# Mathematics

The Mathematics Department recommends that most students take four years of mathematics. Honors, regular, and basic groupings ensure that students are appropriately placed for success. In all math classes, graphing is emphasized for visualizing concepts. Since computing is a discipline that influences nearly all other areas, we suggest that students take a class in computer science, too.

Note: Students are required to have a graphing calculator (TI- 83+, 84+, or Silver Edition). Principia makes these available for loan during the academic year, 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. *

This course covers many concepts of Euclidean geometry, including definitions, postulates, and theorems. Areas of study include angles, parallel lines, triangles, congruency, similarity, polygons, circles, and coordinate geometry. Students revisit the concepts of shape and measurement and combine algebra skills with analytical thinking to prove mathematical ideas. Emphasis is placed on accuracy of the written word and visual models.

#### 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. *

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. This course is a prerequisite for AP Calculus.

#### Problem Solving

*One semester, one half credit.*

This course is primarily focused on problem-solving strategies and using them to solve complex and novel problems. Emphasis is placed on effective group work and clear oral and written communication of solution strategies.

#### 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.

#### Trigonometry

*One semester, one half credit. *

This course explores right-triangle trigonometry, the unit circle, the circular functions, polar coordinates, and vectors. There is a significant focus on applications and modeling.

### 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.

#### 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 course covers 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 more 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.

#### Computer Science 1: Java Programming

*One semester; open to students in grades 10–12. Prerequisite: Introduction to Computer Science *

Students will be introduced to the world of object-oriented programming using the Java programming language. Students will learn to implement core programming principles using Java. They will also learn design principles, syntax and style, and data structures.

#### Computer Science 2: Java Programming

*One semester; open to students in grades 10–12. Prerequisite: Computer Science 1 *

Students will continue programming using Java. They will embark on a deeper exploration of the pillars of object-oriented programming. Additional concepts covered will include arrays, strings, file streams, and algorithms.