# UnLock Math Curriculum

Algebra II is the direct successor to Algebra I and builds on each of the concepts studied within it.

## Curriculum

## Algebra II

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 Introduction to Equations
- 1.2 Multistep & Distributive Part I
- 1.3 Multistep & Distributive Part II
- 1.4 Equations with Multiple Variables
- 1.5 Slope & Rate of Change
- 1.6 Calculating Slope Using a Graph
- 1.7 Calculate Slope Using dydx & Intercepts
- 1.8 Slope-Intercept Form
- 1.9 Equation of a Line
- 1.10 Introduction to Exponents
- 1.11 The Product Property
- 1.12 The Quotient Property
- 1.13 Zero and Negative Exponents
- 1.14 Fractional Exponents
- 1.15 Power of a Power Property
- 1.16 Power of a Product Property
- 1.17 Power of a Fraction
- 1.18 Simplifying Algebraic Expressions with Exponents

Unit 2

### Systems of Linear Equations & Inequalities

- 2.1 Intro to Systems of Linear Equations & Inequalities
- 2.2 Solving a System of Equations by Substitution
- 2.3 Solving a System of Equations by Elimination
- 2.4 Graphing Systems of Linear Equations
- 2.5 Graphing Systems of Inequalities
- 2.6 Linear Programming

Unit 3

### Polynomial Functions

- 3.1 Introduction to Polynomials
- 3.2 Adding & Subtracting Polynomials
- 3.3 Multiplying Polynomials
- 3.4 Dividing Polynomials Using Long Division
- 3.5 Dividing Polynomials Using Synthetic Division
- 3.6 Remainder Theorem
- 3.7 Factor Theorem
- 3.8 Factoring Polynomials Using the GCF
- 3.9 Factoring Using Difference of Squares
- 3.10 Factoring Perfect Square Trinomials
- 3.11 Factoring Trinomials
- 3.12 Factoring Using Sums or Difference of Cubes
- 3.13 Solving Equations Using Factoring

Unit 4

### Functions

- 4.1 Introduction to Functions
- 4.2 Function Notation & Evaluation
- 4.3 Domain of a Function & Interval Notation
- 4.4 Range of a Function & Interval Notation
- 4.5 Adding & Subtracting Functions
- 4.6 Multiplying & Dividing Functions
- 4.7 Composition of Functions
- 4.8 Inverse Functions
- 4.9 Composition and Inverse
- 4.10 Piecewise Functions
- 4.11 Step Functions

Unit 5

### Complex Numbers

- 5.1 Introduction to Imaginary & Complex Numbers
- 5.2 Adding & Subtracting Complex Numbers
- 5.3 Multiplying Complex Numbers
- 5.4 Complex Conjugates
- 5.5 Dividing Complex Numbers
- 5.6 Absolute Value & Complex Numbers

Unit 6

### Polynomial Functions Solving & Graphing

- 6.1 Finding a Polynomial Given the Roots
- 6.2 Location Principle & Multiplicity of Zeros
- 6.3 Rational Root Theorem
- 6.4 The Quadratic Formula
- 6.5 The Complex Conjugate Root Theorem
- 6.6 Fundamental Theorem of Algebra & Descartes Rule of Signs
- 6.7 Graphing Polynomials

Unit 7

### Quadratic Functions

- 7.1 Introduction to Quadratic Functions
- 7.2 Graphing Quadratic Functions in Vertex Form
- 7.3 Solving Quadratics with Square Roots
- 7.4 Solving Quadratics with Completing the Square
- 7.5 Converting Quadratic Function to Vertex Form using Completing the Square
- 7.6 Graphing Quadratic Inequalities
- 7.7 Applications of Quadratics

Unit 8

### Exponential & Logarithmic Functions

- 8.1 Intro to Exponential & Logarithmic Properties
- 8.2 Exponential Growth
- 8.3 Exponential Decay
- 8.4 Logarithmic Functions
- 8.5 Evaluating Logarithmic Functions
- 8.6 Product Property of Logarithms
- 8.7 Quotient Property of Logarithms
- 8.8 Power Property of Logarithms
- 8.9 Exponential-Logarithmic Inverse Properties
- 8.10 Application of Logarithms
- 8.11 The Natural Exponential Function
- 8.12 The Natural Logarithm
- 8.13 Solving Logarithmic Equations

Unit 9

### Exponential & Logarithmic Functions

- 9.1 Introduction to Rational Functions
- 9.2 Direct Variation
- 9.3 Inverse Variation
- 9.4 Joint & Combined Variation
- 9.5 Simplifying Rational Expressions
- 9.6 Adding & Subtracting Rational Expressions
- 9.7 Multiplying Rational Expressions
- 9.8 Dividing Rational Expressions
- 9.9 Complex Fractions
- 9.10 Solving Rational Equations
- 9.11 Graph of a Rational Function
- 9.12 Graph of a Rational Function Continued

Unit 10

### Radical Functions

- 10.1 Introduction to Radical Functions
- 10.2 Simplifying Radicals - Numerical
- 10.3 Simplifying Radicals - Algebraic
- 10.4 Multiplying Radicals
- 10.5 Dividing Radicals
- 10.6 Adding & Subtracting Radicals
- 10.7 Solving Radical Equations
- 10.8 Graphing Radical Functions

Unit 11

### Conic Sections

- 11.1 Introduction to Conic Sections
- 11.2 Distance & Midpoint Formulas
- 11.3 Parabolas Part I
- 11.4 Parabolas Part II
- 11.5 Circles Part I
- 11.6 Circles Part II
- 11.7 Ellipses Part I
- 11.8 Ellipses Part II
- 11.9 Hyperbolas Part I
- 11.10 Hyperbolas Part II
- 11.11 Solving Non Linear Systems

Unit 12

### Statistics & Probability

- 12.1 Introduction to Statistics
- 12.2 Independent & Dependent Events
- 12.3 Measures of Central Tendency
- 12.4 Hisotgrams & Circle Graphs
- 12.5 Stem & Leaf Plots
- 12.6 Box & Whisker Plots
- 12.7 Scatter Plots
- 12.8 Permutations
- 12.9 Combinations
- 12.10 Measures of Dispersion

Unit 13

### Series & Patterns

- 13.1 Introduction to Series & Patterns
- 13.2 Sequences & Series
- 13.3 Arithmetic Sequences
- 13.4 Arithmetic Series
- 13.5 Geometric Sequences
- 13.6 Finite Geometric Series
- 13.7 Infinite Geometric Series
- 13.8 Pascal's Triangle
- 13.9 Binomial Theorem

Unit 14

### Trigonometry

- 14.1 Introduction to Trigonometric Functions
- 14.2 Finding an Unknown Angle
- 14.3 Reciprocal Ratios
- 14.4 Sine Law
- 14.5 Cosine Law
- 14.6 Angles in Standard Position
- 14.7 Special Triangles & Exact Values

Unit 15

### Matrices

- 15.1 Introduction to Matrices
- 15.2 Basic Matrix Operations
- 15.3 Matrix Multiplication
- 15.4 Determinant of a Matrix
- 15.5 Inverse of a Matrix