I can honestly say that coming to Emma Willard is the best decision I ever made. It has helped me not only to strengthen my passion for learning and surrounded me in an environment with others who share that passion, but also allowed me to grow in incredible and unforeseen ways.

Jillian, Emma girl

**M-125 Algebra I**

Year 1 unit

In this course, students expand their notion of a variable and connect it to algebraic and problem-solving techniques. This is a comprehensive course that lays the foundation for both Algebraic Geometry and Algebra II and Trigonometry. Topics include signed numbers, radicals and radical operations, linear equations, systems of linear equations, exponents, the quadratic formula, polynomials, and factoring. Students in this course learn to translate verbal statements into mathematical statements, clarify procedural questions, solidify arithmetic skills, and comprehend the abstraction of the coordinate plane. Class time is used for discussion, developing initiative in problem-solving and perfecting study skills.*Open to: 9/10***M-225 Algebraic Geometry**

Year 1 unit

This course uses a problem-based curriculum that enables students to investigate and prove geometric concepts. Topics include distance in a coordinate plane, the Pythagorean Theorem, angles, parallel and perpendicular lines, planes, vectors, properties of triangles, properties of quadrilaterals, regular polygons, transformations, congruence, similarity, right triangle trigonometry, circles, area, perimeter, volume, and surface area. Proficiency in basic algebra is expected and necessary. Geometry students are active learners, engaging the problem-solving skills learned in Algebra I. The course stresses the connections between algebra and the geometric topics covered. Each student develops the practice of self-assessment so that she is better able to critique her understanding. Class discussion centers around problem sets, and students employ graphing calculators, dynamic computer software, the Internet, and journals as tools in the learning process.*Prerequisite: Algebra I (M-125)**Open to: 9/10/11***M-315 Functions and Trigonometry**

Year 1 unit

This course is a one-year algebra and trigonometry course that satisfies the mathematics graduation requirement for juniors and seniors. Its syllabus includes topics to prepare students for mathematical applications at the college level. If recommended by the department, a student may follow this course with Algebra II and Trigonometry (M-325). If M-315 is taken before the junior year, another year of mathematics must be taken to fulfill the graduation requirement. This course does not serve as a prerequisite for Precalculus (M-450).*Prerequisite: Recommendation of the department**Open to: 10/11/12***M-325 Algebra II and Trigonometry**

Year 1 unit

This course continues to develop independent problem-solving while expanding skills to solve, graph and interpret linear, absolute value, and quadratic equations, as well as higher-degree polynomial functions, inverse functions, logarithmic functions, rational functions, and trigonometric functions. Functions introduce an abstract thought process, and the focus is on solving problems and reading carefully in order to build skills. At this level, students are expected to reason independently and formulate questions based on insights into applications of the algebra previously studied.*Prerequisite: Algebraic Geometry (M-225)**Open to: 9/10/11/12***M-420 Applications of Finite Mathematics**

Year 1 unit

This elective course is designed for students who are interested in learning mathematical modeling techniques that can be applied to real-world problems. Through analysis of applications and the use of technology, students learn the major concepts and tools for collecting, organizing, analyzing, and drawing conclusions from data. This course does not focus on topics from algebra and geometry; rather, after a 1-2 week review of algebra and geometry topics covered on the SAT, the course moves on to topics including set theory, voting and apportionment methods in U.S. history, a review of major functions, combinatorics, probability and statistics, graph theory, and a unit on personal finance including the cost of borrowing money. Assessments include tests and quizzes along with two major projects. This course does not prepare students for taking Precalculus in future years.*Prerequisite: Algebra II and Trigonometry (M-325) or Functions and Trigonometry (M-315) and recommendation of the department**Open to: 10/11/12***M-430 College Algebra and Its Applications**

Year 1 unit

This course explores four major units: functions and their graphs, with an emphasis on transforming functions; exponential and logarithmic functions; trigonometry and trigonometric graphs; and logic, reasoning, and SAT prep, which includes a substantial geometry review. In between these major units, and woven throughout the course, students do mini-projects and read books that apply math to daily life. Although the course is based on traditional algebraic and graphical problem solving, it emphasizes real-world applications wherever possible, including log-log plots, harmonic motion, circular motion, logistic curves, and population growth. Students solve problems daily and keep a semi-weekly mathematical journal. Students who take this course may take Precalculus the following year.*Prerequisite: Algebra II and Trigonometry (M-325) or Functions and Trigonometry (M-315) and recommendation of the department**Open to: 10/11/12***M-450 Precalculus with Statistics**

Year 1 unit

This course is designed for students who have completed the study of basic trigonometry and algebra. In Precalculus, students are introduced to different areas of study in higher-level mathematics. Topics include advanced trigonometry, vectors and their applications to physics, functions, modeling, statistics, analytic geometry, series, and limits. The course assumes that students employ effective questioning skills: not just procedural, but analytical. In addition, students apply a range of methods when problem-solving. This course involves significant independent work, and students are responsible for assessing their progress, seeking help in the Math Learning Center as necessary.*Prerequisite: Algebra II and Trigonometry (M-325) and recommendation of the department**Open to: 10/11/12***M-460 Precalculus with Non-Routine Problems**

Year 1 unit

This course is designed for students who have successfully completed the study of trigonometry and algebra. Students study the various topics of precalculus which include advanced trigonometry, vectors and their applications to physics, functions, probability, statistics, analytic geometry, and sequences and series. In addition, students examine a large number of non-routine problems which will require creative problem-solving skills. The successful student in this course will be proactive both in and out of the classroom, will seek help when necessary, be able to do independent work, use effective questioning skills and frequently enter into or initiate discussions in class, have a natural curiosity to pursue not only the mechanics of problem-solving but also the concepts behind the problem, and readily draw from a variety of problem-solving skills.*Prerequisite: Algebra II and Trigonometry (M-325) and recommendation of the math department**Open to: 10/11/12***M-500 Calculus**

Year 1 unit

This course is designed for students looking for a moderately paced course in calculus. The course covers the traditional topics of differential and integral calculus with special emphasis on applications, and it prepares students well for college and/or continued study in mathematics. This course is not intended to prepare students for the AP examination. *Prerequisite: Precalculus (M-450) and recommendation of the department**Open to: 11/12***M-540 Advanced Placement Statistics**

Year 1.5 units

This course offers a thorough examination of data analysis, data production, and statistical inference. Topics include the normal distribution, correlation and regression, experimental design, sampling distributions, probability theory, confidence intervals, tests of significance, and the Chi-Square Test. Diverse areas such as economics, medicine, and politics are incorporated into discussions of statistical topics. Solution methods for the Advanced Placement exam and assessments in this class employ technology. Also, students should expect significant reading, written analysis, and interpretation as parts of statistical inference. As with other AP courses, additional assignments should be expected over school vacations, and summer work is required. Students in this course are expected to sit for the AP Statistics exam in May.*Prerequisites: Precalculus (M-450) or Precalculus with Non-Routine Problems (M-460) and recommendation of the department**Open to: 11/12***M-550 Advanced Placement Calculus AB**

Year 1.5 units

This course prepares students for the AP Calculus AB exam. It offers a thorough exposure to differential and integral calculus. The course begins with a review of functions and their graphs, followed by derivative functions, limits, continuity, and the definite integral. Derivative rules and applications complete the study of differential calculus, and this is followed by additional work with integrals and their applications. The course finishes with the topics of differential equations and slope fields. All students who take this course are expected to take the AP Calculus AB exam in May. As with other AP courses, additional assignments should be expected over school vacations, and summer work is required.*Prerequisites: Precalculus (M-450) or Precalculus with Non-Routine Problems (M-460) and recommendation of the department**Open to: 11/12***M-560 Advanced Placement Calculus BC**

Fall .75 units

This course is a continuation of AP Calculus AB (M-550), and covers only those topics on the College Board BC topic outline not already presented in Calculus AB. These include integration by parts and by partial fractions, improper integrals, curve length, infinite series, and parametric and polar functions. All students are required to sit for the AP Calculus BC exam in May. In preparation for this exam, there are several weeks of required review sessions in the spring. Students should also expect a substantial summer assignment and possible assignments during school vacations. *Prerequisites: AP Calculus AB (M-550) and recommendation of the department**Open to: 11/12***M-570 Multivariable Calculus**

Spring .75 units

This course covers topics that are typically offered in a third-semester college course in multivariable calculus. These include vectors and surfaces in three-dimensional space, vector-valued functions, partial derivatives, vector fields, and line integrals. It will be a particularly helpful course for students who plan to study engineering, physics, or math in college.*Prerequisite: AP Calculus BC (M-560) and recommendation of the department**Open to: 11/12*