# Mathematics

## 2024-2025

The Cary Academy Upper School Mathematics program strives to provide all students with a greater appreciation for mathematics as a discipline and as an integral part of the world in which we live. Students will be asked to actively participate in their work to develop a deeper understanding of the mathematics.

Throughout the curriculum there will be an emphasis on logical reasoning and deductive skills. In addition, students must recognize that attending to detail is an essential component of producing thoughtful, quality work.

## Mathematics 24-25

wdt_ID | wdt_created_by | wdt_created_at | wdt_last_edited_by | wdt_last_edited_at | Dept. | Course Number | Title | Course Description | Blocks per week | Credits | Term | Grade level(s) |
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1 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH525-SY | ADV Analytics and Statistics | Advanced Analytics and Statistics examines the four core principles of data science: Exploring data, sampling and experimentation, anticipating patterns and statistical inference. There is a heavy focus on using technology including graphing calculators and online simulation tools. This course emphasizes collaboration both in class, through discussion and group work, and out of class, through projects that require students to apply the concepts that are being studied. Many students choose to sit for the Advanced Placement (AP) examination. Prerequisites - grade of "A" in MTH435: Functions and Modelling, or Pre/Corequisite: MTH440 Precalculus, or MTH450: Honors Precalculus or permission of the department chair. | All | 1 | Year | 9,10,11,12 |

2 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH441-SY | Calculus 1 | This course emphasizes an integrated approach to learning Calculus. Students utilize skills developed earlier in their mathematical courses to address conceptual and applied topics related to Calculus including limits, derivatives, and integrals, as well as some of their applications.This course is offered both with and without the ADV designation. Students who qualify for the ADV designation will be notified through their teacher recommendation. Prerequisites: Completion of MTH440: Precalculus with an 85% assessment average and a teacher recommendation, or completion of MTH450: Honors Precalculus and a teacher recommendation, or permission of the department chair. | All | 1 | Year | 9,10,11,12 |

3 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH625-SY | ADV Calculus I & II | This course covers the content of Calculus I ADV as well as Advanced Topics in Calculus. The pace and rigor of this course are intended for students with a commitment to learning advanced mathematics and a desire to pursue advanced mathematics in college. This course is structured using a modified blended model. In addition to regular coursework, students are expected to work during two additional designated periods to complete an online component of the course, requiring both consistent diligence and selfmotivation. Most students choose to sit for the Advanced Placement (AP) examination (Calculus BC). Prerequisite: an assessment average of 95% or higher in Honors Precalculus and a teacher recommendation. | All | 1 | Year | 9,10,11,12 |

4 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH705-SY | ADV Calculus II | In this course, students will be asked to uncover the mathematics together with assistance from the instructor. There are two primary goals of the course. First, having completed a year of the Calculus, students will be asked to revisit topics from the first year with greater attention to depth of knowledge. In addition, students will examine new areas of the Calculus, including but not limited to, Taylor Series and more advanced applications of integration and differential equations. Most students in this course choose to sit for the Advanced Placement (AP) examination (Calculus BC). Prerequisite: Assessment average of 85 or higher in MTH 550: Calculus I and teacher recommendation. | All | 1 | Year | 9,10,11,12 |

5 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH755-SY | ADV Calculus III & Diff. Equations | This course will cover the content of semester courses in college-level Multivariable Calculus (1st half of the year) and Differential Equations (2nd half of the year) and be taught in a blended format. Each week, there will be a mixture of contact periods with the teacher and virtual periods during which to complete online assignments and participate in an online discussion forum. This forum will allow peers to collaborate with each other, with their teacher in a facilitator role. Prerequisite: MTH 625: Calc I & II or MTH705: Advanced Calculus II. | All | 1 | Year | 9,10,11,12 |

6 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH530-SY | ADV Statistical Theory and Application | This course follows the Advanced Statistics curriculum while also integrating a calculus component. This course is designed for students interested in understanding the Calculus foundations of statistics as well as those interested in developing programming skills that can be used in future data science courses. Prerequisite: MTH 441: Calculus I and a teacher's recommendation or MTH450: Honors Precalculus and CPS 305: ADV Computer Science and a teacher's recommendation. | All | 1 | Year | 9,10,11,12 |

7 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH300-SY | Algebra II | Students will develop proficiency with algebraic expressions and equations to further develop the skills necessary to be successful in future math courses. Students will explore in detail the linear, absolute value, quadratic, polynomial, rational, exponential, logarithmic, and piece-wise functions along with their applications. Additional topics may include systems of equations, matrices, and statistics. Prerequisite: MTH 100: Algebra I or MTH 101: Algebra of non-linear functions and MTH 200: Geometry or MTH 250: Honors Geometry. | All | 1 | Year | 9,10,11,12 |

8 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH435-SY | Functions and Modeling | Functions and Modeling introduces students to the concepts and skills that they will encounter in a college math course including function analysis, trigonometry, and statistics. Through collaborative activities students will work to enhance their algebraic understanding of essential concepts necessary for success in college. They will complete projects that illustrate the applications of mathematics in the real world and apply their understanding to a variety of contexts. Prerequisite: MTH300: Algebra II. | All | 1 | Year | 9,10,11,12 |

9 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH200-SY | Geometry | Students proceed through a Euclidean geometry course emphasizing deductive reasoning, sequential analysis, and proof. Logic plays a critical role in the development of properties for planar and spatial figures. Students also perform basic constructions and represent geometric figures in the Cartesian plane. Algebra is reinforced throughout the course. Students also learn to apply geometry to real-world problems. Prerequisite: MTH100: Algebra I or MTH101:Algebra of Non-linear Functions | All | 1 | Year | 9,10,11 |

10 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH350-SY | Honors Algebra II | Students will develop proficiency with a wide range of functions including linear, absolute value, quadratic, polynomial, rational, radical, exponential, logarithmic, and piece-wise. Applications of each of these functions will be explored and connections to Calculus concepts will be made. Additional topics may include conic sections, statistics, systems of equations, and matrices. Prerequisites: An assessment average of 85 or higher in MTH250: Honors Geometry and a teacher's recommendation or an assessment average of 95 or higher in MTH200: Geometry and a teacher's recommendation. | All | 1 | Year | 9,10,11,12 |

11 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH250-SY | Honors Geometry | This honors course will allow students to explore Euclidean geometry with an emphasis on deductive reasoning, sequential analysis, and proof. Logic plays a critical role in the development of properties for planar and spatial figures. Students also perform basic constructions and represent geometric figures in the Cartesian plane. Algebra is reinforced throughout the course. Students also learn to apply geometry to real-world problems. Prerequisite: An assessment average of 95 or higher in MTH 100: Algebra I or MTH101:Algebra of Non-linear Functions and a teacher's recommendation. | All | 1 | Year | 9,10,11 |

12 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH450-SY | Honors Precalculus | Students will expand their understanding of functions that they encountered in Algebra 2 and learn additional functions including trigonometric, polar, and parametric. Additional topics covered include sequences and series, vectors, the binomial expansion, and probability & statistics. Calculus concepts are encountered throughout the year to establish a foundation of skills necessary to be successful in that course. Students will be challenged routinely to think abstractly about the concepts and leverage their algebra skills to solve interesting and challenging problems. Fluency with algebraic manipulations and a thorough understanding of function behavior are required for success in this course. Prerequisite: An assessment average of 85 or higher in MTH350: Honors Algebra II and a teacher's recommendation or an assessment average of 95 or higher in MTH:300 Algebra II and a teacher's recommendation. | All | 1 | Year | 9,10,11,12 |

13 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH381-S1 | Math Contest Topics S1 | This course is designed to help students interested in high school mathematics competitions learn more of the theory behind solving competition. Advanced geometry, probability, combinatorics and number theory are challenging topics, but the fundamentals behind them are often intuitive and accessible to students of all ages. These units will be examined with the specific aim of gathering tools and techniques that are needed to solve challenging high school math competition problems. A strong emphasis will be placed on students working collaboratively to solve fewer, more difficult problems within an extended time frame, as well as finding intuitive shortcuts to reduce time pressure and sometimes learning to work without the aid of a calculator. Students will also learn from each other through student-led presentation of solutions. May be repeated for credit. | One | 0 | Fall | 9,10,11,12 |

14 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH381-S2 | Math Contest Topics S2 | This course is designed to help students interested in high school mathematics competitions learn more of the theory behind solving competition. Advanced geometry, probability, combinatorics and number theory are challenging topics, but the fundamentals behind them are often intuitive and accessible to students of all ages. These units will be examined with the specific aim of gathering tools and techniques that are needed to solve challenging high school math competition problems. A strong emphasis will be placed on students working collaboratively to solve fewer, more difficult problems within an extended time frame, as well as finding intuitive shortcuts to reduce time pressure and sometimes learning to work without the aid of a calculator. Students will also learn from each other through student-led presentation of solutions. May be repeated for credit. | One | 0 | Spring | 9,10,11,12 |

15 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH440-SY | Precalculus | Students will expand their understanding of functions that they encountered in Algebra 2 and learn additional functions including trigonometric, polar, and parametric. Additional topics covered include sequences and series, vectors, the binomial expansion, and probability & statistics. Calculus concepts are encountered throughout the year to establish a foundation of skills necessary to be successful in that course. Prerequisite: MTH 300: Algebra II or MTH 350: Honors Algebra II. | All | 1 | Year | 9,10,11,12 |

16 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH500-S1 | College Math Topics S1 | In this course, you'll master fundamental concepts vital for college success, covering topics like linear equations, functions, proportions, percentages, probability, matrices, quadratic and exponential functions, polynomials, and geometric/trigonometric functions. We'll also explore problem-solving strategies, test-taking tips, and efficient use of Desmos and TI-84 graphing calculators. Prerequisite: Completion of Algebra 1. | 1 day a week | 0 | Fall | 9,10,11,12 |

17 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH500-S2 | College Math Topics S2 | In this course, you'll master fundamental concepts vital for college success, covering topics like linear equations, functions, proportions, percentages, probability, matrices, quadratic and exponential functions, polynomials, and geometric/trigonometric functions. We'll also explore problem-solving strategies, test-taking tips, and efficient use of Desmos and TI-84 graphing calculators. Prerequisite: Completion of Algebra 1. | 1 day a week | 0 | Fall | 9,10,11,12 |

18 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | MTH101-SY | Algebra of Non-linear Functions | This course enhances the foundation laid in the Algebra of linear functions by further cultivating algebraic proficiency, specifically geared towards the exploration of non-linear functions. It delves into quadratic and exponential functions, equipping students with essential skills like factoring and operations involving polynomials, radicals, and exponents. The regular use of technological tools such as Desmos and graphing calculators will be integrated into the learning process, facilitating a hands-on approach to applying and understanding these concepts. | All | 1 | Year | 9,10 |

19 | emi_charboneau | 24/02/2024 01:02 AM | emi_charboneau | 24/02/2024 01:02 AM | Mathematics | ADV: Topics in Data Science Using Linear Algebra | Advanced topics in data science using linear algebra is a year-long course for upper school students, offering an in-depth study of linear algebra's key concepts such as linear independence, matrix operations, vector spaces, eigenvalues, eigenvectors, and various factorizations of matrices. Incorporating computational programming, the course prepares students to apply these concepts in data science and beyond, fostering analytical and problem-solving skills. This course is ideal for students aspiring to excel in STEM and any data-intensive fields, providing a strong foundation for understanding and analyzing complex data structures. Prerequisite: MTH440 Precalculus, or MTH450: Honors Precalculus or permission of the department chair. | All | 1 | Year | 10,11,12 | |

Dept. | Course Number | Title | Course Description | Blocks per week | Credits | Term | Grade level(s) |