# Mathematics

**All potential course offerings in the subject of Mathematics are listed alphabetically below.**

**Please Note: In any given year, whether a course is offered depends on the number of requests received for that course.****Course Descriptions**

**AP CALCULUS AB** | Credits: 1 | Terms: 2 | Course #: 21240

Grades: 11, 12

Prerequisites: Precalculus

Description: Calculus is the study of functions and their behavior. Topics studied include limits, continuity, derivatives, mean value theorems, anti-derivatives and the Fundamental Theorem of Calculus. These will give the student powerful tools for understanding the behavior of functions, and will also provide students with the ability to solve problems in which the important quantities are in a state of continuous change.

**AP CALCULUS BC** | Credits: 1 | Terms: 2 | Course #: 21250

Grades: 12

Prerequisites: AP Calculus AB

Description: This course is an extension of AP Calculus AB. Topics to be learned will be: parametric, polar and vector functions, techniques of anti-differentiation: partial fractions, trig substitution, integration by parts, improper integrals, applications of definite integrals, further study of differential equations, Euler's Method, and a study of sequences and series, including Taylor series and MacLaurin series.

**AP STATISTICS** | Credits: 1 | Terms: 2 | Course #: 22030

Grades: 11, 12

Prerequisites: Math 3

Description: AP Statistics emphasizes statistical sampling techniques and ways of describing the data collected, including ways to determine whether or not the data is clustered in a meaningful way. Also included will be normal probability distributions, hypothesis testing, confidence intervals, and a study of probability. This course is a common requirement for many college majors---not just math.

**CALCULUS 3** | Credits: 1.0 | Terms: 2 | Course #:

Grades: 11, 12

Prerequisites: AP Calculus BC

Description: This course is an extension of AP Calculus AB and BC and takes key concepts of calculus into three dimensions. Topics to be covered include vector, polar, and parametric functions in two and three dimensions, curves and surfaces in two and three dimensions, multivariable functions and their graphs, partial derivatives, analytic geometry, double and triple integrals, line integrals and applications, vector field properties, and crucial theorems of vector calculus.

**COLLEGE ALGEBRA READINESS AND SKILLS** | Credits: 0.5 | Terms: 1 | Course #: 20572

Grades: 11, 12

Prerequisites: Math I, Math II, Math III

Description: This course develops algebraic skills necessary for manipulating expressions and solving equations. Topics in the course include radicals, complex numbers, polynomials, factoring, rational expressions, quadratic equations, absolute value equations and inequalities, systems of linear equations, related applications, and math learning strategies. This course prepares students for College Algebra.

**MATHEMATICS I** | Credits: 1 | Terms: 2 | Course #: 20611

Grades: 9

Prerequisites: Successful completion of 8th grade mathematics

Description: Mathematics I is a year-long course focusing on geometry. The first semester of the course emphasizes transformational geometry and congruence. Students will experiment with transformations in the plane and understand congruence in terms of rigid motion. In addition, students prove geometric theorems and make geometric constructions. Second semester emphasizes properties of dilations and similarity. Students will be expected to prove theorems related to similarity of shapes and understand that similarity is foundational to trigonometry. Students will apply properties of dilation, similarity, trigonometric functions, and the Pythagorean Theorem to solve real world problems. In addition, students will solve problems using area, surface area, and volume formulas.

**MATHEMATICS I SUPPORT** | Credits: 0.5 | Terms: 1 | Course #: 20614

Grades: 9

Prerequisites: Teacher recommendation

Description: This course is designed to provide students with additional support for their Mathematics I class. Students will receive direct instruction for the skills and concepts necessary to achieve competency in the Colorado Academic Standards and Mathematics I.

**MATHEMATICS II** | Credits: 1 | Terms: 2 | Course #: 20612

Grades: 10

Prerequisites: Mathematics I

Description: Mathematics II is an in-depth study of linear, quadratic, and exponential functions. Algebraic concepts include rate of change, domain, range, transformations, and multiple representations of functions. Multiple representations include: graphs, tables, equations, and situations. Significant skills addressed are: equation solving, graphing functions, factoring, completing the square, quadratic formula, and properties of exponents. Logarithms and logarithmic functions will be introduced.

**MATHEMATICS II SUPPORT** | Credits: 0.5 | Terms: 1 | Course #: 20615

Grades: 10

Prerequisites: Teacher recommendation

Description: This course is designed to provide students with additional support for their Mathematics II class. Students will receive direct instruction for the skills and concepts necessary to achieve competency in the Colorado Academic Standards and Mathematics II.

**MATHEMATICS III** | Credits: 1 | Terms: 2 | Course #: 20613

Grades: 11

Prerequisites: Mathematics II

Description: Mathematics III is a year‐long course that will continue the work of Mathematics 2 with the use of real data and modeling using families of functions. This course emphasizes modeling real situations using arithmetic and geometric sequences, linear, exponential, power, root, logarithmic, polynomial, rational, and trigonometric functions. Students will expand on knowledge of quadratics by studying the four conic sections. Students will revisit logarithmic functions as inverse to exponential functions and practice properties of exponents and logarithms as part of the work of the course. Geometric concepts include coordinate geometry and the study of circles and their properties. Students will also complete a unit of study on statistical methods that take variability into account and support informed decisions through quantitative studies designed to answer specific questions.

**MATHEMATICS III** **SUPPORT** | Credits: 0.5 | Terms: 1 | Course #: 20616

Grades: 11

Prerequisites: Teacher recommendation

Description: This course is designed to provide students with additional support for their Mathematics III class. Students will receive direct instruction for the skills and concepts necessary to achieve competency in the Colorado Academic Standards and Mathematics III.

**PERSONAL FINANCE LITERACY** | Credits: 0.5 | Terms: 1 | Course #: 21571

Grades: 12

Prerequisites: Math I, Math II, Math III

Description: The focus of Personal Financial Literacy is the real-world application of computational skills to solve consumer based problems. You will gain budgeting, planning, and life skills while learning to use spreadsheets to manage data and solve problems. Basic arithmetic principles and processes are reviewed and practiced with topics such as banking, saving, investing, home expenses, taxes, budgeting, check writing, benefits/risks of credit cards, and insurance. This course will teach wise money management in these areas. This course is available for college credit.

**PRECALCULUS** | Credits: 1 | Terms: 2 | Course #: 21100

Grades: 11, 12

Prerequisites: Successful completion of Mathematics III or Instructor Approval based on assessment of skills

Description: Precalculus is a thorough development of equations, functions, their graphs, domains, ranges, and composites of functions. Families of functions studied include: exponential, logarithmic, polynomial, rational, trigonometric. Relevant applications offer the opportunity to apply the learning of each of the family of functions. Trigonometry is the study of ratios based on similarity of right triangles using both degree and radian angle measure in the unit circle. Students study trigonometric equations and the applications of periodic functions in a wide variety of fields. The law of sines and the law of cosines are used to solve for unknowns in triangles.