Algebra III:  Curriculum

Chapter 1: Preliminaries

1. Approximations; Calculators
   1. Distinguish between rounding (up, down, rule) and truncating a decimal
   2. Perform arithmetic operations on a calculator
2. Real Numbers
   1. Classify Numbers
   2. Perform arithmetic operations
   3. Know properties of real numbers
   4. Determine the domain of a variable
3. Integer Exponents
   1. Evaluate expressions containing exponents
   2. Work with laws of exponents
   3. Use a calculator to evaluate exponents
   4. Use scientific notation
4. Polynomials
   1. Add and subtract polynomials
   2. Multiply polynomials
   3. Know formulas for special products
   4. Divide polynomials
5. Factoring Polynomials
   1. Factor the difference of squares and the sum and the difference of two cubes
   2. Factor perfect squares
   3. Factor second-degree polynomials (trinomials)
   4. Factor by grouping
6. Rational Expressions
   1. Reduce a rational expression to lowest terms
   2. Multiply and divide rational expressions
   3. Add and subtract rational expressions
   4. Simply complex fractions
7. Square Roots; Radicals
   1. Work with properties of square roots
   2. Rationalize the denominator
   3. Simplify nth roots
   4. Simplify radicals
8. Rational Exponents
   1. Evaluate expressions with fractional exponents
9. Geometry Topics
   1. Use the Pythagorean Theorem and its converse
   2. Know geometry formulas

 

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

1. Linear Equations
   1. Solve a linear equation in one variable
   2. Graph a linear equation
2. Setting Up Equations:  Applications
   1. Translate verbal descriptions into mathematical expressions and models
   2. Write and solve linear models for geometrical figures
   3. Write and solve linear models for simple interest
   4. Write and solve linear models for distance
   5. Write and solve linear models for calculating an average/mean
3. Linear Inequalities
   1. Solve linear inequalities
   2. Solve combined linear inequalities
   3. Write models for linear inequalities in one variable
4. Systems of Linear Equations
   1. Solve systems of linear equations by substitution
   2. Solve systems of linear equations by elimination
   3. Identify inconsistent and dependent linear systems
   4. Write models for linear systems
5. Systems of Linear Inequalities
   1. Graph an inequality
   2. Graph a system of linear inequalities

 

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

1. Quadratic Equations
   1. Solve a quadratic equation by factoring
   2. Solve a quadratic equation using the quadratic formula
   3. Solve applied problems
2. Other Types of Equations
   1. Solve an equation containing radicals
   2. Solve equations in quadratic form
3. Inequalities;  Interval Notation
   1. Convert between forms of :  interval notation, a number line, and an inequality
4. Polynomial and Rational Inequalities
   1. Solve polynomial inequalities
   2. Solve rational inequalities
5. Equations and Inequalities Involving Absolute Value
   1. Solve equations involving absolute value
   2. Solve inequalities involving absolute value

 

Chapter 3:  Graphs

1. Rectangular Coordinates;  Scatter Diagrams
   1. Know the Rectangular/Cartesian Coordinate Plane/System
   2. Find the distance between 2 points using the Distance Formula or Pythagorean Theorem
   3. Find the midpoint of a line segment using the Midpoint Formula
   4. Draw and Interpret Scatter Diagrams
2. Graphs and Equations
   1. Find the Intercepts on a Graph
   2. Identify a Graph as possessing Symmetry with Respect to the (a) x-axis, (b) y-axis, or (c) origin
   3. From a Given Point, Plot a Point that has Symmetry with Respect to the (a) x-axis, (b) y-axis, or (c) origin
   4. From a Given Graph, Sketch a Graph that has Symmetry with Respect to the (a) x-axis, (b) y-axis, or (c) origin
   5. Find the Intercepts from an Equation
   6. Test an Equation for Symmetry with Respect to the (a) x-axis, (b) y-axis, and (c) origin
3. Lines
   1. Calculate and Interpret the Slope of a Line
   2. Graph Lines
   3. Find the Equation of Vertical Lines
   4. Use the Point-Slope Form of a Line; Identify Horizontal Lines
   5. Find the Equation of a Line from Two Points
   6. Write the Equation of a Line in Slope-Intercept Form
   7. Identify the Slope and y-Intercept of a Line from its Equation
   8. Write the Equation of a Line in General Form
4. Parallel and Perpendicular Lines; Circles
   1. Define Parallel Lines
   2. Find Equations of Parallel Lines
   3. Define Perpendicular Lines
   4. Find Equations of Perpendicular Lines
   5. Graph a Circle
   6. Write the Standard Form of the Equation of a Circle
5. Linear Curve Fitting
   1. Distinguish between Linear and Nonlinear Relations
   2. Write the equation of a linear model from a scatter diagram
6. Variation
1. Construct a Model Using Direct Variation
2. Construct a Model Using Inverse Variation
3. Construct a Model Using Joint Variation
4. Construct a Model Using Combined Variation

 

Chapter 4:  Functions and Their Graphs

1. Functions
   1. Determine whether a relationship represents a function
   2. Find the value of a function
   3. Find the domain of a function
   4. Identify the graph of a function
   5. Obtain information from or about the graph of a function
2. More About Functions
   1. Determine where a function is increasing and decreasing
   2. Determine even or odd functions from a graph
   3. Graph certain important functions
   4. Evaluate piece-wise defined functions
3. Graphing Techniques:  Transformations
   1. Graph functions using vertical and horizontal shifts
   2. Graph functions using compressions and stretches
   3. Graph functions using reflections about the x-axis or y-axis
4. Operations on Functions; Composite Functions
   1. Form the sum, difference, product and quotient of 2 functions
   2. Form the composite function and its domain

not complete and subject to change based on student needs