Mathematics

Use this chart in conjunction with the specific course descriptions and prerequisites.

The high school mathematics department at ASL believes that the field of mathematics provides an essential and unique way of interpreting the world around us. We strive to foster an enjoyment of mathematics where students appreciate the beauty, wonder and exactness of this field of study. The goal of the program is for students to understand and appreciate the mathematics they are studying. We envision that each student will be able to interpret, communicate and explore mathematics with confidence.

We aim to provide each student with a solid foundation in mathematics through a challenging curriculum that is appropriate for the age, readiness and needs of each student. The program encourages students to construct and share their own mathematical understandings by asking questions, solving problems and exploring concepts using a variety of methods and tools. We promote collaboration among students and foster cross-curricular connections with other disciplines.

The ASL math curriculum is aligned to the Common Core State Standards (CCSS) and develops the math practices that are an essential part of those standards throughout each course. At every level, students are asked to not only find answers to problems, but to give detailed and thoughtful solutions that demonstrate the learning process and deep understanding of the fundamental concepts. Students learn how to express their solutions mathematically, and also how to explain their understanding through written reflection.

Throughout an ASL high school student's mathematics career, the department endeavors to provide learning experiences that utilize appropriate technology. The graphing calculator equips students with opportunities to explore concepts and topics in depth. Learning to use a graphing calculator effectively and efficiently is, therefore, an integral part of the mathematics curriculum, and students in the High School are expected to have a graphing calculator for use in math courses. We strongly recommend that students use any variety of the Texas Instruments TI-84 Plus calculator.

The mathematics department sponsors the Math Club, which provides motivated students with an opportunity to work on problems that require them to think laterally and creatively and to explore methods outside the curriculum. Students work individually and in small groups in preparation for various math competitions. Participation in contests, including ISMTF mathematics competitions and the UKMT and other mathematical challenges, is open to all students willing to undertake extra work in mathematics.

The mathematics curriculum is differentiated for various levels of student readiness. Families are strongly encouraged to communicate with teachers to determine which courses and pathways are most appropriate for a student. We aim to provide students with a challenging mathematical experience that optimizes their growth as mathematicians in a healthy and manageable way. Teachers use data about an individual student and their preparation to tailor recommendations about which courses are a good fit for that student.

Note on AP Precalculus

ASL does not offer an AP Precalculus course; the content of AP Precalculus is covered in Precalculus with Calculus, and mostly covered in Precalculus with Analysis. Students who wish to take the AP Precalculus exam should consult with a university advisor as to the potential advantages and disadvantages of this course of action. Students who decide to take the exam after consulting with a university advisor should then consult with the math department head and their math teacher for resources and advice to prepare for the exam.

Advanced Math Seminar

1 credit; full year
Standard prerequisite: Completion of AP Calculus AB or completion of/concurrent enrollment in AP Calculus BC

This is a college seminar-style math course that explores a variety of advanced mathematical topics. These vary from year to year, and are tailored to the background of the group of students who take the class. Possible topics include polar and parametric functions, complex analysis, advanced geometry, further topics in calculus, number theory, vectors and space curves. An emphasis is placed on creative and complex problem solving and presenting work to the class with regularity.

Algebra I

1 credit; full year
Standard prerequisites: Math 8 or Pre-algebra

This is a first-year algebra course organized around essential families of functions. The focus is on linear, quadratic and exponential functions with an emphasis on modeling real-world situations using these functions. Solving systems of equations and inequalities and the manipulation of exponents are also included. A major emphasis of the class is on problem-solving and communicating reasoning.

Algebra II

1 credit; full year
Standard prerequisite: Geometry with Proof or Geometry with Algebra

This course strengthens a student's skills as a thinker and problem-solver while deepening understanding of the principles of mathematics, with a focus on the topics of quadratic functions and modeling, linear systems, complex numbers, many graphing concepts including transformations, the properties of exponents, negative and fractional exponents, roots, inverse functions, polynomial arithmetic, advanced factoring techniques, simplifying rational expressions, solving rational equations, exponential and logarithmic functions, and solving non-linear equations. The course culminates with a unit on combinatorics and probability.

Algebra II Foundations

1 credit; full year
Standard prerequisite: Geometry with Algebra

This course serves as a foundational course in algebraic skills and ideas to help students develop greater understanding of topics that may have been challenging in Algebra I. Students study the topics of linear equations and functions, systems of linear equations, quadratic equations and functions, exponents, logarithms, rational functions, rational expressions and equations, polynomials and factoring and probability and combinatorics. The class emphasizes application and reasoning with the goal of preparing students for the multiple approaches to problems that are essential for further study in math.

Algebra II with Trigonometry

1 credit; full year
Standard prerequisite: Geometry with Proof

This rigorous course is designed to stress depth of knowledge and an ability to move from initial standards to higher-level standards at a faster pace. The course includes all of Algebra II as well as a comprehensive unit on trigonometry. The topics of the course and the focus are similar to what is listed for Algebra II, but each unit moves from the initial standards to rich problem solving at a much quicker pace. The emphasis is on mastery of the higher-level concepts and problems. Creative problem solving is a core value of the course, and the units are synthesized into challenging problems that require and build these creative skills.

AP Calculus AB

1 credit; full year
Standard prerequisite: Precalculus with Analysis

This college-level course is the equivalent of the first semester of an American university calculus sequence, based on the standards of the AP Calculus AB curriculum. As in the prerequisite Precalculus with Analysis course, there is a focus on depth of understanding, problem solving, and communication of ideas. Topics include: limits, differential calculus, and integral calculus, with applications throughout. Applications include optimization, function graph behavior, related rates, differential equations, and volumes of revolution. As is required by the AP curriculum, students learn how to apply calculus concepts both with and without the use of calculator technology. All students take the AP Calculus AB exam in May, and additional topics and applications are studied after the completion of that exam.

AP Calculus BC

1 credit; full year
Standard prerequisite: Precalculus with Calculus or AP Calculus AB
This college-level course is the equivalent of the full year of an American university calculus sequence, based on the standards of the AP Calculus BC curriculum. As in the prerequisite Precalculus with Calculus course, students are held to a high standard of retention of prerequisite knowledge and skills as the course moves at a faster pace than AP Calculus AB. Topics include: limits, differential calculus, and integral calculus, with applications throughout. Applications include optimization, function graph behavior, related rates, differential equations, and volumes of revolution.
The course covers all of the topics in AP Calculus AB with more depth of problem solving, along with units on differential equations, additional techniques and applications of the definite and indefinite integral, sequences and series including the power and Taylor series, and the calculus of polar and parametric functions. As is required by the AP curriculum, students learn how to apply calculus concepts both with and without the use of calculator technology. All students take the AP Calculus BC exam in May, and additional topics and applications are studied after the completion of that exam.

AP Statistics

1 credit; full year, Grade 11-12 students
Standard prerequisite: Algebra II or Algebra ll with Trigonometry

This course is a college-level introduction to the major themes of statistics, with an emphasis on four main skills; selecting statistical methods, data analysis, using probability and simulation, and statistical argumentation. It focuses on exploring one and two variable data, probability, randomness and probability distributions, sampling distributions and inferential reasoning. Students learn how to collect and use data from a sample and know what they can generalize about a population from this. All students take the AP Statistics exam in May.

Calculus

1 credit; full year
Standard prerequisite: Precalculus with Statistics or Precalculus with Analysis

This course features the study of differential calculus along with its standard applications to the theory of graphs and related rates. This is followed by the study of integral calculus, the fundamental theorems, and applications to motion, area and volume. Applications to real-world situations and collaborative thinking allow students to grapple with these complex ideas and see their interconnectedness before going into the higher-level problems that are a part of college calculus courses.

Financial Mathematics

1 credit; full year, Grade 11-12 students
Standard prerequisites: Algebra II, Algebra ll with Trigonometry or Algebra II Foundations

This course is a varied, numbers-based elective course that aims to introduce students to a wide range of real-life topics from the world of personal finance. We begin with a discussion of financial goal-setting and planning for the future. Students learn about compound interest in order to understand the concepts of Future Value and Present Value. Students learn how to model annuities and mortgages using spreadsheets and how to use the financial functions embedded within Google Sheets and the T1-84 Financial TVM Solver. This leads into discussions about how to save for retirement, how to distribute an annuity over a fixed time period, and the concept of "discounting". Students investigate credit cards and model simple financial accounting statements. They then create financial statements for their "future selves" based on their personal habits and goals.

The second semester includes activities on how to research the purchase of a house and car, how to finance those large purchases, and how to use credit wisely. The consequences of excessive debt and bankruptcy, as well as the psychological component of risk and investment are central themes. Students study short- and long-term investing options, including participation in a stock market simulation that allows them to buy and sell stocks using "live" data from Wall Street. The role of taxes and insurance in financial planning is also considered. Students apply finance and accounting principles from the first semester to understand how businesses are started, structured, capitalized and valued. Threaded throughout the course are discussions around ethics, lifestyle choices, the role of government in the economy and the psychology of spending.

Geometry with Algebra

1 credit; full year
Standard prerequisite: Algebra I

This course introduces students to plane geometry, the angles and relationships between parallel and perpendicular lines, triangles, quadrilaterals, similarity and congruence, polygons, area and volume, polyhedra and right-triangle trigonometry. A heavy emphasis is placed throughout the course on reviewing and strengthening algebra skills within the realm of geometry.

Geometry with Proof

1 credit; full year
Standard prerequisite: Algebra I

This is a robust geometry course that delves into rich and challenging applications of geometry concepts. It features reasoning and proof, the angles and relationships between parallel and perpendicular lines, triangle congruence, relationships within triangles, similarity, right-triangle trigonometry, quadrilaterals, properties of circles, area and perimeter, polyhedra and surface area and volume. Strong algebra skills are required, as many geometric situations require application of material from Algebra I.

Precalculus with Analysis

1 credit; full year
Standard prerequisite: Algebra II or Algebra ll with Trigonometry

This course continues the Algebra Il curriculum with a focus on depth of understanding, problem solving, and communication of ideas. Through this course, students build a greater appreciation for mathematics and the connected nature of seemingly disparate topics.
Trigonometry topics include, with applications,- unit circle trigonometry, graphing trigonometric functions, analytic trigonometry including work with identities, and the laws of sines and cosines. Other topics include: polynomial functions including division, rational zeros and factors; exponential and logarithmic functions with applications including base e, sequences and series with sigma notation, and conic sections.

Precalculus with Calculus

1 credit; full year
Standard prerequisite: Algebra II with Trigonometry

This rigorous course continues the Algebra II with Trigonometry curriculum, stressing depth of knowledge and an ability to move from initial standards to higher-level ones at a fast pace. Students are held to a high standard of retention of prerequisite knowledge and skills, which allows all of the standards of Precalculus with Analysis to be completed, in addition to vectors, polar equations and parametric equations, a study of limits and differential calculus in preparation for the AP Calculus BC course the following year.

Precalculus with Statistics

1 credit; full year
Standard prerequisite: Algebra II Foundations or Algebra II

This course strengthens and deepens students’ knowledge of material first encountered in Geometry and Algebra II courses. Specifically, students expand upon their knowledge of functions and graphs to include trigonometric, polynomial and rational functions. The function work completes the foundation which students need in order to study calculus. The statistics aspect of the course provides an introduction to one-variable and two-variable statistics (graphical representations of data, linear regression, probability, binomial and normal distribution). This balance of precalculus and statistics topics provides students with real-world applications that help show them how to apply their knowledge in other fields.