Advanced Topics / Pre-Calculus - Syllabus

M.A.S.T. High School @ Homestead



Instructor: Mr.lee

Room: 217



Course Website:


The Following topics will be covered in this course throughout the four nine weeks. The schedule is tentative and flexible, and in the event of unforeseen circumstances the instructor will try to adhere to the syllabus as much as possible and make any necessary adjustments.




I. Relations and Functions A. Functions and Their Graphs B. Linear Functions C. Transformations of Functions D. Composite Functions E. Inverse Functions II. Quadratic Equations A. Complex Numbers B. Quadratic Equations C. Quadratic Functions and Their Graphs D. Systems of Nonlinear Equations in Two Variables III. Polynomial Functions A. Polynomial Functions and Their Graphs B. Dividing Polynomials: Remainder and Factor Theorems C. Polynomial Identities/Theorems D. Zeros of Polynomial Functions IV. Exponential and Logarithmic Functions A. Exponential Functions B. Logarithmic Functions C. Properties of Logarithms D. Exponential and Logarithmic Equations E. Real-World Applications V. Rational Functions A. Rational Expressions B. Rational Equations C. Rational Functions and Their Graphs D. Polynomial and Rational Inequalities. VI. Right Triangle Trigonometry A. Angles and Radian Measure B. Right Triangle Trigonometry C. Real-World Applications D. Trigonometric Functions of Any Angle (Unit Circle) E. Trigonometric Functions of Real Numbers VII. Graphing Trigonometric Functions and Analytic Trigonometry A. Trigonometric Functions and Their Graphs (Sine, Cosine, Tangent) B. Inverse Trigonometric Functions and Their Graphs C. Applications of Trigonometric Functions D. Verifying Trigonometric Identities E. Sum and Difference Formulas VIII. Conic Sections and Analytic Geometry A. Circles B. The Parabola C. The Ellipse D. The Hyperbola E. Real-World Applications IX. Sequences and Series A. Sequences and Sigma/Summation Notation B. Arithmetic Sequences and Series C. Geometric Sequences and Series D. Real World Problems Involving Area and Volume of Circles, Cones and Spheres. X. Probability and Statistics A. Counting Principles, Permutations, and Combinations B. Probability XI. Matrices A. Matrix Solutions to Linear Systems B. Matrix Operations and Applications C. Multiplicative Inverses of Matrices and Matrix Equations D. Determinants and Cramer’s Rule XII. Polar Coordinates A. Polar Coordinates B. Complex Numbers in Polar Form: DeMoivre’s Theorem