# Mathematics

Through the study of mathematics, students discover the language for expressing relationships that order the natural world. At BTA, students cultivate a keen sense of logic and the ability for abstraction so that they can develop advanced analystical skills for examining the world in which they live.

###### The goals of the Mathematics Department are:

- To help students apply mathematics to practical human living, i.e. finance, geometry, algebra, preparation for SAT
- To help students to develop a keen sense of logic and ability for abstraction, i.e. Calculus, geometry proof, and algebraic operation so that they can engage in advanced intellectual activities
- To increase math literacy and inspire students to think rationally
- To help students view the created world with numeric, geometric, and algebraic insight

Emphasis is placed on developing middle school students’ problem solving skills while making mathematics fun and interesting for curious minds. High school students learn through a tradtional battery of Algebra, Pre-Calculus, and AP Calculus AB and BC. Students are also challenged outside the classroom through the math club and the American Math Competitions.

Courses: Transitions Mathematics (Grade 6 or 7) | Pre-Algebra (Grades 6-8) | Algebra (Grades 7-10), Geometry (Grades 8-11) | Algebra II (Grade 9-12) | Pre-Calculus (Grade 10-12) | AP Calculus AB (Grade 11-12) | AP Calculus BC (Grade 12)

#### Transitions Mathematics (Grade 6 or 7)

Students in Transitions Mathematics master the basic concepts of simple functions: addition, subtraction, multiplication, and division. Students will master multiplication and division of 2-digit numbers without a calculator, place value, decimals, and positive and negative numbers. Students also master work with fractions and become proficient with common fraction/decimal equivalency. Students learn how to interpret and create their own graphs and to define various geometric shapes and angles.

#### Pre-Algebra (Grades 6-8)

Pre-algebra prepares students for the study of first-year algebra. A significant portion of the curriculum is spent on reviewing and mastering basic arithmetic skills. Students also broaden and enrich their math background by exploring more abstract topics and concepts, such as proportional reasoning and the volume of three-dimensional shapes, in order to promote the higher-order thinking required in more advanced math courses. An increasing use of variables and methods of isolating the variable are key themes to the course.

#### Algebra (Grades 7-10)

The course is designed to give students a clear and thorough understanding of the foundational concepts within the field of algebra so they are prepared for their continuing study of mathematics. Students learn to relate their understanding of Pre-Algebra with the abstract ideas presented in an Algebra I curriculum. Students develop a thorough knowledge of the traditional methods for solving algebraic problems and also the ability to use these models to solve a wide range of problems.

#### Geometry (Grades 8-11)

Students are instructed in foundational geometrical concepts and learn to apply these concepts. Students hone their algebraic understanding by using algebra to solve a wide range of geometric problems. Students develop their abilities to solve varying forms of geometric proofs. This course is a bridge to many higher level courses in mathematics and provides students the knowledge and experiences to navigate successfully through the upper echelons of mathematics.

#### Algebra II (Grade 9-12)

Advanced Algebra expands on the topics of Algebra 1 and provides further development of the concept of function. Topics include: relations, functions, equations and inequalities; conic sections; polynomials; algebraic fractions (rational functions); logarithmic and exponential functions; sequences and series; counting principles and probability; and introductory trigonometry.

#### Pre-Calculus (Grade 10-12)

Pre-calculus provides a study of polynomial equations, complex numbers, functions, logarithms, circles, trigonometry, transformational geometry, probability and statistics, and sequences and series. Pre-calculus prepares students for further study of calculus. Algebra II, or placement out of Algebra II, is a prerequisite for Pre-calculus.

#### AP Calculus AB (Grade 11-12)

This is a first-semester college-level calculus course that is designed to span one year. Students have the opportunity to earn college credits if they earn a high enough score on the Advanced Placement exam at the end of this course. The instruction covers concepts of limit, derivative, definite integrals, and indefinite integrals. Students are expected to perform high-level thinking and mathematical reasoning. Lessons are taught in lectures, discovery activities, group discussions, and experiments.

*Course Highlights:*

- Two-dimensional pendulum experiment
- Curve sketching puzzles to understand graphical relationships between functions and their derivatives
- Slicing of lemon activity to understand volume of solid by rotation
- A month-long AP Exam preparation

#### AP Calculus BC (Grade 12)

This is a second-semester college-level calculus course that is designed to span one year. Students have the opportunity to earn college credits if they earn a high enough score on the Advanced Placement exam at the end of this course. The instruction covers concepts of convergence and divergence of functions, analysis of infinite series, various integration techniques, analysis of complex, hyperbolic, polar, and parametric functions, and vector calculus. Students are expected to perform high-level thinking and mathematical reasoning. Lessons are taught in lectures, discovery activities, group discussions, and experiments.

*Course Highlights:*

- Intensive review of Calculus AB
- Further discussion on linearity and infinity series
- An intensive AP Exam preparation