Algebra I

Instructor: Paul Prencis

This course is a Regents math course covering the New York State Core Curriculum for Integrated Algebra. The course provides a strong foundation in elementary algebra, functions and their graphs, and statistics. Topics include: equations and inequalities, operations with polynomials, factoring and quadratics, and systems of equations, with emphasis on using these skills to solve contextual problems. Students will take the New York State Integrated Algebra Regents exam in June.

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Introduction to Linear Models

• What is a linear model
  
• Creating a linear model
• Evaluating linear models
• Using linear models to predict future events
• Examples
• • Cell phone
  • Taxi cab
  • Sales commision
    

Solving Linear Equations

• Solving Equations Using More Than One Operation (4.1)
• Simplifying Each Side of an Equation (4.2) 
• Solving Equations That Have the Variable in Both Sides (4.3)
• Properties of Operations (2.2)
• Using Formulas to Solve Problems (4.4)
• Solving for a Variable in Terms of Another Variable (4.5)
• Transforming Formulas (4.6)
• The Integers (1.1)
• The Rational numbers (1.2)
• Absolute Value (1.2)
• Solving Equations with Fractional Coefficients (14.6)
• Applications 

Solving Linear Inequalities

• Properties and Graphing of Inequalties (4.7)
• Finding and Graphing the Solution Set of an Inequality (4.8)
• Solving Inequalities with Fractional Coefficients (14.7)
• Using Inequalties to Solve Problems (4.9)

Types of Linear Applications

• Coin Problems
• Distance Problems
• Whole in two parts
• Consecutive integer Problems
• Mixture/Weighted Average Problems
• Perimeter
• Complementary and Supplementary Problems (7.2)
• Inequality Problems

Graphs of Linear Functions

• Graphing Number Pairs (2.8)
• Sets, RelationsFunctions (9.1)
• Graphing Linear Functions Using Their Solutions (9.2)
• The Intercepts of a Line (9.6)
• The Slope of a Line (9.4)
• Graphing Linear Functions Using Their Slopes (9.7)
• The Point-Slope Form of a Line
• Graphing a Line Parallel to an Axis (9.3)
• The Slopes of Parallel and Perpendicular Lines (9.5)
• Writing an Equation Given Slope and One Point (10.1)
• Writing an Equation Given Two Points (10.2)
• Writing an Equation Given the Intercepts (10.3)
• Graphing First-Degree Inequalities in Two Variables (9.9)
• Graphs Involving Absolute Value (9.10)

Operations and Factoring Polynomials

• Adding and Subtracting Algebraic Expression (5.1)
• Multiplying Powers That Have the Same Base (5.2)
• Multiplying by a Monomial (5.3)
• Dividing Powers That Have the Same Base (5.5)
• The Square of a Monomial (11.3)
• Negative and Zero Exponents (5.6)
• Multiplying Polynomials (5.4)
• Multiplying the Sum and the Difference of Two Terms (11.4)
• Multiplying Binomials (11.6)
• Dividing Polynomials by Monomials (5.8)
• Scientific Notation (5.7)
• Prime Factorization (11.1)
• Factoring by using the GCF (11.2)
• Factoring by the Difference of two Squares (11.5)
• Factor by Grouping
• Factoring Trinomials (11.7)
• Factoring Completely (11.8)

Quadratic Functions

• Factoring Completely (11.8)
• Solving Quadratic Equations (13.1)
• The Graph of a Quadratic Equation (13.2)
• Finding Roots from a Graph (13.3)

Graphical Systems

• Solving Linear Systems of Equations Graphically (10.4)
• Solving Quadratic Linear Systems Graphically (13.4)
• Solving Quadratic Linear Inequalties Graphically (10.8)

Algebraic Systems

• Using Addition to Solve a System of Linear Equations (10.5)
• Using Substitution to Solve a System of Linear Equations (10.6)
• Algebraic Solution of a Quadratic Linear System (13.5)
• Using Systems of Equations to Solve Verbal Problems (10.7)

Algebraic Fractions

• The Meaning of an Algebraic Fraction (14.1)
• Reducing Fractions to Lowest Terms (14.2)
• Multiplying Fractions (14.3)
• Dividing Fractions (14.4)
• Adding or Subtracting Algebraic Fractions (14.5)
• Solving Equations with Fractional Coefficients (14.6)
• Solving Inequalities with Fractional Coefficients (14.7)
• Solving Fractional Equations (14.8)

Ratio and Proportion

• Ratio (6.1)
• Using a Ratio to Express a Rate (6.2)
• Verbal Problems Involving Ratio (6.3)
• Proportion (6.4)
• Direct Variation (6.5)
• Percent and Percentage Problems (6.6)
• Changing Units of Measure (6.7)
• Precision and Accuracy (1.5)

Radicals and The Pythagorean Theorem

• Radicals and the Rational Numbers (12.1)
• Radicals and the Irrational Numbers (12.2)
• Finding the Principal Square Root of a Monomial (12.3)
• Simplifying a Square-Root Radical (12.4)
• Addition and Subtraction of Radicals (12.5)
• Multiplication of Square-Root Radicals (12.6)
• Division of Square-Root Radicals (12.7)
• The Pythagorean Theorem (8.1)

Trigonometry

• The Sine, Cosine, Tangent  Ratios (8.2, 8.4)
• Applications of Trigonometric Ratios (8.3,8.5,8.6)

Area and Volume

• Areas of Irregular Polygons   (7.6)
• Surface Area of Solids  (7.7)
• Volumes of Solids  (7.8)

Regents Review