# Mathematics

Placement Requirements

The placement process for new students is different from that for returning students. Please review the placement requirements for the appropriate group at the links below.

All placements are subject to review by the head of the department.

## Department Courses

### Algebra

### Geometry

### Intermediate Algebra, Advanced Algebra, Trigonometry, and Precalculus

### Calculus, Statistics, and Beyond

Statistics Honors is available to those who have completed a Calculus course. Students who take Algebra in grade 9 can take Calculus. In fact, our top students who start in Algebra can take AP Calculus AB in grade 12. There is also an opportunity to take our non-AP Calculus course.

### Math Paths

The study of Mathematics offers learning paths. The Math Paths Diagram provides a few of the most common paths. Other paths are possible and students can move between paths. Students may freely choose to move to a less challenging path than was is described in the Math Paths Diagram.

*To move to a more challenging path*, students need to:- receive a strong recommendation from their math teacher at Stevenson
- have earned a 95% or better in the Stevenson math course.
- In addition, extra summer work may be required, as is the case for the move from Advanced Algebra / Trigonometry / Precalculus (AATP) to AP Calculus AB.

### Math 4: Semester Courses for Grade 12

## Mathematics Course Descriptions

## Algebra

*Available to: qualified students, see placement requirements link above*

This rigorous course emphasizes skill-building and the development of a positive mindset for lifelong learning in mathematics and beyond. Students develop a strong foundation in algebraic topics such as probability, linear functions, exponents and radicals, quadratic functions, factoring polynomials, and inequalities. They learn and practice new skills in collaboration with their peers and are pushed to connect the material to the world as they know it. We introduce topics covered in Geometry with an eye for opportunities to integrate algebraic skills; for example, they might need to first apply a geometric theorem such as the sum of the angles in a triangle to produce a quadratic formula to be solved, then decide whether one, both, or none of the resulting solutions makes sense. Students will also engage with hands-on technology such as Desmos and Geogebra. Students in Algebra will usually continue on to take Geometry.

## Algebra Honors

*Type: honors*

*Available to: qualified students, see placement requirements link above*

This course is the first in the honors sequence for highly motivated and skilled students. Students develop a strong foundation in topics covered in Algebra while having their knowledge enhanced with additional problem sets that focus on more advanced concepts designed to provide a challenge for even the strongest students. Using mathematical puzzles and abstract concepts, students learn by exploration and collaboration while preparing themselves for future honors math courses. This course prepares students for Geometry Honors.

For specific topics covered, see course description for Algebra.

## Geometry A

*Available to: qualified students, see placement requirements link above*

In this course students continue to strengthen their understanding of the fundamentals of elementary algebra with an intensive review of algebraic topics before beginning their formal study of geometry. Students learn in a supportive environment that enables them to learn at an appropriate instructional pace. The skills developed in this course help to prepare students for courses in advanced algebra. Students in Geometry A are usually placed into Intermediate Algebra or Advanced Algebra / Trigonometry / Precalculus (AATP).

## Geometry

*Available to: qualified students, see placement requirements link above*

In this comprehensive geometry course, students develop spatial and deductive reasoning skills through an exploration of 2D and 3D shapes, congruent and similar figures, formal geometric vocabulary, basic structuring of mathematical proofs, and trigonometric identities. All geometric topics are discussed with a connection to the coordinate plane with an emphasis on strengthening students’ algebraic skills. In preparation for future courses, students will be introduced to concepts such as logarithmic and exponential functions, polynomials, and imaginary numbers. Students learn in collaboration with their peers and have ample opportunity for hands-on practice and feedback. In addition to a rigorous study of Euclidean Geometry, they spend time doing constructions in Geogebra to strengthen their understanding of geometry through real-life applications. Students in Geometry usually continue on to take Precalculus.

## Geometry Honors

*Type: honors*

*Available qualified students, see placement requirements link above*

This course is the second in the honors sequence for highly motivated and skilled students. In addition to reviewing previously studied topics covered in Algebra Honors, students will continue to have their knowledge enhanced with problem sets that focus on practical application and real-life examples. The problem sets are designed to provide a challenge for even the strongest students and to prepare students for participation in optional math contests. Students move through fundamental concepts and the new topics at a brisk pace by spending less time on general practice, and more time engaging with more challenging problems. Students in Geometry Honors usually continue on to take Advanced Algebra / Trigonometry / Precalculus Honors (AATP Honors).

For specific topics covered, see course description for Geometry.

## Summer Geometry

*Type: summer*

*Available to: high school students who have completed Algebra 1*

*Schedule: three and a half hours a day, five days a week for five weeks in the summer*

*Special Notes: Students taking this course are still expected to take a full load of courses in the following year. The course is in-person and our dorms are closed, so students must provide their own housing and meals.*

For information about the Summer Geometry course, please click here.

## Intermediate Algebra

*Available to: qualified students, see placement requirements link above*

In this course, students will learn not only about algebra, but also how to use algebra to describe and make predictions about authentic situations. The text used for this course contains data that describe hundreds of real-life questions. While working with data, students are able to make connections to foundational mathematical concepts and how mathematics impacts their daily lives. For example, in one project students collect data and then use linear regression to explain the relationships within the data, making predictions about what results they might have achieved had they collected more data. Students also embark upon other exploratory topics and learn to leverage different types of technology, most notably Desmos and graphing calculators, in their pursuit of becoming better problem solvers.

Students in this course usually go on to Advanced Algebra / Trigonometry / Precalculus (AATP) or Math 4: Semester Mathematics Courses For Grade 12.

Students in this course usually go on to Advanced Algebra / Trigonometry / Precalculus (AATP) or Math 4: Semester Senior Mathematics Courses.

## Advanced Algebra / Trigonometry / Precalculus (AATP)

*Available to: qualified students, see placement requirements link above*

This course covers all techniques, methods, and concepts usually covered in an algebra and trigonometry course, as well as the concepts presented in a traditional precalculus course. During the fall semester, students are introduced to advanced algebra concepts such as quadratic functions, polynomial functions, exponential and logarithmic functions, and systems of linear and nonlinear equation systems. The second half of the year features a detailed study of trigonometry including graphs, trigonometric equations and trigonometric identities. Throughout the year, students expand their knowledge of algebra and geometry and become familiar with concepts that they will encounter in calculus. Students in this course usually go on to take Calculus.

## Advanced Algebra / Trigonometry / Precalculus Honors (AATPH)

*Available to: qualified students, see placement requirements link above*

This course is the third in the honors sequence for highly motivated and skilled students. Students completing Geometry Honors are well prepared to take this course. This course covers advanced algebra, trigonometry and the concepts needed to provide students for calculus. The course broadens and deepens advanced algebra concepts such as quadratic functions, polynomial functions, exponential and logarithmic functions, conic sections, and systems of linear and nonlinear equations. Students continue working on supplemental problem sets to enhance problem-solving skills, and we introduce non-traditional topics such as number system conversion. The course concludes with a detailed study of trigonometry including graphs, trigonometric equations and trigonometric identities. Graphing calculators and technology are integrated into the curriculum through projects and discussions of real-world problems, such as modeling population change. Throughout the year, students collaborate in an environment that encourages participation from all. Students who complete this course usually go on to take AP Calculus AB or Calculus.

## Calculus

*Available to: qualified students, see placement requirements link above*

This course introduces students to the elements of differential and integral calculus with an emphasis on building upon and subsequently mastering skills learned in prior math courses. Students will use limits in their study of differential calculus and do a thorough examination of the tangent line problem. Students will apply differentiation techniques such as power, chain, product, and quotient rules. Once the techniques are mastered, students will apply their knowledge to authentic problems involving optimization. They will also explore applications of integral calculus, which include calculating the area under a curve and the fundamental theorem of calculus. This comprehensive course prepares graduating grade 12 students for college-level mathematics courses and younger students for AP Calculus AB.

## AP Calculus AB

*Type: Honors*

*Available to: qualified students, see placement requirements link above*

AP Calculus AB is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems. This comprehensive course requires students to use definitions and theorems to build arguments and justify conclusions. Students learn to solve problems expressed graphically, numerically, analytically and verbally to build a deeper understanding of the presented topics. Students use online resources such as Desmos and the AP Classroom along with graphing calculators to enhance their knowledge of the concepts while preparing for the AP exam in May, and the possibility of taking AP Calculus BC the following year.

## AP Calculus BC

*Type: Honors*

*Available to: qualified students, see placement requirements link above*

This fast-paced college-level course covers the topics presented in AP Calculus AB in greater depth, as well as infinite series, including the Taylor series. Students also investigate functions defined by polar and parametric equations and vectors. They use topics such as the logistic growth model and related rates to apply their work to real world situations. Using calculus, they are able to calculate the carrying capacity of a pack of wolves, or how fast the volume of a balloon is changing when inflated or deflated. Students use online resources such as Desmos and the AP Classroom along with graphing calculators to enhance their knowledge of the concepts while preparing for the AP Exam.

## Multivariable Calculus

Available to: qualified students, see placement requirements link above

Multivariable Calculus is reserved for students who have completed AP Calculus BC. In colleges this course is commonly called Calculus III, and it expands the calculus concepts to multiple variables, and to multiple dimensions. The first part of the course introduces vector calculus basics such as the definition of a vector, its magnitude and direction, dot and cross products, and their geometrical interpretation. These concepts are then applied to 3-dimensional shapes, including lines, planes, and quadrics (ellipsoids, spheres, cones, paraboloids etc.). The second phase of the course focuses on calculus concepts with multiple variables to calculate arc length, surface area and volume by using line, double and triple integrals in Cartesian, polar, cylindrical and spherical coordinate systems. The course concludes by making connections to real-life problems such as Green’s, Divergence, and Stokes’ Theorems.

## Statistics Honors

*Type: honors*

*Available to: qualified students, see placement requirements link above*

Statistics is a growing field of study that has applications in many industries and academic fields such as psychology, life sciences, economics, astronomy, finance, sports and more. Paying close attention to local, national and global events, this honors course introduces students to the descriptive and inferential statistical methods that allow them to be competent consumers and handlers of data. Throughout the year students will explore several statistical themes such as producing data with experimental design, exploring data with descriptive statistics, anticipating patterns using probability, and learning about a population from sample data using statistical inference. Students will engage with these concepts through activities, simulations, projects. current events, and real-world data sets. Also, they will develop familiarity with technological tools that will help them access, display, analyze and interpret data. Deep engagement in the coursework will help students to further develop their problem-solving, critical thinking, and communication skills, as well as prepare them for further studies and applications of statistics at the university level.

*Available to: Grade 12 students*

*Schedule: **each meets during a single semester.*

The semester grade 12 mathematics course offerings can change from year to year.

The registrar will work with rising grade 12 students to request particular semester math courses in May of grade 11.

## Personal Finance

This semester course gives students the opportunity to learn about essential elements of personal finance that they are likely to encounter as young adults both during and after college. Students learn about interest, the present and future value of money, debt, basic banking, investing, loans, retirement savings, insurance, and taxes. Throughout this course, students explore the nature of growth and decay, and compound interest. Overall, the course focuses on solving math problems related to financial literacy, providing students with the basic knowledge and tools they will need to apply their problem-solving abilities to their financial life. Throughout the course, students will engage in budgeting and stock investing simulations using an online application called Personal Finance Lab.

## Statistics

This introductory statistics course will introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data, as well as provide them with opportunities to apply what they have learned to real data sets. Students will develop statistical strategies from a wide variety of sources including experiments, sample surveys and other observational studies. Students will study probability and simulation to aid in their understanding of statistics and to aid in constructing models of chance. Also, students will study the properties of sampling distributions in order to construct confidence intervals and carry out hypothesis tests. Throughout the course, students will use technological tools such as graphing calculators, and spreadsheets to organize, display and analyze data.This course helps prepare students for an introductory course in statistics at the college level, and helps them become discerning consumers of data.