ALGEBRA 1

Mr. P. Nelson

pnelson0502@yahoo.com

General Course Description

Algebra, which can be described as the language of mathematics, is the foundation of all advanced mathematics. It is the first mathematics course that teaches the basic structure and abstract nature of mathematics. More specifically, Algebra is a branch of mathematics in which we are concerned with the manipulation of symbolic combinations of objects - in particular, numbers. We are especially interested in quantitative properties and how to equate one combination of numbers with another. The course provides an introduction to the basics of algebra, which include the real numbers, and functions on the Cartesian plane. In particular, linear, exponential, and quadratic functions are emphasized with applications. Topics include sequences, inequalities, systems of equations/inequalities with emphasis on problem-solving. Much time and emphasis will also be placed on factoring polynomials, an essential skill needed to transition to more advanced math courses. If time permits, we will also delve into elementary logic and proof-writing in preparation for geometry.

Materials Needed

• Notebook paper

• Graph paper

• #2 pencils

• Scientific calculator

• Ruler

Desmos Scientific Calculator: https://www.desmos.com/scientific

Course Material

The lecture summaries should not be used as a substitute for participating in class. Students should still take their own notes.

Handouts

• Coordinate Grids

• Translating Words to Variable Expressions and Equations

• Properties of the Real Numbers

• Perfect Squares and Square Roots to Remember & Memorize

• Cartesian Plane: Points and Lines

• Classic Puzzle Problems

• Union and Intersection of Sets

• Guidelines for Factoring Completely

• Completing the Square Procedure

Lecture Summaries

• Numerical and Variable Expressions

• The Real Numbers and their Properties

• Solving Equations

• Problem-Solving

• Transforming Formulas

• Distance-Rate-Time Problems

• Exponents, Numerical Expressions, and Exponent Rules

• Ratio and Proportion

• Negative Exponents and Scientific Notation

• The Cartesian Plane, Linear Equations, and Function Families

• Relations and Functions

• Arithmetic and Geometric Sequences

• Direct and Inverse Variations

• Solving Systems of Equations

• Linear Inequalities; Set Theory: Union & Intersection

• Exponential Functions: Growth and Decay

• Radical Expressions

• Polynomial Expressions

• Introduction to Proof

• Factoring Polynomials

• Quadratic Functions and Equations