# Math Department

University High School’s math curriculum is comprehensive and features classes ranging from Algebra I to Multivariate Calculus & Differential Equations. Three of those courses are AP-level courses — AP Statistics, AP Calculus AB, and AP Calculus BC.

To graduate from University High School, students must earn six credits (one credit is earned each semester) in math.

## 2020-21 Math Course Descriptions

##### Algebra I

This course will strongly emphasize number sense, working with fractions and decimals daily. Throughout the course, students will increase their ability to work with challenging algebraic equations and to interpret data They will work with increasingly complex problems and applications of the mathematical ideas they are learning. Students are expected to start building a deeper understanding of the algebraic concepts and to start looking at why problems are set up the way they are, not simply memorizing a single approach to a problem. They will begin to truly see mathematics in the world around them. Different tools, such as graphing calculators and Desmos, allow for exploring mathematical ideas in a way that is not practical by hand. By the end of the year, students should be more comfortable with their ability to manipulate numbers and solve mathematical equations.

##### Geometry

Geometry is the oldest and most studied field of mathematics, largely due to its intuitive base. It is about shapes and figures and their relationships to one another. This course builds on the topics discussed in Algebra I and explores in detail the many different geometric figures and the complexity that can be pulled out of these seemingly simple figures. The purpose of this course is to explore these different figures, make conjectures about them, and then experiment with the conjectures using inductive and deductive approaches. This course focuses on hands-on activities in the development and testing of these conjectures. These hands-on activities may make use of different types of technology, ranging from paper and pencil to the graphing calculator, GeoGebra, and Desmos. By the end of this course, students will have an understanding of geometry as a coherent system of interrelated ideas and a thorough sense of how these ideas are developed, tested, and verified. Students who complete Geometry should advance to Algebra II or Algebra II with Trigonometry, based on recommendations from their current math teacher and a discussion with their mentor.

##### Algebra II

This year-long course builds on the foundation laid in Algebra I and Geometry. Students are expected to think deeply about the foundation of the subject, instead of just memorizing facts. Students will learn about the importance of functions in mathematics and their applications with real-world examples. Students will practice skills in preparation for standardized tests like the SAT and ACT and to ensure success in their future college courses. Topics in the class include:

- Relations and functions
- Linear and absolute value equations and inequalities
- Matrices
- Quadratic equations and functions
- Polynomials
- Algebraic fractions
- Logarithmic and exponential functions
- Conic sections (without transformations)
- Arithmetic and geometric sequences
- Counting principles, probability, and statistics

It is strongly recommended that students who complete Algebra II advance to Functions & Trigonometry paired with either Finite Math A, Finite Math B, or Probability & Statistics. If a student has an additional year of high school, they may be eligible to take AP Statistics based on a teacher recommendation.

##### Algebra II with Trigonometry

In this year-long course, students will learn about the importance of functions in mathematics and apply them to real-world examples. The course develops advanced algebraic skills such as systems of equations, sequences and series, probability, advanced polynomials, rational functions, complex numbers, quadratics, logarithmic and exponential functions, and conic sections. In addition, students will study trigonometric functions using the Unit Circle, triangle trigonometry, and graphs of sinusoidal functions.

Students are expected to think deeply about the foundation of the subject, instead of just memorizing facts. Technology, in the form of graphing calculators and computer graphing applications, is an integral part of the course. Students are encouraged to purchase a TI-83 or 84 calculator (Plus or Silver editions). Traditional paper and pencil skills are also taught to reinforce the understanding of concepts and ensure students are not dependent on their calculators. Nearly every exam will include a calculator and a non-calculator portion.

Students who complete Algebra II with Trigonometry are eligible to take Precalculus and/or AP Statistics the following year.

##### Functions & Trigonometry

This course will focus on building students’ mathematical skills. Students are expected to think deeply about the foundation of the subject, instead of just memorizing facts. This course covers topics from algebra and trigonometry at a level and emphasis appropriate for students who are preparing for mathematics courses at the college level. This is the recommended course after students complete Algebra II and is intended for students who are not pursuing AP mathematics courses. Students will practice skills required for solid scores on standardized tests like the SAT and ACT and success in their future college courses. Topics in the class include parent functions and transformations, triangle trigonometry, the Unit Circle, basic trigonometric curves, and law of sines and law of cosines. Students will need a scientific calculator.

##### Finite Mathematics

This course covers a wide variety of real-world problems that can be modeled and solved using quantitative means. In science and industry, mathematical models are the major tools for analyzing and solving problems: What is a cost-efficient route for a garbage truck? How are flights scheduled to maximize profits? How can the future value of a stock be found? How long can renewable resources last? These are only a few of the problems we will learn to solve. By doing mathematics on practical problems, students gain the tools needed to understand and use the power of mathematics in the modern world. Topics covered will include graph theory, election theory, apportionment, and finance. Students will need a scientific calculator.

##### Probability & Statistics

This semester-long class will cover some of the topics addressed in AP Statistics but will not go as deep as the AP Statistics curriculum does. The class will spend approximately half of the semester working on probability and half learning about descriptive statistics. The probability section will cover basic probability, conditional probability, probability decision trees, and the many ways you use probability in everyday life. The statistics portion of the class will concentrate on how to use statistics to describe large sets of data, interpreting statistics, and understanding and creating visual displays of data. In addition, the class will spend a good deal of time on experimental design and how one correctly and creatively designs surveys and observational studies. Students in this class may, with the recommendation of the teacher, take AP Statistics the following year.

##### Precalculus

Algebra is the generalization of arithmetic, and calculus is the study of the dynamics of functions. Precalculus bridges the gap between the two, both in terms of content and approach. The course reviews topics from advanced algebra, focusing on graphing and functions. Students also study trigonometric functions, polar functions, and conics—all tools that help better describe the world in mathematical terms. The course also includes a review of exponential and logarithmic functions. Precalculus is not a required course; students who elect to take this course should understand that it is demanding. Precalculus goes beyond the ability to deal successfully with equations and formulas. It requires a commitment to understanding and explaining the rationale of the topics covered.

##### AP Calculus AB

AP Calculus AB is a college-level course. The text used is a college-level text, and students are expected to work at a rapid pace. The curriculum followed is the curriculum outlined by the organization that administers the Advanced Placement exam in May. Technology, in the form of graphing calculators, is an integral part of the course. Students are encouraged to purchase a TI-83 or 84 calculator (Plus or Silver editions). Students are required to think “outside of the box” in AP Calculus AB, putting many different ideas together in order to solve a problem.

The course begins with a short review of pertinent material covered in Precalculus. The first semester is used to discover how the derivative of an equation is found and how that derivative is used. There are many applications of the derivative, and the students are exposed to a variety of these situations. In the second semester, students work with integrals. Again, they are expected to use their knowledge to solve a wide range of applications.

The course is a rigorous one, but it is one that, with effort, can be successfully completed. It prepares students for a college-level calculus class, and in many instances, a student can place out of a college class with a good score on the AP exam in May.

The class’s major topics include:

- Limits and their properties
- Differential calculus
- Applications of derivatives
- Integral calculus
- Applications of integration

Differential equations

##### AP Calculus BC

This course will begin with a review of AP Calculus AB material. This course will then cover integration techniques (including partial fractions and integration by parts), improper integrals, Euler’s method, volume of solids of revolution, arc length, area of surfaces of revolution, review of sequences and series, tests for convergence, Taylor & Maclaurin polynomials & approximations, power series, Taylor & Maclaurin series, review of parametric equations & polar coordinates, arc length in parametric & polar coordinates, review of polar graphs, area in polar coordinates, logistic functions, review of trigonometric functions & identities, and solving integrals using trigonometric substitutions. This course will also cover in-depth examples and real-world applications of said material. Students will also explore an introduction to additional topics in mathematics including, but not limited to, game theory, differential equations, and linear algebra. Students should take this course if they are interested in more mathematics after AP Calculus AB and if they are interested in exploring advanced mathematics in preparation for a technical or math-heavy degree at the college level.

##### Multivariate Calculus & Differential Equations

Multivariate Calculus and Differential Equations will cover a number of other topics beyond the AP Calculus BC curriculum, including calculating volumes by using shells, surfaces of revolution, and centers of mass and centroids. The course also explores topics that are studied in a typical college-level third semester calculus course, including vectors and vector valued functions, differentiation in several variables, optimization in several variables, multiple integration, and line and surface integrals. The course concludes with an introduction to differential equations. Topics may include solving exact first-order equations, solving second-order homogeneous and non-homogeneous linear equations, and exploring applications to various scientific fields.

##### AP Statistics

The AP Statistics course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. The students use computer-based statistics programs as well as a graphing calculator in this course; technology is an important part of mathematics at this level. The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes:

- Exploring data: describing patterns and departures from patterns
- Sampling and experimentation: planning and conducting a study
- Anticipating patterns: exploring random phenomena using probability and simulation
- Statistical inference: estimating population parameters and testing hypotheses

This course is a rigorous one, but it is one that can be completed successfully with work.