Pre-calculus syllabus and online practice

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Functions

• Functions and Relations
• Domain and Range
• Even and odd functions
• Transformation of functions
• Trigonometric equations 

Trigonometry

• Graphs of Sine and cosine
• Transformations of sine and cosine
• Inverse trigonometric functions
• Sinusoidal equations and models
• Angle addition
• Using trigonometric identities

Polynomials

• Addition and subtraction of polynomials 
• Division of polynomials
• Binomial theorem
• Graphs of polynomial functions  and solving equations
• Graphing rational functions and reciprocal functions

Exponential and Logarithms

• Applications of exponential functions
• Logarithms
• Solving exponential and logarithmic equations
• Graphing logarithmic functions

Conic sections

• Feature of a circle
• Equations of a circle
• Center, radii, focii of an ellipse
• Focus and directrix of a parabola
• Hyperbola

Vectors

• Introduction to vectors
• Operations with vectors
• Applications of vectors

Complex numbers

• Complex numbers and imaginary numbers
• The complex plane: Complex numbers
• Addition, Subtraction and Multiplication of complex numbers
• Distance and midpoint of complex numbers
• Complex conjugates and dividing complex numbers
• Identities with complex numbers
• Absolute value and angle of complex numbers
• Polar form of complex numbers, multiplication and division

Matrices

• Introduction
• Representing linear systems of equations with augmented matrices
• Matrix row operations
• Row-echelon form and Gaussian elimination
• Addition, Subtraction, Multiplication of Matrices
• Multiplying matrices by scalars
• Properties of matrix addition & scalar multiplication
• Properties of matrix multiplication
• Matrices as transformations
• The determinant of a 2×2 matrix
• Finding the inverse of a matrix using its determinant
• Solving equations with inverse matrices
• Model real-world situations with matrices

Note: Any other topic as per inputs by students provided during the course will be covered