In math, precalculus is the course that includes algebra, trigonometry, functions, and geometry. It prepares students for the calculus; thus, the name is pre-calculus.
It primarily focuses on understanding how mathematical functions behave and how they are used to solve real-world problems.
Prerequisites
- Real numbers
- Laws of Exponents
- Factoring polynomials
- Quadratic equations
- Equations & Inequalities
- Systems of equations
1. Functions
- Introduction
- Domain and Range
- Function notation
- Types of Functions
- Rate of change
- Transformations
- Composite functions
- Inverse functions
- Real-Life Applications
2. Polynomial & Rational Functions
- Polynomial Functions
- Graphing Polynomials
- End behavior
- Zeros of Polynomial
- Rational functions
- Asymptotes
- Polynomial/rational inequalities
- Polynomials Real-Life Applications
3. Exponential & Logarithmic Functions
- Exponential Functions
- Logarithms
- Laws of Log
- Solving exponential
- Log Functions
- Log equations
- Exponential growth/decay
- Applications
4. Trigonometry
- Angles & Radians
- Basics of Trigonometry
- Unit circle
- Trig functions
- Identities
- Graphing trig functions
- Inverse trig functions
- Solving trig equations
- Law of Sines & Cosines
- Applications of Trigonometry
5. Sequences & Series
- Arithmetic Sequence
- Geometric Sequences
- Summation Notation
- Series
- Partial sums
- Binomial theorem
6. Complex Numbers
- Introduction
- Value of i
- Complex number arithmetic: (Add & Subtract | multiply | Divide)
- Complex conjugates
- Complex zeros of polynomials
- Fundamental Theorem of Algebra
- Real-Life Applications
7. Vectors
8. Matrices
- Introduction
- Matrix operations
- Solving systems with matrices
- Determinants
- Cramer's Rule
- Inverse matrices
- Real-Life Applications
9. Conic Sections
10. Probability & Combinatorics
- Permutations & combinations
- Basic probability
- Binomial probability
- Probability in Real-Life