# Mathematics

"Students' experiences in mathematics provide the skills and knowledge necessary to be able to select from a variety of post-secondary options and future career choices."

The Brooks School Mathematics Department seeks to provide the most meaningful educational experience our students will have in their lives. Whether a student enters our curriculum in Algebra 1 or in Honors Advanced Precalculus, we accept students where they are and then work to help each student grow to meet their achievement goals.

The Mathematics Department firmly believes that students’ experiences in mathematics provide the skills and knowledge necessary to be able to select from a variety of post-secondary options and future career choices. Guided by our vision, the mathematics curriculum balances the development of procedural skills, conceptual understanding of mathematical ideas, appropriate use of technology, and opportunities for critical thinking and problem solving.

The small class sizes at Brooks School encourage effective collaboration with peers and builds each students’ ability to communicate mathematical reasoning. Teachers help students develop the reasoning and problem-solving skills necessary to think critically and encourage mathematical modeling in which students make choices about how to use mathematics to create representations of a real-world process. Brooks School sets high expectations for all students and provides the support necessary to help them meet those expectations.

## Math Courses

- First-Year Algebra
- Geometry
- Second-Year Algebra
- Pre-Calculus
- Advanced Pre-Calculus
- Honors Advanced Pre-Calculus and Differential Calculus
- Calculus
- Probability & Statistics
- AP Statistics
- AP Calculus (AB)
- AP Calculus (BC)
- Multivariable Calculus
- AP Computer Science Principles
- Engineering: Product Design
- Engineering: Digital Design
- Computer Programming & Coding Through Apps
- Independent Study

## First-Year Algebra

The first semester introduces the language of algebra and functions while emphasizing reading, writing, and evaluating algebraic expressions. In addition, it deals with the fundamental operations of polynomials, linear equations, and linear inequalities. The second semester covers linear systems, quadratic equations, factoring, fractional equations, radicals, and radical equations.

## Geometry

The first semester introduces students to the terms, definitions, postulates, and theorems that form the basis of Euclidean geometry. It also explores the notion of formal proofs. Topics covered include parallel lines, congruent triangles, similar triangles, right triangles, and polygons. The second semester covers right triangle trigonometry, oblique triangle trigonometry, circles, area of planar figures, surface areas and volumes of three-dimensional objects, and an introduction to vectors and/or matrices. In both semesters, students utilize Geometer Sketchpad.

## Second-Year Algebra

The first semester reviews, reinforces, and explores more deeply the concepts of a First-Year Algebra course. The concept of functions, particularly linear and quadratic functions, is more fully developed. The second semester explores the logarithmic, exponential, rational, irrational, and variation functions. The study of sequences, series, and probability completes the course. There is an emphasis on modeling realistic examples from life and using the full capabilities of the graphing calculator.

## Pre-Calculus

This is a two-semester course that serves as an introduction to the elements of Pre-Calculus. It is designed for students who have not been recommended for the Advanced Pre-Calculus course. It is also designed for those who may be interested in pursuing the non-Advanced Placement Calculus course or math electives during the following year. Topics include the study of polynomial, exponential, logarithmic and trigonometric functions. The graphing calculator is used extensively, and students create mathematical models to solve realistic problems. The syllabus also includes some preparation for the SAT subject tests.

## Advanced Pre-Calculus

The first semester of this course continues the study begun in second year algebra of the modeling of linear, quadratic, logarithmic, exponential, and variation functions. Composite and inverse functions are also examined. The trigonometric and circular functions are also introduced in this course. The second semester studies trigonometric equations and identities; non-right triangle trigonometry; conic sections; complex numbers; polar numbers, equations and graphs; parametric equations and graphs; sequences and series; probability; and vectors.

## Honors Advanced Pre-Calculus and Differential Calculus

## Calculus

## Probability & Statistics

Students develop the skills to collect, analyze and interpret data, as well as develop proficiency in the use of spreadsheets. We are inundated by numbers that communicate powerful messages. As a citizen in today's society, one must be able to interpret the real story behind the numbers. Likewise, given the overwhelming amount of data available to us, we must be able to make sense of the data – to tell its story. This is not a math-intensive course, but rather a class focused on building analytic skills and writing stories about data. Students complete several projects, at least one of which is based on data of the student's own choosing.

## AP Statistics

This year long course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes in the AP Statistics course: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding. All students are required to take the Advanced Placement examination.

## AP Calculus (AB)

This course follows closely the syllabus as outlined by the Advanced Placement program of The College Board. The first semester includes the topics of limits and derivatives with attention given to the concept of rate of change, optimization and graphing techniques. The second semester continues with work in the trigonometric, exponential and logarithmic functions. It also explores the concept of the integral and all of its applications including the fundamental theorem of calculus. Students need to have done honors-level work in Pre-Calculus and must have departmental permission to gain entrance to this course. All students are required to take the Advanced Placement examination.

## AP Calculus (BC)

This course continues the study of calculus begun in the second semester of Honors Advanced Pre-Calculus and Differential Calculus. After completing the course work as defined in AP Calculus (AB), students proceed to the more advanced topics for the Advanced Placement BC Examination. These topics include infinite series, Taylor series, differential equations, delta-epsilon proofs, vector analysis, length of curves, surface area, advanced integration techniques, and parametric functions.

## Multivariable Calculus

The first semester of this full-year course includes vector algebra and geometry, cylindrical and spherical coordinates, three-dimensional surfaces, vector functions, velocity and acceleration, speed, tangent and normal vectors, arc length and curvature. The second semester covers functions of several variables, partial differentiation, grad, div, curl, tangent plane, normal line, level curves/surfaces, extrema and Lagrange's method, multiple integrals, change of variables, Jacobian applications, vector analysis, and more complex differential equations.

## AP Computer Science Principles

This yearlong course introduces students to the foundational concepts of computer science and computational thinking, and explores how computing and technology impact our world. As outlined by the Advanced Placement program of the College Board, students will focus on the “7 Big Ideas” -- creativity, abstraction, data and information, algorithms, programming, the Internet, and global impact. All students are required to take the Advanced Placement examination, which consists of a written exam and two artifacts.

## Engineering: Product Design

Students have a hands-on introduction to the product design process from conceptualization to prototype construction through 3D printer and testing. Students learn many skills including engineering graphics communications, technical sketching, and CAD (ComputerAided Design). Students work in groups and learn to function effectively in a team. (NOT OFFERED IN 2019-2020)

## Engineering: Digital Design

Students have a hands-on introduction to the principles and practices of digital design, one of the first core courses in the discipline of electrical and computer engineering in college. Students study topics such as analog vs. digital, different number systems, Boolean algebra, transistor network design, combinational circuits, sequential circuits and more. Design methodology using both discrete components (using breadboard) and hardware description languages (using FPGA) is implemented in the laboratory portion of the course. (NOT OFFERED IN 2019-2020)

## Computer Programming & Coding Through Apps

Students are introduced to programming with creating an app in mind, either iOS or Android. Students explore simple coding through their TI calculators and transition to learning MIT’s AppInventor, a GUI-based coding. After gaining some experience in simple programming, students learn Java or Objective-C and eventually create apps starting with classic games such as Tic-Tac-Toe or Flappy Bird. (NOT OFFERED IN 2019-2020)