EQUATIONS WITH RADICALS AND EXPONENTS SIMPLIFIED PROBLEM SOLVER

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Continuation of study of basic concepts of algebra. Topics include brief review of elementary algebra, solutions of second-degree equations, radicals, complex numbers, rational expressions, polynomial expressions, rational exponents and roots, systems of equations and inequalities. |

**Topics outline:**

- I. Review Topics (appropriate review topics can be covered as each core topic is introduced):

- 1. Elementary Algebra

- (1). Arithmetical operations on integers and rationals

- (2). Terminology: associative, commutative and distributive properties; subsets of reals

- 2. Linear Equations in One Variable

- (1). Addition and multiplication principles introduced and used in solution process with integral coefficients/constants and parentheses

- (2). Solution process with rational and decimal coefficients/constants and parentheses

- (3). Formula evaluation and rearrangement (literal coefficients/constants)

- (4). Word problems (age, coin, geometric, consecutive integers)

- 3. Graphs of Lines in Two Variables

- II. Core Topics:

- 1. Linear Inequalities

- (1). Review number line graphing of solution

- (2). Compound inequality statements

- 2. Absolute Value (linear domains)

- (1). Solving equations c |ax + b| + d = e

- (2). Solving inequalities c |ax + b| + d is less than e and c |ax + b| + d is greater than e

- (3). Number line graphing of solution

- 3. Systems of Equations

- (1). Point-slope form

- (2). Slope-intercept form

- (3). Slope of parallel and perpendicular lines

- (4). Formula for the distance between two points

- (5). Elimination and substitution techniques for 2x2 and 3x3 systems

- (6). Graphical interpretation of 2x2 and 3x3 systems, including inconsistent and dependent systems

- (7). Appropriate word problems (as in A II d, motion, interest)

- (8). Sketching linear inequalities in two variables

- 4. Polynomials

- (1). Properties of integral exponents

- (2). Four basic operations (including long division)

- (3). Factoring common factors

- (4). Factoring by grouping (including multi-termed factor)

- (5). Factoring a x^2 + b x + c

- (6). Special products and factoring (perfect square trinomials, difference of two squares, sum/difference of two cubes)

- 5. Rational Expressions

- (1). Lowest term reduction

- (2). Four basic operations on rational expressions

- (3). Equations involving rational expressions

- (4). Complex fractions

- (5). Variation

- (6). Appropriate word problems (motion, work, etc.)

- 6. Rational Exponents and Roots

- (1). Exponential properties applied to rational exponents

- (2). Simplified radical form

- (3). Four basic operations on radical expressions

- (4). Equations with radicals

- (5). Four basic operations on complex numbers

- 7. Quadratic Equations

- (1). Solution by factoring

- (2). Completing the square

- (3). Quadratic formula usage and discriminant

- (4). Quadratic form equations

- (5). Graphing parabolas

- (6). Word problems

- solve the following types of equations: linear equations, quadratic equations, absolute-value equations, equations involving rational expressions, equations involving radicals, systems of two equations in two unknowns, systems of three equations in three unknowns;
- solve the following types of inequalities: linear inequalities, absolute-value inequalities, systems of linear inequalities in two variables;
- graph the following: lines, parabolas, linear inequalities in two variables;
- perform the elementary operations on the following: polynomials, rational expressions, complex numbers, radicals;
- simplify algebraic expressions including: reducing to lowest terms, complex fractions, algebraically rewriting results using basic definitions, laws of exponents, distributive law, factoring, and other basic properties of real numbers; rationalize the denominator;
- set up and solve word problems which apply linear equations, quadratic equations, equations involving rational expressions;
- interpret the basic relationships linking linear equations and linear inequalities in two variables, and parabolic equations to their graphs such as: solution sets, slope, parallel and perpendicular lines, forms of equations of lines, x-intercepts, y-intercepts, intersection of lines.

**Course Objectives:**

- Upon successful completion of this course, students should be able to:

- Individual work of a student
- participation in problem solving in class,
- preparation of the assigned homeworks and reading.

- Instructor's office hours.
- Free tutoring and use of computer software in the Academic Skills Center, Academic Wing of the Multipurpose Building, Room MA 129. (Hours are posted on door. You must sign in each time you use the Skills Center.)

**Procedures for accomplishing the Course Objectives:**

**Student Requirements for completion of the course:**

- Students must attend class, do homework assignment, take all the quizzes and the comprehensive final exam.

**Grading:**

- There will be approximately 15 -- 20 quizzes, given regularly (at least once a week) in class. They will last no more than 20 minutes each and will cover current material. There will be a final exam at the end of the course. It will cover all the material of the course. If a test (i.e. a quiz or the final exam) is missed, then the grade 0 is assigned for that test.

- Final score of a student =

- sum of all quiz scores (out of 75 possible)

- +

- the final exam score (out of 25 possible).

- Letter grade of a student =

- A, if the final score is 90 and above;

- B+, if the final score is 85 -- 89;

- B, if the final score is 80 -- 84;

- C+, if the final score is 75 -- 79;

- C, if the final score is 70 -- 74;

- D+, if the final score is 65 -- 69;

- D, if the final score is 60 -- 64;

- F, if the final score is below 60;

- W, if the student withdraws officially, by returning a withdrawal slip with my signature to the Registrar's Office before mid-semester (as defined by the academic calendar).

**Attendance:**

- All students are expected to attend every session of each course for which they are registered. Students are responsible for all that transpires in class whether or not they are in attendance. The College defines excessive absence or lateness as more than the equivalent of one week of class meetings during the semester. Excess absence or lateness may lead to failure in a course or removal from the class roster.

**Make-ups:**

- Make-up tests will be given only for documented emergencies, and then only at my discretion and convenience. However, if you have a good reason, please do ask for consideration.

**Disruptions:**

- Disruptive behaviors, as defined by the Student Handbook, will not be tolerated. College policy allows for the removal of disruptive students from class for the remainder of a class session in progress. Repeated disruptions in the classroom will lead to disciplinary action as specified in the Student Handbook. Pagers and cell phones are to be turned off at all times. If anyone wishes to reach you in an emergency, he or she should call the Mathematics Department Secretary (see the phone number above).

**Use of Calculators:**

- Use of calculators is

- not allowed --- in the class and during the final exam;

- not recommended --- during home work.

**Students with special needs:**

- If you are a student who has a disability and need reasonable accommodations, then please give me an advance notice about your special needs. If you have specific questions about obtaining these accommodations, you can call the Counselling Center at (631) 851-6250.

Contact the webmaster | Sun Jan 22 17:45:30 2006 |