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Many advanced math concepts and theories are not covered in algebra, geometry and other courses in a student’s high school math curriculum. Precalculus commonly focuses on properties of functions along with the study of trigonometric, logarithmic and exponential functions. It includes topics about sequences, limits and other concepts crucial to the study of calculus.
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Below are the topics often included in the Precalculus syllabus:
|Linear Equations||The Distribution Property
Parallel and Perpendicular Lines in Graphs of Linear Equations
|Inequalities||Systems of Inequalities
Graph Absolute Value Inequalities
|Absolute Value Equations||Transformations
|Complex Numbers||Imaginary Numbers
Operations with Complex Numbers
Graphing Complex Numbers
|Systems of Linear Equations||Solving Systems of Linear Equations|
|Quadratic Functions||Definition of Quadratic Equations
Greatest Common Factor
Multiplication Property Of Zero
Solving Quadratics not in the Standard Form
Completing the Square
Factoring Quadratic Equations
|Geometry for Precalculus||Area and Circumference of a Circle
Midpoint and Distance Formula
The Pythagorean Theorem
|Functions||Domain and Range of a Function
Power of a Function
Operations with Functions
Factoring Polynomials in Quadratic Form
Long and Synthetic Division
Remainder and Factor Theorem
|Rational Expressions||Operations of Rational Expressions
Solve Rational Equations
|Exponential and Logarithmic Functions||Exponential growth and decay
Inverse of logarithmic functions
|Trigonometric Functions and Graphs||Sine and cosine Functions
Special Right Triangles
Graphing sine and cosine transformations
Determining trigonometric identities using graphs
|Trigonometric Equations||Inverse Trigonometric Functions
|Trigonometric Identities & Applications||Basic Trigonometric Identities
Law of Cosines
Law of Sines
Formulas for sine, cosine and tangent
|Vectors, Matrices and Determinants||Operations on Vectors
Operations on Matrices
Inverse of a matrix
|Mathematical Sequences and Series||The sigma and factorial notation.
|Polar Coordinates and Parameterization and Conic Sections||Conversion between polar and rectangular coordinates.
Graph of functions in polar coordinates.
De Moivre’s Theorem
Parametric and Rectangular forms of equations.
Graphs of parabolas, ellipses and hyperbolas
|Limits & Continuity||Intermediate Value Theorem
Graphs to Define Limits
Determine Limits of Functions
Limits for Asymptotes and Infinity
Practice is essential in precalculus and will lead to successful performance on exams. Tests and quizzes are given every precalculus topic studied.
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