Math 105: Precalculus Algebra

Learn about mathematical modeling, quadratic functions, complex numbers and more in this precalculus algebra course. Make sure you have a solid grasp of these concepts by taking the self-assessment quizzes that follow each lesson. 

About the Course

Topics covered in this precalculus algebra course range from basic mathematical modeling to an introduction to derivatives. You'll learn to solve various types of equations and inequalities both symbolically and graphically.

The experienced, knowledgeable instructors for this precalculus algebra course have developed several video lessons for you to view. Each category, such as complex numbers or geometry basics, is divided into several chapters, allowing the concepts to be presented more in depth. Each lesson also gives you the opportunity to test your knowledge through quizzes and practice exams.

Course Topics

Mathematical ModelingWrite and solve equations that relate a 2-dimensional figure's side lengths, perimeter and area. Write and solve real-life models, such as cost determination and d=rt. Evaluate economic equilibrium and profit functions from linear models. Find minimum and maximum values of quadratic models.
Linear Equations & InequalitiesGraph and write linear equations. Use point-slope formula to find the equation of a line. Graph 1- and 2-variable inequalities. Use a system of equations.
Quadratic FunctionsFactor quadratic equations. Complete the square. Solve quadratic equations by factoring or by using the quadratic formula. Graph quadratic inequalities and systems of quadratic inequalities and identify the regions that satisfy the inequalities or systems.
Rational Expressions & FunctionsAdd, subtract, multiply and divide rational expressions. Solve rational equations. Graph rational functions that consist of polynomials of various degrees. Identify asymptotes, domain and range algebraically and graphically.
Polynomial Functions of a Higher DegreeAdd, subtract, multiply and divide polynomials. Identify and evaluate polynomials in quadratic form. Factor polynomials using the remainder, factor and rational zero theorems as well as synthetic division. Determine how many solutions a polynomial has based on the degree of the polynomial. Write a polynomial equation using given zeros of a function and the concept of complex conjugate pairs.
Absolute Value Equations & Inequalities Evaluate absolute value expressions. Solve and graph absolute value equations and inequalities.
Complex NumbersAdd, subtract, multiply and divide complex numbers. Graph complex numbers on the complex plane. Solve quadratics with complex numbers as the solution.
Geometry BasicsDetermine the area and circumference of a circle. Graph circles. Rewrite a general second-degree equation in standard form. Use the distance and midpoint formulas.
Functions OverviewGraph basic functions. Determine the domain and range of a function. Write and graph power functions. Graph square root and cube root functions. Graph and find the domain of piecewise functions. Shift graphs on a plane.
Function OperationsAdd, subtract, multiply and divide functions. Graph functions of functions. Understand how the domain and range of one function affects the domain and range of another function. Graph inverse functions. Identify 1-to-1 functions algebraically and graphically. Recognize the relationship between domain and range of a 1-to-1 function and its inverse.
Graph SymmetryDetect symmetry graphically, numerically and algebraically. Define even and odd functions algebraically and identify them graphically.
Exponential & Logarithmic FunctionsTranslate an exponential function horizontally and vertically. Define the natural base and graph natural base functions. Evaluate logarithms. Rewrite logarithmic equations in exponential form and vice versa. Graph a logarithmic function and identify its vertical asymptote, domain and range. Solve logarithmic and exponential equations. Use the change-of-base formula to evaluate logarithmic expressions. Calculate rate and exponential growth.
Introduction to the DerivativeLearn about velocity and rate of change as well as slopes and rate of change.

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