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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:
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
Trigonometry Functions & Graphs
- Sine and cosine Functions
- Unit Circles
- Special Right Triangles
- Graphing sine and cosine transformations
- Determining trigonometric identities using graphs
Trigonometry Equations
- Inverse Trigonometric Functions
- Sinusoidal Functions
Trigonometry 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
- Determinants
- Gaussian elimination
- Linear Programming
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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