## Mathematics

#### High School

Mathematics is the universal language. It allows all to make sense of the natural world—to observe, quantify, analyze, make connections, and solve problems in every field of study (course descriptions follow).

The ability to comprehend, develop, and utilize mathematical concepts is invaluable throughout life; all global citizens need strong fluency in this area. Achieving this ability is best done by learning to draw reasonable conclusions from information found in various sources. Whether from observation, words, data, or graphs, students use the tools of mathematics to analyze information and become adept at problem solving. Students are encouraged to welcome new challenges, question and justify their conjectures and solutions, test the reasonableness of those solutions, develop facility with and understanding of mathematical operations and procedures, and use them appropriately to make sense of the world.

The High School mathematics requirement is four full years of math. Students also have the opportunity to take more than one math course when their schedule allows for it. The mathematics curriculum encompasses the traditional high school courses of Algebra 1 through AP Calculus AB and BC, with additional courses in statistics and advanced level calculus.

#### Algebra 1 - College Prep

##### Algebra 1 - College Prep [1 credit]

Prerequisites: Placement exam and/or departmental approval

This course is designed for the student with average math aptitude and skills. Topics covered in this course include equation solving, operations with polynomials, word problems, linear equations and their graphs, fractions, factoring and radicals. Emphasis is placed on skills and on applying the basic algebraic concepts to problems.

#### Algebra 1 - Accelerated

##### Algebra 1 - Accelerated [1 credit]

Prerequisites: Placement exam and/or departmental approval

This course is designed for the student who has had some algebra and shows above average math aptitude. The course includes the development of mathematical skills such as operating with polynomials, solving and graphing linear and quadratic equations, solving and graphing systems of linear equations, factoring, and working with radicals. Real life applications are stressed.

#### Algebra 1 - Honors

##### Algebra 1 - Honors [1 credit]

Prerequisites: Placement exam and/or departmental approval

This course is designed for the student who has had some algebra and shows a high math aptitude. This course includes the study of mathematical concepts such as operations with polynomials, solving and graphing equations, systems of equations, factoring, quadratics, and radicals. Real life applications are stressed with great emphasis on word problems.

#### Geometry - Honors

##### Geometry - Honors [1 credit]

Prerequisites: Placement exam and/or departmental approval

This course is designed for the student who has a high mathematical aptitude and has learned the skills of algebra 1 in grammar school. Topics of algebra will be reviewed. Students will study the logical structure of geometry through theorems, postulates, deductive reasoning, and proofs. The course includes the study of plane, and solid geometry.

#### Geometry - College Prep

##### Geometry - College Prep [1 credit]

Prerequisites: Algebra 1 College Prep and/or departmental approval

This course is designed for the student who has completed the algebra 1 course. It includes the study of plane and solid geometry. Students will study the logical structure of geometry through theorems, postulates, deductive reasoning.

#### Geometry/Algebra 2 - Accelerated

##### Geometry/Algebra 2 - Accelerated [1 credit]

Prerequisites: Algebra 1 Accelerated and/or departmental approval

This course is designed for the student who has completed a course in algebra 1 and shows above average mathematical ability. It includes the study of plane and solid geometry for about three-fourths of the year. Students will study the logical structure of geometry through theorems, postulates, deductive reasoning, and proofs. It includes the study of plane, coordinate and solid geometry. Students also begin the study of algebra 2 developing skill working with linear equations and solving systems of linear equations and inequalities.

#### Geometry/Algebra 2 - Honors

##### Geometry/Algebra 2 - Honors [1 credit]

Prerequisites: Algebra 1 Honors and/or departmental approval

This course is designed for the mathematically inclined student who has completed a course in algebra 1, shows exceptionally high mathematical ability and can handle a fast pace of intensive work. Students are placed in this course based on previous grades and ability**. **It includes the study of plane, coordinate, and solid geometry.** **Students will study the logical structure of geometry through theorems, postulates, deductive reasoning, and proofs. The remainder of the school year is spent on topics from algebra 2, developing skill working with linear equations, quadratic and polynomial functions, and solving systems of linear equations and inequalities.

#### Algebra 2 - Honors

##### Algebra 2 Honors [1 credit]

Prerequisites: Geometry Honors and/or departmental approval.

This course is designed for the mathematically inclined student who has completed a course in geometry, and shows high mathematical ability. It includes the study of polynomial functions, conic sections, exponential and logarithmic functions, and complex numbers. The skill of applying these advanced algebraic concepts to real world problems is included.

#### Algebra 2/Trigonometry - Honors

##### Algebra 2/Trigonometry - Honors [1 credit]

Prerequisites: Geometry Honors and/or departmental approval.

This course is designed for the mathematically inclined student who has completed a course in geometry, shows exceptionally high mathematical ability and can handle a fast pace of intensive work. It includes the study of polynomial, conic sections, exponential and logarithmic functions, complex numbers, and trigonometric functions. Emphasis is placed on the skill of applying these advanced algebraic concepts to real world problems.

#### Algebra 2/Trigonometry - College Prep

##### Algebra 2/Trigonometry - College Prep [1 credit]

Prerequisites: Geometry College Prep and/or departmental approval

This course is designed for the student who has completed a full course of Geometry. It includes the study of polynomial functions, exponential and logarithmic functions, trigonometric functions, and solving systems of equations and inequalities.

#### Trigonometry/Precalculus - Accelerated

##### Trigonometry/Precalculus - Accelerated [1 credit]

Prerequisites: Geometry/Algebra 2 Accelerated and/or departmental approval

This course is a continuation of Geometry/Algebra 2. It includes the study of quadratic functions, radicals, rational functions, matrices, polynomial functions, series and sequences, conic sections, exponential and logarithmic functions and trigonometric functions.

#### Trigonometry/Precalculus Honors

##### Trigonometry/Precalculus Honors [1 credit]

Prerequisites: Geometry/Algebra 2 Honors and/or departmental approval

This course is a continuation of Geometry/Algebra 2. It will include the study of conic sections, exponential and logarithmic functions, series and sequences, and trigonometric functions. Additional precalculus topics include, advanced algebra, limits and simple derivatives.

#### Precalculus - Honors

##### Precalculus - Honors [1 credit]

Prerequisites: Algebra 2/Trigonometry Honors and/or departmental approval

This course is designed for the student who has completed a course in Algebra 2 and Trigonometry, and has shown high mathematical ability. The course includes the study of exponential and logarithmic functions, transformations, trigonometric functions, advanced algebra, vectors, polar coordinates, complex numbers, matrices and limits.

#### Statistics/Intro to Calculus - College Prep

##### Statistics/Intro to Calculus - College Prep [1 credit]

Prerequisites: Algebra 2/Trigonometry College Prep and/or departmental approval

This course is designed for the student who has completed at least Algebra 2 and Trigonometry. Topics will include measures of central tendency and variation, probability, binomial distributions, the central limit theorem, linear regression, chi-square. Emphasis will be on applied problems in business, psychology, biology and the social sciences. The course will include an introduction of Calculus with the study of limits and derivatives.

#### Statistics/Intro to Calculus - Accelerated

##### Statistics/Intro to Calculus - Accelerated [1 credit]

Prerequisites: Trig/Precalculus Accelerated and/or departmental approval

This course is designed for the student who has completed a course in Trig/Precalculus and has above average mathematical ability. Topics will include measures of central tendency and variation, probability, binomial distributions, the central limit theorem, linear regression, chi-square tests. Emphasis will be on applied problems in business, psychology, biology and the social sciences. The pace and depth of study will be more rigorous than the similar college prep course and will include an introduction of Calculus with the study of limits and derivatives.

#### AP Statistics

##### AP Statistics [1 credit]

Prerequisites: AP Calculus AB, Precalculus Honors, or Trig/Precalculus Honors and/or departmental approval

Advanced Placement statistics is equivalent to a first year college statistics course. The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Topics will include measures of central tendency and variation, probability, binomial distributions, the central limit theorem, linear regression, chi-square tests, and an introduction to calculus. Emphasis will be on applied problems in business, psychology, biology and the social sciences. Course content will include preparation for the Advanced Placement Statistics exam.

#### Calculus - Accelerated

##### Calculus - Accelerated [1 credit]

Prerequisites: Trig/Precalculus Honors or Trig/Precalculus Accelerated and/or departmental approval.

Calculus Accelerated includes the review and study of functions, analytic geometry, and advanced algebra. The object of the course is to develop methods of finding and applying the derivative and integral as a limit. The calculus of polynomial, trigonometric and exponential functions will be studied, and applied to problems involving analytic geometry, science and economics.

#### Calculus Honors

##### Calculus Honors [1 credit]

Prerequisites: Precalculus Honors or Trig/Precalculus Honors or Trig/Precalculus Accelerated and/or departmental approval.

Calculus Honors expands the study of functions, analytic geometry, and advanced algebra. The course will develop methods of finding and applying the derivative and integral as a limit, studying the calculus of polynomial, trigonometric, exponential and logarithmic functions and applying it to problems involving analytic geometry, science and economics. The pace and level of difficulty of problems is significantly more challenging than the accelerated level.

#### AP Calculus AB

##### AP Calculus AB [1 credit]

Prerequisites: This course is open to juniors who have completed Algebra 2/Trigonometry Honors with departmental approval, and also to seniors who have completed Precalculus Honors, Trigonometry/Pre-Calculus Honors and/or departmental approval.

AP Calculus AB includes methods of finding and applying the derivative and integral as a limit, studying the calculus of polynomial, trigonometric, exponential, logarithmic and inverse functions and applying it to problems involving analytic geometry, science and economics. The syllabus is determined by the AP College Board, and necessitates a rigorous and challenging pace. Preparation for the Advanced Placement Calculus AB Exam is extensive.

#### AP Calculus BC

##### AP Calculus BC [1 credit]

Prerequisites: AP Calculus AB and/or departmental approval

Advanced Placement Calculus BC is equivalent to a first-year college Calculus course. The student begins the course in his junior year with AP Calculus AB, and completes the course in his senior year. To cover this amount of material, the student must devote a good deal of time to study each day. The course is partially lecture with the stress being on the student's independent study and completing assignments. Course topics include but are not limited to: parametric, polar and vector functions; integration by parts, partial fractions, and improper integrals; the logistic growth model; and infinite series*. *Preparation for the Advanced Placement Calculus BC Exam is included.

#### Multivariable Calculus with Differential Equations (Formerly Calculus 5)

## Multivariable Calculus with Differential Equations (formerly Calculus 5) [1 credit]

Prerequisites: AP Calculus AB and BC and/or departmental approval

During the first semester after covering some preliminary topics on trigonometric substitutions, areas of surfaces of revolution, center of mass, work, fluid pressure, and the binomial series, the main topics are vector algebra, vector calculus, partial derivatives, multiple integrals, line integrals, and surface integrals as well as applications of these concepts.

The second semester is a course on ordinary differential equations beginning with the complex exponential function, homogeneous and non-homogeneous linear differential equations and systems of those, including applications to various types of harmonic motion and electric circuits. Separable, Bernoulli, exact, and Euler differential equations with some applications are covered as well as graphical solutions of autonomous equations, series solutions, and numerical methods employing a graphing calculator. If time permits, the Laplace transform is introduced.