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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 Expression 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 Graphs 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 Composition of 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 Graphs of Polynomials 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 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 Logarithmic and Exponential 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 models (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