High School Math Course Descriptions

Pre-Algebra serves as a bridge between basic arithmetic and algebraic thinking. Students explore fundamental concepts including integers, rational numbers, ratios, proportions, percent applications, basic geometry, and the introduction of variables and simple equations. This course emphasizes problem-solving strategies and develops the mathematical reasoning necessary for success in Algebra I. Mastery of Pre-Algebra concepts provides the essential foundation for all subsequent high school mathematics courses.

Algebra I introduces students to the language of algebra and its applications. The course covers:

• Solving linear equations and inequalities
• Graphing linear functions and systems of equations
• Operations with polynomials
• Factoring techniques
• Solving quadratic equations
• Introduction to exponential functions
• Basic data analysis and statistics

Students develop analytical thinking skills and learn to model real-world situations using algebraic expressions and equations. This core course is typically required for high school graduation and provides the foundation for all advanced mathematics study.

Geometry introduces students to the study of shapes, size, relative position, and properties of space. Key components include:

• Parallel and perpendicular lines
• Triangle congruence and similarity
• Properties of quadrilaterals and other polygons
• Right triangle trigonometry
• Circle theorems and circumference, area calculations
• Surface area and volume of three-dimensional figures
• Coordinate geometry and transformations
• Geometric proofs using deductive reasoning

This course emphasizes visual thinking, spatial reasoning, and logical argumentation. Geometry integrates algebraic concepts with geometric properties, allowing students to see connections between mathematical disciplines.

Algebra II expands on the concepts introduced in Algebra I while introducing new advanced topics. The curriculum typically includes:

• Solving linear, quadratic, and higher-degree equations
• Systems of equations and inequalities
• Polynomial functions and operations
• Rational expressions and equations
• Exponential and logarithmic functions
• Introduction to trigonometry and trigonometric functions
• Complex numbers
• Sequences and series
• Conic sections
• Probability and combinatorics

Algebra II develops students' abstract thinking skills and provides the mathematical foundation needed for pre-calculus and calculus. Many colleges consider Algebra II essential for college preparation.

Pre-Calculus bridges the gap between algebraic mathematical concepts and calculus. The course combines elements of algebra, geometry, and trigonometry to prepare students for calculus. Key topics include:

• Functions and their graphs (polynomial, rational, exponential, logarithmic)
• Trigonometric functions, identities, and equations
• Analytic trigonometry
• Systems of linear equations and matrices
• Sequences, series, and probability
• Introduction to limits and continuity
• Introduction to derivatives
• Vectors and parametric equations
• Polar coordinates and complex numbers

Pre-Calculus emphasizes function analysis and problem-solving techniques that provide the necessary skills for calculus and other advanced mathematics courses at the college level.

Calculus I introduces the fundamental concepts of differential and integral calculus. The course covers:

• Limits and continuity
• Derivatives and their applications including rates of change
• Techniques of differentiation
• Applications of derivatives (optimization, related rates, curve sketching)
• Definite integrals and the Fundamental Theorem of Calculus
• Antiderivatives and basic integration techniques
• Introduction to applications of integration (area, volume)

Calculus I is often taken by students who have excelled in previous mathematics courses and wish to pursue STEM fields or other mathematically-intensive disciplines in college. The course emphasizes both conceptual understanding and problem-solving techniques.

Building on Calculus I, this course continues the study of calculus focusing on integration techniques and applications. Topics typically include:

• Advanced integration techniques
• Applications of integration (work, fluid pressure, center of mass)
• Sequences and series
• Convergence tests for infinite series
• Power series and Taylor polynomials
• Parametric equations and polar coordinates
• Introduction to differential equations

Calculus II challenges students to apply calculus concepts to more complex mathematical models and provides a deeper understanding of the power and elegance of calculus.

This introductory statistics course explores fundamental concepts of data analysis and probability. Key components include:

• Data collection methods and experimental design
• Descriptive statistics (measures of center, spread, and position)
• Graphical displays of data
• Probability concepts and distributions
• Sampling distributions
• Confidence intervals
• Hypothesis testing
• Correlation and linear regression
• Applications in various fields

Statistics emphasizes the process of statistical thinking, data analysis, and interpretation rather than calculation techniques. This course is valuable for students interested in social sciences, business, medicine, or any field that utilizes data-driven decision making.

Discrete Mathematics focuses on mathematical structures that are fundamentally discrete rather than continuous. The course typically covers:

• Logic and proof techniques
• Sets, functions, and relations
• Combinatorics and counting principles
• Graph theory
• Recurrence relations
• Introduction to algorithms
• Number theory basics
• Boolean algebra

This course is particularly relevant for students interested in computer science, information technology, and mathematical logic. Discrete Mathematics develops skills in problem-solving, logical reasoning, and algorithmic thinking.

Financial Mathematics applies algebraic and statistical concepts to real-world financial situations. The curriculum typically includes:

• Budgeting and personal financial management
• Banking and interest calculations
• Credit and loans
• Understanding taxes
• Investment fundamentals
• Insurance concepts
• Retirement planning
• Basic economic principles
• Risk assessment and probability

This practical mathematics course prepares students for financial decision-making in adulthood. It demonstrates how mathematical concepts apply to everyday financial situations and develops critical thinking skills for evaluating financial opportunities.

This applied mathematics course focuses on using mathematics to solve real-world problems. Topics may include:

• Mathematical modeling techniques
• Applied geometry and measurement
• Linear and exponential models
• Statistics and probability in context
• Applications in science, engineering, and social sciences
• Decision-making using mathematical analysis
• Project-based learning experiences

This course emphasizes the practical application of mathematics rather than theoretical development. Students work on projects that require mathematical analysis to solve authentic problems from various disciplines.