Courses and Content

A breakdown of each math course and its main content

Basic Arithmetic: Addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals.
Ratios and Proportions: Understanding and solving problems involving ratios, proportions, and percent.
Integers: Operations with positive and negative numbers.
Variables and Expressions: Introduction to algebraic expressions and simple equations.
Basic Geometry: Understanding shapes, areas, and volumes.Statistics: Introduction to data representation and basic probability.

Linear Equations and Inequalities: Solving and graphing linear equations and inequalities.
Functions: Understanding and working with functions, including domain and range.
Systems of Equations: Solving systems of linear equations using various methods.
Polynomials: Operations with polynomials and factoring.
Quadratic Equations: Solving quadratic equations by factoring, completing the square, and using the quadratic formula.
Rational Expressions: Simplifying and performing operations with rational expressions.

Basic Geometric Shapes: Properties and classifications of different shapes (triangles, quadrilaterals, circles).
Congruence and Similarity: Understanding and proving congruence and similarity in geometric figures.
Theorems and Proofs: Key geometric theorems (e.g., Pythagorean Theorem) and writing formal proofs.
Circles: Properties of circles, arcs, chords, and angles.
Coordinate Geometry: Using the coordinate plane to solve geometric problems.
Surface Area and Volume: Calculating surface area and volume for various 3D shapes.

Complex Numbers: Introduction to and operations with complex numbers.
Polynomials: Advanced operations, factoring, and polynomial functions.
Rational Expressions and Equations: Working with more complex rational expressions and solving rational equations.
Exponential and Logarithmic Functions: Understanding and applying exponential growth and decay, and solving logarithmic equations.
Sequences and Series: Arithmetic and geometric sequences, series, and their sums.
Conic Sections: Properties and equations of parabolas, ellipses, and hyperbolas.

Advanced Functions: Detailed study of polynomial, rational, exponential, logarithmic, and piecewise functions.
Systems of Equations and Inequalities: Solving more complex systems, including nonlinear systems.
Matrices: Basic operations with matrices and applications.
Determinants: Calculating and interpreting determinants.
Complex Numbers: Further exploration of complex numbers and their applications.
Sequences and Series: More in-depth study of sequences and series, including binomial theorem.

Functions and Their Graphs: In-depth study of functions, including transformations and inverses.
Trigonometry: Trigonometric functions, identities, and equations; and applications.
Analytic Geometry: Study of conic sections in more depth.
Polynomial and Rational Functions: Detailed study of their properties and behavior.
Vectors: Basic concepts of vectors and their applications.
Limits and Continuity: Introduction to the concept of limits and continuity.

Limits and Derivatives: Fundamental concepts of limits and derivatives, including differentiation rules and applications.
Integrals: Introduction to integration, techniques of integration, and applications.
Fundamental Theorem of Calculus: Relationship between differentiation and integration.
Series and Sequences: Study of infinite series and sequences, including convergence and divergence.
Multivariable Calculus: Basics of calculus involving functions of more than one variable (if covered).
Applications: Applications of calculus in real-world problems, including optimization and modeling.