AHS Course Descriptions

Grades 9, 10  5 credits

Algebra I Curriculum A is the first course in a four-year college preparatory sequence. This course addresses the standards of the current state framework with major emphasis on the Algebra domain and the Functions domain. Students will investigate patterns, relations, and functions, simplify polynomials, and solve linear and quadratic equations, inequalities, and systems of equations. Students will also study powers and roots in accordance with standards from the Number and Quantity domain. Content areas including scatter plot, line of best fit, and basic counting principles connect to the Statistics and Probability domain. The following topics are covered:

• Expressions and Equations: writing, modeling, and solving

• Graphs: from statistics to graphing equations

• Lines: slope, graphs, parallel lines, solving systems, and modeling

• Functions: naming, definition, graphs, tables

• Exponents and Radicals: squares, cubes, roots, expressions and functions

• Polynomials: identities, factoring to solve

• Quadratics: quadratic formula, graphs, applications

Suggested Entry Criteria: Understand the concepts and skills of Math 8 or equivalent.

Next Course: Geometry Curriculum A or Geometry Curriculum H.

Grades 9, 10  5 credits

This accelerated course addresses the requirements of the current state framework, with major emphasis on the Geometry domain. Major content areas from this domain include the study of angles, polygons, polyhedrons, and circles, recognizing and applying properties of similarity and congruence, calculating measurements, and demonstrating and applying transformations. Students will also identify and apply trigonometric ratios and the Pythagorean theorem. The Statistics and Probability domain is addressed as students determine sample spaces using counting principles to find probability. Additionally, all students will participate in the year-long Math Fair project. The following topics are covered:

• Congruence and Proof

• Similarity

• Circles

• Using Similarity

• Coordinates and Vectors

• Optimization

Suggested Entry Criteria: Mastery of the concepts and skills of Algebra I.

Next course: Algebra II Curriculum H or Algebra II Curriculum A.

Grades 9, 10, 11, 12  5 credits

In this course, students study a full geometry curriculum. Major content areas include the study of lines, angles, polygons, circles, and congruence and similarity relationships. Students apply area and volume formulas to solve problems as well as use inductive and deductive reasoning processes to justify conclusions. Students will also work in the coordinate plane with transformations, distance and midpoint formulas, and parallel and perpendicular lines. The Number and Quantity domain is addressed as students work with powers and roots and use estimation in problem solving. Students use sample spaces to find simple probabilities, which is consistent with the standards of the Statistics and Probability domain. The following topics are covered:

• Congruence and Proof

• Quadrilaterals

• Area, Surface Area, Volume

• Similarity

• Circles

• Using Similarity

• Coordinates and Vectors

• Optimization

Suggested Entry Criteria: Successful completion of Algebra l.

Next course: Algebra II Curriculum H or Algebra II Curriculum A.

Grades 10, 11, 12  5 credits

Algebra II Curriculum H is the second course in a four-year honors mathematics sequence. Students continue to demonstrate higher order thinking skills by applying concepts to challenging problems and ‘real-world’ problems. This honors course addresses the current state framework with emphasis on the Algebra domain and Functions domain. Consistent with the content standards of these domains, students expand their knowledge of functions to include exponential, logarithmic, trigonometric, and polynomial functions using discrete and recursive models. They will expand their knowledge of equation solving to include multiple methods of solving quadratics, linear systems in three variables, and linear programming problems. The Number and Quantity domain is addressed as students study complex numbers and finite graphs, extend the real number system to rational exponents, and study its structure and properties. Students work in the coordinate plane studying quadratic relationships as they address the standards of the Geometry domain. The standards in the Statistics and Probability domain are addressed as students interpret data to find a model to fit the data. Additionally, all students will participate in the year-long Math Fair project. The following topics will be covered in the course:

• Systems and matrices

• Quadratic functions

• Rational expressions

• Polynomials

• Exponential and logarithmic functions

• Statistics

• Trigonometric functions

• Radicals

• Complex numbers

A TI-83+ or TI-84 graphing calculator or equivalent is required.

Suggested Entry Criteria: Mastery of the concepts and skills of Geometry.

Next course: Pre-Calculus Curriculum H, Pre-Calculus Curriculum A, Statistics Curriculum A, or AP Statistics.

Grades 10, 11, 12  5 credits

Algebra II Curriculum A is the third course in a four-year college preparatory sequence that further develops and strengthens the concepts and skills of Algebra I and extends these concepts and skills into the traditional topics of Algebra II. The course is aligned with the current state framework and primarily focuses on the Algebra domain and the Functions domain. Students apply their knowledge in problem solving applications. Technology is integrated into the course to support problem solving. The following topics are covered:

• Linear, quadratic, and exponential functions

• Graphs

• Inequalities

• Polynomials

• Rational expressions

• Systems of equations

• Graph translations

• Radicals

• Complex numbers

A TI-83+ or TI-84 graphing calculator or equivalent is highly recommended.

Suggested Entry Criteria: Successful completion of Geometry.

Next Course: Pre-Calculus Curriculum H, Pre-Calculus Curriculum A, Statistics Curriculum A, or AP Statistics.

Grades 11, 12  5 credits

Pre-Calculus Curriculum H is the third course in a four-year honors mathematics sequence. It is a rigorous course focusing on mathematical relations and their graphs, inverses, and applications. Topics studied include polynomial, trigonometric, exponential and logarithmic functions, matrices, polar coordinates, complex numbers, sequences, series and conics (and as time permits, combinations, permutations, probability and statistics.) The course is designed to emphasize theory and mathematical structure. Additionally, all students will participate in the year-long Math Fair project. The following topics are covered:

• Trigonometric Functions

• Analytic Trigonometry

• Vectors

• Exponential and Logarithmic Functions

• Polynomials and Reciprocal Functions

• Limits

A TI-83+ or TI-84 graphing calculator or equivalent is required.

Suggested Entry Criteria: Mastery of the concept and skills of Algebra II.

Next Course: AP Calculus BC, AP Calculus AB, Calculus Curriculum H, AP Statistics, or Statistics Curriculum A.

Grades 11, 12  5 credits

Pre-Calculus Curriculum A addresses the same topics as Pre-Calculus Curriculum H at a modified level of rigor. Topics studied include polynomial, trigonometric, exponential and logarithmic functions, matrices, polar coordinates, complex numbers, sequences, series and conics. The following topics are covered:

• Trigonometric Functions

• Analytic Trigonometry

• Vectors

• Exponential and Logarithmic Functions

• Polynomials and Reciprocal Functions

• Limits

A TI-83+ or TI-84 graphing calculator or equivalent is highly recommended.

Suggested Entry Criteria: Mastery of the concepts and skills of Algebra II.

Next Course: AP Calculus AB, Calculus Curriculum H, AP Statistics, Statistics Curriculum A.

Grade 12  5 credits

Calculus BC covers the BC syllabus set by the College Board as preparation for the Advanced Placement Test in Calculus. Calculus BC represents college-level mathematics for which most colleges grant advanced placement and/or credit. Most colleges and universities offer a sequence of several courses in calculus, and entering students are placed within this sequence according to the extent of their preparation. The content of Calculus BC is designed to allow students to receive credit for and placement beyond one full year of calculus at many colleges; however, college credit and placement decisions are made by individual colleges, based primarily on the student's score on the AP Calculus (BC) exam. Students are required to take the Advanced Placement Exam at the BC level (cost approx. $100) in May. In addition, students will be invited to participate in the competitive Math Exam Program of the Math Department, taking both the Math Olympiad and the AMC Exams. The following topics are covered:

• Limits and continuity

• Differentiation

• Applications of differentiation

• Integration and accumulation of change

• Differential equations

• Applications of integration

• Parametric equations, polar coordinates, and vector-valued functions

• Infinite sequences and series

A TI-83+ or TI-84 graphing calculator or equivalent is required.

Suggested Entry Criteria: Mastery of the concepts and skills of Pre-Calculus Curriculum H.

Grade 12  5 credits

Calculus AB covers the AB syllabus set by the College Board as preparation for the Advanced Placement Test in Calculus. Calculus AB represents college-level mathematics for which most colleges grant advanced placement and/or credit. Most colleges and universities offer a sequence of several courses in calculus, and entering students are placed within this sequence according to the extent of their preparation. The content of Calculus AB is designed to allow students to receive credit for and placement beyond one semester of calculus at many colleges; however, college credit and placement decisions are made by individual colleges, based primarily on the student's score on the AP Calculus (AB) exam. Students are required to take the Advanced Placement Exam at the AB level (cost approx. $100) in May. In addition, students will be invited to participate in the competitive Math Exam Program of the Math Department, taking both the Math Olympiad and the AMC Exams. The following topics are covered:

• Limits and continuity

• Differentiation

• Applications of derivatives

• Integration

• Fundamental theorem of calculus

A TI-83+ or TI-84 graphing calculator or equivalent is required.

Suggested Entry Criteria: Mastery of the concepts and skills of Pre-Calculus.

Grade 12  5 credits

Calculus Curriculum H completes the advanced sequence with an emphasis on functions, their derivatives and antiderivatives. Students are introduced to the basic topics in calculus, including limits, simple derivatives, and their applications to functions and problem solving. Applications of the derivative and integral are introduced throughout the course. The following topics are covered:

• Limits and continuity

• Differentiation

• Applications of derivatives

• Integration

A TI-83+ or TI-84 graphing calculator or equivalent is highly recommended.

Suggested Entry Criteria: Mastery of the concepts and skills of Pre-Calculus.

Grade 11, 12  5 credits

AP Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes:

• Exploring Data: Describing patterns and departures from patterns

• Sampling and Experimentation: Planning and conducting a study

• Anticipating Patterns: Exploring random phenomena using probability and simulation

• Statistical Inference: Estimating population parameters and testing hypotheses

The content of AP Statistics is designed to allow students to receive credit for and placement beyond one semester of introductory statistics at many colleges; however, college credit and placement decisions are made by individual colleges, based primarily on the student's score on the AP Statistics exam. Students are required to take the Advanced Placement Exam in Statistics (cost approx. $100) in May.

A TI-83+ or TI-84 graphing calculator or equivalent is required.

Suggested Entry Criteria: The successful completion of Algebra II Curriculum A, at a minimum.

Grade 11, 12  5 credit

Statistics A is an introduction to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The level of rigor is reduced from that of the AP Statistics course. The following topics are covered:

• Organizing Data

• Averages and Variation

• Regression and Correlation

• Elementary Probability Theory

• Normal Distributions

• Sampling Distributions

• Estimation

• Hypothesis Testing

A TI-83+ or TI-84 graphing calculator or equivalent is highly recommended.

Suggested Entry Criteria: The successful completion of Algebra II Curriculum A.

Grade 11, 12  5 credits

Quantitative Reasoning A is a modified mathematics course that follows Algebra I, Geometry, and Algebra II. The course emphasizes probability, statistics and financial applications, and it prepares students to use algebra, geometry, recursively defined functions, and discrete mathematics to model a range of situations and solve problems. The following topics are covered:

• Modeling Games

• Probability

• Statistics

• Using Recursive and Explicit Functions in Models and Decision Making

• Personal Finance.

The TI-83+ or TI-84 graphing calculator or equivalent is highly recommended.

Suggested Entry Criteria: Understand the concepts and skills of Algebra II.

Computer Science and CADD

A list of courses offered can be found on the Computer Science website found here.

Grades 11 and 12  2.5 credits

Linear algebra is the study of linear systems of equations, vector spaces, and linear transformations. Solving systems of linear equations is a basic tool of many mathematical procedures used for solving problems in science and engineering. In this class we will concentrate on the mathematical theory and methods of linear algebra. The student will become competent in solving linear equations, performing matrix algebra, calculating determinants, and finding eigenvalues and eigenvectors. On the theoretical side, the student will come to understand a matrix as a linear transformations relative to a basis of a vector space.

Suggested Entry Criteria: Algebra II or equivalent

Grades 11 and 12 2.5 credits

This is an introductory course in Number Theory for students interested in mathematics. The course begins with the basic notions of integers and sequences, divisibility, and mathematical induction. It also covers standard topics such as Prime Numbers; the Fundamental Theorem of Arithmetic; Euclidean Algorithm; the Diophantine Equations; Congruence Equations and their Applications (e.g. Fermat’s Little Theorem); Multiplicative Functions (e.g. Euler’s Phi Function); Application to Encryption and Decryption of Text.

Suggested Entry Criteria: Algebra II or equivalent