This course prepares students for success in calculus. A brief review of college algebra topics is presented including linear, polynomial, radical, rational and absolute value, functions, and equations. Students also examine systems of equations, exponential, logarithmic, and trigonometric functions as well as analytic geometry. In addition, students are introduced to sequences and series.
Review all topics and objectives from Weeks One through Six.
Introduction to Functions
Use different methods to find the roots of polynomials.
Graph functions including inverse functions.
Analyze graphs of functions including inverse functions.
Examine the notion of function and its notation.
Apply the use of functions to real-world situations.
Apply the fundamental theorem of algebra.
Trigonometric Equations, Law of Sines, Law of Cosines, and Polar Coordinates
Convert equations between polar and rectangular.
Convert coordinates between polar and rectangular.
Solve oblique triangles using the Laws of Sines and Cosines.
Solve trigonometric equations.
Trigonometric Functions and Identities
Manipulate trigonometric identities.
Analyze values of inverse trigonometric functions.
Describe the graphs of trigonometric functions.
Apply trigonometric functions to solve right triangles.
Use the unit circle to find the values of trigonometric functions.
Construct the unit circle.
Convert angle measures between degrees and radians.
Systems of Equations
Calculate solutions using Cramer’s rule.
Calculate solutions using inverse matrices.
Calculate solutions using Gaussian elimination.
Solve systems of linear equations in three variables.
Solve systems of linear equations in two variables.
Conic Sections, Sequences, and Series
Solve geometric sequences and series.
Solve arithmetic series.
Use sequence and summation notation.
Examine how transformations affect conic sections.
Differentiate among the equations for conic sections.
Rational, Logarithmic, and Exponential Functions
Apply exponential and logarithmic functions to real-world problems.
Analyze graphs of exponential and logarithmic functions.
Analyze the relationship between exponential and logarithmic functions.
Solve exponential and logarithmic functions.
Identify the vertical, horizontal, and slant asymptotes of a rational function.
Determine the domain of a rational function.
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