Pre-calculus syllabus and online practice

  • Functions

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


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


    • 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


    • 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


    • 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