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 is 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 mathematics for all four of their years in the Upper School. 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 Mathematics Courses 

Math 9

Grade: 9 

Mathematics 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. 

Math 9-1

This course explores advanced algebraic and geometric content through an emphasis on problem solving, reasoning, and proof. Topics include graph theory, laws of exponents and radicals, the algebra of rational expressions, quadratic equations, Euclidean and coordinate geometry, and unit-circle trigonometry.

Math 9-2, 9-3, 9-4

These courses explore algebra, geometry, and the connections between the two, with an emphasis on developing students' ability to solve problems through a variety of approaches. Topics include algebra, coordinate geometry, systems of equations, trigonometry, quadratic functions, and combinatorics, with a consistent focus throughout on reasoning and proof.

Math 10

Grade 10 - Required

This course is required at one of three levels: Math 10-1, Math 10-2, or Math 10-3.

Math 10-1

Students expand upon the understanding of algebra and geometry gained in Math 9-1. 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 10-2 and 10-3

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, polynomial functions and complex numbers, statistics, and Euclidean geometry.

Math 11C, Math 11D

Grade 11

These courses emphasize applications of mathematics and may include the following areas:  algorithms, exponential functions, logarithms, trigonometric functions, transformations of functions, polynomial functions, combinatorics and probability, and further topics in geometry.

Advanced Calculus (Accelerated)

Grade 12

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 our 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 (AP) 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.

Prerequisite: Calculus

Advanced Elective: Mathematical Modeling

Grades 9-12

In this course, students will learn and use advanced mathematical topics and methods such as difference equations, dynamical systems, geometric similarity, model fitting and assessment, graph theory, dimensional analysis, probabilistic modeling, linear algebra, and linear programming. They will study problems motivated by population biology, chemistry, finance, economics, and physics, and through these problems will develop mathematical tools that are both beautiful and useful.

Prerequisite: Permission of the department

Calculus (Accelerated)

Grades 11-12

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 (AP) Calculus AB exam.

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

Calculus and Modeling

Grade 11

This course emphasizes mathematical modeling in a wide variety of contexts, introducing the major concepts of  differential and integral calculus as tools. Students who complete this course will be ready for an accelerated senior-year course in which they complete the content in a typical first-semester calculus course.

Prerequisite: Math 10B

Fall Semester Mathematics Courses

Calculus I

Grade 12

Students will begin the course by considering the "tangent line problem" and go on to study limits and develop a definition of the derivative. At the same time, they will examine rational functions, using the language and techniques of limits to help understand the graphs of these functions. Before applying the derivative to real-life problems, students will learn a variety of techniques for taking derivatives, all the while strengthening their algebra skills.

Prerequisite: Math 11-2 or permission of the department

Discrete Mathematics I

Grades 10-12

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. We 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.

Statistics I

Grades 10-12

Students study topics in descriptive statistics: good and bad ways to display data, comparing data sets according to center, shape, and spread, the normal distribution, sampling techniques and survey design, simulations, and correlation.

Spring Semester Courses

Calculus 2

Grade 12

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

Discrete Mathematics 2

Grades 10-12

Discrete Mathematics 2 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 1 is nota prerequisite.)

Statistics 2

Grades 10-12

Topics may include probability, experimental design, confidence intervals, and hypothesis testing.

Prerequisite: Statistics 1