Mathematics

Algebra I

This year-long course is reserved for students new to The Agnes Irwin School. The focus of this course is to provide a solid foundation for higher study of mathematics, as it is a critical element in secondary mathematics. This course includes recognizing and developing patterns using tables, graphs and equations, while covering the following topics: linear, quadratic, rational, radical, and exponential functions.

Algebra IB

This course is the second half of the foundation course for Upper School mathematics and consists of the traditional college-preparatory program. Topics include polynomials, factoring, exponents and exponential functions, quadratic, radical and rational equations and functions. Students are also introduced to basic geometry concepts in an algebraic framework.

Geometry

This is a study of Euclidean Geometry concentrating on geometric reasoning, lines, angles, triangles, polygons, and circles. Students solve problems using the Pythagorean Theorem and right triangle trigonometry and find the areas and volumes of plane and solid figures. Note: Geometry is offered over the summer and requires the recommendation of the Mathematics Department.

Geometry Accelerated

Geometry Accelerated covers the topics of Geometry at an increased level of depth and rigor. Students are challenged to explore geometric properties and theorems in dynamic software. Prerequisite: B in Algebra I Part II, and recommendation of the Mathematics Department.

Algebra II

This course expands upon many of the topics from Algebra I, but at a deeper and more complex level. Students enrolled in this course examine topics such as quadratic and polynomial functions and equations, systems of equations, complex numbers, radical, rational, exponential and logarithmic functions. Prerequisite: C– in Algebra IB. Students who need to strengthen their algebra skills may be recommended for summer work.

Algebra II Accelerated

Algebra II Accelerated involves a more rigorous dive into the topics of Algebra II, covering the content in greater depth and at a faster pace. The course covers additional topics such as sequences, combinatorics, probability, conic sections, and basic trigonometry. Prerequisite: B in Algebra I Part II or A in both Algebra IB and Geometry and recommendation of the Mathematics Department.

Algebra II Honors

Algebra II Honors covers the topics of Algebra II Accelerated at a heightened pace and requires students to be more independent learners and thinkers in all aspects of the class. Students enrolled in this course should have a strong background in Algebra and an ability to creatively problem solve. Prerequisite: B in Algebra I Honors and Geometry Honors, or A in both Algebra I Accelerated and Geometry Accelerated, and recommendation of the Mathematics Department.

Precalculus

This course strengthens students’ algebraic foundations while introducing them to new and challenging concepts. Topics addressed include polynomial, rational, exponential, and logarithmic equations and functions, and unit circle trigonometry. Students also get a preview into the concepts of Calculus. Prerequisite: B in Algebra II.

Precalculus Accelerated

Precalculus Accelerated offers a more rigorous approach to the topics of Precalculus, covering additional topics such as graphing trigonometric functions and inverse trigonometry. Prerequisite: B in Algebra II Accelerated and recommendation of the Mathematics Department.

Precalculus Honors

Precalculus Honors is a fast-paced and challenging course that prepares students for Honors Calculus I. The course covers trigonometry, logarithmic, exponential and algebraic functions, sequences and series, limits, and analytic geometry. Prerequisite: B in Algebra II Honors and recommendation of the Mathematics Department.

Calculus

This course begins with the concept of the limit and explores the techniques of differential and integral Calculus. Students learn about the many applications of Calculus, including its use in business and physics. Students enrolled in this course should have a strong mastery of Algebra. Prerequisite: B in Precalculus Accelerated or A- in Precalculus and recommendation of the Mathematics Department.

Calculus I Honors

Calculus I Honors offers a more rigorous approach to the topics of Calculus, covering additional topics such as derivatives of inverse trig functions, linear approximation, and slope fields. It is an intensive, college-level course intended to prepare students for advanced standing upon entering college. Prerequisite: B+ in Precalculus Honors and recommendation of the Mathematics Department.

Calculus II Honors

The Calculus II Honors course picks up where Calculus I Honors left off, completing the study of single variable Calculus. The remainder of the course is dedicated to the study of Multivariable Calculus. In addition to procedural problems (partial derivatives, multiple integrals, line and surface integrals) an emphasis is placed on proofs and applications. Students gain a deeper understanding of Calculus and the emphasis on proofs prepares them for a rigorous college course. Note: This course will run in the 2022-2023 school year and is offered every other year, alternating with Linear Algebra Honors. Prerequisite: B+ in Calculus I Honors and recommendation of the Mathematics Department.

Note: Economics is listed as a cross-curricular elective on page 36.

Chaotic Dynamical Systems

This college-level course involves the study of systems that change over time. This course focuses on discrete dynamical systems that exhibit chaotic behavior, including experiments using computer software to simulate and analyze dynamical systems. Emphasis is placed on mathematical and computer graphics foundations behind fractal images and the relationship between chaotic dynamics and fractal geometry. Prerequisite: Successful completion of Calculus.

Linear Algebra Honors

Linear Algebra is a college-level course, focusing on vector spaces, linear transformations, and matrices. This course covers a broad range of applications, from physics and engineering to economics and social sciences to game theory. In addition to a rigorous exploration of mathematical content, this course pays particular attention to using new methods of proof and developing the skills of reading a “real” math text. Note: This course will run in the 2023-2024 school year and is offered every other year, alternating with Calculus II Honors. Prerequisite: B+ in Calculus I Honors and recommendation of the Mathematics Department.

Statistics and Probability

Americans are bombarded with statistics on a daily basis, from political polls to discussions of failing public schools to health epidemics. Students discuss the collection, analysis, and depiction of data, with a special focus on how one might use statistics to make claims and predictions that may be useful as well as misleading. Topics covered include combinatorics and probability and how probabilities can be used in conjunction with statistics to make decisions. Prerequisite: Algebra II.

Statistics and Probability Honors

This course serves as a rigorous, college-level introduction to statistics. Students are introduced to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Prerequisite: B+ in Algebra II Accelerated or Precalculus Accelerated or B in Algebra II Honors or Precalculus Accelerated, and recommendation of the Mathematics Department.