Description
Curriculum
Instructor
Pre-Calculus typically covers a range of mathematical concepts that prepare students for studying calculus. Some of the key topics include:
- Functions and Graphs:
- Types of functions: linear, quadratic, polynomial, rational, exponential, logarithmic, trigonometric, and inverse functions.
- Graph transformations and asymptotes.
- Domain, range, and behavior of functions.
- Composition of functions.
- Polynomials:
- Polynomial functions, degree, and end behavior.
- Factoring polynomials and finding zeros/roots.
- The Remainder and Factor Theorems.
- Rational Functions:
- Simplifying rational expressions.
- Identifying vertical and horizontal asymptotes.
- Graphing rational functions.
- Exponential and Logarithmic Functions:
- Properties of exponents and logarithms.
- Solving exponential and logarithmic equations.
- Applications of growth and decay.
- Trigonometry:
- Unit circle and radian measure.
- Trigonometric identities (Pythagorean, sum/difference, double-angle).
- Graphing sine, cosine, and tangent functions.
- Inverse trigonometric functions.
- Solving trigonometric equations.
- Law of Sines and Law of Cosines.
- Complex Numbers:
- Operations with complex numbers (addition, subtraction, multiplication, division).
- Polar form of complex numbers.
- De Moivre’s Theorem.
- Vectors:
- Operations with vectors (addition, subtraction, scalar multiplication).
- Dot product and cross product.
- Applications of vectors in geometry.
- Sequences and Series:
- Arithmetic and geometric sequences.
- Finding the sum of finite and infinite series.
- Introduction to sigma notation.
- Matrices (optional in some curriculums):
- Basic matrix operations (addition, multiplication, inverse).
- Solving systems of equations using matrices.
- Conic Sections:
- Parabolas, ellipses, and hyperbolas.
- Equations and graphing conic sections.
- Identifying conic sections from their equations.
- Limits and Continuity (Introduction to Calculus):
- Understanding the concept of a limit.
- Continuity and the behavior of functions near a point.
These topics build a strong foundation for calculus and further advanced mathematics.
Review
