Math 103 Topic Coverage

Fall 2013 Page 1 of 5 Cuyamaca College Topic Coverage for Math 103 – Intermediate Algebra (3 units)

Prerequisite: Credit in MATH 090 or equivalent

Course Materials: . Web-Enhanced Course - You will be doing your homework, lab assignments, and exam reviews online; therefore, you will need to purchase the Access Code for MyMathLab from online at mymathlab.com ($91.30 for the life-time of the edition, non-refundable) or from the Cuyamaca Bookstore (prices on campus may vary depending on the option you go with: $110.65, $114.30, or $178.55). o Course ID needed to enroll: . o You must be enrolled in MyMathLab by ??? you fill in date or you will be dropped from the course. . Textbook – Beginning and Intermediate Algebra by Bittinger and Ellenbogen, Custom Edition for Grossmont and Cuyamaca College . Calculator – A Scientific Calculator is required (graphing calculators ok). No other calculating device will be allowed during exams!

Course Description: This course explores graphic, numeric, analytic and applied problems on topics including linear, quadratic, exponential and logarithmic functions, exponents and radicals. It also covers the selection and application of appropriate graphing utility and/or computer program to interpret, model and analyze data, graphs and/or application problems. Additional topics include systems of equations, algebraic fractions, radicals, complex numbers, and equations involving inequalities and absolute value.

Course Objectives (Expected Student Learning Outcomes) - Students will be able to: Course Objectives Students will be able to: 1) Simplify or reorganize expressions by: a. Performing operations on rational expressions b. Performing operations on radical expressions c. Applying properties of rational exponents d. Applying properties of logarithms and/or 2) Solve each of the following: a. Absolute value equations b. Quadratic equations 1. By extracting roots 2. By completing the square 3. Using the quadratic formula c. Rational equations d. Radical equations e. Exponential equations f. Logarithmic equations and/or g. Absolute value linear inequalities 3) Solve system of two or three equations a. by graphing for two unknowns b. by substitution c. by elimination 4) Apply critical thinking and mathematical reasoning to analyze, translate and solve real-world problems applicable to vocation and professional fields and related disciplines (responses should include a correct interpretation of the solution using appropriate language and units) 5) Simplify or reorganize functions given a a. Sum b. Difference c. Product and/or d. Quotient 6) Inspect and analyze a graph in order to a. Evaluate the function **The instructor reserves the right to modify topic coverage as deemed appropriate while abiding by the established SLO’s** Fall 2013 Page 2 of 5 b. Determined the domain and range of a function 7) Given a quadratic function identify and/or interpret a. The coordinate of the vertex b. The shape of the graph and/or c. The max or min of a quadratic function 8) Find the domain and range of the following functions: a. Polynomial functions and/or b. Rational functions. 9) Apply coursework management skills to succeed in this class 10) Make consistent and regular preparations to maximize learning inside and outside the classroom.

Student Learning Outcomes Students will be able to: 1) Simplify or reorganize expressions 2) Solve equations 3) Solve systems of two or three equations. 4) Solve application problems 5) Simplify or reorganize functions by operations 6) Inspect and analyze a graph 7) Graph a quadratic function and identify its defining elements. 8) Find the domain and range of functions

Chapter 9 – Elementary Algebra Review o 9.1 – Introduction to Algebraic Expressions . The Real Numbers . Operations on Real Numbers . Algebraic Expressions o 9.2 – Equations, Inequalities, and Problem Solving . Solving Equations and Formulas . Solving Inequalities . Problem Solving o 9.3 – Introduction to Graphing and Functions . Points and Ordered Pairs . Graphs and Slope . Linear Equations . Functions o 9.4 – Systems of Equations in Two Variables . Solving Systems Graphically . Solving Systems Algebraically . Applications . Solving Equations by Graphing - SKIP o 9.5 – Polynomials . Exponents . Polynomials . Addition and Subtraction of Polynomials . Multiplication of Polynomials . Division of Polynomials - SKIP o 9.6 – Polynomial Factorizations and Equations . Common Factors and Factoring by Grouping . Factoring Trinomials . Factoring Special Forms . Solving Polynomial Equations

Chapter 7 – Rational Expressions and Equations o 7.1 – Rational Expressions **The instructor reserves the right to modify topic coverage as deemed appropriate while abiding by the established SLO’s** Fall 2013 Page 3 of 5 . Simplifying Rational Expressions . Factors That Are Opposites o 7.2 – Multiplication and Division . Multiplication . Division o 7.3 – Addition, Subtraction, and Least Common Denominators . Addition When Denominators Are the Same . Subtraction When Denominators Are the Same . Least Common Multiples and Denominators o 7.4 – Addition and Subtraction with Unlike Denominators . Adding and Subtracting with LCDs . When Factors Are Opposites o 7.5 – Complex Rational Expressions - SKIP o 7.6 – Solving Rational Equations . Solving a New Type of Equation . A Visual Interpretation - SKIP o 7.7 – Applications Using Rational Equations and Properties . Problems Involving Work - SKIP . Problems Involving Motion . Problems Involving Proportions - SKIP

Chapter 10 – Inequalities o 10.1 – Graphical Solutions and Compound Inequalities - SKIP o 10.2 – Absolute-Value Equations and Inequalities . Equations with Absolute Value . Inequalities with Absolute Value o 10.3 – Inequalities in Two Variables . Graphs of Linear Inequalities . Systems of Linear Inequalities o 10.4 – Polynomial Inequalities and Rational Inequalities - SKIP

Chapter 11 – More on Systems o 11.1 – System of Equations in Three Variables – KEEP IT SIMPLE o 11.2 – Solving Applications: Systems of Three Equations - SKIP o 11.3 – Elimination Using Matrices - SKIP o 11.4 – Determinants and Cramer’s Rule - SKIP o 11.5 – Business and Economics Applications . Break-Even Analysis . Supply and Demand

Chapter 12 – Exponents and Radical Functions o 12.1 – Radical Expressions, Functions, and Models . Square Roots and Square-Root Functions . Expressions of the Form a2 . Cube Roots . Odd and Even nth Roots . Radical Functions and Models o 12.2 – Rational Numbers as Exponents . Rational Exponents . Negative Rational Exponents . Laws of Exponents . Simplifying Radical Expressions – KEEP IT SIMPLE o 12.3 – Multiplying Radical Expressions . Multiplying Radical Expressions . Simplifying by Factoring . Multiplying and Simplifying **The instructor reserves the right to modify topic coverage as deemed appropriate while abiding by the established SLO’s** Fall 2013 Page 4 of 5 o 12.4 – Dividing Radical Expressions . Dividing and Simplifying . Rationalizing Denominators or Numerators with One Term o 12.5 – Expressions Containing Several Radical Terms . Adding and Subtracting Radical Expressions . Products and Quotients of Two or More Radical Terms . Rationalizing Denominators and Numerators with Two Terms . Terms with Differing Indices - SKIP o 12.6 – Solving Radical Equations . The Principle of Powers . Equations with Two Radical Terms o 12.7 – The Distance Formula, the Midpoint Formula, and Other Applications . Using Pythagorean Theorem . Two Special Triangles - SKIP . The Distance Formula and the Midpoint Formula - SKIP o 12.8 – The Complex Numbers . Imaginary Numbers and Complex Numbers . Addition and Subtraction . Multiplication . Conjugates and Division . Powers of i

Chapter 13 – Quadratic Functions and Equations o 13.1 – Quadratic Equations . The Principle of Square Roots . Completing the Square . Problem Solving – FIND X-INTERCEPTS o 13.2 – The Quadratic Formula . Solving Using the Quadratic Formula . Approximating Solutions o 13.3 – Studying Solutions of Quadratic Equations - SKIP o 13.4 – Applications Involving Quadratic Equations . Solving Problems . Solving Formulas - SKIP o 13.5 – Equations Reducible to Quadratic - SKIP o 13.6 – Quadratic Functions and Their Graphs . The Graph of f(x) = ax2 . The Graph of f(x) = a(x - h)2 . The Graph of f(x) = a(x - h)2 + k o 13.7 – More About Graphing Quadratic Functions . Finding the Vertex . Finding Intercepts o 13.8 – Problem Solving and Quadratic Functions . Maximum and Minimum Problems . Fitting Quadratic Functions to Data - SKIP

Chapter 14 – Exponential Functions and Logarithmic Functions o 14.1 – Composite Functions and Inverse Functions – Keep light just so Expo and Log make sense . Composite Functions . Inverse and One-to-One Functions . Finding Formulas for Inverses . Graphing Functions and Their Inverses . Inverse Functions and Composition - SKIP o 14.2 – Exponential Functions . Graphing Exponential Functions . Equations with x and y Interchanged - (save as intro to 14.3) . Applications of Exponential Functions o 14.3 – Logarithmic Functions . Graphs of Logarithmic Functions **The instructor reserves the right to modify topic coverage as deemed appropriate while abiding by the established SLO’s** Fall 2013 Page 5 of 5 . Common Logarithms . Equivalent Equations . Solving Certain Logarithmic Equations o 14.4 – Properties of Logarithmic Functions . Logarithms of Products . Logarithms of Powers . Logarithms of Quotients . Using Properties Together o 14.5 – Natural Logarithms and Changing Bases o 14.6 – Solving Exponential and Logarithmic Equations . Solving Exponential Equations . Solving Logarithmic Equations o 14.7 – Applications of Exponential and Logarithmic Functions . Applications of Logarithmic Functions - SKIP . Applications of Exponential Functions

Chapter 15 – Conic Sections o 15.1 – Conic Sections: Parabolas and Circles . Parabolas . Circles o 15.2 – Conic Sections: Ellipses . Ellipses Centered at (0,0) . Ellipses Centered at (h,k) o 15.3 – Conic Sections: Hyperbolas . Hyperbolas . Hyperbolas (Nonstandard Form) - SKIP . Classifying Graphs of Equations o 15.4 – Nonlinear Systems of Equations - SKIP

Chapter 16 – Sequences, Series, and the Binomial Theorem o 16.1 – Sequences and Series . Sequences . Finding the General Terms . Sums and Series . Sigma Notation . Graphs of Sequences - SKIP o 16.2 – Arithmetic Sequences and Series . Arithmetic Sequences . Sum of the First n Terms of an Arithmetic Sequence . Problem Solving - SKIP o 16.3 – Geometric Sequences and Series . Geometric Sequences . Sum of the First n Terms of a Geometric Sequence . Infinite Geometric Series - SKIP . Problem Solving - SKIP o 16.4 – The Binomial Theorem - SKIP

**The instructor reserves the right to modify topic coverage as deemed appropriate while abiding by the established SLO’s**