksheet ANSWERS 10:15

Minimums and Maximums of Quadratic Functions Worksheet ANSWER Videos and ANSWERS

76 Section 4: Quadratic Functions - Quiz 00:38

Section 4: Quadratic Functions - Quiz (Answers under Resources)

77 Section 4 - Brain Candy 03:14

Section 4 - Brain Candy

Midterm 2

78 PRACTICE Midterm 2 00:00

PRACTICE Midterm 2

79 PRACTICE Midterm 2 ANSWERS 00:00

PRACTICE Midterm 2 ANSWERS

80 Midterm 2 (pdf) 00:00

Midterm 2 (Answers under Resources)

Section 5: Polynomial Functions

81 Lesson 1 - Fundamental Theorem of Algebra 07:12

Fundamental Theorem of Algebra

82 Lesson 2 - Polynomial Function Definition 03:22

polynomial functions

83 Lesson 3 - What is a Polynomial Function? 04:44

Polynomial Functions

84 Polynomial Function Worksheet ANSWERS 03:55

Polynomial Function Worksheet ANSWER Videos and ANSWERS

85 Lesson 4 - Function Arithmetic 06:35

86 Function Arithmetic Worksheet ANSWERS 06:10

Function Arithmetic Worksheet ANSWER Videos and ANSWERS

87 Lesson 5 - Finding a “Zero” of a Function 04:45

a "zero" of a function

88 “Zeros” of a Function Worksheet ANSWERS 05:54

Finding a “Zero” of a Function Worksheet ANSWER Videos and ANSWERS

89 Lesson 6 - Multiplicities of a Zero 01:54

Multiplicities of a Zero

90 Multiplicities of a Zero Worksheet ANSWERS 03:39

Multiplicities of a Zero Worksheet ANSWER Videos and ANSWERS

91 Lesson 7 - The Factor and The Remainder Theorems 02:14

Theorems

92 Lesson 8 - Polynomial Division 05:02

Polynomial Division

93 Polynomial Division Worksheet ANSWERS 08:32

Polynomial Division Worksheet ANSWER VIDEOS and ANSWERS

94 Lesson 9 - Synthetic Polynomial Division 08:24

Synthetic Polynomial Division

95 Lesson 9b - Synthetic Polynomial Division example 04:31

Synthetic Polynomial Division

96 Synthetic Polynomial Division Worksheet 00:00

Synthetic Polynomial Division Worksheet

97 Synthetic Polynomial Division Worksheet ANSWERS 11:12

Synthetic Polynomial Division Worksheet ANSWER Videos and ANSWERS

98 Lesson 10 - Difference Quotient Function 06:32

Difference quotient

99 Difference Quotient Function Worksheet ANSWERS 05:05

Difference Quotient Function Worksheet ANSWER Videos and ANSWERS

100 Lesson 11 - Average Rate of Change Function 04:49

Average Rate of Change

101 Average Rate of Change Worksheet ANSWERS 07:22

Average Rate of Change Function Worksheet ANSWER Videos and ANSWERS

102 Lesson 12 - Function Composition 04:38

Function Composition

103 Function Composition Worksheet ANSWERS 06:08

Function Composition Worksheet ANSWER Videos and ANSWERS

104 Lesson 14 - One-to-one and Onto Functions 11:25

Onto and One-to-one functions

 

 

105 One-to-one and Onto Worksheet ANSWERS 06:36

One-to-one and Onto Functions Worksheet ANSWER Videos and ANSWERS

106 Lesson 15 - Inverse Functions 05:13

Inverse functions

107 Inverse Functions Worksheet ANSWERS 07:00

Inverse Functions Worksheet ANSWER Videos and ANSWERS

108 Section 5: Polynomial Functions Quiz 01:19

Section 5: Polynomial Functions Quiz (Answers under Resources)

109 Section 5 - Brain Candy 04:01

Section 5 - Brain Candy

Section 6: Exponents and Logarithms

110 Lesson 1 - Rules of Exponents (Review) 02:06

Rules of Exponents

111 Lesson 2 - Rational Exponents 08:36

Rational Exponents

112 Rational Exponents Worksheet ANSWERS 05:14

Rational Exponents Worksheet ANSWER Videos and ANSWERS

113 Lesson 3 - Exponential Equations 02:56

Exponential equations

114 Powers of Numbers 00:00

Powers of Numbers

115 Exponential Equations Worksheet ANSWERS 10:25

Exponential Equations Worksheet ANSWER Videos and ANSWERS

116 Lesson 4 - Properties of Exponential Functions 04:48

Exponential functions

117 Lesson 5 - Exponential Function in Excel 01:09

Excel macro for graphing exponential functions

118 Lesson 6 - Exponential Formulas (pdf) 00:55

A few exponential equations for your perusal.

119 Lesson 7 - Logarithms: General 09:41

Exponential equations into logarithm equations

120 Lesson 8 - Properties of Logarithmic Functions 08:33

Properties of Log Functions

121 Lesson 9 - Algebraic Properties of Logarithms 11:48

Algebraic Properties of Logarithms

122 Lesson 10 - Logarithms: Change of Base Rule 03:23

Change of Base Formula

123 Lesson 11 - Solving Log Equations 01:59

Solving Log Equations

124 Log Equations Worksheet ANSWERS 18:44

Solving Log Equations Worksheet ANSWER Videos and ANSWERS

125 Lesson 12 - Euler's Number 03:33

Euler's Number

126 Lesson 13 - Logarithms - Solving Natural Log Equations 02:01

Solving natural log equations

127 Lesson 14 - Graphing Logarithmic Functions in Excel 09:46

Graphing log functions in Excel

128 Lesson 15 - Applications (INTEREST problems only) 10:46

Applications of Exponential and Log Equations (INTEREST problems only)

129 Exponents and Logarithms Worksheet 05:05

Some harder log problems worked out

130 Exponents and Logarithm Worksheet ANSWERS 18:14

Exponents and Logarithm Formulas Worksheet ANSWER Video and ANSWERS

131 Section 6: Exponents and Logarithms Quiz 00:44

Section 6: Exponents and Logarithms Quiz (Answers under Resources)

132 Section 6 - Brain Candy 05:33

Section 6 - Brain Candy

Midterm 3

133 PRACTICE Midterm 3 (pdf) 00:00

PRACTICE Midterm 3 (pdf)

134 PRACTICE Midterm 3 ANSWERS (pdf) 00:00

PRACTICE Midterm 3 ANSWERS (pdf)

135 Midterm 3 (pdf) 00:00

Midterm 3 (Answers under Resources)

Section 7: Systems of Linear Equations

136 Lesson 1 - Systems of Linear Equations 03:27

Systems of Linear Equations

137 Lesson 2 - Graphing Systems of Linear Equations 10:47

Graphing Systems of Linear Equations

138 Graphing Systems of Linear Equations ANSWERS 07:22

Graphing Systems of Linear Equations Worksheet ANSWER Videos ANSWERS

139 Lesson 3 - Solving by Substitution 05:09

Solving by Substitution

140 Solving by Substitution ANSWERS 05:14

Solving by Substitution Worksheet ANSWER Video and ANSWERS

141 Lesson 4 - Gaussian Elimination 04:27

Guass

142 Gaussian Elimination Worksheet ANSWERS 14:10

Gaussian Elimination Worksheet ANSWER Videos and ANSWERS

143 Lesson 5 - Consistent and Independent Systems 06:15

Consistent and Independent System (3 variables)

144 Lesson 6 - Inconsistent Systems 03:35

Inconsistent System (3 variables)

145 Lesson 7 - Dependent and Consistent Systems 05:34

Dependent and consistent system (3 variables)

146 Systems with 3 Variables Worksheet ANSWERS 19:38

Systems with 3 Variables Worksheet ANSWER Videos and ANSWERS

147 Lesson 8 - A Coffee Mixture Problem 04:14

Coffee mixture problem

148 Lesson 9 - Changing a System into a Matrix 01:59

Changing a System into a Matrix

149 Lesson 10 - The Matrix - Aij Identifying Rows and Columns 01:10

Identifying Entries in a Matrix

150 Lesson 11 - Determinants of a Matrix 06:42

Discriminants

151 Lesson 12 - Scalars 01:07

Scalars

152 Determinants and Scalars Worksheet ANSWERS 06:35

Determinants of a Matrix and Scalars Worksheet ANSWERS

153 Lesson 13 - The Augmented Matrix 01:37

The Augmented Matrix

154 Lesson 14 - Row Echelon Form 04:17

Row Echelon Form matrix

155 Lesson 15 - Reduced Row Echelon Form 05:12

Reduced Row Echelon Form Matrix

156 Lesson 16 - Solving a 3 x 4 matrix 04:34

Solving a 3 x 4 Matrix

157 Augmented Matrices Worksheet ANSWERS 15:45

Solving Augmented Matrices Worksheet ANSWER Videos and ANSWERS

158 Lesson 17 - Use a Matrix to Find a Quadratic Equation 06:09

The Vandermonde Matrix

159 Use a Matrix to Find a Quadratic Equation ANSWERS 08:44

How to Use a Matrix to Find a Quadratic Equation Worksheet ANSWER Videos and ANSWERS

160 Lesson 19 - Properties of Matrices 02:48

Properties of Matrices

161 Lesson 20 - Matrix Addition and Subtraction 04:40

Matrix addition and subtraction

162 Lesson 21 - Matrix Multiplication (non-square matrices) 06:44

Multiplying matrices (non-square)

163 Lesson 22 - Multiplying Matrices (square matrices) 03:17

Multiplying square matrices

164 Matrix Arithmetic Worksheet ANSWERS 06:15

Matrix Arithmetic Worksheet Worksheet ANSWER Video and ANSWERS

165 Lesson 23 - The Identity Matrix 01:44

The Identity Matrix

166 Lesson 24 - Matrix Inverses 03:42

Inverse Matrix

167 Matrix Inverses Worksheet ANSWERS 08:44

Matrix Inverses Worksheet ANSWER Videos and ANSWERS

168 Lesson 25 - Eigenvalues and Eigenvectors 06:24

Eigenvalues and Eigenvectors

169 Section 7: Systems of Linear Equations Test (in pdf format) 00:00

Section 7: Systems of Linear Equations Test (in pdf format)  (Answers under Resources)

170 Section 7 - Brain Candy 06:57

Section 7 - Brain Candy

Section 8: Sequences

171 Lesson 1 - Sequences 08:23

Sequences

172 Lesson 2 - The nth Term 03:40

The nth Term

173 Lesson 3 - Arithmetic Sequences: Finding the nth Term 02:04

Arithmetic Sequences: Finding the nth Term

174 Lesson 4 - Geometric Sequences: Finding the nth Term 03:49

Geometric Sequences: Finding the nth Term

175 Sequences: Finding the nth Term ANSWERS 30:29

Sequences: Finding the nth Term Worksheet ANSWER Videos and ANSWERS

176 Lesson 5 - Summation Notation 03:57

Summation

177 Lesson 6 - Summation of Arithmetic Sequences 02:10

Summation arithmetic sequence

178 Lesson 7 - Summation of Geometric Sequences When |r| ≥ 1 02:30

Summation of a geometric sequence with r greater than 1

179 Lesson 8 - Summation of Geometric Sequences When |r| < 1 03:04

Summation geometric sequence with r less than 1

180 Summation of Sequences ANSWERS 14:08

Summation of Sequences Worksheet ANSWER Videos and ANSWERS

181 Lesson 9 - Principal of Mathematical Induction (PMI) 07:54

Principal of Mathematical Induction (PMI)

182 Principal of Mathematical Induction ANSWERS 03:48

Principal of Mathematical Induction Worksheet ANSWER Videos and ANSWERS

183 Lesson 10 - The Binomial Theorem 09:57

Binomial Theorem

184 The Binomial Theorem Worksheet ANSWERS 03:36

The Binomial Theorem Worksheet ANSWER Videos and ANSWERS

185 Section 8: Sequences Test (in pdf format) 00:00

Section 8: Sequences Test (in pdf format) (Answers under Resources)

186 Section 8 - Brain Candy 02:46

Section 8 - Brain Candy

Final Exam (cumulative)

187 PRACTICE Final Exam 00:00

PRACTICE Final Exam

189 PRACTICE Final Exam ANSWERS 00:00

PRACTICE Final Exam ANSWERS

190 Final Exam (pdf) 00:00

Final Exam - cumulative (Answers under Resources)

COURSE LEARNING OUTCOMES

Upon successful completion of this course, students will be able to:

  • Write out and describe sets using set-theory notation
  • Solve intersections and unions of sets; Venn Diagrams
  • Understand the Fundamental Graphing Theory
  • Determine the x-intercepts and y-intercepts of polynomial functions
  • How to reflect a point and a line across an axis and/or the origin
  • Find midpoints and distance between any two given points
  • Apply Coordinate Geometry to explore geometric shapes on the Cartesian plane
  • Determine if a relation is also a function
  • How to graph relations
  • How to graph using set-building notation
  • Identify the domain and range of a function
  • Solve and graph linear equations and inequalities
  • Apply step-wise functions
  • Solve and graph absolute value equations and inequalities
  • Factor polynomials, solve and graph quadratic equations and inequalities
  • Calculate with complex numbers, conjugates, discriminants, and real solutions
  • Solve quadratic equations by Completing the Square, and with the Quadratic Formula
  • Solve application problems including quadratic models and optimization   
  • Understand and apply the Fundamental Theorem of Algebra
  • Determine which functions are polynomial functions and which are not
  • Find all of the “zeros” (Real and/or Complex) of a polynomial function
  • Define multiplicities of zeros for polynomial functions
  • Understand and apply the Factor and Remainder Theorem
  • Perform operations on functions, including addition, subtraction, multiplication and division
  • Perform synthetic division with polynomial functions
  • Understand and apply the Difference Quotient Function
  • Find the average rate of change of functions
  • Successfully compose functions and define their domains and ranges
  • Understand what makes a function one-to-one and/or onto
  • Calculate the inverse of a polynomial function, including the domain and range
  • Understand and apply the Properties of Exponential Functions 
  • How to graph exponential functions using MS Excel
  • Reduce and calculate with radicals and fractional exponents
  • Solve quadratic, radical, polynomial, and rational equations 
  • Understand and apply the Properties of Logarithmic Functions
  • Apply the rules of logarithms to expand logarithms, or to write logarithmic expressions as a single log
  • Solve equations and applications involving exponential and logarithmic functions
  • How to graph logarithmic functions using MS Excel
  • Calculate with Euler’s number (e) 
  • To solve logarithmic equations with the Change of Base rule
  • Apply exponential and logarithmic properties to real-world problems
  • Solve systems of linear equations using the Substitution and/or the Gaussian Elimination method
  • Translate systems of linear equations into matrices
  • Find determinants of 2 x 2 and 3 x 3 matrices
  • To convert any augmented matrix into reduced-row echelon form
  • Identify if a matrix is consistent and/or dependent
  • Understand what the Identity Matrix is and how it is used
  • Perform arithmetic with matrices
  • Find inverses of matrices
  • Find Eigenvalues and Eigenvectors of 3 x 3 matrices
  • To calculate information from a sequence (arithmetic and geometric) such as the sum, nth term and other information
  • To use the Principal of Mathematical Induction to prove or disprove statements with Natural numbers
  • To apply the Binomial Theorem
  • Brain Candy

 

TARGET AUDIENCE

This is a robust 11th grade algebra course that was designed for high school students planning on attending, and graduating from, college. 

 

COURSE REQUIREMENTS

Students taking this course should ALREADY have basic algebra skills, i.e., arithmetic with fractions, decimals, and percents; arithmetic with integers (a negative multiplied by a negative is a positive); how to algebraically move a variable and/or a constant from one side of an equation to the other side; you know - the absolute basics of algebra. A graphing calculator would be nice but not necessary. A calculator that can calculate exponents and logarithms is needed. 

 

THIS COURSE INCLUDES

  •  140+ video tutorials
  •  Guided homework worksheets covering every concept (answer sheets with video explanations)
  •  8 tests (one for each section)
  •  3 Midterms + 3 Practice Midterms (with answers)
  •  1 Final Exam + 1 Practice Final Exam (cumulative, with answers)

 

COURSE CONCEPTS

 

Basic Algebra Review

  • Basic Algebra Review

 

Introductory Set Theory

  • Lesson 1 – Set Theory
  • Lesson 2 - Sets of Numbers
  • Lesson 3 – Symbols Used in Set Theory
  • Lesson 4 - Set Notation
  • Lesson 5 - Subsets
  • Lesson 6 - Unions and Intersections of Sets
  • Lesson 7 - Venn Diagrams

 

The Cartesian Plane and Coordinate Geometry

  • Lesson 1 - The Cartesian Plane
  • Lesson 2 - The Fundamental Graphing Principle
  • Lesson 3 - Vertical and Horizontal Lines on a Graph
  • Lesson 4 - Reflections on a Graph
  • Lesson 5 - Intercepts
  • Lesson 6 - Midpoints
  • Lesson 7 - Distance Formula
  • Lesson 8 - Finding points on a graph with a fixed distance
  • Lesson 9 - Triangle XYZ is a right triangle
  • Lesson 10 - Find the third vertex of a 30-60-90-degree triangle
  • Lesson 11 - Find the fourth point of a square
  • Lesson 12 - Area of circle and a triangle
  • Lesson 13 - Right triangle problem without coordinates

 

Functions (General) and Graphing

  • Lesson 1 - Relations
  • Lesson 2 - Graphing Relations using Set Notation
  • Lesson 2b - Set notation in a plane
  • Lesson 3 - Function notation
  • Lesson 4 - Domains and Ranges of Functions
  • Lesson 5 - Linear Functions: Slope
  • Lesson 6 - Linear Functions Graphing
  • Lesson 7 - Linear Equations: Solving
  • Lesson 8 - Linear inequalities: Graphing
  • Lesson 9 - Linear Functions Worksheet
  • Lesson 10 - Step-wise Functions (Piece-wise)
  • Lesson 11 - Absolute Value Functions
  • Lesson 12 - Absolute Value Inequalities
  • Lesson 13 - Absolute Value Inequalities Graphing

 

Quadratic Functions

  • Lesson 1 - Graphing Quadratic Functions
  • Lesson 2 - Graphing Quadratic Functions with x intercepts
  • Lesson 3 - Imaginary Numbers
  • Lesson 4 - Complex Numbers
  • Lesson 5 - Graphing Quadratic Equations with no x intercepts
  • Lesson 6 - Solving Quadratic Equations by Completing the Square
  • Lesson 7 - Solving Quadratic Equations using the Quadratic Formula
  • Lesson 8 - Graphing Quadratic Inequalities
  • Lesson 9 - Minimums and maximums of quadratic functions
  • Lesson 10 - Optimization of quadratic functions word problems

 

 Polynomial Functions 

  • Lesson 1 - Fundamental Theorem of Algebra
  • Lesson 2 - Polynomial Function Definition
  • Lesson 3 - What is a Polynomial Function?
  • Lesson 4 - Function Arithmetic
  • Lesson 5 - Finding a “Zero” of a Function
  • Lesson 6 - Multiplicities of a Zero
  • Lesson 7 - The Factor and The Remainder Theorems
  • Lesson 8 - Polynomial Division
  • Lesson 9 - Synthetic Polynomial Division
  • Lesson 9b - Synthetic Polynomial Division another example
  • Lesson 10 - Difference Quotient Function
  • Lesson 11 - Average Rate of Change Function
  • Lesson 12 - Function Composition
  • Lesson 14 - One-to-one and Onto Functions
  • Lesson 15 - Inverse Functions

 

Exponents and Logarithms

  • Lesson 1 - Rules of Exponents
  • Lesson 2 - Rational Exponents
  • Lesson 3 - Exponential Equations
  • Lesson 4 - Properties of Exponential Functions
  • Lesson 5 - Graphing an Exponential Function in Excel
  • Lesson 6 - Exponential Formulas (pdf)
  • Lesson 7 - Logarithms: General
  • Lesson 8 - Properties of Logarithmic Functions
  • Lesson 9 - Algebraic Properties of Logarithms
  • Lesson 10 - Solving Logarithmic Equations
  • Lesson 11 - Euler's Number
  • Lesson 12 - Logarithms - Solving Natural Logarithmic Equations
  • Lesson 13 - Graphing Logarithmic Functions in Excel
  • Lesson 14 - Applications (INTEREST problems only)
  • Lesson 15 - Logarithms: Change of Base Rule
  • Lesson 16 - Some Exponential and Logarithmic Problems Worked Out

 

 Systems of Equations

  • Lesson 1 - Systems of Linear Equations
  • Lesson 2 - Graphing Systems of Linear Equations
  • Lesson 3 - Solving by Substitution
  • Lesson 4 - Gaussian Elimination
  • Lesson 5 - Consistent and Independent Systems (3 variables)
  • Lesson 6 - Inconsistent Systems (3 variables)
  • Lesson 7 - Dependent and Consistent Systems (3 variables)
  • Lesson 8 - Coffee mixture problem
  • Lesson 9 - Changing a System into a Matrix
  • Lesson 10 - The Matrix - Aij Identifying Rows and Column
  • Lesson 11 - Determinants of a Matrix
  • Lesson 12 - The Augmented Matrix
  • Lesson 13 - Row Echelon Form
  • Lesson 14 - Reduced Row Echelon Form
  • Lesson 15 - Solving a 3 x 4 matrix
  • Lesson 16 - Matrix - Inconsistent and/or Dependent
  • Lesson 17 - How to Use a Matrix to Find a Quadratic Equation
  • Lesson 18 - Scalars
  • Lesson 19 - Properties of Matrices
  • Lesson 20 - Matrix Addition and Subtraction
  • Lesson 21 - Matrix Multiplication (non-square matrices)
  • Lesson 22 - Multiplying Matrices (square matrices)
  • Lesson 23 - The Identity Matrix
  • Lesson 24 - Matrix Inverses
  • Lesson 25 - Eigenvalues and Eigenvectors

 

Sequences

  • Lesson 1 - Sequences
  • Lesson 2 - The nth Term
  • Lesson 3 - Arithmetic Sequences: Finding the nth Term
  • Lesson 4 - Geometric Sequences: Finding the nth Term
  • Lesson 5 - Summation Notation
  • Lesson 6 - Summation of Arithmetic Sequences
  • Lesson 7 - Summation of Geometric Sequences When |r| ≥ 1
  • Lesson 8 - Summation of Geometric Sequences When |r| < 1
  • Lesson 9 - Principal of Mathematical Induction (PMI)
  • Lesson 10 - The Binomial Theorem
  • Teacher: Richard
  • Areas of expertise: Algebra, Statistics and Probability, Trigonometry, Calculus, Discrete Math, Linear Algebra, How to Teach Math (for future Math instructors), Business Math, and others.
  • Education: BA in Mathematics (SDSU), MA in Curriculum and Instruction Emphasis in Math Instruction (SDSU), BCLAD Teaching Credential (SDSU)
  • Interests: Watching students succeed in mathematics, Emerging Learning Technologies, Puzzles, Soduko, Space Exploration, Science Fiction, Zombie movies (good ones, not those cheap ones!), Music, Video Production, Website Construction, World Peace, Family, others
  • Skills: I have an easy non-threatening approach to the teaching/learning of mathematics. I break down the harder concepts into easier to understand steps. I am one of those weirdos who actually loves math. I see math like art and/or music - it gives me goose bumps!
  • Associations: TODOS: Mathematics For All Greater San Diego Math Teachers Association National Council of Math Teachers (NCTM) Hispanic Association of Colleges and Universities (HACU) White House Initiative on Educational Excellence for Hispanic Americans’ Hispanic Family Learning Initiative
  • Issues I care about: I am very concerned with how our country has watered down math education in our public schools. There is no doubt that the courses that keeps students from succeeding in high school and/or college are all mathematics courses. I don't blame the students - I blame the educators; not the teachers, but the Educational Leaders who make the big decisions. Public school teachers have zero choice in what and how to teach math.

I have been a Math Learning Specialist and Director of our University's Tutoring Center for the last 15 years. I have personally worked with thousands of struggling math students. I have also taught all of the math courses that our school offers, at both undergraduate and graduate level. A very sad fact is that around 90% of our incoming students are not prepared for college level mathematics. For some strange reason, students who are not successful at math in high school believe that they will understand it when they get to college - just the opposite is true. Students who master the concepts covered in this 11th grade course will succeed in their math courses in college.

What you should know before beginning this course

What you should already know before beginning this course

Section 1: Set Theory Quiz ANSWERS

Section 1: Set Theory Quiz ANSWERS

Section 2: Cartesian Plane and Coordinate Geometry Quiz ANSWERS

Section 2: Cartesian Plane and Coordinate Geometry Quiz ANSWERS

Section 3: Functions (General) and Graphing Quiz ANSWERS

Section 3: Functions (General) and Graphing Quiz ANSWERS

Section 4: Quadratic Functions Quiz ANSWERS

Section 4: Quadratic Functions Quiz ANSWERS

Section 5: Polynomial Functions Quiz ANSWERS

Section 5: Polynomial Functions Quiz ANSWERS

Section 6: Exponents and Logarithms Quiz ANSWERS

Section 6: Exponents and Logarithms Quiz ANSWERS

Section 7: Systems of Linear Equations Test ANSWERS

Section 7: Systems of Linear Equations Test ANSWERS

Section 8: Sequences Test ANSWERS

Section 8: Sequences Test ANSWERS

Midterm 1 ANSWERS

Midterm 1 ANSWERS

Midterm 2 ANSWERS

Midterm 2 ANSWERS

Midterm 3 ANSWERS

Midterm 3 ANSWERS

Final Exam ANSWERS

Final Exam ANSWERS

Graphing Linear Equations (pdf)

Graphing Linear Equations (pdf)

Graphing blanks for practice

Graphing blanks for practice

Basic Geometry Formulas

Basic Geometry Formulas used in this course.

List of Powers 2 - 20

List of Powers 2 - 20 - KNOW THEM!

Systems of Linear Equations: Example

Systems of Linear Equations: Example

Preset Color