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Mathematics 125

Intermediate Algebra

IntermediateAlgebra

Overview

Topics include laws of exponents, radicals, equations in onevariable (linear, quadratic, and some of higher degree), systems ofliner equations, imagineries, grraphical representations, logarithms,binomial theorem.

Video Lesson Descriptions (Lessons 1-13)


Lesson 1- The Power of Algebra
Offers a basic overview of algebra and its components, and reviews thecomutative, associative, and distributive properties for addition andmultiplication.    
 
Lesson 2- Polynomials
Introduces the basic terminology of polynomials, the procedures forsimplifying a polynomial, and methods for adding, subtracting, andmultiplying polynomials.    

Lesson 3- Solving and GraphingEquations
Demonstrates the four problem-solving techniques—verbal, symbolic,numeric, and graphic.    

Lesson 4- Linear Equations
Reviews the general strategy for solving linear equations andintroduces formulas used for solving word problems involvingconsecutive integers, consecutive even integers, and consecutive oddintegers.    

Lesson 5- Solving by Factoring
Introduces the rate-time-distance formula and describes some commonstrategies for solving applied problems involving rates andtimes.    

Lesson 6- Inequalities andAbsolute Values
Explains and demonstrates how to formulate and solve linearinequalities by offering two scenarios: how to determine the exam scoreneeded in order to receive an A in the class, and how to choose thebest alternative between two salary plans.    

Lesson 7- Graphs of Equationsand Functions
Explains the Cartesian coordinate systme and introduces the interceptmethod for graphing linear equations.    

Lesson 8- Systems of Equations
Describes systems of linear equations and their solution throughsubstitution or elimination method.    

Lesson 9- Graphing Inequalities
Illustrates the steps of graphing a linear inequality in theplane.    

Lesson 10- Introduction toQuadratic Equations
Introduces the standard form of a quadratic equation, reviews squareroot properties, and demonstrates the solution of quadraticequations.    

Lesson 11- The Quadratic Formula
Shows how to derive a general formula that can be used to solve anyquadratic equation and explores various real-worldapplications.    

Lesson 12- Graphing QuadraticEquations
Presents three methods for graphing a quadratic equation in twovariables: plotting points using a table of values, finding the vertexand the intercepts, and applying geometric transformations.   

Lesson 13- Rational Expressions
Explains the procedures for working with fractions involvingpolynomials.

Video Lesson Descriptions (Lessons 14-26)


Lesson 14- The Algebra ofFunctions
Illustrates the different ways that functions can be specified: by atable, a set of ordered pairs, a graph, or an equation.   

Lesson 15- Graphing Functions   
Includes examples of how to graph linear, quadratic, and higher degreefunctions.    

Lesson 16- Exponents and RadicalExpressions
Explains how exponents help student manage very large numbers and verysmall numbers using scientific notation.    

Lesson 17- Exponential Functions
Discusses mathematical models of exponential growth anddecay.    

Lesson 18- Logarithmic Functions
Demonstrates how logarithms can be used to solve for an unknown thatappears in an exponent.    

Lesson 19- Properities ofLogarithms
Introduces the five key properties of logarithms, which are derivedfrom the properties of exponents.    

Lesson 20- Exponential andLogarithmic Equations
Reviews the properties and methods used in solving exponential andlogarithmic equations.    

Lesson 21- Systems of LinearEquations and Matrices
Teaches students how to solve sets of three equations in three unknownsusing linear equations and matrices.    

Lesson 22- Operations on Matrices
Introduces the algebraic operations on matrices.    

Lesson 23- Conic Sections
Defines the properties and graphs of the many shapes—circles, ellipses,parabolas, and hyperbolas—that originate as sections of acone.    

Lesson 24- Sequences and Series
Offers an overview of numerical sequences and the sum of their terms,known as series.    

Lesson 25- The Binomial Formulaand Counting
Introduces counting principles required in computingprobabilities.    

Lesson 26- Permutations,Combinations & Probability
Explains the calculation of probability using permutations andcombinations.