# Mathematics

The mathematics curriculum promotes the optimal mathematical development of each student. Through innovative, challenging, and differentiated instruction we seek to develop student’s problem-solving and critical thinking skills and foster an appreciation for the power and beauty of mathematics.

Students are encouraged to question, think, reason, compute, and communicate mathematically to solve real-world problems with enthusiasm, confidence, and creativity.

## Course Descriptions

## Algebra | Geometry | Precalculus | Calculus

#### Algebra I

*Full year*. Students use graphical, symbolic, tabular, and numerical representations as they solve problems involving unknown quantities. Linear equations and linear relationships are examined in great detail, and conceptual understanding is emphasized throughout the course. The

graphing calculator is utilized and required. Students are introduced to quadratic equations, factoring, and irrational numbers.

#### Geometry

*Full year. Prerequisite: Algebra I*. In this course, students will study parallelism, congruence,

similarity, polygons, circles, area, volume, and transformations. Particular emphasis is placed on inductive and deductive reasoning, logic, and proof. Students will use Geometer’s Sketchpad to explore relationships and formulate conjectures. Concepts of Algebra I are reinforced, including linear equations, graphing, and solving systems. Students are introduced to

right triangle trigonometry and counting principles. Algebraic applications of geometry and problem solving are greatly emphasized.

#### Honors Geometry

*Full year. Prerequisite: Algebra I and qualification*. In this course, students will study all of the topics in Geometry but with more theory and in greater depth. A mastery of many algebraic skills will be necessary for students to succeed and meet the demands of this rigorous course. Particular emphasis is placed on inductive and deductive reasoning, logic, proof, and

independent problem-solving. Students will use Geometer’s Sketchpad to explore relationships and formulate conjecture.

#### Algebra II

*Full year. Prerequisite: Geometry. *Algebra II is an extension of Algebra I with new topics

including transformations, higher-order polynomials, exponential, and logarithmic functions. Emphasis is placed on describing relations in multiple ways, developing problem-solving skills, and communicating understanding in verbal and written formats. Students investigate concepts and solve both with and without the use of the graphing calculator.

#### Honors Algebra II

*Full year. Prerequisite: Geometry or Honors Geometry and qualification*. Includes much of the same material as Algebra II plus a unit on trigonometry and rational functions, but with

more theory and in greater depth. Significant emphasis is placed on communication (verbal, partner and written) as well as on applications and problem-solving.

#### Honors Algebra II and Precalculus

*Full year. Prerequisite: Honors Geometry, and recommendation of department.* This course covers topics in Honors Algebra II and Honors Precalculus. The pace will be greater and

independent thinking and reasoning will be emphasized throughout the course. Students will be expected to investigate concepts and apply their knowledge in a variety of ways. Technology will be used extensively, and students will be required to explore many ideas outside of class time.

#### Algebra III/Trigonometry

*Full year. Prerequisite: Algebra II.* This alternative to Precalculus is a comprehensive review

and extension of Algebra II topics with a study of functions, their graphs and applications. Topics covered include matrices, trigonometry, conics, sequences and series, probability, and statistics. Much of the course content is similar to that of Pre-calculus, but material is presented at a slower pace. Please note that students in Algebra III/Trigonometry are not eligible to qualify for AP Calculus.

#### Precalculus

*Full year. Prerequisite: Algebra II.* This course is a study of functions and graphs including

trigonometry, higher order polynomials, exponents, logarithms, analytic geometry, sequences and series, and transformations, also including some principles of probability. Students continuously seek understanding by communicating through use of words, tables, graphs and

Algebra. *Please note: students who have completed Algebra III/Trigonometry are not eligible to enroll in Precalculus. Students should continue to Intro to Calculus & Statistics (below).*

#### Honors Precalculus

*Full year. Prerequisite: Algebra II or Honors Algebra II and qualification*. This course provides an in-depth examination of polynomial, exponential, logarithmic, power, rational, and trigonometric functions (graphs, equations, and applications) in preparation for AP Calculus. Students

communicate their understanding in verbal and written formats. In addition, students thoroughly explore sequences and series, probability, counting methods, and polar graphing, and begin the study of limits, derivatives, and continuity.

#### Intro to Calculus

*Full year. Prerequisite: Pre-calculus or Algebra III/Trigonometry*. The first semester of this course is devoted to developing an understanding of elementary statistics – graphing and describing data, using data to draw conclusions, and gathering data through surveys and experiments.

Students also study normal distributions in depth, including standardizing normal variables and calculating probabilities. In the second semester, students analyze selected topics from Differential Calculus, including limits, continuity, differentiability, and finding and applying

derivatives. The final portion of the course focuses on financial mathematics such as investments, exponential models of growth for compound interest, and Business Calculus.

#### Dynamic Math

*Full year. Prerequisite: Algebra III/Trigonometry or Precalculus*. Mathematical methods can be applied to solve problems in a variety of fields, from biology to computer science to

business. This course focuses on applied math problem-solving by utilizing topics such as matrices, sequences and series, trigonometry, and data analysis. Through project-based learning, students will research and learn about applications of mathematics and statistics in exercise science, dietetics, and kinesiology. Data collection methods and statistical analyses will be employed in the context of decision science and optimization. While the brain navigates through the math, the body will not remain at rest. The student’s work through each unit will

culminate in a mathematically-supported fitness program that will be executed during a class period. This course is guaranteed to grow your brain, appreciation for math, and physical and mental wellness! The course is open to students in grade 12.

## Advanced Math Options

#### AP Statistics

*Full year. Prerequisite: Pre-calculus or Honors Pre-calculus and qualification*. A secondary school equivalent of a one-semester introductory, non-Calculus based college course in Statistics. Four broad conceptual themes emerge in the course: (1) Exploring Data: observing patterns and

departures from patterns, (2) Planning a Study: deciding what and how to measure, (3) Anticipating Patterns in Advance: producing models using probability and simulation, and (4) Statistical Inference: confirming models. Students are expected to sit the AP Statistics

exam at the end of the course.

#### Advanced AP Statistics and R and R Studio

*Full year. Prerequisite or Corequisite: AP Calculus BC*. R is a programming language and statistics software environment used for all aspects of data analysis. RStudio® is a free, open-source integrated development environment that facilitates the use of R. Widely used in

higher education, science, government, and industry, these tools easily manipulate and visualize complex data. Advanced AP Statistics with R and Rstudio® embeds the standard AP Statistics curriculum in these statistical software packages. Students interested in this course

should have strong analytic skills, the ability to reason conceptually, and be comfortable in a rapid-paced learning environment.

#### AP Calculus "AB"

*Full year. Prerequisite: Pre-calculus or Honors Pre-calculus and qualification*. A college-level study that begins with limits and continuity and continues with a study of derivatives and their

applications, integration and some applications of definite integrals, as well as a limited number of techniques of integration. A year-long course designed to prepare the student to take the AP Calculus AB exam. Students who March 2022 13 take AP Calculus (AB) prior to their senior year may not take AP Calculus “BC” in any subsequent year. Students are expected to sit the AP Calculus exam at the end of the course.

#### AP Calculus "BC"

*Full year. Prerequisite: Honors Pre-calculus and qualification*. This college-level study begins with the applications of derivatives and continues with integrals and their applications, techniques of integration, infinite series, the calculus of parametric and polar functions, as well as the

calculus of two-dimensional vectors. The course content is approximately equivalent to the first two semesters of college-level Calculus. Students are expected to sit the AP Calculus exam at the end of the course.

#### Mathematic Analysis

*Fall semester. Prerequisite: BC Calculus or currently enrolled in BC Calculus*. This course introduces advanced students to the rigors of mathematical proof and logic. The course content covers countable and uncountable sets, properties of Rn, convergence of sequences and series, limits and their properties, continuous functions, and a careful development of the foundations for differentiation and integration.

#### Probability Theory

*Spring semester. Prerequisite: BC Calculus or currently enrolled in BC Calculus*. This course is designed for students who are curious to explore research topics in advanced mathematics. The course content covers measure theory, convergence of distributions and probability measures. We will explore foundational theorems of probability theory including the Borel-Cantelli Lemma, Fubini’s theorem and several important limit theorems. Students will be required to complete a significant research project as part of this course.

#### IB Applications SL

*Full year. IB students only. *Please see the IB section for more information.

#### IB Analysis SL

*Full year, IB students only. Please see the IB section for more information.*

#### IB Analysis HL

*Full year. IB students only. Please see the IB section for more information.*

#### Linear Algebra

*Fall semester. Please note that this course is offered in alternate years and is not offered in the 2022-23 academic year. Prerequisite: AP Calculus (AB or BC) and qualification*. This course covers an exhaustive study of systems of equations, determinants, vector spaces, linear

transformations, orthogonality and eigen values. Applications will be emphasized, and technology will be utilized throughout the course.

#### Multivariable Calculus

*Spring semester. Please note that this course is offered in alternate years and is not offered in the 2022-23 academic year. Prerequisite: BC Calculus or currently enrolled in BC Calculus*. This course will include a study of vectors, motion along a curve, partial derivatives, multiple integrals, vector calculus and the divergence, gradient and curl of a vector field. Students will be expected to apply knowledge obtained from AB or BC Calculus when solving or evaluating problems and expressions. Much of the focus of the course will be in three-dimensional space.