1. Advanced Number Systems and Operations
    - Rational, irrational, and real numbers: understanding properties and operations.
    - Expressions involving radicals and rational exponents.
  2. Algebra and Equations
    - Solving linear equations, inequalities, and systems of equations in two variables.
    - Quadratic equations: factoring, solving by quadratic formula, and completing the square.
    - Manipulating and simplifying complex algebraic expressions.
  3. Coordinate Geometry and Graphs
    - Equations of lines, circles, and parabolas in Cartesian coordinates.
    - Finding slopes, intercepts, and intersections.
    - Graphing and interpreting linear and quadratic functions.
  4. Functions and Analysis
    - Domain, range, and behavior of linear, quadratic, and exponential functions.
    - Exploring real-world applications of functions (growth and decay models).
  5. Geometry and Measurement
    - Pythagorean theorem, similarity, congruence, and properties of polygons.
    - Calculating area, surface area, and volume of various complex geometric figures.
    - Basic trigonometric ratios (sine, cosine, tangent) and solving triangle problems.
  6. Trigonometry and Unit Circle
    - Exploring trigonometric identities, relationships, and solving trigonometric equations.
    - Applying the unit circle for evaluating trigonometric functions.
    - Practical problems involving angles and distances.
  7. Probability and Combinatorics
    - Fundamental counting principles, permutations, combinations, and binomial coefficients.
    - Calculating probabilities of independent, dependent, compound, and conditional events.
  8. Data Analysis and Statistics
    - Representing data visually (histograms, scatter plots, box plots).
    - Measures of central tendency and variability, including standard deviation.
    - Applying statistics to interpret real-life data.
  9. Conic Sections and Advanced Graphing
    - Understanding circles, ellipses, parabolas, and hyperbolas.
    - Graphing and analyzing conic sections and their equations.
  10. Practical and Complex Applications
    - Real-world applications and advanced word problems involving multiple mathematical concepts.
    - Integrating algebra, geometry, trigonometry, and statistics to solve practical, interdisciplinary problems.