# Mathematics

We recommend that most students take four years of mathematics. Basic, regular, and honors groupings ensure students are appropriately placed for success. We suggest that students also take a class in computer science. ** Note: **Students require a graphing calculator (TI-83+, 84+, or Silver Edition). Principia makes these available for loan if needed.

### Minimum Required Sequence

#### Algebra 1

*Two semesters, one credit. *

Core topics of beginning algebra are taught, with an emphasis on linear functions. Simplifying algebraic expressions, solving linear equations, and solving systems of equations are important topics. Quadratic functions and equations are also explored. These topics are consistently applied to real world situations.

#### Geometry

*Two semesters, one credit. Prerequisite: Algebra 1. *

Concepts of Euclidean geometry, including definitions, postulates, and theorems are covered in this course. Areas of study include angles, parallel lines, triangles, congruency, similarity, polygons, circles, and coordinate geometry. Students revisit concepts of shape and measurement and combine algebra skills with analytical thinking to prove mathematical ideas. Accuracy of the written word and visual models is emphasized.

#### Algebra 2

*Two semesters, one credit. Prerequisite: Geometry *

This course develops proficiency with algebraic expressions, especially linear and quadratic forms. Powers, roots, polynomials, exponential and logarithmic functions, conic sections, and probability are also explored. These topics are consistently applied to real-world situations.

### Electives

#### Financial Math

*One semester, one half credit. *

This course includes the fundamentals of personal finance, and also focuses on mathematical problem solving in the financial realm. Topics include: saving, budgeting, debt, investing, insurance, and taxes, among others.

#### Precalculus

*Two semesters, one credit. Prerequisite: Algebra 2.*

This course includes the advanced algebra necessary for calculus, including polynomial, rational, exponential, and logarithmic functions. There is also a significant focus on the study of trigonometry in connection with circular functions, triangles, polar coordinates, and vectors. Transformations of graphs, mathematical modeling of data, and linear algebra are also explored.

#### Statistics

*One semester, one-half credit. *

This introduction to the study of statistics includes data collection and analysis, probability and probability distributions, and basic statistical inference. Modern technology eliminates much of the calculation formerly needed and allows for the investigation of more realistic problems.

### Advanced / AP Electives

#### Calculus AB: Advanced Placement

*Two semesters, one credit. Prerequisite: Precalculus. *

This college-level class will prepare students to take the AB form of the Advanced Placement Calculus exam. Both differential calculus and integral calculus are studied, with significant emphasis on the fundamental theorem of calculus. Algebraic, trigonometric, and transcendental functions are studied along with their applications.

#### College Precalculus (Dual Credit)

*Two semesters, one credit. Prerequisite: Algebra 2. Upon completion of this course, students receive credit at both the Upper School and Principia College.*

This course investigates properties of functions, techniques for solving equations and inequalities and graphing. Emphasizes polynomial, rational, algebraic, exponential, logarithmic, and circular functions as well as conic sections and trigonometry.

#### Advanced Calculus

*Two semesters, one credit. May be offered as an independent. Pre-requisite: Calculus AB. *

Additional study in calculus for students who have successfully completed Calculus AB. Topics of study include additional techniques of integration, polar and vector functions, and the study of series. Much emphasis will be given to problem solving. Students will be sufficiently prepared to take the BC form of the Advanced Placement Calculus Exam.

#### Statistics: Advanced Placement

*Two semesters, one credit. Prerequisite: Precalculus. *

This introduction to the study of statistics includes exploratory data analysis, planning a study, probability and probability distributions, and statistical inference. Modern technology eliminates much of the calculation formerly needed and allows for the investigation of realistic problems. Students completing this course are sufficiently prepared to take the AP exam.

### Computer Science

#### Introduction to Computer Science

*One semester; open to all students in grades 9–12 *

Students will learn the basic programming concepts including input and output, conditional statements, loops, and variables using Scratch and Swift programming languages. Students will also gain a deeper understanding of how computers work and discuss current events through the lens of technology.

#### Introduction to App Development

*One semester; one half credit. Prerequisite: Introduction to Computer Science or equivalent programming experience.*

This course will help students build a solid foundation in programming fundamentals using the Swift programming language. Students will explore and learn programming and coding principles through guided and independent exploration of the language tools using Swift Playgrounds, supplemented by classroom instruction. Students are also introduced to user interface design principles. These tools will serve as the foundation needed to build a basic iOS app from scratch.

#### Advanced Placement: Computer Science A

*Two semesters, one credit. Prerequisite: Introduction to Computer Science or approval of instructor*

This course covers fundamental topics that include problem solving, design strategies, data structures, approaches to process-ing data (algorithms), analysis of potential solutions, and the ethical and social implications of computing. It emphasizes object-oriented and imperative problem solving and design using the Java programming language. The techniques represent proven approaches for developing solutions that can scale up from small, simple problems to large, complex ones.