College Algebra Math Chapter R Review Elem. College Algebra Instructor: Dr. Chekad Sarami

Course Number & Name:MATH 123 College Algebra Course Number & Name:MATH 123 College Algebra Semester Hours of Credit:3 Semester Hours of Credit:3 Days/Time Class Meets: MWF Days/Time Class Meets: MWF Room/Bldg. SBE 108 Room/Bldg. SBE 108 Instructors Name: Dr. Chekad Sarami Instructors Name: Dr. Chekad Sarami Office Location: SBE 334 Office Location: SBE 334 Office Telephone: Office Telephone: address: address: Office Hours: M 2-3 pm, TR 2:00-3:30, F 2-3 pm and 4-5 pm Office Hours: M 2-3 pm, TR 2:00-3:30, F 2-3 pm and 4-5 pm Final : Wednesday, December 7, Time: 6-8pm Final : Wednesday, December 7, Time: 6-8pm

COURSE DESCRIPTION: Mathematics 123 is a college level algebra course containing topics as follows: Sets, the real number system, exponents, radicals, polynomials, equations, inequalities, relations and functions, graphing, exponential and logarithmic functions. Prerequisites: High School Algebra I, II, and Plane Geometry or equivalent, and satisfactory placement score. Mathematics 123 is a college level algebra course containing topics as follows: Sets, the real number system, exponents, radicals, polynomials, equations, inequalities, relations and functions, graphing, exponential and logarithmic functions. Prerequisites: High School Algebra I, II, and Plane Geometry or equivalent, and satisfactory placement score. Graphical Calculator is Required! Graphical Calculator is Required!

GRADING SCALE: HW and Three Take-Home Tests (lowest chapter test score is dropped) 65% HW and Three Take-Home Tests (lowest chapter test score is dropped) 65% Group Projects: 10% Group Projects: 10% Instructor Option: 5% Instructor Option: 5% Final Exam (Cumulative) 20% Final Exam (Cumulative) 20% Total: 100

Student Tips I. Prior to the beginning of the semester: Begin each course with a positive attitude and open mind. Begin each course with a positive attitude and open mind. Determine why you are taking this course; graduation requirement, prerequisite for another course, your job demands this course, to improve your GPA. These are all- important reasons—remind yourself of this throughout the course. Determine why you are taking this course; graduation requirement, prerequisite for another course, your job demands this course, to improve your GPA. These are all- important reasons—remind yourself of this throughout the course. Plan your school, work, and recreation schedule to allow plenty of long blocks of time to study. Plan your school, work, and recreation schedule to allow plenty of long blocks of time to study. Plan or designate a study area that is quiet and where you won’t be interrupted. Plan or designate a study area that is quiet and where you won’t be interrupted. Purchase your textbook, calculator and any supplies before the semester begins or on the first day of class. Purchase your textbook, calculator and any supplies before the semester begins or on the first day of class.

II. During the semester: II. During the semester: Make an exaggerated effort the first couple of weeks—get off to a fast start. Make an exaggerated effort the first couple of weeks—get off to a fast start. Attend all classes—your teacher needs you there in order to "teach you." Attend all classes—your teacher needs you there in order to "teach you." Work all assignments as they are assigned. Mathematics courses are usually building courses, meaning each section builds on the concept that you have worked and understood all of the material in the previous section(s). Work all assignments as they are assigned. Mathematics courses are usually building courses, meaning each section builds on the concept that you have worked and understood all of the material in the previous section(s). Complete only one assignment at a time (in a block of time). Allow time for each assignment to "soak in" before attempting the next assignment. Complete only one assignment at a time (in a block of time). Allow time for each assignment to "soak in" before attempting the next assignment. Ask questions. Prepare a list of questions to ask in class, if the teacher allows, or in the teacher’s office or in a math help center. Ask questions. Prepare a list of questions to ask in class, if the teacher allows, or in the teacher’s office or in a math help center. Get help outside of class. You many want to go your teacher’s office or you may prefer to go to a help center. Get help outside of class. You many want to go your teacher’s office or you may prefer to go to a help center. Form study groups with 3 or 4 other students from your class. Form study groups with 3 or 4 other students from your class.

III. Prior to a test: Plan ahead—set aside plenty of study time, beginning several days before the test date. Go through the material presented/homework assignments. Select 2 or 3 problems of each type presented and write yourself a "practice test." For any areas that you feel are weak, select additional practice exercises and/or get help on these areas. 1-2 hours prior to taking the test, work a few problems—get your mind thinking mathematics.

IV. After a test: Go over your test. Study any questions which you missed—learn how to answer (work) these questions immediately. Keep your old tests in a safe place, as you will want to study them again prior to the final exam.

V. How to approach homework assignments: Read back through your class notes, including reworking all examples, before you attempt your homework assignments and read through the reading material in the text, working the examples in the text. As you are working through your homework, check your answers. Remember that you can check your answers to the odd problems from the back of the text. If you miss a problem, try reworking it rather than trying to find your mistake. Then compare your work. If you still miss it, look for a similar example in the reading material in that section. Using your own pencil and paper, work through that example and compare to the example in the text. Ask for HELP!

Properties of Real Numbers Rules of Signs a(-b) = -(ab) = (-a)b (-a)(-b) = ab - ( -a) = a

Properties of Real Numbers Cancellation Properties Zero – Product Property If ab = 0, then a = 0 or b = 0 or, both.

Properties of Real Numbers Arithmetic of Quotients

Arithmetic of Quotients: Example 1

Arithmetic of Quotients: Example 2

The Real Number Line The negative real numbers are the coordinates of points to the left of the origin 0. The real number zero is the coordinate of the origin O. The positive real numbers are the coordinates of points to the right of the origin O.

Example of Domain The result is read “The set of all real numbers z such that z is not equal to –3”

Example: The Pythagorean Theorem Show that a triangle whose sides are of lengths 6, 8, and 10 is a right triangle. We square the length of the sides: Notice that the sum of the first two squares (36 and 64) equals the third square (100). Hence the triangle is a right triangle, since it satisfies the Pythagorean Theorem.

For a rectangle of length L and width W: For a triangle with base b and altitude (height) h: Geometry Formulas For a circle of radius r (diameter d = 2r)

Geometry Formulas For a rectangular box of length L, width W, and height H: For a sphere of radius r: For a right circular cylinder of height h and radius r:

Exponents: Basic Definitions If a is a real number and n is a positive integer,

Examples:

Laws of Exponents

Example:

Simplify the expression. Express the answer so only positive exponents occur.

Using your calculator For Scientific Calculators: Evaluate: Keystrokes: 3.4 = For Graphing Calculators: Evaluate: Keystrokes: 3.44= ^

Monomial Coefficient Degree

Coefficients: 2, 0, -3, 1, -5 Degree: 4

The process of expressing a polynomial as a product of other polynomials is called factoring. Example Multiply: Factoring is the same process in reverse

Factor: Notice that each term in this trinomial has a greatest common factor of 3x.

Special Formulas When you factor a polynomial, first check whether you can use one of the special formulas shown in the previous section. Difference of Two Squares: Perfect Squares: Sum of Two Cubes: Difference of Two Cubes:

Example: Factor Completely:

Look for factors of 18 whose sum is 11.

Factors of , -1 5, -2 -5, 2 -10, 1 Sum

Factor By Grouping:

Absolute Value is needed here, since the principal square root produces a positive value. Example:

Product Property of Square Roots Example:

Rationalize the denominator in each expression

The principal nth root of a real number a, symbolized by is defined as follows: where a > 0 and b > 0 if n is even and a, b are any real numbers if n is odd Examples:

Properties of Radicals

Simplify: