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Beginning Algebra Syllabus

PROGRAMS & CERTIFICATES FOR WHICH THIS COURSE IS REQUIRED:
NONE
PROGRAMS & CERTIFICATES FOR WHICH THIS COURSE IS AN ELECTIVE:
NONE
COURSE ACCEPTED AS TRANSFER CREDIT BY:
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RECOMMENDED CLASS SIZE: 20

RATIONALE: DEPARTMENT STANDARD FOR ENTRY
LEVEL REMEDIAL COURSES

FREQUENCY OF OFFERING: 3 X YEAR
TERMS NORMALLY OFFERED: FALL SPRING SUMMER

LAB FEE: NONE

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RATIONALE FOR COURSE :
This course introduces and develops basic knowledge of algebraic structures that serve as a foundation for other mathematics courses. In addition, problem solving skills are developed that are useful in other disciplines.

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COURSE DESCRIPTION:
This course is designed for students who have never taken algebra. Topics include simplification of algebraic expressions, order of operations , solutions and graphs of linear equations, systems of two linear equations in two unknowns , simple linear inequalities, compound linear inequalities, absolute value equations and inequalities, polynomial arithmetic, integer exponents, and scientific notation. Techniques include numerical, analytical and graphical methods. Credits in this course will not satisfy any degree or certificate requirements. This course is offered Satisfactory / Unsatisfactory only.
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GENERAL COURSE GOALS:
1. Introduce students to mathematics as a symbolic language and structure that is useful in solving real-world problems.
2. Develop a basic understanding of how to use algebraic skills to model and solve real-world problems.
3. Develop students' ability to translate between English and Math.
4. Develop students' confidence to solve problems analytically.
5. Develop algebraic, graphical, and numerical techniques for solving problems.
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COURSE OBJECTIVES:
Upon completion of the course, the student should be able to:

1. Evaluate algebraic expressions.
2. Solve a linear equation in one variable by using appropriate methods : applying addition, subtraction, multiplication, and division axioms in sequence, removing grouping symbols, clearing fractions.
3. Solve literal equations and formulas and demonstrate their use in solving real-world problems.
4. Graph a linear equation in two variables.
5. Find the slope of a line and describe the slope as an average rate of change.

6. Write the equation of a line given two points or a point and a slope.
7. Determine if two lines are parallel or perpendicular geometrically and analytically.
8. Use linear equations and their graphs to model and solve real-world problems.
9. Use graphing to solve a system of two linear equations in two unknowns.
10. Use substitution and elimination to solve a system of two linear equations in two unknowns.

11. Solve application problems involving a system of two linear equations in two unknowns.
12. Express intervals on the real number line using interval notation.
13. Solve simple linear inequalities, graph their solution set on the number line, and express the solution set using interval notation.
14. Use simple linear inequalities to model and solve real-world problems.
15. Solve simple linear inequalities in two variables and graph the solution set.

16. Solve compound linear inequalities, graph their solution set on the number line, and express the solution set using interval notation.
17. Use compound linear inequalities to model and solve real-world problems.
18. Solve equations and inequalities involving absolute values.
19. Use absolute value equations and inequalities to model and solve real-world problems.
20. Add, subtract, multiply, and divide polynomials .

21. Simplify expressions involving integer exponents.
22. Perform scientific notation and standard form conversions and use scientific notation in performing computations.
23. Communicate about algebra/mathematics in writing.
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COURSE OUTLINE:

I. Introduction to algebra
A. Review of real number arithmetic
 a. Addition, subtraction, multiplication and division
 b. Positive exponents
 c. Order of operations
B. The meaning of variable and constant
C. Translating between English and Math
D. Evaluating algebraic expressions
E. Simplifying algebraic expressions
 a. Commutative, associative, and distributive properties .

II. Linear equations
A. Linear equations and the addition rule
B. Linear equations and the multiplication rule
C. Solving linear equations by combining rules
D. Solving literal equations and formulas
E. Applications and problem solving (including geometry and percent applications)

III. Graphing
A. The rectangular coordinate system
 a. Plotting ordered pairs
 b. Quadrants
B. Graphing linear equations
 a. Finding x- and y- intercepts and graph
 b. Slope
  1. Geometric interpretation
  2. Slope as a rate of change
 c. Slope - intercept form of a line
 d. General form of a line
C. Writing linear equations
 a. Given two points
 b. Given a point and a slope
D. Parallel and perpendicular lines
E. Modeling with linear equations

IV. Systems of two linear equations in two unknowns
A. Graphical solution
B. Substitution and elimination
C. Applications involving systems of two linear equations in two unknowns

V. Simple Linear Inequalities
A. Interval notation
B. Simple linear inequalities and the addition rule
C. Simple linear inequalities and the multiplication rule
D. Solving simple linear inequalities by combining rules
E. Applications and problem solving
F. Solving simple linear inequalities in two variables and graphing the solution set

VI. Compound linear inequalities
A. Solving compound inequalities
 a. Involving "and" (intersection)
 b. Involving "or" (union)
B. Applications involving compound linear inequalities

VII. Absolute value equations and inequalities
A. Absolute value equations
B. Absolute value inequalities
C. Applications involving the absolute value

VIII. Polynomials
A. Polynomial Arithmetic
 a. Addition and subtraction of "like" terms
 b. Multiplication and properties of exponents
 c. Long division

IX. Integer exponents
A. Definition and properties of integer exponents
B. Scientific notation

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