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## Math

### Mathematics I • Year

Darrow's Math sequence begins with this course, taught non-traditionally. Topics include number sense, linear, absolute-value, and quadratic functions. This is the first year of an integrated, student-centered, and problem-based four-year Math program. In class, students utilize the Harkness method by presenting their solutions to problems and, with the teacher’s facilitation, identify key concepts and surprising connections between mathematical ideas as they emerge.

### Mathematics II • Year

Darrow's Math sequence continues with this course, taught non-traditionally. Math II will cover a variety of topics that would be included in a traditional Geometry, Algebra II, Pre-Calculus course, as well as Calculus subtopics. This course is taken during the second year of Darrow’s integrated, student-centered, and problem-based four-year Math program. In class, students utilize the Harkness method by presenting their solutions to problems and, with the teacher’s facilitation, identify key concepts and surprising connections between mathematical ideas as they emerge.In Math II, students develop problem-solving skills that will facilitate the rest of their math career at Darrow as well as a lifelong understanding of real-world math concepts and applications. **For all 10th graders **

### Algebra II • Year

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 • Year

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 • Year

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

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

### Advanced Calculus • Year

Advanced Calculus students will continue where they left of in Calculus, beginning with conics, parametric equations, and polar coordinates. They will then continue on to an in-depth study of vectors and vector-valued functions, partial derivatives, multiple integration, and differential equations if time permits. Prerequisites: Calculus.

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