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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
Dilations Reflections |
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 Parabolas 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 Radical Functions Operations with Functions Graphing Functions One-On-One Functions Polynomial Functions |
Symmetry | Graphic Symmetry
Algebraic Symmetry Numerical Symmetry |
Polynomials | Binomial Theorem
Factoring Polynomials in Quadratic Form Dividing Polynomials 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
Natural base Logarithmic properties Inverse of logarithmic functions |
Trigonometric Functions and Graphs | Sine and cosine Functions
Unit Circles Special Right Triangles Graphing sine and cosine transformations Determining trigonometric identities using graphs |
Trigonometric Equations | Inverse Trigonometric Functions
Sinusoidal Functions |
Trigonometric Identities & Applications | Basic Trigonometric Identities
Pythagorean Identities Double-Angle 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. Arithmetic sequences Geometric sequences Mathematical Induction Binomial Theorem Pascal’s Triangle |
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. Locus 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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