Mathematics

The fundamental purpose of this Common Core course is to formalize and extend the mathematics that students learned in middle grades. The students will continue to apply the eight mathematical practices of the Common Core through their study of linear, quadratic, and exponential functions. In particular, they will compare and contrast these families of functions through in-depth analysis. In addition, other topics include systems of equations, inequalities, polynomials, data analysis and statistics, exponent rules, and radicals.

The fundamental purpose of this course is to formalize and extend students’ geometric experiences from the middle grades. Students explore more complex geometric situations, deepening their understanding of geometric relationships and mathematical modeling, moving towards formal mathematical arguments. Topics include dimension, measurement, congruency, similarity, right triangle trigonometry, circles, 2-D and 3-D shapes, transformation, and probability.

For further clarification between Geometry and Honors Geometry, click here.

The fundamental purpose of this Common Core course is to formalize and extend student’s geometric experiences from the middle grades. Students explore more complex geometric situations and deepen their explanations of geometric relationships, including formal mathematical arguments and proof. Beyond the standard Geometry curriculum above, students will investigate analytic trigonometry, theorems about circles, advanced volume concepts, transformations, logic, and probability concepts related to geometry.  Honors Geometry requires students to be able to think deeply about mathematics.

For further clarification between Geometry and Honors Geometry, click here.

The fundamental purpose of this Common Core course is to build on previous work with quadratic, and exponential functions. Students extend their repertoire of functions to include polynomial, rational, radical, trigonometric and logarithmic functions. Students work closely with the expressions that define the functions, learn how to use transformations to graph functions, and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic, rational, polynomial, exponential, logarithmic and trigonometric equations.  Students will explore concepts of matrices including operations, inverses, and determinants. In addition, students will use matrices to solve equations.

For further clarification between Algebra II and Honors Algebra II, click here.

The fundamental purpose of this Common Core course is to formalize and extend concepts studied in Algebra I. Students will deeply explore and justify mathematical concepts and claims. Beyond the standard Algebra II curriculum above, students will fully investigate matrices and explore all six trigonometric functions, as well as exploring arithmetic and geometric sequences and series.

For further clarification between Algebra II and Honors Algebra II, click here.

This course re-introduces and delves more deeply into linear, quadratic, and exponential functions, progressing to root and logarithmic functions – all from a data-analysis perspective. The three main types of functions, while review, will be introduced from a 'new' perspective. This approach will be the idea of a transformation. Traditional functions that will be discussed include polynomials and rational functions, with an emphasis on transformations of parent functions. Lastly the course will invest deeply into trigonometry covering the majority of components of that topic: basic right triangle trigonometry, different units of measure, standard position angles, unit circle, applications of right triangle trigonometry, graphing the six trigonometric functions and the inverse trigonometric functions (with transformations), real-world modeling and applications of trigonometric functions, inverse trigonometric values, some basic identities and corresponding proofs and applications, area of a triangle, and the Laws of Sine and Cosine. Topics will also include the complex number system.  

Mathematics Applications and Interpretation/ IB Mathematics Applications and Interpretation SL focus on important interconnected mathematical topics.  The syllabus focuses on: placing more emphasis on student understanding of fundamental concepts than on symbolic manipulation; giving greater emphasis to developing students’ mathematical reasoning rather than performing routine operations; and solving mathematical problems embedded in a wide range of contexts.  There is an emphasis on applications of mathematics and statistical techniques. The course is designed to offer students with varied mathematical backgrounds and abilities the opportunity to learn important concepts, to gain an understanding of a wide variety of mathematical topics, and to develop more sophisticated mathematical reasoning.  Topics of study include number and algebra; statistics and probability; geometry and trigonometry, calculus and functions. Students in the IB section will create an individual piece of work (the Project) involving the collection of information or the generation of measurements and subsequent analysis and evaluation.

This is a calculator-required class.  Students will explore all mathematical topics using the technology of a graphing calculator.  The calculator will be required for all parts of this class including the internal assessment and both parts of the external assessment.

To be awarded International Baccalaureate (IB) for this course, students must complete all Internal & External exams. Please consider this requirement when making your selections for course registration. Exam fees are paid for by the Upper Arlington School District.

IB SL Calculus follows the International Baccalaureate Standard Level curriculum and is designed for students who anticipate a need for a sound mathematical background in preparation for their future studies. Calculus, including elementary differentiation and integration, is a primary topic of study. Other course topics include algebra, functions and equations, trigonometry, vectors, statistics and probability. Students will be expected to write two IB Papers, as well as one internal IB assessment.  

To be awarded International Baccalaureate (IB) for this course, students must complete all Internal & External exams. Please consider this requirement when making your selections for course registration. Exam fees are paid for by the Upper Arlington School District.

Precalculus develops the skills, properties, and representations of concepts prerequisite to the study of calculus. There is an increased focus on application and conceptual understanding through the study of the following topics: functions (including continuity and limits), rational functions, trigonometric functions, exponential and logarithmic functions, sequences and series, conic sections, polar coordinates and graphs, and vectors.

Honors Precalculus is designed for honors students (see note on Honors Program) who anticipate a need for a solid mathematical background for their future studies. This course will meet the curricular prerequisites for AP Calculus AB, AP Calculus BC, IB Mathematics SL/AP, and IB Mathematics HL/AP. Students are expected to possess a solid understanding of mathematics concepts developed in Honors Algebra II and previous courses. This course discusses all non-calculus content from the IB HL curriculum.  The emphasis of this course is the theory and applications of core topics that include functions and equations, trigonometry, vectors, conic sections, polar coordinates, probability and statistics, and proof techniques.

For further clarification between Precalculus and Honors Precalculus, click here.

AP Calculus AB is designed to develop the students’ understanding of the concepts of calculus and provide experience with its methods and applications. This challenging and demanding course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally.

Connections among these representations are also important. Through the use of the unifying themes - function analysis, limits, derivatives, integrals, approximation, and applications and modeling - the course becomes a cohesive whole rather than a collection of unrelated topics.

In addition to meeting the philosophy and goals of the AP program, this course is also intended to fulfill the requirements of the International Baccalaureate Standard Level curriculum. 

To be awarded Advanced Placement (AP) credit for this course, students must complete the accompanying AP exam. Please consider this requirement when making your selections for course registration. Exam fees are paid for by the Upper Arlington School District.

To be awarded International Baccalaureate (IB) for this course, students must complete all Internal & External exams. Please consider this requirement when making your selections for course registration. Exam fees are paid for by the Upper Arlington School District.

AP Calculus BC is an extension of AP Calculus AB rather than an enhancement; common topics require a similar depth of understanding, but at an accelerated pace.

As with Calculus AB, this course is designed to develop the students’ understanding of the concepts of calculus and provide experience with its methods and applications. This challenging and demanding course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Connections among these representations are also important. Through the use of the unifying themes - function analysis, limits, derivatives, integrals, approximation, and applications and modeling - the course becomes a cohesive whole rather than a collection of unrelated topics.

In addition to meeting the philosophy and goals of the AP program, this course is also intended to be the second year of the International Baccalaureate Higher Level curriculum. IB students will be expected to complete internal IB assessments. IB students will also be expected to write two IB Papers. Review of selected topics from previous mathematics courses may be assigned during the summer. 

To be awarded Advanced Placement (AP) credit for this course, students must complete the accompanying AP exam. Please consider this requirement when making your selections for course registration. Exam fees are paid for by the Upper Arlington School District.

To be awarded International Baccalaureate (IB) for this course, students must complete all Internal & External exams. Please consider this requirement when making your selections for course registration. Exam fees are paid for by the Upper Arlington School District.

AP Statistics introduces 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 through identifying and describing patterns, planning and designing statistical samples and experiments, exploring random phenomenon by utilizing probability theory and simulation, and drawing conclusions through formal statistical inference. Important components of the course include the use of technology, student-designed data collection projects, in-class data analysis activities, cooperative group problem-solving, and writing, as a part of concept-oriented instruction and assessment. This course can be taken as an elective or as one of the four (4) math credits required for graduation.

To be awarded Advanced Placement (AP) credit for this course, students must complete the accompanying AP exam. Please consider this requirement when making your selections for course registration. Exam fees are paid for by the Upper Arlington School District.

Continue introduction to integral calculus: integration of exponential, logarithmic, trigonometric, inverse trigonometric functions, volume and surface area of solids of revolution, arc length, and methods of integration. Also includes L'Hospital's Rule and Improper Integrals. Analyze plane curves given parametrically or in polar coordinates, and their differential and integral calculus. Infinite sequences and series, and their sum and/or convergence, conic sections, vectors in the plane and in space. Applications to problems in science and engineering. Not open to students with credit for MATH 1157 and above.

This course is considered for College Credit Plus.

A continuation of the calculus sequence, this course provides an introduction to multivariable calculus: Vector-valued functions and motion in the plane and in space, functions of several variables, partial derivatives, directional derivatives, gradients, extrema, multiple integrals, line integrals, Green’s theorem, parametric surfaces, divergence theorem, and Stokes theorem. Applications to problems in science and engineering.

This course is considered for College Credit Plus.

Financial Mathematics focuses on developing students’ understanding of fundamental concepts in mathematics within the context of business finance. Mathematical concepts explored in the course include functions (especially linear, quadratic, exponential, and piecewise), displays of data, modeling and interpreting data, regression, solving equations and systems of equations, deriving and applying formulas, and others. Business and financial topics addressed in the course include investing, banking services, credit, time value of money, financing (annuities, loans, mortgages, etc.), and retirement. Students will consider the underlying mathematical methods involved in these topics as well as gain experience in their practical application.

The course Statistics allows students to see real-world applications of mathematics.  The course themes of collecting, analyzing, and interpreting data encourages understanding and applying statistical procedures commonly used in sciences and the media.  Real-world examples and group activities with a mastery assessment process give students the chance to display proficiency in basic data collection and analysis in one semester.