**T Mykut**

Course Objectives for Alg III

Algebra III: Curriculum

Chapter 1: Preliminaries

- Approximations; Calculators
- Distinguish between rounding (up, down, rule) and truncating a decimal
- Perform arithmetic operations on a calculator

- Real Numbers
- Classify Numbers
- Perform arithmetic operations
- Know properties of real numbers
- Determine the domain of a variable

- Integer Exponents
- Evaluate expressions containing exponents
- Work with laws of exponents
- Use a calculator to evaluate exponents
- Use scientific notation

- Polynomials
- Add and subtract polynomials
- Multiply polynomials
- Know formulas for special products
- Divide polynomials

- Factoring Polynomials
- Factor the difference of squares and the sum and the difference of two cubes
- Factor perfect squares
- Factor second-degree polynomials (trinomials)
- Factor by grouping

- Rational Expressions
- Reduce a rational expression to lowest terms
- Multiply and divide rational expressions
- Add and subtract rational expressions
- Simply complex fractions

- Square Roots; Radicals
- Work with properties of square roots
- Rationalize the denominator
- Simplify
*n*th roots - Simplify radicals

- Rational Exponents
- Evaluate expressions with fractional exponents

- Geometry Topics
- Use the Pythagorean Theorem and its converse
- Know geometry formulas

Chapter 2 (1,2,6)/Chapter 8 (1,7): Linear

- Linear Equations
- Solve a linear equation in one variable
- Graph a linear equation

- Setting Up Equations: Applications
- Translate verbal descriptions into mathematical expressions and models
- Write and solve linear models for geometrical figures
- Write and solve linear models for simple interest
- Write and solve linear models for distance
- Write and solve linear models for calculating an average/mean

- Linear Inequalities
- Solve linear inequalities
- Solve combined linear inequalities
- Write models for linear inequalities in one variable

- Systems of Linear Equations
- Solve systems of linear equations by substitution
- Solve systems of linear equations by elimination
- Identify inconsistent and dependent linear systems
- Write models for linear systems

- Systems of Linear Inequalities
- Graph an inequality
- Graph a system of linear inequalities

Chapter 2 (3,4,5,7,8): Equations and Inequalities

- Quadratic Equations
- Solve a quadratic equation by factoring
- Solve a quadratic equation using the quadratic formula
- Solve applied problems

- Other Types of Equations
- Solve an equation containing radicals
- Solve equations in quadratic form

- Inequalities; Interval Notation
- Convert between forms of : interval notation, a number line, and an inequality

- Polynomial and Rational Inequalities
- Solve polynomial inequalities
- Solve rational inequalities

- Equations and Inequalities Involving Absolute Value
- Solve equations involving absolute value
- Solve inequalities involving absolute value

Chapter 3: Graphs

- Rectangular Coordinates; Scatter Diagrams
- Know the Rectangular/Cartesian Coordinate Plane/System
- Find the distance between 2 points using the Distance Formula or Pythagorean Theorem
- Find the midpoint of a line segment using the Midpoint Formula
- Draw and Interpret Scatter Diagrams

- Graphs and Equations
- Find the Intercepts on a Graph
- Identify a Graph as possessing Symmetry with Respect to the (a) x-axis, (b) y-axis, or (c) origin
- From a Given Point, Plot a Point that has Symmetry with Respect to the (a) x-axis, (b) y-axis, or (c) origin
- From a Given Graph, Sketch a Graph that has Symmetry with Respect to the (a) x-axis, (b) y-axis, or (c) origin
- Find the Intercepts from an Equation
- Test an Equation for Symmetry with Respect to the (a) x-axis, (b) y-axis, and (c) origin

- Lines
- Calculate and Interpret the Slope of a Line
- Graph Lines
- Find the Equation of Vertical Lines
- Use the Point-Slope Form of a Line; Identify Horizontal Lines
- Find the Equation of a Line from Two Points
- Write the Equation of a Line in Slope-Intercept Form
- Identify the Slope and y-Intercept of a Line from its Equation
- Write the Equation of a Line in General Form

- Parallel and Perpendicular Lines; Circles
- Define Parallel Lines
- Find Equations of Parallel Lines
- Define Perpendicular Lines
- Find Equations of Perpendicular Lines
- Graph a Circle
- Write the Standard Form of the Equation of a Circle

- Linear Curve Fitting
- Distinguish between Linear and Nonlinear Relations
- Write the equation of a linear model from a scatter diagram

- Variation
- Construct a Model Using Direct Variation
- Construct a Model Using Inverse Variation
- Construct a Model Using Joint Variation
- Construct a Model Using Combined Variation

Chapter 4: Functions and Their Graphs

- Functions
- Determine whether a relationship represents a function
- Find the value of a function
- Find the domain of a function
- Identify the graph of a function
- Obtain information from or about the graph of a function

- More About Functions
- Determine where a function is increasing and decreasing
- Determine even or odd functions from a graph
- Graph certain important functions
- Evaluate piece-wise defined functions

- Graphing Techniques: Transformations
- Graph functions using vertical and horizontal shifts
- Graph functions using compressions and stretches
- Graph functions using reflections about the x-axis or y-axis

- Operations on Functions; Composite Functions
- Form the sum, difference, product and quotient of 2 functions
- Form the composite function and its domain

not complete and subject to change based on student needs

Alg II