# Mathematics

The math department’s goal is for students to develop the necessary perseverance to work through challenging problems using critical thinking while taking personal responsibility for their individual learning. In addition to competency in math fundamentals, classes encourage an appreciation for the study of math and its applications in the world.

The math program is rigorous but flexible, serving the needs of students of all abilities. Students from any freshman math class are given the opportunity to accelerate eventually into Advanced Placement Calculus classes. The curriculum is designed to give students a solid foundation in math so they can succeed in Calculus and college level math. Calculators are only used in advanced classes.

- Algebra I
- Intermediate Algebra
- Freshman Geometry
- Geometry
- Algebra II/Trigonometry
- Algebra III/Trigonometry
- Precalculus
- Introduction to Calculus
- AP Calculus AB
- AP Calculus BC
- AP Statistics
- Multivariable Calculus

## Algebra I

The course emphasizes a multi-representational approach with concepts and problems expressed according to the Rule of 4: (1) graphically (2) numerically (3) analytically (4) verbally. Topics include order of operations, evaluation of expressions, using rules of exponents, radical expressions and equations, solving and graphing linear equations and inequalities, modeling with word problems, quadratic functions, the quadratic formula, polynomial, rational and exponential functions, ratio, proportion, elementary statistics and probability. (1 Credit) Placement by Math Department

## Intermediate Algebra

This course builds upon core algebraic concepts and moves at an accelerated pace through the study of expressions, equations, and functions to prepare students for advanced mathematics courses. Topics including linear, quadratic, exponential, logarithmic, polynomial, and trigonometric functions will be studied to provide the foundation needed for the future study of calculus. Applications to real-world problems will be studied in conjunction with each unit when appropriate. A TI-84 graphing calculator is required. (1 Credit) Prerequisites: Placement into this course is determined by the chair of the math department and is based on the student’s performance on the Math Placement Exam.

## Freshman Geometry

Freshmen Geometry covers a mixture of Euclidean geometry and algebra. The Geometry portion of the course includes definitions, axioms, postulates, angle and line relationships, properties of parallel lines, congruence theory, triangles, Euclid’s proof of the Pythagorean Theorem, circles, perimeter and area of plane figures, surface area and volume of solids, similarity, ratio, proportion, geometric constructions and algebraic applications. This course has a primary focus on geometric proof, both direct and indirect. A straightedge and compass are required.

The algebra section of the course covers a variety of Algebra II/Trigonometry topics including, but not limited to, radicals, factoring, rational and piecewise functions, systems of equations, and trigonometry. (1 Credit) Prerequisites: Placement into this course is determined by the chair of the math department and is based on the student’s performance on the Math Placement Exam.

## Geometry

This first course in geometry uses Euclid’s Elements as the text. Topics include definitions, axioms, postulates, angle and line relationships, properties of parallel lines, congruence theory, triangles, Euclid’s proof of the Pythagorean Theorem, circles, perimeter and area of plane figures, surface area and volume of solids, similarity, ratio, proportion, geometric constructions and algebraic applications. This course has a primary focus on geometric proof, both direct and indirect. A straightedge and compass are required. (1 Credit) Prerequisites: Algebra 1 or Intermediate Algebra; Placement by Math Department

## Algebra II/Trigonometry

This course is a continuation of the study of algebra focusing on the study of functions and an introduction to the study of trigonometry. With the help of the graphing calculator, we will examine a wide variety of functions, including polynomial, rational, exponential, logarithmic, and trigonometric functions. In addition to understanding the graphs of functions, we will also study modeling and applying functions with practical applications. Solving equations and systems of equations will be integral to the course of study this year. Other topics include factoring, exponents, radicals, solving polynomial equations, polynomial division, elementary probability, inverse functions, and complex numbers. During our study of trigonometry, the course will include trigonometric ratios, graphing trigonometric functions, solving trigonometric equations, using trigonometric identities, transformations, inverse trigonometric functions, and the Laws of Sines and Cosines. A TI-84 graphing calculator is required (1 Credit) Prerequisites: Successful completion of Geometry or by placement exam administered by the Math Department.

## Algebra III/Trigonometry

This is an accelerated course of study designed to help students master precalculus mathematics. Material covered in this course includes traditional advanced algebra and trigonometry topics, plus material from our precalculus course of study. This course emphasizes a multi-representational approach, with concepts and problems expressed according to the “rule of four.” That is, students will express functions and other mathematical concepts (1) graphically, (2) numerically, (3) analytically, and (4) verbally. A TI-84 graphing calculator is required. (1 credit) Prerequisites: Successful completion of Geometry or by placement exam administered by Math Department; Placement by Math Department chairperson.

## Precalculus

The course emphasizes a multi-representational approach with concepts and problems expressed according to the Rule of 4: (1) graphically (2) numerically (3) analytically (4) verbally. An exploration at a greater level of abstraction of the elementary functions (linear, quadratic, polynomial and rational) and their transformations, the transcendental functions: exponential, trigonometric functions and their inverses and logarithmic functions, composition, asymptotic behavior, polar coordinates, complex numbers, solving and graphing systems of equations and inequalities, elementary probability and statistics, and modeling with word problems. A TI-84 graphing calculator is required. Prerequisites: Algebra II/Trig. Placement by Math Department.

## Introduction to Calculus

This course is divided into two parts. Part I is a study of the elementary functions – polynomial, rational, linear, logarithmic, trigonometric and inverse trigonometric – and rates of change – with an eye towards calculus. Topics are examined according to the Rule of 4: (1) graphically (2) numerically (3) analytically (4) verbally. Part II is a beginning study of the calculus of a single variable. Topics include limits, continuity, derivatives, and anti-derivatives. The use of technology is an important part of this course. A TI-84 graphing calculator is required. (1 Credit) Prerequisites: Successful completion of Algebra III/Trig or placement by the Math department.

## AP Calculus AB

The course follows the Advanced Placement AB Calculus syllabus. The course emphasizes a multirepresentational approach with concepts and problems expressed according to the Rule of 4: (1) graphically (2) numerically (3) analytically (4) verbally. Topics include limits and continuity, differentiation and integration with applications, the Fundamental Theorem of Calculus, numerical approximations and elementary differential equations. The use of technology is an important part of this course. A TI-84 graphing calculator is required. Students are required to sit for the AP Exam. Prerequisites: Completion of Algebra III or Introduction to Calculus: Placement by the Math Department.

## AP Calculus BC

This course covers all the topics in the Advanced Placement BC Calculus syllabus and goes beyond. The course emphasizes a multi-representational approach with concepts and problems expressed according to the Rule of 4: (1) graphically (2) numerically (3) analytically (4) verbally. Topics include vectors and vector-valued functions, parametric equations, polar functions and polar area, differentiation, integration and the Fundamental Theorem of Calculus, improper integrals, sequences and series, Taylor expansions with Lagrange Error Bound, logistic differential equations.

Topics covered beyond the BC syllabus include integral applications to physics and engineering, biology and economics – work, electricity, energy, hydrostatic force, moments, centers of mass, Poiseuille’s Law, cardiac output, consumer surplus, present and future value – surface area, probability, advanced techniques of integration, epsilon-delta definition of limit, curvature, modeling using differential equations, predator-prey systems and Fourier series. A TI-84 graphing calculator is required. Students are required to sit for the AP Exam. (1 credit) Prerequisite: Completion of AB Calculus: Placement by the Math Department

## AP Statistics

The Advanced Placement Statistics course of study introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes, as follows.

1. Exploring Data. Describing patterns and departures from patterns.

2. Sampling and Experimentation. Planning and conducting a study.

3. Anticipating Patterns. Exploring random phenomena and using probability.

4. Statistical Inference. Estimating population parameters and testing hypotheses.

All students participating in this course will take the nationwide AP Statistics Exam in the spring. Students who successfully complete the course and the AP Exam may be eligible to receive credit, advanced placement, or both for a one-semester introductory college statistics course. A TI-84 graphing calculator is required. (1 credit) Prerequisites: Successful completion of Algebra II or III, and approval of the Math Department chairperson.

## Multivariable Calculus

Multivariable Calculus, also known as Calculus III, is an extension of the concepts of single variable calculus to several variables. In single variable calculus, students are accustomed to finding the area under a curve. In multivariable calculus, students will find the volume under a surface. Instead of evaluating single integrals, students will evaluate double and triple integrals. Students will do a lot of graphing in threedimensional space, and most of the topics covered will be explored in three-dimensions.

Topics of the class include vectors and vector valued functions in 2-space and 3-space, cylindrical and spherical coordinates, partial derivatives, limits, continuity, differentiability, directional derivatives, the gradient, maxima and minima, optimization using Language multipliers, parametric surfaces, double and triple integrals, change of variables and the Jacobian, line integrals, vector fields, surface integrals and the classical theorems of Green, Gauss and Stokes. (1 credit) Prerequisites: AP Calculus BC

## Faculty

Mr. Patrick Butcher

Mr. John DeCaro

Mr. Kevin Dorn

Mr. Tim Wisecarver