## 2016-2017 Monarch High School Course Selections - Mathematics

Level 9 – 12

Course Length: 2 semesters

Prerequisite: None

Credits: 10

Algebra 1 is an introduction to abstract reasoning and algebraic symbolism. Students will solve equations and systems of equations, and they will use functions to represent patterns and make predictions. The focus is on linear, exponential, and quadratic functions in problem-solving situations. Students will engage daily with the Standards for Mathematical Practice. Students will also employ algebraic methods to summarize data and to compare data sets.

Level: 9 – 12

Course Length: 2 semesters

Prerequisite: M25 in middle school

Credits: 10

Advanced Algebra 1 is an in-depth study of algebraic symbolism, systems of equations, graphing, problem-solving, and probability and statistics. The students will build upon their previous knowledge to further understand the characteristics and representations of various functions, and relations including: linear, exponential, and quadratic equations, inequalities, complex numbers, and rational algebraic expressions. As an advanced course, this course goes beyond the curriculum expectations of a standard course offering by increasing the depth and complexity. Students are engaged in dynamic, high‐level learning via the Standards for Mathematical Practice. The pace of an advanced course may be faster than that of the Algebra 1 course.

Level: 9 – 12

Course Length: 2 semesters

Prerequisite: M31 or M35

Credits: 10

Geometry presents a thorough study of the structure of the postulational system and development of formal synthetic proof. It considers the topics of congruence, parallelism, perpendicularity, properties of polygons, similarity, and the relationships of circles, spheres, lines, and planes with respect to space as well as the plane. Basic principles of probability will be introduced. The maintenance of algebraic skills will be emphasized.

Level: 9 – 12

Course Length: 2 semesters

Prerequisite: M35

Credits: 10

Advanced Geometry presents a thorough study of the structure of the postulate system and development of formal two-column proof. It considers the topics of congruence, parallelism, perpendicularity, properties of polygons, similarity, and the relationships of circles, spheres, lines, and planes with respect to space as well as the plane. Basic principles of probability will be introduced. Use of algebraic skills is expected. As an advanced course, this course goes beyond the curriculum expectations of a standard course offering by increasing the depth and complexity. Students are engaged in dynamic, high‐level learning via the Standards for Mathematical Practice. The pace of an advanced course may be faster than that of the M41 Geometry course.

Level: 10-12

Course Length: 2 semesters

Prerequisite: M31 or M41

Credits: 10

Algebra 2 emphasizes the structure of algebra. The students will study complex numbers, relations and functions, solutions to polynomial, radical, rational, exponential and logarithmic functions. Statistics and circular trigonometry are also covered. They will apply their studies to develop understandings of how these topics relate to one another through the Standards for Mathematical Practice.

Level: 10-12

Course Length: 2 semesters

Prerequisite: None

Credits: 10

M55, Advanced Algebra 2, emphasizes the structure of algebra. The students will study complex numbers, relations and functions, solutions to polynomial, radical, rational, exponential, logarithmic and basic trigonometric functions. Statistics and circular trigonometry are also covered. They will apply their studies to develop understandings of how these topics relate to one another. As an advanced course, this course goes beyond the curriculum expectations of a standard course offering by increasing the depth and complexity through the Standards for Mathematical Practice. Students are engaged in dynamic, high‐level learning. The pace of an advanced course may be faster than that of M51 Algebra 2 course.

Level: 11 -12

Course Length: 1 year

Prerequisite: M41 or M43

Credits: 10

Discrete Mathematics allows for students to explore 20th century applications of mathematics. The curriculum is practical in nature and includes apportionment, graph theory, fair division, matrices and their applications to problem solving, and probability and statistics. Students will specifically explore mathematics as it applies to current world events and discoveries.

Level: 11-12

Course Length: 2 semesters

Prerequisites: M51 or M55

Credits: 10

Mathematics at the Pre‐Calculus level focuses on exponential, logarithmic, and trigonometric functions, conic sections, systems of equations solved by matrices and limits of functions as a precursor to the study of Calculus. Problem solving, representations, reasoning, communication, and connections within and outside of mathematics underline all of the teaching and learning at the Pre‐Calculus level.

Level: 10-12

Course Length: 2 semesters

Prerequisites: M55

Credits: 10

Mathematics at the Advanced Pre‐Calculus level focuses on solving and modeling with exponential, logarithmic, parametric and trigonometric functions and their inverses. The complex number system is fully developed. Conic sections, systems of equations solved through matrices, and an introduction to vectors and sequences and series are also included. Limits of functions are taught as a precursor to Calculus. Problem solving, representations, reasoning, communication, and connections within and outside of mathematics underline all of the teaching and learning at the Pre‐Calculus level. As an advanced course, this course goes beyond the curriculum expectations of the M61 Pre-Calculus course offering by increasing the depth and complexity. Students are engaged in dynamic, high‐level learning via the Standards for Mathematical Practice. The pace of an advanced course may be faster than that of the M61 Pre-Calculus course.

Level: 11-12

Course Length: 2 semesters

Prerequisites: M61 and M64 or M62 and M63

Credits: 10

AP Calculus AB is the equivalent of the first semester of college Calculus. It examines the theory of limits, differentiation, functional analysis, and integration. Students develop problem solving skills through application. Students may take the advanced placement exam and possibly receive college credit.

Level: 10-12

Course Length: 2 semesters

Prerequisite: M62, M63

Credits: 10

AP Calculus BC involves the content of Calculus AB plus further application of differentiation and integration. AP Calculus BC is roughly the equivalent of the content taught in the first and second semesters of college Calculus, including polar coordinates, differential equations, infinite series, and integration techniques. Students may take advanced placement exams and possibly receive college credit.

Level: 10-12

Course Length: 2 semester sequence

Prerequisites: M51 or M55

Credits: 10

This course is designed to be equivalent to a one-semester, introductory, non-calculus based college course in statistics. The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: 1) exploring data: observing patterns and departures from patterns, 2) planning a study: deciding what and how to measure, 3) anticipating patterns: producing models using probability and simulation, 4) statistical inference: confirming models. Students who successfully complete the course and AP exam may receive college credit and/or advanced placement for a one-semester college statistics course.

Level: 11-12

Course Length: 1 semester

Prerequisite: M66 or teacher rec

Credits: 5

M87 Calculus 2 is equivalent to the third semester of college Calculus. Topics include transcendental functions, methods of integration, improper integrals, infinite series and polar coordinates. Students completing this course will have thorough understanding of exponential, logarithmic, and inverse trigonometric functions and infinite series as well as the applied use of these mathematical concepts.

Level: 11-12

Course Length: TBD

Prerequisite: TBD

Credits: TBD

The M88 Calculus 3 course is the equivalent of the fourth semester of college Calculus. Topics include vectors, vector-valued functions, partial differentiation, multiple integration and vector calculus. Students completing this class will have a thorough understanding of calculus applied to multi-variable functions, vector-valued functions and vector fields.

Level: 11-12

Course Length: 2nd semester

Prerequisite: M87

Credits: 5

The M92 Intermediate Algebra course provides students an opportunity to continue learning Algebraic topics to prepare for either Algebra 2 or other fourth year math course offerings. Students will study algebraic expressions and equations, functions and relations, systems of equations, quadratic functions, polynomial functions, and exponential and logarithmic functions,.

**M31 Algebra 1**Level 9 – 12

Course Length: 2 semesters

Prerequisite: None

Credits: 10

Algebra 1 is an introduction to abstract reasoning and algebraic symbolism. Students will solve equations and systems of equations, and they will use functions to represent patterns and make predictions. The focus is on linear, exponential, and quadratic functions in problem-solving situations. Students will engage daily with the Standards for Mathematical Practice. Students will also employ algebraic methods to summarize data and to compare data sets.

**M35 Algebra 1, Advanced**Level: 9 – 12

Course Length: 2 semesters

Prerequisite: M25 in middle school

Credits: 10

Advanced Algebra 1 is an in-depth study of algebraic symbolism, systems of equations, graphing, problem-solving, and probability and statistics. The students will build upon their previous knowledge to further understand the characteristics and representations of various functions, and relations including: linear, exponential, and quadratic equations, inequalities, complex numbers, and rational algebraic expressions. As an advanced course, this course goes beyond the curriculum expectations of a standard course offering by increasing the depth and complexity. Students are engaged in dynamic, high‐level learning via the Standards for Mathematical Practice. The pace of an advanced course may be faster than that of the Algebra 1 course.

**M41 Geometry**Level: 9 – 12

Course Length: 2 semesters

Prerequisite: M31 or M35

Credits: 10

Geometry presents a thorough study of the structure of the postulational system and development of formal synthetic proof. It considers the topics of congruence, parallelism, perpendicularity, properties of polygons, similarity, and the relationships of circles, spheres, lines, and planes with respect to space as well as the plane. Basic principles of probability will be introduced. The maintenance of algebraic skills will be emphasized.

**M43 Geometry, Advanced (Weighted)**Level: 9 – 12

Course Length: 2 semesters

Prerequisite: M35

Credits: 10

Advanced Geometry presents a thorough study of the structure of the postulate system and development of formal two-column proof. It considers the topics of congruence, parallelism, perpendicularity, properties of polygons, similarity, and the relationships of circles, spheres, lines, and planes with respect to space as well as the plane. Basic principles of probability will be introduced. Use of algebraic skills is expected. As an advanced course, this course goes beyond the curriculum expectations of a standard course offering by increasing the depth and complexity. Students are engaged in dynamic, high‐level learning via the Standards for Mathematical Practice. The pace of an advanced course may be faster than that of the M41 Geometry course.

**M51 Algebra 2**Level: 10-12

Course Length: 2 semesters

Prerequisite: M31 or M41

Credits: 10

Algebra 2 emphasizes the structure of algebra. The students will study complex numbers, relations and functions, solutions to polynomial, radical, rational, exponential and logarithmic functions. Statistics and circular trigonometry are also covered. They will apply their studies to develop understandings of how these topics relate to one another through the Standards for Mathematical Practice.

**M55 Algebra 2, Advanced (Weighted)**Level: 10-12

Course Length: 2 semesters

Prerequisite: None

Credits: 10

M55, Advanced Algebra 2, emphasizes the structure of algebra. The students will study complex numbers, relations and functions, solutions to polynomial, radical, rational, exponential, logarithmic and basic trigonometric functions. Statistics and circular trigonometry are also covered. They will apply their studies to develop understandings of how these topics relate to one another. As an advanced course, this course goes beyond the curriculum expectations of a standard course offering by increasing the depth and complexity through the Standards for Mathematical Practice. Students are engaged in dynamic, high‐level learning. The pace of an advanced course may be faster than that of M51 Algebra 2 course.

**M58 Discrete Math**Level: 11 -12

Course Length: 1 year

Prerequisite: M41 or M43

Credits: 10

Discrete Mathematics allows for students to explore 20th century applications of mathematics. The curriculum is practical in nature and includes apportionment, graph theory, fair division, matrices and their applications to problem solving, and probability and statistics. Students will specifically explore mathematics as it applies to current world events and discoveries.

**M61 Pre-Calculus**Level: 11-12

Course Length: 2 semesters

Prerequisites: M51 or M55

Credits: 10

Mathematics at the Pre‐Calculus level focuses on exponential, logarithmic, and trigonometric functions, conic sections, systems of equations solved by matrices and limits of functions as a precursor to the study of Calculus. Problem solving, representations, reasoning, communication, and connections within and outside of mathematics underline all of the teaching and learning at the Pre‐Calculus level.

**M62 Pre-Calculus Advanced (Weighted)**Level: 10-12

Course Length: 2 semesters

Prerequisites: M55

Credits: 10

Mathematics at the Advanced Pre‐Calculus level focuses on solving and modeling with exponential, logarithmic, parametric and trigonometric functions and their inverses. The complex number system is fully developed. Conic sections, systems of equations solved through matrices, and an introduction to vectors and sequences and series are also included. Limits of functions are taught as a precursor to Calculus. Problem solving, representations, reasoning, communication, and connections within and outside of mathematics underline all of the teaching and learning at the Pre‐Calculus level. As an advanced course, this course goes beyond the curriculum expectations of the M61 Pre-Calculus course offering by increasing the depth and complexity. Students are engaged in dynamic, high‐level learning via the Standards for Mathematical Practice. The pace of an advanced course may be faster than that of the M61 Pre-Calculus course.

**M65****AP****Calculus AB (Weighted)**Level: 11-12

Course Length: 2 semesters

Prerequisites: M61 and M64 or M62 and M63

Credits: 10

AP Calculus AB is the equivalent of the first semester of college Calculus. It examines the theory of limits, differentiation, functional analysis, and integration. Students develop problem solving skills through application. Students may take the advanced placement exam and possibly receive college credit.

**M66 AP Calculus BC (Weighted)**Level: 10-12

Course Length: 2 semesters

Prerequisite: M62, M63

Credits: 10

AP Calculus BC involves the content of Calculus AB plus further application of differentiation and integration. AP Calculus BC is roughly the equivalent of the content taught in the first and second semesters of college Calculus, including polar coordinates, differential equations, infinite series, and integration techniques. Students may take advanced placement exams and possibly receive college credit.

*.***M69 AP Statistics (Weighted)**Level: 10-12

Course Length: 2 semester sequence

Prerequisites: M51 or M55

Credits: 10

This course is designed to be equivalent to a one-semester, introductory, non-calculus based college course in statistics. The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: 1) exploring data: observing patterns and departures from patterns, 2) planning a study: deciding what and how to measure, 3) anticipating patterns: producing models using probability and simulation, 4) statistical inference: confirming models. Students who successfully complete the course and AP exam may receive college credit and/or advanced placement for a one-semester college statistics course.

**M87 Calculus 2 (Weighted)**Level: 11-12

Course Length: 1 semester

Prerequisite: M66 or teacher rec

Credits: 5

M87 Calculus 2 is equivalent to the third semester of college Calculus. Topics include transcendental functions, methods of integration, improper integrals, infinite series and polar coordinates. Students completing this course will have thorough understanding of exponential, logarithmic, and inverse trigonometric functions and infinite series as well as the applied use of these mathematical concepts.

**M88 Calculus 3 (Weighted)**Level: 11-12

Course Length: TBD

Prerequisite: TBD

Credits: TBD

The M88 Calculus 3 course is the equivalent of the fourth semester of college Calculus. Topics include vectors, vector-valued functions, partial differentiation, multiple integration and vector calculus. Students completing this class will have a thorough understanding of calculus applied to multi-variable functions, vector-valued functions and vector fields.

**M92 Intermediate Algebra**Level: 11-12

Course Length: 2nd semester

Prerequisite: M87

Credits: 5

The M92 Intermediate Algebra course provides students an opportunity to continue learning Algebraic topics to prepare for either Algebra 2 or other fourth year math course offerings. Students will study algebraic expressions and equations, functions and relations, systems of equations, quadratic functions, polynomial functions, and exponential and logarithmic functions,.