## Math Courses

Algebra is the foundational skill for manipulating quantitative relationships involving equality, inequality, and correlation. It is a symbolic language that also allows one to solve problems from the physical, natural, and business worlds. Students strengthen their understanding of algebra when they continuously make this connection between abstraction and real-world contexts through their use of equations, tables, graphs, diagrams, and narratives. The primary topics in this course include: terminology and properties of the set of real numbers; creating, simplifying, and translating algebraic expressions; writing, solving, and graphing linear equations (including proportions and inequalities); the rules and properties of linear functions; systems of linear equations; performing operations with polynomials, especially factoring; solving absolute value equations; and an introduction to solving and graphing quadratic functions. Students are assessed primarily through lectures, nightly homework assignments, and quizzes and tests. At Darrow, Algebra I is the first in the series of three required yearlong courses, typically followed by Geometry and then Algebra II.

Geometry is essential as a means to giving students the quantitative skills to describe and measure the 2D and 3D world. It is a fundamental part of understanding such diverse applications as visual arts, navigation, construction, design, and architecture. It is also the classic manner of fostering the mathematical skill of logical reasoning and proof. And it provides a visual means of reinforcing and enhancing the algebraic skills that were stressed in Algebra I and will be expanded upon in Algebra II. Thus, at Darrow, Geometry is the second in the series of three required year-long courses. The primary topics in this course include: a review of the properties of points, lines, angles, and polygons; an introduction to logical statements and proof; parallel and perpendicular lines; triangle congruence; ratios and proportions; right triangle trigonometry; properties of quadrilaterals; properties of circles, arcs and chords; two dimensional measurement involving perimeter, circumference, and area; and properties of three-dimensional solids, as well as measurement of these solids involving surface area and volume. In addition to lectures, nightly homework assignments, quizzes, and tests, students are assessed through lab exercises involving Geometer’s Sketchpad, a computer drawing program that can be used both analytically and creatively.

Algebra II is distinguished from Algebra I in two ways. First, it emphasizes an increased level of proficiency in the fundamental skill set of manipulating variables and equations, such as graphing, factoring, and simplifying. Second, it stresses the central importance of functions in understanding any quantitative relationship. Each new unit covers a different “family” of functions and explores the overlapping ways of describing their properties, graphing their key points and end behavior, solving their roots and modeling their applications in real-world phenomena. The primary topics in this course include: a review of linear functions and inequalities; solving systems of linear equations graphically, algebraically, and with matrices; quadratic functions; higher-degree polynomial functions; and rational exponent and radical functions. Depending on the class, time is spent on exponential and logarithmic functions, as well as an introduction to the unit circle and trigonometric functions. In each unit, the TI-84 graphing calculator is used extensively, both as a utility for calculations as well as a tool for exploring function properties. At Darrow, Algebra II is the last in the series of three required year-long courses, typically preceded by Algebra I and then Geometry. Most students continue on to our higher-level elective courses, depending on the year they complete Algebra II, as well as their post-high school goals and interests. Students who successfully complete Algebra II are well-prepared for the mathematics portion of the SAT.

Pre-Calculus is an in-depth study of functions and ways in which they can be manipulated. Course topics include, but are not limited to: combinations and composition of functions, graphing transformations, exponential and logarithmic functions, trigonometry, rational functions, conic sections, and an introduction to limits. Pre-Calculus prepares students for Calculus by providing them with greater understanding of fundamental concepts of Algebra.

Prerequisite: Algebra II

Calculus is an advanced mathematics topic that requires abstract thought. The first semester is devoted to the derivative as defined by the slope of a curve; students begin by investigating limits and use this concept through formal proofs to define derivative. As the semester continues, students look at increasingly complex ways in which to take derivatives of various common functions. During the second semester, students investigate the integral, as defined by area under a curve. This study begins with a look at Riemann sums and antiderivatives, and progresses to more complex ways in which to take integrals, including substitution, integration by parts, algebraic identities, and improper integrals. The second semester ends with the study of practical applications of the integral.

Prerequisite: Pre-Calculus or permission of Math Department Chair.

This is a one-semester course which must be taken in conjunction with Statistics. In Probability, students will learn about questions such as: What is the probability of winning the lottery? What is the probability that my child will have blue eyes? and What is the probability of a sports team winning if it goes into overtime? Together the class will discover the answers to these questions, as well as more that involve combinations, permutations, expected value, and how they relate to various other topics in mathematics.

Prerequisite: Algebra II

Statistics is the mathematical science of collecting, describing, and analyzing data from the real world. The first half of the semester is devoted to descriptive statistics, which includes topics such as measurements of central tendency and dispersion, normal distribution, random sampling, coefficient of correlation, an introduction to linear regression, and discussions of causation vs. causality. The second half of the semester focuses on inferential statistics, which are used to test hypotheses and make generalizations about the strength of the data sample. Students will analyze and discuss current events in the media that rely on statistical information for their central message, and gain an understanding of how to both consume and present statistical information.

Prerequisite: Algebra II

In the year long course we will be studying many advanced topics. These may include: more advanced differential equations, parametric equations, polar equations, vectors, more advanced applications of derivatives and antiderivatives, advanced matrix algebra, more advanced series and sequences, and more that will be decided amongst the class.

This course is open to those who have completed Calculus.