Algebra I Honors

This course is an accelerated version of Algebra I designed for the highly motivated student who has mastered the skills and understands the concepts covered in previous Mathematics courses. Traditional topics will be covered in more depth and at a faster pace. The topics include:

• Functions and Their Graphs
• Algebraic Concepts and Equations
• Equations and Inequalities
• Graphing and Writing Linear Equations
• Systems of Equations and Inequalities
• Quadratic Equations and Functions
• Exponents and Exponential Functions
• Polynomials
• Rational Expressions and Functions
• Matrices and Matrix Operations

In addition to these topics, the honors class will also include an introduction to Probability & Statistics, Symbolic Logic, and the basic concepts of Geometry. Problem solving will be emphasized throughout the course. Students will sometimes be expected to learn material from additional reading and/or solving problems on their own. Typical classes will include a minimal review of homework and previously covered material.

COMPETENCY GOAL 1:  The learner will perform operations with numbers and expressions to solve problems. Objectives:

• Write equivalent forms of algebraic expressions to solve problems.
• Apply the laws of exponents.
• Operate with polynomials.
• Factor polynomials.
• Use formulas and algebraic expressions, including iterative and recursive forms, to model and solve problems.
• Model and solve problems using direct variation.

COMPETENCY GOAL 2:  The learner will describe geometric figures in the coordinate plane algebraically. Objectives:
Find the lengths and midpoints of segments to solve problems.
Use the parallelism or perpendicularity of lines and segments to solve problems.

COMPETENCY GOAL 3: The learner will collect, organize, and interpret data with matrices and linear models to solve problems. Objectives:

• Use matrices to display and interpret data. 
• Operate (addition, subtraction, scalar multiplication) with matrices to solve problems.
• Create linear models for sets of data to solve problems.
• Interpret constants and coefficients in the context of the data.
• Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

COMPETENCY GOAL 4: The learner will use relations and functions to solve problems. Objectives:

• Use linear functions or inequalities to model and solve problems; justify results.
• Solve using tables, graphs, and algebraic properties.
• Interpret constants and coefficients in the context of the problem.
• Graph, factor, and evaluate quadratic functions to solve problems.
• Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify results.
• Graph and evaluate exponential functions to solve problems.

COMPETENCY GOAL 5: The learner will be able to apply basic geometric properties to solve problems. Objectives :

• Understand periodic data and use it to solve problems.
• Apply the properties of the sine, cosine, and tangent
• functions to solve basic geometric problems.
• Understand and apply the properties of right triangles to solve related problems.

COMPETENCY GOAL 6 : The learner will be able to apply the basic principles of probability and statistics to analyze and solve problems. Objectives :

• Analyze the distribution of data by determining the mean, median, mode, and standard deviation of the data.
• Apply statistical principles and methods to sample surveys.
• Use basic probability and the normal distribution to model and analyze data.

COMPETENCY GOAL 7: The learner will use symbolic logic to analyze and solve logical problems. Objectives :

• Understand and apply the logical  and,  or,  and  not  to solve logical problems.
• Understand and use Venn Diagrams to solve logical problems.
• Create and use truth tables to analyze logical problems.