# Mathematics

Learn to explore mathematics with confidence from Algebra 1 all the way through to post-calculus. The curriculum is designed for a range of student interests and aptitudes. Math is interactive and collaborative at Fountain Valley, where learning often takes place outside the classroom. You may find yourself in geometry class measuring the height of the flagpole using the sextant you’ve just made, or building a keystone arch using the 3D printer. Or perhaps measuring the volume of the pond in Algebra 2 and calculating the recommended maximum speed on the school road’s curves in Multivariable Calculus. Our goal is to encourage you to be a capable and confident mathematician and in turn, a better thinker.

### List of 15 items.

• #### Algebra I

This course is designed for students who have not yet completed Algebra I before arriving at FVS or have just taken a pre‑algebra class. The nature of real numbers is explored through the study of postulates, solving equations and inequalities, system of equations, graphing, exponents, radicals, factoring, probability, statistics, and an extensive study of lines.
• #### Geometry

The visual and practical nature of geometry enables students to develop the tools of logic. These skills will then be used in the more abstract study of analytical geometry and beyond. Students taking this course study points, lines and planes, and they discover relationships between geometric shapes, such as congruence and similarity. Additionally, proofs are used to establish properties of different types of quadrilaterals.
• #### Geometry Honors

Prerequisite: A‑ average in Algebra I and teacher recommendation.
The visual and practical nature of geometry enables students to develop the tools of logic. These skills will then be used in the more abstract study of analytical geometry and beyond. Students taking this course study points, lines and planes, and they discover relationships between geometric shapes, such as congruence and similarity. Additionally, proofs are used to establish properties of different types of quadrilaterals. This honors class will cover additional topics with more depth and at a faster pace than the traditional Geometry class.
• #### Algebra II

A solid understanding of algebra is key for success in future math courses. This class will build upon the algebra that students have already learned with the goal of delving deeper into many algebraic concepts. Topics covered include solving equations, transformations of graphs, lines, systems of equations, exponents, factoring, and an extensive study of quadratics.
• #### Honors Algebra II

Prerequisite: Grade of A‑ or higher in Algebra I and teacher recommendation.
Some students may need to take an algebra placement test. A solid understanding of algebra is key for success in future math courses. This class will build upon the algebra that students have already learned with the goal of delving deeper into many algebraic concepts. Topics covered include solving equations, transformations of graphs, lines, systems of equations, probability, logarithms, exponents, factoring, and an extensive study of quadratics. This Honors class will cover additional topics with more depth and at a faster pace than the traditional Algebra II class.
• #### Functions, Statistics, and Trigonometry

This class is designed to give students a greater understanding of algebra topics that are important for college and beyond. Topics covered include transformations, both graphically and algebraically, logarithms, statistics, probability, modeling regression curves, sequences and series, rational functions, and trigonometry, including the Law of Sines and Cosines. An emphasis will be placed on the use of these skills and their practical applications.
• #### Precalculus

Prerequisite: Grade of A or higher in Algebra II, B or higher in Honors Algebra II, or an A or higher in Functions, Statistics, and Trigonometry, and teacher recommendation.
Numerous topics that the students have been exposed to are covered in more depth to prepare the students for the study of higher‑level mathematics. Review topics include the shapes and transformations of graphs, polynomials, and exponential and logarithmic functions. An extensive study of trigonometry with its applications is included as well as an introduction to probability, statistics, matrices, sequences, and series.
• #### Honors Precalculus

Prerequisite: Grade of A‑ or higher in Honors Algebra II and teacher recommendation.
Precalculus is designed for the strong math student and Honors Precalculus is designed for the exceptional math student. Numerous topics that the students have been exposed to are covered in more depth to prepare the students for the study of higher‑level mathematics. Review topics include the shapes and transformations of graphs, polynomials, and exponential and logarithmic functions. An extensive study of trigonometry with its applications is included as well as study of limits and the derivative. This class moves at a much faster pace than the Precalculus class in order for students to be eligible to enroll in Advanced Calculus BC the following year
• #### Statistics

This course presents statistics as a key tool for understanding the world through data. The four major themes of the course are: (1) analyzing data, (2) understanding chance behavior (probability), and (3) drawing conclusions and making predictions from data. The course emphasizes conceptual understanding, clear communication and critical thinking over calculations and algorithms. The statistical concepts and techniques you acquire will prove invaluable in higher‑level studies in the natural sciences, social sciences, health sciences and business. It will also serve as a preparation for college level statistics. Overall, the study of statistics will help you to become a more effective consumer of information.

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Prerequisite: teacher recommendation.

Statistics is the art and science of collecting, organizing, analyzing, and drawing conclusions from data. In Advanced Statistics, the focus will be on four major themes: exploratory data analysis, designing studies, probability models and simulation, and statistical inference. Advanced Statistics is designed to be at least as comprehensive as any one‑semester, college introductory statistics course. This AP level class is designed so that a student who completes additional work outside of class will be prepared to take the AP Statistics exam.

Prerequisite: Grade of B‑ or higher in Precalculus or a C+ or higher in Honors Precalculus and teacher recommendation.
This class explores differential and integral calculus. The theory behind the derivative and the integral, as well as applications of each, is covered in depth. This AP level class is designed so that a student will be prepared to take the AP Calculus AB exam. A student who does not take the AP exam will be required to take a final exam in May.

Prerequisite: teacher recommendation.
This class will have a summer assignment and will begin with a very quick review of the calculus topics covered in Honors Precalculus. The new topics that will be covered include more involved techniques of integration, differential equations, infinite series, and calculus for polar and parametric curves. This AP level class is designed so that a student will be prepared to take the AP Calculus BC exam. A student who does not take the AP exam will be required to take a final exam in May.
• #### Honors Linear Algebra

Prerequisite: teacher recommendation
Linear Algebra is a branch of mathematics that studies vector spaces. This class will explore vectors, systems of linear equations, matrices, eigenvalues and eigenvectors, and vector spaces.
• #### Financial Math/Economic Reasoning

Math skills are necessary in many life situations. This course is designed to enhance understanding of basic, practical math applications. Students gain practical math competence through real‑world examples that may include areas of budgeting, major purchases, investments, compound interest, taxes, credit cards, salaries and retirement, and finances of everyday living.
• #### Honors Discrete Mathematics

Prerequisite: teacher recommendation
Based on student and teacher interest, this class will dabble with inner product spaces, number theory, AMC questions, mathematical modeling through the MathWorks Math Modeling Challenge, proof writing, and mathematical induction.

### List of 6 members.

• #### Blake Pelton

Mathematics Department Chair, Mathematics Faculty
(719) 649-3638
• #### Debra Prantl

Mathematics Faculty
(719) 391-5343
• #### Sam Harrison

Mathematics Faculty
(719) 391-5346
• #### Scott Lebo

Teacher
(719) 391-5345
• #### Matt Jones

Math Faculty
• #### Azamat  Zhaksylykov

STEM Faculty FVS is a private, college-preparatory, co-ed, day and boarding school for grades 9-12 in Colorado Springs.