MAT1023

College Algebra with Applications

MAT 1023 College Algebra with Applications. (3-0) 3 Credit Hours. (TCCN = MATH 1314)

Prerequisite: Satisfactory performance on a placement examination. Topics include algebraic expressions; equations; inequalities over the real numbers; relations, functions and graphs; polynomial and rational functions; systems of linear equations and inequalities; complex numbers; and matrices and determinants. A wide range of applications will be included in this course. Students majoring in areas that require MAT 1214 Calculus I are encouraged to take MAT 1073 instead of MAT 1023. (Formerly MTC 1023. Credit can be earned for only one of the following: MAT 1023, MTC 1023, MAT 1063, MTC 1073, or Mat 1073. NOTE: For the purpose of the Three-Attempt Rule, these courses are considered to be equivalent and additional fees may be charged for the third or subsequent attempt to take any of these courses in any combination.) This course is designed for majors outside sciences and engineering. May apply toward the Core Curriculum requirement in Mathematics. Generally offered: Fall, Spring, Summer. Course Fees: LRC1 $12; LRS1 $45; STSI $21.

Date	Section	Topic	Pre-requisite	Student Learning Outcome
Week 1	P.1	Algebraic Expressions	Review concepts from high school algebra and/or developmental math course in Chapter P	Evaluate and simplify algebraic expressions
Week 1	P.2	Exponential Properties and Scientific Notation	Review basic properties of exponents and rational exponents and the connection between radical notation and rational exponents	Use the rules for exponents to simplify exponential expressions
Week 1	P.3	Radical & Rational Exponent	Review the connection between radical notation and rational exponents	Evaluate and simplify radical expressions Understand and use rational exponents
Week 2	P.4	Polynomials	Review concepts from high school algebra and/or developmental math course in Chapter P	Understand the vocabulary and operations of polynomial expressions
Week 2	P.5	Factoring Polynomials	Review techniques for factoring	Use a general strategy for factoring polynomials
Week 2	P.6	Rational Expressions	Review finding LCD and what operations need a LCD. Simplify fractions	Specify numbers that must be excluded from the domain and use operations of addition, subtraction, multiplication, and division of rational expressions
Week 3	1.1	Graph of equations	Review definition and computation of slope	Graph equations and determine intercepts
Week 3	1.2	Linear and Rational Equations	Differentiate between algebraic expression and algebraic equation	Solve linear equations including those involving fractions and variables in the denominator
Week 3	1.3	Models and Applications	Discuss strategies for solving word problems	Use linear equations to solve application problems and solve for a variable
Week 3	1.4	Complex Numbers	Intro. to imaginary and complex numbers	Perform operations with complex numbers and Square roots of negative numbers
Week 4		Review and Test I: Chapter P and 1.1-1.4
Week 5	1.5	Quadratic Equations	Recognize quadratic equations	Solve quadratic equations by factoring, square root property, completing the square, and the quadratic formula
Week 5	1.6	Other Types of Equations	Recognize polynomial, radical, rational exponent, and absolute value equations	Solve polynomial, radical, and rational exponent, and absolute value equations
Week 6	1.7	Linear and Absolute Value Inequalities	Basic knowledge of Inequality symbols and interval notation	Use interval notation Find union and intersection Solve linear and absolute value inequalities Solve compound inequalities
Week 6	2.1	Functions	Knowledge of Cartesian co-ordinate system, and representations of functions	Identify functions and find domain, range, and intercepts of functions
Week 6	2.1	Graphs	Knowledge of Cartesian co-ordinate system, and representations of functions	Graph functions by plotting points Evaluate functions
Week 6	2.2	More on Functions and Their Graphs	Be familiar with terms such as increasing, decreasing, minimum, and maximum in regard to a graph (ex. Average fuel efficiency over time)	Identify increasing, decreasing, and constant functions: relative max and min Identify even and odd functions and recognize their symmetries; understand and use piecewise functions
Week 7	2.3	Linear Functions and Slope	Review concept of slope from perspective of students’ previous knowledge	Calculate slope Write the point-slope and slope-intercept forms of the equations of a line Graph lines by plotting points and by using intercepts Model data
Week 7	2.4	More on Slope	Have students explain terms: parallel and perpendicular lines	Find slopes and equations of parallel and perpendicular lines Interpret slope as rate of change Find average rate of change
Week 7	2.5	Single Transformations of Functions	Review graphs of common functions	Recognize graphs of common functions Use horizontal and vertical shifts to graph functions Use reflections, stretching and shrinking to graph functions
Week 8	2.6	Combinations of Functions/Composite Functions	Knowledge of the domain of a function Addition, subtraction, multiplication and division of algebraic expressions	Find the domain of functions Combine functions using the algebra of functions form composite functions and determine the domain Write functions as compositions
Week 8	2.7	Inverse Functions	Knowledge of inverse operations in algebra Definition of function and domain of a function	Verify inverse functions Find the inverse of a function Use the horizontal line test to determine if a functions has an inverse
Week 9		Review and Test II: Sec. 1.5-1.6 and Chapter 2
Week 10	3.1	Quadratic Functions	Able to factor quadratic equations, and graph basic parabolas and transformations	Recognize characteristics of parabolas including minimum or maximum values and applications
Week 10	3.2	Polynomial Functions and Their Graphs	Able to factor polynomial equations	Identify polynomial functions and recognize characteristics of their graphs Determine end behavior Identify zeros and their multiplicities Use the Intermediate Value Theorem Understand the relationship between degree and turning points and graph the function
Week 10	3.3	Dividing Polynomials	Know steps in long division, and factor polynomials	Use long division and synthetic division to divide polynomials
Week 10	3.3	Remainder and Factor Theorem	Know steps in long division, and factor polynomials	Evaluate a polynomial using the Remainder Theorem Use the Factor Theorem to solve a polynomial equation
Week 11	5.1	Systems of Linear Equations in Two Variables	Combine equations/like terms	Solve linear systems by substitution and the addition method Identify systems that do not have exactly one ordered-pair solution
Week 11	5.5	Systems of Inequalities (optional-if time permits)		Graph a linear inequality in 2 variables Graph a nonlinear inequality in 2 variables Graph a system of inequalities
Week 12	Review for Test 3	Topics for TEST III: Chapters 3 and 5
Week 13	4.1	Exponential Functions	Recognize and/or review exponential functions Identify domain of functions	Evaluate exponential functions including those with a base e Graph exponential functions Use compound interest formulas
Week 13	4.2	Logarithmic Functions	Recognize and/or review logarithmic functions Identify domain of functions	Change from log to exponential form and vice versa Evaluate logs; use basic log properties Graph logarithmic functions and identify the domain Use common and natural logarithms
Week 14	4.3	Logarithmic Properties	Know properties of exponents	Use product, quotient, and power rules Expand and condense logarithmic expressions Use change of base property
Week 14	4.4	Exponential and Logarithmic Equations	Understand properties of logarithms	Use like bases and logarithms to solve exponential equations Use the definition of a logarithm to solve log equations Use the one-to-one property of logs to solve equations Solve application problems
Week 14	4.5	Exponential Growth and Decay (Modeling Data) (Optional-if time permits)	Understand exponential and logarithmic equations	Model exponential growth and decay Use logistic growth models and exponential model in base e
Week 15	Review	Review for Final