 # Mathematics

The goals of the CRMS Mathematics Department are to provide students with the tools to be logical thinkers and to help them gain a solid foundation in problem-solving. The department aims to help students become more confident in their mathematical abilities as well as appreciate ways in which the math they are studying relates to the world around them. Emphasis is placed on both mastery of mathematical operations and understanding of the underlying reasoning of the operations themselves. All topics are explored visually, symbolically, and verbally. Class work, homework, quizzes, tests, and projects are designed to develop critical thinking. Graphing calculators and computer technology are an integral part of the curriculum and are regularly used as tools to help students further comprehend the topics being studied. Completing three years of math and passing Algebra II are the minimum requirements, but students are encouraged to continue math classes up to and including their senior year.

Algebra I
This course develops both the fundamental skills of algebra and the context for the practical application of math. Students learn algebraic manipulation, graphing, and mathematical modeling. Algebraic manipulation topics include simplifying and solving linear and polynomial expressions and equations. These algebraic topics are applied to linear and quadratic modeling. Students use a calculator, computers, and the web to gain better understanding of the topics.

Geometry
This course begins by introducing concepts of plane and coordinate geometry through such topics as angles, triangles, lines, circles, polygons, area similarity, congruence, and right-triangle trigonometry. The second semester includes an introduction to perimeter, area, surface area, and volume by deriving formulae and solving problems. Students learn deductive reasoning using proof to expand fundamental geometric concepts by writing logical arguments and justifying conclusions. Throughout the year, geometric constructions serve to illustrate many of the topics. Furthermore, students utilize the graphing calculator as a vehicle to increase understanding through exercises and projects.
Prerequisite: Algebra I.

Algebra II
This course builds on the foundation of Algebra I and Geometry to prepare students for future math courses. Students study various classes of functions. Applying the functions to real-world situations through mathematical modeling provides students with an answer to the question, “What is all this algebra good for?” Integrated throughout the year are the fundamental algebraic skills of graphing, solving equations, and simplifying expressions. The graphing calculator is used as a tool for discovering and for making connections between the symbolic, numerical, and geometric representations of algebraic concepts.
Prerequisite: Geometry

Precalculus
This course explores functions and their applications. Emphasis is put on the use of polynomial, rational, exponential, logarithmic, and trigonometric functions. Operations, transformations, and inverses of functions are explored fully. Students are expected to use multiple representations of functions to solve problems, including algebraic, graphical, numerical, and verbal methods. The graphing calculator is used as a tool to explore new concepts as well as to solve problems in different ways. Students are assessed in a variety of ways, including tests, quizzes, projects, and presentations.
Prerequisite: Algebra II

AP Calculus AB
This course is centered on the four central concepts to be mastered in the first-semester college course in calculus: limit, derivative, definite integral, and indefinite integral. For each concept, students are asked to know the precise definition and be able to apply the concept and its associated skills to a variety of novel problems. There are three ways these concepts are presented to the student: graphically, algebraically, and verbally. Students may earn college credit through successful performance on the Calculus AB Advanced Placement examination.
Prerequisite: Precalculus

AP Calculus BC
This course serves as either an advanced first-year calculus course or as an extension of AP Calculus AB. First-year calculus students will be placed in AP Calculus BC vs. AP Calculus AB based on their interest, performance in Precalculus, and teacher recommendation. The course continues to emphasize a multi-representational approach to calculus. Topics covered include: more sophisticated methods of integration, polar and parametric curves, polynomial approximations and infinite series, and vector-valued functions. Students may earn college credit through successful performance on the Calculus BC Advanced Placement examination.
Prerequisite: Precalculus

Independent Study in Mathematics
Students can select from a variety of advanced mathematical topics and texts depending on their goals: preparation for fundamental collegiate mathematics, exposure to a broad set of mathematical methods, in-depth study of a particular set of concepts and methods, application of mathematics to a specific scientific specialty, etc. Students meet in a weekly seminar with the Chair of the Department of Mathematics and are expected to work diligently outside this seminar time.
Prerequisite: AP Calculus BC and approval from Academic Dean and Mathematics Chair.

To learn more about Colorado Rocky Mountain School, please join our mailing listrequest information or apply now. ## Academics # Mathematics

The goals of the CRMS Mathematics Department are to provide students with the tools to be logical thinkers and to help them gain a solid foundation in problem-solving. The department aims to help students become more confident in their mathematical abilities as well as appreciate ways in which the math they are studying relates to the world around them. Emphasis is placed on both mastery of mathematical operations and understanding of the underlying reasoning of the operations themselves. All topics are explored visually, symbolically, and verbally. Class work, homework, quizzes, tests, and projects are designed to develop critical thinking. Graphing calculators and computer technology are an integral part of the curriculum and are regularly used as tools to help students further comprehend the topics being studied. Completing three years of math and passing Algebra II are the minimum requirements, but students are encouraged to continue math classes up to and including their senior year.

Algebra I
This course develops both the fundamental skills of algebra and the context for the practical application of math. Students learn algebraic manipulation, graphing, and mathematical modeling. Algebraic manipulation topics include simplifying and solving linear and polynomial expressions and equations. These algebraic topics are applied to linear and quadratic modeling. Students use a calculator, computers, and the web to gain better understanding of the topics.

Geometry
This course begins by introducing concepts of plane and coordinate geometry through such topics as angles, triangles, lines, circles, polygons, area similarity, congruence, and right-triangle trigonometry. The second semester includes an introduction to perimeter, area, surface area, and volume by deriving formulae and solving problems. Students learn deductive reasoning using proof to expand fundamental geometric concepts by writing logical arguments and justifying conclusions. Throughout the year, geometric constructions serve to illustrate many of the topics. Furthermore, students utilize the graphing calculator as a vehicle to increase understanding through exercises and projects.
Prerequisite: Algebra I.

Algebra II
This course builds on the foundation of Algebra I and Geometry to prepare students for future math courses. Students study various classes of functions. Applying the functions to real-world situations through mathematical modeling provides students with an answer to the question, “What is all this algebra good for?” Integrated throughout the year are the fundamental algebraic skills of graphing, solving equations, and simplifying expressions. The graphing calculator is used as a tool for discovering and for making connections between the symbolic, numerical, and geometric representations of algebraic concepts.
Prerequisite: Geometry

Precalculus
This course explores functions and their applications. Emphasis is put on the use of polynomial, rational, exponential, logarithmic, and trigonometric functions. Operations, transformations, and inverses of functions are explored fully. Students are expected to use multiple representations of functions to solve problems, including algebraic, graphical, numerical, and verbal methods. The graphing calculator is used as a tool to explore new concepts as well as to solve problems in different ways. Students are assessed in a variety of ways, including tests, quizzes, projects, and presentations.
Prerequisite: Algebra II

AP Calculus AB
This course is centered on the four central concepts to be mastered in the first-semester college course in calculus: limit, derivative, definite integral, and indefinite integral. For each concept, students are asked to know the precise definition and be able to apply the concept and its associated skills to a variety of novel problems. There are three ways these concepts are presented to the student: graphically, algebraically, and verbally. Students may earn college credit through successful performance on the Calculus AB Advanced Placement examination.
Prerequisite: Precalculus

AP Calculus BC
This course serves as either an advanced first-year calculus course or as an extension of AP Calculus AB. First-year calculus students will be placed in AP Calculus BC vs. AP Calculus AB based on their interest, performance in Precalculus, and teacher recommendation. The course continues to emphasize a multi-representational approach to calculus. Topics covered include: more sophisticated methods of integration, polar and parametric curves, polynomial approximations and infinite series, and vector-valued functions. Students may earn college credit through successful performance on the Calculus BC Advanced Placement examination.
Prerequisite: Precalculus

Independent Study in Mathematics
Students can select from a variety of advanced mathematical topics and texts depending on their goals: preparation for fundamental collegiate mathematics, exposure to a broad set of mathematical methods, in-depth study of a particular set of concepts and methods, application of mathematics to a specific scientific specialty, etc. Students meet in a weekly seminar with the Chair of the Department of Mathematics and are expected to work diligently outside this seminar time.
Prerequisite: AP Calculus BC and approval from Academic Dean and Mathematics Chair.

To learn more about Colorado Rocky Mountain School, please join our mailing listrequest information or apply now.
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