# Mathematics

SEM's math program prepares students for success in college math classes by providing them with a strong foundation in mathematics, developing and refining students' critical thinking skills through reasoning, problem-solving, and oral and written communication of mathematical concepts. The math curriculum is coordinated with the science curriculum to teach the necessary math skills required for Physics and Chemistry.

All students use graphing calculators (T1-84 Plus), and instruction is supplemented by the use of interactive white boards in all classes. Student laptops provide individual access to a variety of software that supports instruction. Electronic notebooks allow teachers to view and comment upon student notes and written assignments.

**Departmental requirements:** 3 years and a fourth year in either math or science. Students may also choose to take two math electives senior year.

**Course of Study by Year:**

Freshman: Algebra 1 or *Geometry

Sophomore: Geometry or *Intermediate Algebra

Junior: *Intermediate Algebra or *Pre-Calculus

*Honors sections available

**Mathematics Department Chair: **** Dr. Dolores Pasciak**

**Course Descriptions**

Includes electives, though not all elective courses are offered each year or trimester. Students may also enroll in additional math electives and AP's offered through SEM's membership in the Online School for Girls.

- Algebra 1
- Geometry
- Honors Geometry
- Intermediate Algebra
- Honors Intermediate Algebra with Trigonometry
- Honors Precalc
- Topics of Precalculus
- Introduction to Calculus
- AP Statistics
- AP Calculus AB and BC
- Financial Algebra A, B, and C

## Algebra 1

Algebra 1 is a full year course that includes the following topics: equations and inequalities, systems of equations and inequalities, linear and quadratic functions, exponents and exponential functions, polynomials and factoring, radical expressions and equations, and rational expressions and functions. As with all SEM math courses, a TI-84 Plus calculator is required.

## Geometry

Geometry is a full year course that is an algebra-based approach to geometry. The algebra topics covered include: solving equations, factoring, operations with polynomials, operations with radicals, rational expressions, and systems of equations. These topics are taught with the understanding that this may be some students’ first exposure to the topics and therefore more time is spent on these fundamentals. The geometry topics covered are graphing linear equations, angle relationships with parallel lines, right triangle trigonometry, proving triangles similar and congruent, relationships within triangles, properties of quadrilaterals, circles, area, surface area and volume.

## Honors Geometry

Honors Geometry covers the same topics as in Geometry, but moves at a much faster pace and explores more challenging application problems. The algebra topics are reviewed in Honors Geometry with the expectation that students already have a basic understanding of that material from a previous Algebra course. Due to the accelerated pace of the class, more time is available at the end of the year to explore additional topics, including, but not limited to, probability and statistics, transformations, and parabolas.

## Intermediate Algebra

Prerequisite: successful completion of Geometry

This full year course continues the study of the topics started in Algebra 1 and Geometry. Students study linear systems of equations, quadratic functions, complex numbers, conic sections, matrices, polynomial functions, radical functions, rational exponents, rational functions, and logarithmic and exponential functions.

## Honors Intermediate Algebra with Trigonometry

Prerequisite: minimum grade of A in Geometry or minimum grade of B- in Honors Geometry and teacher recommendation.

Students in Honors Intermediate Algebra with Trig cover the same topics as in Intermediate Algebra, but move at a much faster pace and explore more challenging application problems. Honors Intermediate Algebra with Trig also includes the study of trigonometry, including the unit circle, trigonometric equations, trig identities, and trig functions.

## Honors Precalc

Prerequisites: minimum grade of B- in Honors Intermediate Algebra with Trigonometry and teacher recommendation.

Honors Precalculus is a full year course which focuses on the study of the twelve basic functions and their graphs. Students study linear, trigonometric, rational and polynomial functions, conic sections, systems of equations, matrices, parametric equations, vectors, motion, sequences, series, statistics and the concept of limits, which is a bridge to Calculus. Honors Precalculus also focuses on the applications of each topic that is covered, which is an essential skill in Calculus. Students are encouraged to approach problems in a variety of ways: algebraically, graphically, numerically, and verbally.

## Topics of Precalculus

Prerequisite: successful completion of Intermediate Algebra or Honors Intermediate Algebra with Trigonometry.

Topics of Precalculus is a full year course in which students study trigonometric, polynomial and rational functions, analytic trigonometry, vectors, parametrics, polar coordinates, conics, systems of equations, matrices, sequences, and probability.

## Introduction to Calculus

Prerequisite: successful completion of Topics of Precalculus or Honors Precalculus.

Introduction to Calculus is a year-long, academically rigorous course that is designed to support topics studied in calculus. This course will provide opportunities for students to be involved in experiences that apply concepts of Calculus. These concepts include: functions, graphs, limits, differentiation, and applications of differentiation and integration. This course encourages geometrical, numerical, verbal, and analytic expression of concepts, results and problems, while incorporating appropriate technology, manipulatives, and graphing calculators. This course is not an AP Calculus class, however it is an introduction to Calculus and would be suited for someone who is looking to take Calculus I as a freshman in college.

## AP Statistics

Prerequisite: minimum grade of B- in Honors Precalc or A- in Precalc Topics.

AP Statistics is a full year course that introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, planning a study, anticipating patterns, and statistical inference. Students learn to use computer software programs for statistics and their graphing calculators to draw graphs and analyze data. Students are required to take the AP exam.

## AP Calculus AB and BC

Prerequisite: minimum grade of B+ in Honors Precalculus for AP Calculus AB or minimum grade of A- in Honors Precalculus for AP Calculus BC.

This full year course studies the four main topics of Calculus: limits, derivatives, integrals and definite integrals, as well many applications of these operations to word problems. AP Calculus AB is the equivalent of the first semester of college calculus, while AP Calculus BC covers the material in the first two semesters of college calculus. Currently, all AP Calculus students meet together to learn the initial material. After mastering derivatives, the AP Calculus BC students meet for additional class time to cover applications of limits, derivatives, integrals, series and sequences, parametric functions, vectors, and polar functions. Both courses end with an AP exam that consists of multiple choice and short answer questions. AB and BC students take separate exams, but the BC students get separate scores for the AB and BC portions, allowing them to earn credit for only the first semester if they didn’t master all of the topics.

## Financial Algebra A, B, and C

Prerequisite: Successful completion of Intermediate Algebra or Honors Intermediate Algebra with Trigonometry.

Financial Algebra is a college preparatory mathematical modeling course that is algebra-based, applications-oriented, and technology-dependent. It incorporates topics and skills from Algebra and Geometry, combining algebraic and graphical approaches, to connect math to students’ everyday life, equipping them to make sound financial decisions. The mathematics topics in this course were developed using the Common Core State Standards in Mathematics and the NCTM Curriculum and Evaluation Standards, and are introduced and applied in an as-needed format in the financial settings covered. Students are encouraged to use a variety of problem-solving skills and strategies in real-world contexts, and to question outcomes using mathematical analysis and data to support their findings. It provides students a motivating, young-adult centered financial context for understanding and applying the mathematics they are guaranteed to use in the future. Each trimester of Financial Algebra is independent of the others, so students may take one, two, or all three trimesters: Financial Algebra A: Banking Services and Consumer Credit, Financial Algebra B: Automobile Ownership and Employment Basics, Financial Algebra C: Independent Living and Preparing a Budget.