COURSE TITLE: Algebra I
COURSE DESCRIPTION: In Algebra I students study the relations and properties of real numbers. A substantial portion of the course focuses on an understanding of simplification techniques, methods of solving equation, inequalities and graphing. This is a college preparatory course.
Prerequisite: Placement based on Placement Test scores and Math Chairperson recommendation.
COURSE REQUIREMENT/REQUIRED MATERIALS:
A. Textbook
B. Pencil
C. A notebook dedicated only to Algebra
D. A pocket folder for math papers only.
E. Loose leaf paper
F. A TI 83+ Graphing Calculator
COURSE OBJECTIVES/STUDENT OUTCOMES:
1) Students will become familiar with the Real Number System.
Upon completing this goal the student will be able to:
* evaluate algebraic and numerical expressions using the rules for
order of operations
* identify the subsets of real numbers and relationships among them
* add, subtract, multiply and divide using real numbers
2) Students will learn the methods for solving equations and
inequalities in one variable.
Upon completing this goal the student will be able to:
* solve a linear equation in one variable
* solve equations that involve absolute value and graph their
solution sets
* solve quadratic equations by factoring
* solve fractional equations
* solve radical equations
* solve inequalities and graph their solution sets
* solve and graph inequalities that involve absolute value
* solve word problems that involve equations and inequalities in
one variable
3) Students will acquire an understanding of the nature of polynomials.
Upon completing this goal the student will be able to:
* add, subtract, multiply and divide polynomials
* simplify expressions with positive and negative exponents
* express numbers in scientific notation
* find the products and quotients of numbers expressed in
scientific notation
* identify the degree of a polynomial
* arrange the terms of a polynomial in ascending and descending order
* factor monomials into prime factors
* factor binomials and trinomials either by extracting common factors
or by using FOIL
* use grouping techniques to factor polynomials with four or more terms
4) Students will gain an understanding of the techniques for working
with rational expressions.
Upon completing this goal, the student will be able to:
* simplify rational expressions
* multiply and divide rational expressions
* add and subtract rational expressions
5) Students will discern the differences and similarities among
functions and relations.
Upon completing this goal, the student will be able to:
* show relations as sets of ordered pairs, mappings, tables,
graphs and equations
* identify the domain and range of a relation
* determine whether a given relation is a function
* calculate functional values for a given function
* write an equation to represent a relation, given a chart of values
6) Students will experience graphing linear equations and
inequalities with two variables.
Upon completing this goal, the student will be able to:
* graph linear equations
-by making a table and plotting points
-by using x- and y-intercepts
-by using the slope and y-intercept
* find the slope of a line
-when given two points
-when given the equation of a linear relation
* write a linear equation in standard and slope-intercept form given
-the coordinates of two points on the line
-the slope and the y-intercept
-the coordinates of a point on the line and the slope of the line
* determine whether two lines are parallel or perpendicular
* find the coordinates of the midpoint of a line segment
* graph lines using the graphing calculator
* graph linear inequalities
7) Students will develop the methods for solving systems of
equations and inequalities.
Upon completing this goal, the student will be able to:
* solve a system of linear equations
-by graphing by hand and using a graphing calculator
-by the substitution method
-by the elimination method
* determine whether a system of equations has one solution,
no solution or infinitely many solutions algebraically and graphically
* solve a system of inequalities by graphing
* use a system of two linear equations in two variables to solve
word problems
8) Students will gain an understanding of the properties of radicals.
Upon completing this goal, the student will be able to:
* simplify square roots
* find approximate value for square roots
* simplify radical expressions
* use the Pythagorean Theorem
* distinguish rational and irrational numbers
* add, subtract, multiply and divide radical expressions
* solve radical equations
* use the distance formula
COURSE OUTLINE:
A. Simplify
1) Order of operations
2) Combine like terms
3) Polynomials - multiply and divide
4) Rational expressions - factoring
a) Monomials
b) Binomials
c) Trinomials
d) Four terms
B. Graphing
1) On a number line
a) sets of numbers
b) inequalities
2) On a coordinate plane
a) points
b) Functions and relations
1. linear equations
2. linear inequalities
C. Linear equations
1) slope
a) given the graph
b) given two points
c) given the equation
2) write linear equation in the form y = mx + b
a) given slope and y-intercept
b) given slope and point on the line
c) given y-intercept and point on the line
d) given two points
e) given parallel to other line through point
f) given perpendicular to other line through point
D. Solve
1) One variable
a) linear equation
b) proportion
c) quadratic equation
d) absolute value
e) rational - fractional equation
f) radical equation
2) More than one variable
a) literal equations
b) systems of linear equations
1. solve graphically
2. solve by substitution
3. solve by elimination (addition)
3) Inequalities
a) single variable
b) compound
c) absolute value
E. Verbal Expressions and sentences
1) one variable
a) linear
1. consecutive integers
2. proportions
b) inequalities
c) quadratic
2) two variables - systems of equations
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