Algebra I

Algebraic Foundations

• Overview and history of algebra. Introduction to variables. Substitution to variables. Substitution and evaluating expressions. Combining like terms. Introduction to equivalent expressions. Division by zero. 

Solving Equations & Inequalities

• Linear equations with variables on both sides. Linear equations with parenthesis. Analyzing the number of solutions to linear equations. Linear equations with unknown coefficients. Multi-step inequalities. Compound inequalities. 

Working with Units

• Rate conversions. Appropriate units. Word problems with multiple units. 

Linear Equations & Graphs

• Two-variable linear equation introduction. Slope. Horizontal and vertical lines. X-intercepts and y-intercepts. Applying intercepts and slopes. 

Forms of Linear Equations

• Introduction to slope-intercept form. Graphing slope-intercept equations. Writing slope-intercept equations. Point-slope form. Standard form. Summary forms of two-variable linear equations. 
  

Systems of Equations

• Introduction to systems of equations. Solving systems of equations with substitution. Equivalent systems of equations and the elimination method. Number of solutions to systems of equations. Systems of equation word problems. 

Inequalities (Systems & Graphs)

• Checking solutions of two-variable inequalities. Graphing two-variable inequalities. Modeling with linear inequalities. 

Functions

• Evaluating functions. Inputs and outputs of a function. Functions and equations. Interpreting function notation. Introduction to the domain and range of a function. Determining the domain of a function. Recognizing functions. Maximum and minimum points. Intervals where a function is positive, negative increasing or decreasing. Interpreting features of graphs. Average rate of change. Average rate of change word problems. Introduction to inverse functions.

Sequences

• Introduction to arithmetic sequences. Constructing arithmetic sequences. Introduction to geometric sequences. Constructing geometric sequences. Modeling with sequences. General sequences.

Absolute Value & Piecewise Functions

• Graphs of absolute value functions. Piecewise functions. 

Exponents & Radicals

• Exponents properties review. Radicals. Simplifying square roots. 

Exponential Growth & Decay

• Exponential vs. linear growth. Exponential expressions. Graphs of exponential growth. Exponential vs. linear growth over time. Exponential growth and decay. Exponential functions from tables and graphs. Exponential vs. linear models.

Quadratics. Multiplying & Factoring.

• Multiplying monomials by polynomials. Multiplying binomials. Special products of binomials. Introduction to factoring. Factoring quadratics introduction. Factoring quadratics by grouping. Factoring quadratics with difference of squares. Factoring of quadratics with perfect squares. Strategies in factoring quadratics.

Quadratic Functions & Equations

• Introduction to parabolas. Solving and graphing with factored form. Solving by taking the square root. Vertex form. Solving quadratics by factoring. The quadratic formula. Completing the square. Quadratic standard form. Features and forms of quadratic functions. Transforming quadratic functions.

Irrational Numbers

• Irrational numbers. Sums and products of rational and irrational numbers. Proofs concerning irrational numbers.