# Mathematics

The study of math develops and refines critical-thinking skills. Logical reasoning, problem solving, and the ability to organize information enhance each girl’s ability to think critically, and these skills become tools for lifelong success. The math program prepares students for success in college math classes by giving them a strong foundation in mathematics, including reasoning, problem-solving skills, and the ability to communicate mathematical ideas verbally and in writing. We provide four years of sequential instruction; our goal is to have every girl reach her maximum potential as she moves through our program. We coordinate with the science teachers to teach math skills required in physics and chemistry. Our Advanced Placement Calculus class allows the science department to offer calculus-based AP Physics.

The math sequence includes Algebra, Geometry, Intermediate Algebra, and Precalculus. Honors sections are available for Geometry, Intermediate Algebra, and Precalculus. Senior year electives include AP Calculus AB/BC (for students in the Honors Program), AP Statistics, Introduction to Derivatives, and Financial Algebra. While the graduation requirement is three years of math with a fourth year of either math or science, nearly all students take four years of math, and some technically complete a fifth by taking two math classes in senior year.

All students use graphing calculators, 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 4th year in either math or science

**Course of study by year:**

Freshman: Algebra 1 or Geometry

Sophomore: Geometry or Intermediate Algebra

Junior: Intermediate Algebra or Pre-Calculus

**Mathematics Department Chair: **** Dolores Pasciak**

**Course Descriptions**

Including current electives, though not all

elective courses are offered each year or trimester.

**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

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 Trig

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 Trig

Topics of Precalculus is a full year course in which students study trigonometric, polynomial and rational functions, analytic trigonometry, vectors, parametrics, conics, systems of equations, matrices, sequences, and probability. Students will have mastered the following skills by the end of the year: identifying properties of trigonometric graphs, proving trig identities, solving trig equations, converting between radians and degrees, working with polar coordinates, and solving a system of 3 equations with matrices.

**Introduction to Derivatives**

Prerequisite: successful completion of Topics of Precalculus or Honors Precalculus

Introduction to Derivatives 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. Appropriate technology, including manipulatives and graphing calculators, will be used regularly for instruction and assessment. 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. There are two levels of AP Calculus: AB and BC. 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. AP Calculus BC applies the concepts of limits, derivatives and integrals to series and sequences and parametric, vector and polar functions. Currently, all AP Calculus students meet together to learn the first set of material. After mastering derivatives, the AP Calculus BC students meet for additional class time to cover applications of the other functions mentioned above. 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: student must be a senior who has successfully completed Intermediate Algebra or Honors Intermediate Algebra with Trig

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, allowing them the opportunity to view the world of finance through a mathematical lens. The mathematical formulas, functions, and pictorial representations used assist students in making sense of the financial world around them and equip them with the ability to make sound financial decisions. The mathematics topics contained 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.*