Algebra 1

Jacob Carroll, Sep 26, 2019

Within this book, students will build onto their knowledge and skills for mathematics from grades 6-8. A foundation of linear relationships, number and operations, and proportionality. Students will study linear, quadratic, and exponential functions and their related transformations, equations, and associated solutions. Students will connect functions and their solutions to both mathematical and real-world situations.

Table of Contents

  1. Mathematical process standards
    1. Student Expectations
    2. Algebra Symbols
    3. Mental Math Game
    4. Similarity in Everyday Life
  2. Linear Functions, Equations, and Inequalities
    1. Properties of Linear Functions
    2. f(x) Transformations
    3. Parameter Changes to a Linear Function
    4. Solving Linear Equations
    5. graph linear inequalities in two variables
    6. Solving 2x2 Systems of Equations
  3. Quadratic Functions and Equations
    1. Properties of a Quadratic
    2. f(x)=x^2 Transformations
    3. Domain and Range of Quadratics
    4. Completing the Square
    5. Standard Form vs. Vertex Form
    6. Quadratic Formula Calculator
  4. Exponential Functions and Equations
    1. Properties of an Exponential Function
    2. Exponential Growth and Decay
    3. Exponential Functions
    4. Domain and Range of Exponentials
  5. Number and Algebraic Methods
    1. Factoring Trinomials
    2. Multiplying Binomials
    3. Plotting a Point
    4. Simplifying Radicals (II)
    5. Reflecting a Triangle over the X & Y Axis

1.

Mathematical process standards

The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

  • 1. Student Expectations
  • 2. Algebra Symbols
  • 3. Mental Math Game
  • 4. Similarity in Everyday Life

1.1.

Student Expectations

A. apply mathematics to problems arising in everyday life, society, and the workplace;[br]B. use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem -solving process and the reasonableness of the solution;[br]C. select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; [br]D. communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;[br]E. create and use representations to organize, record, and communicate mathematical ideas;[br]F. analyze mathematical relationships to connect and communicate mathematical ideas; and[br]G. display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
– Jacob Carroll

1.2.

–

1.3.

–

1.4.

–

2.

Linear Functions, Equations, and Inequalities

  • 1. Properties of Linear Functions
  • 2. f(x) Transformations
  • 3. Parameter Changes to a Linear Function
  • 4. Solving Linear Equations
  • 5. graph linear inequalities in two variables
  • 6. Solving 2x2 Systems of Equations

2.1.

Properties of Linear Functions

– Jacob Carroll

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

3.

Quadratic Functions and Equations

  • 1. Properties of a Quadratic
  • 2. f(x)=x^2 Transformations
  • 3. Domain and Range of Quadratics
  • 4. Completing the Square
  • 5. Standard Form vs. Vertex Form
  • 6. Quadratic Formula Calculator

3.1.

Properties of a Quadratic

– Jacob Carroll

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

4.

Exponential Functions and Equations

  • 1. Properties of an Exponential Function
  • 2. Exponential Growth and Decay
  • 3. Exponential Functions
  • 4. Domain and Range of Exponentials

4.1.

Properties of an Exponential Function

Exploring the many properties of an exponential function.
– Jacob Carroll, biiancasn5

4.2.

–

4.3.

–

4.4.

–

5.

Number and Algebraic Methods

  • 1. Factoring Trinomials
  • 2. Multiplying Binomials
  • 3. Plotting a Point
  • 4. Simplifying Radicals (II)
  • 5. Reflecting a Triangle over the X & Y Axis

5.1.

Factoring Trinomials

– Jacob Carroll

5.2.

–

5.3.

–

5.4.

–

5.5.

–

Information