 Algebra Archives - UnLock Math

# UnLock Math Algebra

Develop critical thinking skills, including problem solving, logic, patterns, and deductive and inductive reasoning. ## Pre-Algebra

Total Units: 16

Pre-Algebra builds off of Foundations and prepares students for a successful algebraic education. Unlock Pre-Algebra will explain in an easy to understand method as what seems complex becomes understandable. The course reviews topics such as integers, fractions, decimals, percent, and geometry, while introducing students to new topics.

Unit 1

### Whole Numbers

1. 1.1 Introduction to Whole Numbers
2. 1.2 Place Value of Whole Numbers
3. 1.3 Rounding Whole Numbers
4. 1.4 Roman Numerals
5. 1.5 Patterns

Unit 2

### Integers

1. 2.1 Introduction to Integers
2. 2.2 Integers & Absolute Value
3. 2.3 Graphing Integers on a Number Line
4. 2.4 Comparing & Ordering Integers
6. 2.6 Subtracting Integers
7. 2.7 Multiplying Integers
8. 2.8 Dividing Integers

Unit 3

### Variables and Expressions

1. 3.1 Introduction to Variables & Expressions
2. 3.2 Writing Expressions
3. 3.3 Evaluating Expressions
4. 3.4 Order of Operations
5. 3.5 Equivalent Expressions
6. 3.6 Evaluating Expressions using Substitution
7. 3.7 Properties of Real Numbers
8. 3.8 Like Terms
9. 3.9 Distributive Property

Unit 4

### Rational Numbers

1. 4.1 Introduction to Rational Numbers
2. 4.2 Divisibility
3. 4.3 Factors & Multiples
4. 4.4 Prime Numbers
5. 4.5 Prime Factors
6. 4.6 Exponents
7. 4.7 Greatest Common Factor
8. 4.8 Least Common Multiple

Unit 5

### Fractions

1. 5.1 Introduction to Fractions
2. 5.2 Equivalent Fractions & Simplifying
3. 5.3 Mixed Numbers & Improper Fractions
4. 5.4 Multiplying Fractions
5. 5.5 Reciprocals
6. 5.6 Fractions - Relating Multiplication & Division
7. 5.7 Fractions - Cancelling to Simplify Multiplication
8. 5.8 Adding & Subtracting with Like Denominators
9. 5.9 Comparing Fractions
10. 5.10 Adding & Subtracting with Unlike Denominators

Unit 6

### Equations

1. 6.1 Introduction to Equations
2. 6.2 Problem Solving with Equations
3. 6.3 Solving Equations Using Addition & Subtraction
4. 6.4 Solving Equations Using Multiplication & Division
5. 6.5 Solving Equations Using Reciprocals
6. 6.6 Solving Multi-Step Equations with Variables on Both Sides
7. 6.7 Solving Multi-Step Equations with Fractions
8. 6.8 Writing Equations

Unit 7

### Inequalities

1. 7.1 Introduction to Inequalities
2. 7.2 Graphing Inequalities on a Number Line
3. 7.3 Adding & Subtracting Inequalities
4. 7.4 Multiplying & Dividing Inequalities
5. 7.5 Conjunctions & Disjunctions
6. 7.6 Solving Inequalities

Unit 8

### The Coordinate Plane

1. 8.1 Introduction to the Coordinate Plane
2. 8.2 Graphing a Coordinate Point
3. 8.3 Using a Table of Values
4. 8.4 First Differences
5. 8.5 X and Y Intercepts & Standard Form
6. 8.6 Classifying Slope
7. 8.7 Calculating Slope
8. 8.8 Slope-Intercept Form
9. 8.9 Graphing Inequalities
10. 8.10 Changing Forms: Standard to Slope

Unit 9

### Decimals

1. 9.1 Introduction to Decimals
2. 9.2 Decimals and Estimation
3. 9.3 Decimals to Fractions
4. 9.4 Fractions to Decimals
5. 9.5 Scientific Notation
6. 9.6 Repeating & Terminating Decimals

Unit 10

### Percent

1. 10.1 Introduction to Percent
2. 10.2 Decimals and Percent
3. 10.3 Finding Percent of a Number
4. 10.4 Simple Interest
5. 10.5 Compound Interest
6. 10.6 Discount Solving Percent Equations
7. 10.7 Percent of Change

Unit 11

### Polynomials

1. 11.1 Introduction to Polynomials
3. 11.3 Subtracting Polynomials
4. 11.4 Multiplying Polynomials
5. 11.5 Common Factoring

Unit 12

### Triangles

1. 12.1 Introduction to Triangles
2. 12.2 Triangle Classifications
3. 12.3 Square Roots
4. 12.4 Pythagorean Theorem

Unit 13

### 2D Geometry

1. 13.1 Introduction to 2D Geometry
2. 13.2 Parallel & Perpendicular Lines
3. 13.3 Classifying Polygons
4. 13.4 Interior Angles of Polygons
5. 13.5 Exterior Angles of Polygons
6. 13.6 Perimeter
7. 13.7 Area
8. 13.8 Circumference of a circle
9. 13.9 Area of a Circle
10. 13.10 Area of Irregular Shapes
11. 13.11 Perimeter of Irregular Shapes

Unit 14

### 3D Geometry

1. 14.1 Introduction to 3D Geometry
2. 14.2 Surface Area of a Rectangular Prism
3. 14.3 Surface Area of Pyramids
4. 14.4 Surface Area of Cylinders
5. 14.5 Volume of Rectangular Prisms
6. 14.6 Volume of Cylinders & Triangular Prisms
7. 14.7 Volume of Pyramids & Cones
8. 14.8 Volume and Surface Area of a Sphere

Unit 15

### Analyzing Data

1. 15.1 Introduction to Analyzing Data
2. 15.2 Line Graphs and Pictographs
3. 15.3 Bar Graphs
4. 15.4 Stem-and-Leaf Plots
5. 15.5 Measures of Central Tendency Part I
6. 15.6 Measures of Central Tendency Part II
7. 15.7 Box-and-Whisker Plots
8. 15.8 Circle Graphs

Unit 16

### Probability and Statistics

1. 16.1 Introduction to Probability & Statistics
2. 16.2 Ratio and Proportion
3. 16.3 Unit Rate and Proportion
4. 16.4 Simple Probability
5. 16.5 Independent Events
6. 16.6 Dependent Events
7. 16.7 Fundamental Counting Principle ## Algebra I

Total Units: 12

It expands on material introduced in Pre-Algebra while introducing functions, systems of linear equations and trigonometry. The primary goal of Algebra I is for students to develop beyond understanding rudimentary mathematical operations to comprehend more abstract algebraic ideas.

Unit 1

### Equations

1. 1.1 Introduction to Equations
2. 1.2 Solving Equations - Adding & Subtracting
3. 1.3 Solving Equations - Multiplying & Dividing
4. 1.4 Two Step Equations
5. 1.5 Multistep & Distributive Part I
6. 1.6 Multistep & Distributive Part II
7. 1.7 Equations with Multiple Variables
8. 1.8 Solving Percent Equations
9. 1.9 More Applications

Unit 2

### Linear Functions

1. 2.1 Introduction to Linear Functions
2. 2.2 Graphing Coordinate Point
3. 2.3 Relations and Linear Functions Pt I
4. 2.4 Relations and Linear Functions Pt II
5. 2.5 Direct Variation
6. 2.6 Slope & Rate of Change
7. 2.7 Calculating Slope
8. 2.8 Slope-Intercept Form
9. 2.9 X and Y Intercepts & Standard Form
10. 2.10 Calculate Slope using dydx and Intercepts
11. 2.11 Equation of a Line
12. 2.12 Special Lines
13. 2.13 Cost vs Time Functions
14. 2.14 Distance vs Time

Unit 3

### Inequalities & Absolute Value Functions

1. 3.1 Introduction to Inequalities & Absolute Value Functions
2. 3.2 Writing Solution Sets
3. 3.3 Graphing 1D
4. 3.4 Solving Multistep
5. 3.5 Compound Inequalities
6. 3.6 Solving Compound Inequalities
7. 3.7 Inequalities in 2D
8. 3.8 Absolute Value
9. 3.9 Graphing Absolute Value Functions

Unit 4

### Exponential Functions

1. 4.1 Introduction to Exponents
2. 4.2 The Product Property
3. 4.3 The Quotient Property
4. 4.4 Zero and Negative Exponents
5. 4.5 Fractional Exponents
6. 4.6 Power of a Power Property
7. 4.7 Power of a Product Property
8. 4.8 Power of a Fraction
9. 4.9 Order of Operations with Exponents – Numeric
10. 4.10 Simplifying Algebraic Expressions with Exponents
11. 4.11 Scientific Notation Part I
12. 4.12 Scientific Notation Part II
13. 4.13 Scientific Notation Part III
14. 4.14 Exponential Decay
15. 4.15 Exponential Growth

Unit 5

### Polynomials

1. 5.1 Introduction to Inequalities
3. 5.3 Subtracting Polynomials
4. 5.4 Adding & Subtracting Polynomials With More Than One Variable
5. 5.5 Multiplying Polynomials
6. 5.6 Common Factoring
7. 5.7 Factoring Polynomials Using The GCF
8. 5.8 Factoring Perfect Square Trinomials
9. 5.9 Factoring Difference Of Squares
10. 5.10 Factoring Trinomials
11. 5.11 Solving Equations Using Factoring
12. 5.12 Graphing The Cubic Function

Unit 6

1. 6.1 Introduction To Quadratic Functions
3. 6.3 Graphing Quadratic Function - Vertex Form
4. 6.4 Solving Equations with Square Roots
5. 6.5 Solving by Completing the Square
6. 6.6 Converting Quadratic Functions Into Vertex Form Using Completing the Square

Unit 7

### Rational Functions

1. 7.1 Introduction to Rational Functions
2. 7.2 Simplifying Rational Expressions
3. 7.3 Adding & Subtracting Rational Expressions
4. 7.4 Multiplying Rational Expressions
5. 7.5 Dividing Rational Expressions
6. 7.6 Graph of a Rational Function

Unit 8

1. 8.1 Introduction to Radical Functions
2. 8.2 Prime Factors
3. 8.3 Square Roots
4. 8.4 Simplifying Radicals – Numerical
5. 8.5 Simplifying Radicals – Algebraic

Unit 9

### Transformations

1. 9.1 Introduction to Transformations
2. 9.2 Domain of Parent Functions
3. 9.3 Range of Parent Functions
4. 9.4 Translations
5. 9.5 Reflections
6. 9.6 Vertical Stretches & Compressions
7. 9.7 Horizontal Stretches & Compressions
8. 9.8 Summary on Transformations
9. 9.9 Multiple Transformations

Unit 10

### Systems of Equations & Inequalities

1. 10.1 Introduction to Systems of Linear Equations & Inequalities
2. 10.2 Graphing Systems of Linear Equations
3. 10.3 Graphing Inequalities
4. 10.4 Graphing Systems of Inequalities
5. 10.5 Evaluating Expressions using Substitution
6. 10.6 Solving a System of Equations by Substitution
7. 10.7 Solving Systems of Equations by Elimination
8. 10.8 Identifying Types of Systems using Equations
9. 10.9 Writing an Equation
10. 10.10 Applications of Systems of Equations & Inequations

Unit 11

### Trigonometry

1. 11.1 Introduction to Trigonometry
2. 11.2 Sine Ratio
3. 11.3 Cosine Ration
4. 11.4 Tangent Ratio

Unit 12

### Probability

1. 12.1 Introduction to Probability
2. 12.2 Simple Probability
3. 12.3 Fundamental Counting Principle
4. 12.4 Independent Events
5. 12.5 Dependent Events
6. 12.6 Compound Probability
7. 12.7 Experimental & Theoretical Probability
8. 12.8 Set Theory & Venn Diagrams
9. 12.9 Set Theory - Intersection and Union ## Algebra II

Total Units: 15

Emphasis on functions returns as the functional families learned in Algebra I are studied in more detail. Algebra II expands on quadratic, polynomial, exponential, radical and rational functions and introduces logarithmic functions. Students learn how to use and operate on complex numbers so that complex solutions of quadratic and polynomial functions can be considered. This course focuses on more abstract and theoretical concepts, allowing students to improve their critical thought processes. The primary goal of this course is for students to own a strong understanding of all types of functions and prepare them for Pre-Calculus.

Unit 1

### Review of Equations & Exponents

1. 1.1 Introduction to Equations
2. 1.2 Multistep & Distributive Part I
3. 1.3 Multistep & Distributive Part II
4. 1.4 Equations with Multiple Variables
5. 1.5 Slope & Rate of Change
6. 1.6 Calculating Slope Using a Graph
7. 1.7 Calculate Slope Using dydx & Intercepts
8. 1.8 Slope-Intercept Form
9. 1.9 Equation of a Line
10. 1.10 Introduction to Exponents
11. 1.11 The Product Property
12. 1.12 The Quotient Property
13. 1.13 Zero and Negative Exponents
14. 1.14 Fractional Exponents
15. 1.15 Power of a Power Property
16. 1.16 Power of a Product Property
17. 1.17 Power of a Fraction
18. 1.18 Simplifying Algebraic Expressions with Exponents

Unit 2

### Systems of Linear Equations & Inequalities

1. 2.1 Intro to Systems of Linear Equations & Inequalities
2. 2.2 Solving a System of Equations by Substitution
3. 2.3 Solving a System of Equations by Elimination
4. 2.4 Graphing Systems of Linear Equations
5. 2.5 Graphing Systems of Inequalities
6. 2.6 Linear Programming

Unit 3

### Polynomial Functions

1. 3.1 Introduction to Polynomials
2. 3.2 Adding & Subtracting Polynomials
3. 3.3 Multiplying Polynomials
4. 3.4 Dividing Polynomials Using Long Division
5. 3.5 Dividing Polynomials Using Synthetic Division
6. 3.6 Remainder Theorem
7. 3.7 Factor Theorem
8. 3.8 Factoring Polynomials Using the GCF
9. 3.9 Factoring Using Difference of Squares
10. 3.10 Factoring Perfect Square Trinomials
11. 3.11 Factoring Trinomials
12. 3.12 Factoring Using Sums or Difference of Cubes
13. 3.13 Solving Equations Using Factoring

Unit 4

### Functions

1. 4.1 Introduction to Functions
2. 4.2 Function Notation & Evaluation
3. 4.3 Domain of a Function & Interval Notation
4. 4.4 Range of a Function & Interval Notation
5. 4.5 Adding & Subtracting Functions
6. 4.6 Multiplying & Dividing Functions
7. 4.7 Composition of Functions
8. 4.8 Inverse Functions
9. 4.9 Composition and Inverse
10. 4.10 Piecewise Functions
11. 4.11 Step Functions

Unit 5

### Complex Numbers

1. 5.1 Introduction to Imaginary & Complex Numbers
2. 5.2 Adding & Subtracting Complex Numbers
3. 5.3 Multiplying Complex Numbers
4. 5.4 Complex Conjugates
5. 5.5 Dividing Complex Numbers
6. 5.6 Absolute Value & Complex Numbers

Unit 6

### Polynomial Functions Solving & Graphing

1. 6.1 Finding a Polynomial Given the Roots
2. 6.2 Location Principle & Multiplicity of Zeros
3. 6.3 Rational Root Theorem
5. 6.5 The Complex Conjugate Root Theorem
6. 6.6 Fundamental Theorem of Algebra & Descartes Rule of Signs
7. 6.7 Graphing Polynomials

Unit 7

1. 7.1 Introduction to Quadratic Functions
2. 7.2 Graphing Quadratic Functions in Vertex Form
3. 7.3 Solving Quadratics with Square Roots
4. 7.4 Solving Quadratics with Completing the Square
5. 7.5 Converting Quadratic Function to Vertex Form using Completing the Square

Unit 8

### Exponential & Logarithmic Functions

1. 8.1 Intro to Exponential & Logarithmic Properties
2. 8.2 Exponential Growth
3. 8.3 Exponential Decay
4. 8.4 Logarithmic Functions
5. 8.5 Evaluating Logarithmic Functions
6. 8.6 Product Property of Logarithms
7. 8.7 Quotient Property of Logarithms
8. 8.8 Power Property of Logarithms
9. 8.9 Exponential-Logarithmic Inverse Properties
10. 8.10 Application of Logarithms
11. 8.11 The Natural Exponential Function
12. 8.12 The Natural Logarithm
13. 8.13 Solving Logarithmic Equations

Unit 9

### Exponential & Logarithmic Functions

1. 9.1 Introduction to Rational Functions
2. 9.2 Direct Variation
3. 9.3 Inverse Variation
4. 9.4 Joint & Combined Variation
5. 9.5 Simplifying Rational Expressions
6. 9.6 Adding & Subtracting Rational Expressions
7. 9.7 Multiplying Rational Expressions
8. 9.8 Dividing Rational Expressions
9. 9.9 Complex Fractions
10. 9.10 Solving Rational Equations
11. 9.11 Graph of a Rational Function
12. 9.12 Graph of a Rational Function Continued

Unit 10

1. 10.1 Introduction to Radical Functions
2. 10.2 Simplifying Radicals - Numerical
3. 10.3 Simplifying Radicals - Algebraic

Unit 11

### Conic Sections

1. 11.1 Introduction to Conic Sections
2. 11.2 Distance & Midpoint Formulas
3. 11.3 Parabolas Part I
4. 11.4 Parabolas Part II
5. 11.5 Circles Part I
6. 11.6 Circles Part II
7. 11.7 Ellipses Part I
8. 11.8 Ellipses Part II
9. 11.9 Hyperbolas Part I
10. 11.10 Hyperbolas Part II
11. 11.11 Solving Non Linear Systems

Unit 12

### Statistics & Probability

1. 12.1 Introduction to Statistics
2. 12.2 Independent & Dependent Events
3. 12.3 Measures of Central Tendency
4. 12.4 Hisotgrams & Circle Graphs
5. 12.5 Stem & Leaf Plots
6. 12.6 Box & Whisker Plots
7. 12.7 Scatter Plots
8. 12.8 Permutations
9. 12.9 Combinations
10. 12.10 Measures of Dispersion

Unit 13

### Series & Patterns

1. 13.1 Introduction to Series & Patterns
2. 13.2 Sequences & Series
3. 13.3 Arithmetic Sequences
4. 13.4 Arithmetic Series
5. 13.5 Geometric Sequences
6. 13.6 Finite Geometric Series
7. 13.7 Infinite Geometric Series
8. 13.8 Pascal's Triangle
9. 13.9 Binomial Theorem

Unit 14

### Trigonometry

1. 14.1 Introduction to Trigonometric Functions
2. 14.2 Finding an Unknown Angle
3. 14.3 Reciprocal Ratios
4. 14.4 Sine Law
5. 14.5 Cosine Law
6. 14.6 Angles in Standard Position
7. 14.7 Special Triangles & Exact Values

Unit 15

### Matrices

1. 15.1 Introduction to Matrices
2. 15.2 Basic Matrix Operations
3. 15.3 Matrix Multiplication
4. 15.4 Determinant of a Matrix
5. 15.5 Inverse of a Matrix