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Mathematics

We believe that inquiry and the construction of knowledge are essential elements of each student’s educational experience. Park’s mathematics program provides opportunities for students to become more mathematically aware, capable, and confident.

Mathematics enables students to develop a better understanding of our world, to create and discover patterns and ideas, and to appreciate a compelling form of inquiry and argument. Making the connections between different areas of mathematics is a major component of our department’s program. We believe the study of mathematics as a unified body of knowledge that emphasizes problem solving and generalization. Applications will engage students and promote their ability to communicate and reason mathematically. To these ends, all Park students take courses that allow them to become better problem-solvers. Students learn algebra, geometry, trigonometry, and other topics through a discovery process and are routinely expected to apply these concepts in novel situations.

REQUIREMENTS

Two years of mathematics are required for graduation. However, most Park students complete three years of mathematics, and almost every senior takes at least one elective. Students cover the material on the SAT Subject Test in mathematics by the end of 11th grade. 

Students are placed in appropriate mathematics classes by the Mathematics Department and are encouraged to visit the Mathematics/Science Office for assistance from faculty members at any time; peer tutors are also available. 

A TI-83+ or TI-84+ graphing calculator is required for all classes. 

Note: Our goal is for students to take the math courses most appropriate for them. Each level within the core curriculum in grades 9, 10, and 11 will appear as Math 9, Math 10, and Math 11 on student transcripts.

Full Year Courses 

Math 9

Grade: 9 

Mathematic courses in the 9th Grade explore algebra, geometry, and the connections between the two. Throughout, there is an emphasis on problem solving, reasoning, and proof. Students are sectioned by interest and ability, with the different classes varying in pace and level of abstraction. Topics for more advanced sections include Euclidean geometry and unit-circle trigonometry. Topics for all 9th Grade sections include algebra, coordinate geometry, systems of equations, trigonometry, quadratic functions, and combinatorics.

Math 10-1

Grade: 10 

Students expand upon the understanding of algebra and geometry gained in Math 9. They explore exponential and logarithmic functions, combinatorics, sequences and series, graphical transformations, polynomials and rational functions, circular motion and the trigonometric functions, trigonometric identities, complex numbers, and begin the study of infinitesimal processes.

Math 10-B

Grade: 10 

Students expand upon the understanding of algebra and geometry gained in Math 9. They explore exponential and logarithmic functions, combinatorics, sequences and series, graphical transformations, polynomials and rational functions, circular motion and the trigonometric functions, trigonometric identities, and complex numbers. Students will continue to review and practice algebra skills throughout. Those completing this course will likely begin studying calculus in spring semester of their junior year.

Math 10-C, Math 10-D

Grade: 10

These courses examine algebra, geometry, and discrete mathematics but in greater depth than the previous year, with a continuing emphasis on developing students’ ability to solve problems through a variety of approaches. Topics may include graph theory, geometric sequences and series, radicals and laws of exponents, the algebra of rational expressions, exponential functions, further study of quadratic equations and complex numbers, statistics, and synthetic geometry.

Calculus (Acc)

Grades: 11-12

Prerequisite: Math 10-1 or permission of current math teacher.

Concepts and applications of differential and integral calculus are presented. For juniors, a month-long final project, requiring considerable independent work, concludes the course. Students who complete the course successfully are prepared to take the Advanced Placement Calculus AB exam.

Math 11-2, Math 11-3, Math 11-4                                    

Grade: 11

These courses emphasize applications of mathematics and may include the following areas: algorithms, logarithms, trigonometric functions, transformations of functions, trigonometric identities, probability and counting methods, and/or statistics.

Advanced Calculus (Acc)

Grade: 12

Prerequisite: Calculus

In Calculus, students are introduced to the concepts surrounding limits, and learn how they can be applied to develop the theory of differentiation (rates of change) and integration (accumulation), which culminates in the fundamental theorems of calculus. Advanced Calculus continues to develop the techniques of differentiation and integration. In this curriculum, the class plans to cover indeterminate forms; logarithmic and implicit differentiation; related rates; integration by parts; partial fraction decomposition; improper integrals; parametric and polar equations; vector calculus as it applies to position, velocity, and acceleration; differential equations and population models; sequences; Taylor and power series. These topics should cover the vast majority of the Advanced Placement Calculus BC exam, and will provide a strong foundation for students interested in taking it. In addition to the aforementioned core topics, the class may often take occasional tangents into other areas of higher mathematical study. These topics may include different systems of numbers; different sizes of infinity; mathematical physics; multivariable calculus; and Fourier series.

linear algebra

Grades: 9-12

Prerequisite: permission of the department.

Linear Algebra is a wonderful field of mathematics: it lives squarely in that sweet spot where beauty and “extreme usefulness” overlap. The subject begins with a deep exploration of strategies for solving systems of linear equations, moving to the powerful realm of vectors, vector spaces, and linear transformations. Applied linear algebra empowers much of modern computational sciences such as Google’s famed PageRank algorithm, computer graphics and animations, and Computerized Axial Tomography (as in CAT scans). This class will provide a balance of theory and application and computation.

Fall Semester Courses

Discrete Mathematics I

Grades: 11-12

Discrete Mathematics is a contemporary branch of mathematics that focuses on various problems, topics, and algorithms that often have whole-number outcomes. Topics are grounded in real applications. This course focuses on the mathematical perspective of fairness, value, and individual perception. Students will study a wide variety of voting methods and examine “fair division” algorithms through the lens of entitlement and estates, apportionment, and an array of continuous cases.

Functions and Calculus I

Grade: 12

Prerequisite:  Math 10-1, 11-2, or permission of the current mathematics teacher.

Students begin by considering the “tangent line problem” and go on to study limits and develop a definition of the derivative, eventually applying derivative to real-life problems. Along the way, they examine polynomial and rational functions, using the language and techniques of calculus to help understand the graphs of these functions.

Statistics I

Grades: 11-12

Students are introduced to the four key components of data exploration: observing patterns and departures from patterns, planning a study (deciding what and how to measure), anticipating patterns (producing models using probability and simulation), and statistical inference (confirming models).

Spring Semester Courses

Discrete Mathematics II

Grades: 11-12

Discrete Mathematics II will focus primarily on applications that can be analyzed with the help of matrices. After a quick study of what matrices are, and how they work, students will use them as tools to study a variety of applications. They will model and predict population growths, take an introductory study into cryptography, and study expected probabilities through board game construction. (Note: Discrete Mathematics I is not a prerequisite.)

Functions and Calculus II

Grades: 12

Prerequisite:  Functions and Calculus I.

Students continue to use the lens of calculus to study functions and their graphs. Topics may include optimization problems, related rate problems, the area under a curve, the definition of an integral, and the Fundamental Theorem of Calculus.

Statistics II

Grades: 11-12

Prerequisite:  Statistics I.

Students explore statistical inference, with an emphasis on estimating the parameters of a population distribution and testing hypotheses about a population parameter. The probability models used in these inference situations are the normal distribution (bell curve), the t-distribution, and the chi-square distribution. Depending on time and interest, students may conduct a project in which they collect and analyze data.