Mathematics Department

Students will engage in the foundational study of algebraic concepts and practices. Algebra I provides a comprehensive introduction to essential algebraic principles, equipping students with the skills necessary for success in future mathematics courses and beyond. The curriculum emphasizes the development of algebraic thinking and problem-solving skills, preparing students for higher-level mathematics. Throughout the course, students will explore linear equations and inequalities, learning to solve and graph both on the coordinate plane. Students will also investigate systems of equations, understanding how to find solutions using various methods, including substitution and elimination. An essential component of Algebra I is the study of functions, in which students will analyze linear and quadratic functions, recognizing the characteristics and applications of each.

Additionally, students will delve into polynomials, learning to perform operations such as addition, subtraction, multiplication, and factoring. The course will also cover exponential functions and their applications in real-world scenarios, reinforcing the importance of mathematics in everyday life. A TI-84 calculator is required for all high school mathematics courses at DCA. Prerequisite: PreAlgebra

Students will engage in the study of functions: linear, quadratic, polynomial, exponential, rational, and logarithmic. These functions are studied symbolically, graphically, and numerically. Through the use of mathematical modeling, data analysis, matrices, and algorithmic thinking, students will view algebra as a problem-solving tool. The course is designed to prepare students for introductory collegiate mathematics courses. Students will deepen work in problem-solving, with an emphasis on applying learned techniques to novel, more advanced situations. An emphasis will be placed on developing good study habits, utilizing the language of mathematics, and growing a deeper understanding of the interconnectedness of mathematics principles to other fields of study including the natural sciences, social-behavioral sciences, and business. A TI-84 calculator is required for all mathematics courses at DCA. Prerequisites: Algebra I and Geometry

Students will engage in a deep study of functions: linear, quadratic, polynomial, exponential, rational, and logarithmic. These functions are studied symbolically, graphically, and numerically. Strong emphasis will be placed on graphing techniques both with and without technology. Through the use of in-depth mathematical modeling, data analysis, matrices, and algorithmic thinking, students will view algebra as a problem-solving tool. Students will construct logical and valid proof throughout the course. 

Coursework at the honors level necessitates increased student participation, persistence, and performance. Students will be expected to utilize formal and informal concepts to self-critique work and adjust work habits accordingly. Honors math students should expect to read in the content area outside of class and demonstrate a high level of topic understanding in the application of algebraic concepts to solve complex problems. A TI-84 calculator is required for all mathematics courses at DCA. Prerequisites: a minimum grade of 84/B in both 8th Grade Honors Algebra I (or at least a 90/B+ in College Prep Algebra I) and at least an 84/B in Honors Geometry (or at least a 90/B+ in CP Geometry) and teacher approval.

Students will engage in a comprehensive coverage of formal geometric concepts. Topics studied in this course include points, lines, and planes, similarity and congruence of polygons, right triangle relationships including trigonometry, area and volume, constructions and transformations, circles, and quadrilaterals. The development of the discovery of ideas, the formulation and investigation of conjectures, and problem-solving that requires multi-step thinking and logical reasoning will be emphasized. This course focuses on both the content and form of geometry, with emphasis on the techniques of formal proof and the application of geometric concepts to solve complex problems. 

Students will learn to become proficient in sound reasoning and problem-solving, with an emphasis on applying learned techniques to novel situations. An emphasis will be placed on developing good study habits, utilizing the language of mathematics, and growing a deeper understanding of the interconnectedness of mathematics principles to other fields of study. A TI-84 calculator is required for all mathematics courses at DCA. Prerequisite: Algebra I

Students will engage in a comprehensive coverage of trigonometry and an introduction to calculus concepts. Topics studied in this course will include an in-depth development of the unit circle and its properties, the six trigonometric functions and their inverses, graphing techniques, modeling, utilization and manipulation of trig identities, solving trigonometric equations, vectors, parametric equations, and polar functions. Students will be introduced to concepts of continuity, limits, equations of tangent lines, and basic derivatives. To enhance visualization of mathematical concepts and encourage exploration of alternative solution methods, students will develop a high level of proficiency with a graphing calculator, a tablet, and multiple computer software programs. 

Coursework at the honors level necessitates increased student participation, persistence, and performance. Students will be expected to utilize formal and informal proof to self-critique work and adjust work accordingly. Honors math students should expect to read in the content area outside of class and demonstrate a high level of topical understanding in the application of precalculus and introductory calculus concepts to solve complex problems. All honors precalculus students will be prepared to perform well on college entrance exams and enter college-level mathematics studies. Those who earn a minimum of a 93 along with Pre-calculus teacher recommendation will be prepared to undertake ADVANCED PLACEMENT (AP®) CALCULUS AB senior year. A TI-84 calculator is required for all mathematics courses at DCA. Prerequisites: At least an 84/B average in Honors Algebra I, Honors Algebra II, and Honors Geometry or at least a 90/B+ average in College Prep Algebra II, and teacher approval.

Students will engage in a study of trigonometry and advanced pre-calculus concepts. Topics studied in this course will include an in-depth development of the unit circle and its properties, the six trigonometric functions and their inverses, graphing techniques, modeling, utilization and manipulation of trig identities, solving trigonometric equations, vectors, parametric equations and polar functions. Students will be introduced to concepts of continuity and limits. To enhance visualization of mathematical concepts and encourage exploration of alternative solution methods, students will develop a high level of proficiency with a graphing calculator, a tablet, and multiple computer software programs.

Students will deepen work in problem-solving, with an emphasis on applying learned techniques to novel, more advanced situations. An emphasis will be placed on developing good study habits, utilizing the language of mathematics, and growing a deeper understanding of the interconnectedness of mathematics principles to other fields of study including the natural sciences, social-behavioral sciences, and business. Upon completion, students will be prepared to perform well on college entrance exams and enter college-level mathematics studies.  A TI-84 calculator is required for all mathematics courses at DCA. Prerequisites: Algebra I, II, and Geometry.

Course Overview: AP® Calculus AB is equivalent to a first-semester college calculus course. Topics include functions, limits and continuity, derivatives, and integrals. The course will focus on applying the skills and concepts of calculus to modeling and solving problems across multiple representations. Students will maintain a College Board/AP® Calculus AB account and will complete assigned work in the account throughout the year to prepare for the AP® exam. All students enrolled in this course are required to take the AP® exam, incurring its associated costs. A TI-84 calculator is required for all mathematics courses at DCA and this meets the calculator requirements for AP® Calculus AB. Students will also be expected to use the AP® Calculus calculator found on the AP® website in preparation for the exam. Prerequisites: Honors Algebra I, Honors Geometry, Honors Algebra II, and Honors Pre-Calculus; Enrollment is subject to departmental review based teacher approval and a minimum average of 93 in Honors PreCalculus.

1 semester, 0.5 credit

An introduction to statistics and probability, including topics and procedures which may be required in general education (e.g. psychology) and business. Basic focus on the fundamentals of statistical measurement and analysis, descriptive and inferential. Illustrative topics include probability, frequency distributions. Introduction to sampling theory, hypothesis testing, and confidence intervals, linear regression, and correlation. Dual Enrollment courses require tuition to be paid to the college or university in addition to DCA tuition. Students may utilize the Dual Enrollment Grant through the TN Education Lottery Programs for approximately $500 per course for 5 semester courses' tuition. Three hours, offered fall semester, through Welch College. Prerequisites: Completion or enrollment in PreCalculus, at least an 84/B average in previous Honors mathematics courses or a minimum of 90/B+ in previous CP math courses, and a minimum ACT Composite score of 18 and ACT Math Subject score of 18 as set by Welch College.