# Mathematics

The ability to reason and analyze with mathematical skills and techniques is central to Baylorâ€™s philosophy. Baylor recognizes the importance of understanding mathematical concepts in multiple ways in order to develop methods to handle familiar and unfamiliar problems. The ability to convey mathematical understanding analytically, orally, in writing and through collaborative processes is also an important part of a mathematics education. Baylor further recognizes the importance of integrating available technology into its mathematics curriculum at every grade level and the importance of graphing calculators in mathematics instruction (the Texas Instruments TI-84+ and TI-84+C graphing calculators are used in all classes).

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Mathematics Requirements**

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*Four credits are required. Students must take a full year of Mathematics at each grade level.*

### CLASSES

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**Algebra I**

This course in first-year algebra stresses the use of symbols to represent variable quantities, patterns in data, techniques for manipulating algebraic expressions with exponents, and methods for solving equations and inequalities. The emphasis is on linear relationships and linear functions. Graphical representations and applications to problem-solving are ulitized throughout the course. The graphing calculator is used to enhance the understanding of functions.

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**Geometry**

This is a course in plane geometry with additional topics in solid geometry, analytic geometry, coordinate geometry, and transformations. Deductive reasoning is used to build concepts of points, lines, planes, parallelism, congruence, and similarity. While being introduced to methods of proof and critical thinking within a logical system, students learn how to solve problems within two-dimensional and three-dimensional models.

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**Honors Geometry**

Geometry Honors covers the outline of Geometry in greater detail and at a faster pace and includes additional topics not covered in regular sections. Increased emphasis is placed on solid geometry and on more elaborate proofs. The honors class is offered to highly motivated students who have excelled in Algebra I and who have demonstrated the ability to do advanced work in their previous math classes. Departmental approval is required for enrollment.

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**Algebra II**

This course advances the understanding of functions and algebraic models for problem solving. Topics include linear and non-linear systems, the real number system and its properties, quadratic and higher order polynomial functions, rational functions, functions with rational exponents, and basic statistics, and probability theory. Students are presented with a wide variety of problem-solving techniques including symbolic manipulation and graphical analyses, which are complemented by use of the graphing calculator.

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**Algebra II with Trigonometry**

Building upon a mastery of Algebra I, this course deepens the study of linear and non-linear systems. Topics include real and complex numbers, quadratic and higher order polynomial functions, power, radical, and rational functions, trigonometry with the unit circle using degree measure, matrix methods, and applications in statistics and discrete mathematics. Students are presented with a wide variety of problem-solving techniques including symbolic manipulation, matrices, graphical analyses, and modeling both by hand and using the graphing calculator as a tool to aid understanding.

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**Algebra II Honors with Trigonometry**

Algebra II Honors covers the outline of Algebra II with Trigonometry in greater detail and at a faster pace and includes additional topics normally not covered until Precalculus. Students are expected to be able to solve challenging problems that integrate geometry and algebra. Particular emphasis is placed on problems that involve applications of critical thinking. The honors section is offered to highly motivated students who have excelled in Algebra I and Geometry and who have demonstrated the ability to do advanced work in their previous math classes. Departmental approval is required for enrollment.

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**Precalculus**

This course builds on concepts presented in previous math courses and is a more rigorous treatment of advanced topics from algebra and geometry. Topics include function analysis in both real and complex number systems, advanced methods in problem-solving and graphical analysis, exponential and logarithmic functions, and trigonometric function analysis using radian measure. Additional topics include sequences and series, statistical reasoning, and limit definitions of asymptotes. The graphing calculator is used to enhance the understanding of the mathematical concepts.

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**Precalculus Honors**

Precalculus Honors covers the outline of Precalculus in greater detail and at a faster pace and includes additional topics normally not covered in regular sections of Precalculus. An introduction to differential and integral calculus is presented at the end of the course to prepare students for AP Calculus. The honors section is offered to highly motivated students who have excelled in Algebra II with Trigonometry and who have demonstrated the ability to do advanced work in their previous math classes. Departmental approval is required for enrollment.

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**Math Electives**

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**Trigonometry and Analysis**

This course is designed for those who have completed Algebra II or those who can profit from additional study of trigonometry and functions. Transformations of polynomial and rational functions provide a foundation for the study of advanced functions including logarithmic, exponential, and trigonometric functions. Problem-solving techniques using applications of function analysis include prediction based on algebraic, numerical, and graphical models. A review of right triangle trigonometry leads to defining trigonometry in terms of the unit circle. The course emphasizes understanding and problem solving using the graphing calculator as a tool for discovery and conceptual understanding.

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**Honors Abstract Mathematics**

Topics covered in this capstone course include mathematical proof as a basis for the rigor and elegance of mathematics, linear algebra and vector spaces, non-Euclidean geometries, a brief introduction to both multivariate calculus and differential equations, group theory and transformations, and graph theory. The course is designed to challenge those students whose background has included honors mathematics courses throughout high school. Students must be strong, independent, mathematical thinkers who have displayed exceptional reasoning and who express specific interest in pursuing theoretical mathematics. Prerequisite: AP Calculus BC. Permission to register for the course concomitant with AP Calculus BC may be petitioned. Registration must be approved by the Math Department Chair.

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**AP Courses in Mathematics**

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**AP Statistics**

This is an Advanced Placement course that follows the syllabus prepared by the College Board. The course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data, including data exploration, probability and simulation, and statistical inference. Prerequisite: Strong performance in Precalculus and approval by the department. Highly motivated students who have completed Algebra II with a strong performance and who will be taking Precalculus concurrently may also enroll in AP Statistics with departmental approval. Departmental approval is required for enrollment.

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**AP Calculus AB**

This is an Advanced Placement course in single variable calculus that follows the syllabus prepared by the College Board. The course builds on a rigorous treatment of topics covered in Precalculus and includes differential and integral calculus with applications. Prerequisite: Strong performance in Precalculus and permission of department chair. Departmental approval is required for enrollment.

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**AP Calculus BC**

This course covers all of the topics of the AB course in somewhat greater depth and rigor. In addition, some infinite series and vector topics are included. The course follows the College Board syllabus for Calculus BC. Prerequisite: Precalculus Honors and permission of the department chair. The Precalculus Honors requirement may be waived in unusual circumstances after approval by the department chair.

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**Math Courses lasting a semester.**

All of these are semester-long courses. They may be taken as electives or to fulfill the requirements for mathematics.

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**Calculus I**

This course in single variable calculus is intended for students who have completed Precalculus and plan to take first semester calculus in college. The course provides a firm foundation in the concepts and topics in differential calculus and prepares students for the rigorous pace of a semester course in college. Specific topics include limits, derivatives of polynomial, trigonometric, and transcendental functions, and curve sketching.

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**Calculus II**

Calculus II is a course that continues the study of calculus begun in Calculus I. Extending the understanding of derivatives to integral calculus, the course provides a foundation in calculus that prepares students for a complete first semester calculus course in college. The course focuses on integral calculus and applications of integration. Specific topics include area approximations, basic integration through integration by parts, connecting derivatives and antiderivatives, and applications of integration.

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**Discrete Math I**

This course lays the mathematical foundation for future courses in math and computer science such as data structures, algorithms, and database theory and for mathematics courses such as linear algebra, logic and set theory, and number theory. Specific topics include logical form and logical equivalence, conditional statements, valid and invalid arguments, digital logic circuits, modular arithmetic, graphs and trees. It is designed for students who have an interest in computer science and are interested in looking at math in an entirely new way. This course is designed for students who have completed Trig and Analysis. It may be taken concurrently with Precalculus.

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**Discrete Math II**

This course focuses on reasoning and symbolic logic. It is designed for students who may want to pursue the study of computer science and/or applied mathematics in college. Students who have completed either Precalculus or Discrete Math I may take the course. Topics include direct proof, proof by counterexample, set theory, binary relations, and group theory with graphing including isomorphisms, homomorphisms, abelian groups, and Cayley digraphs.

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**Finite Mathematics**

This course in foundational mathematics addresses topics not found in a traditional precalculus sequence. Topics include elementary probability including combinatorics and Markov chains, linear systems and matrix algebra, linear programming, and financial mathematics. This course is designed for students who have completed Trig and Analysis. It may be taken concurrently with Precalculus.

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**Workshop Statistics**

This course in hands-on statistics provides a basic understanding of descriptive and inferential statistics using the TI 84+ graphing calculator. Applications of statistical concepts include graphing and data presentation, exploring types of probability distributions, and using sampling methods to both describe and make inferences about a population. These topics are taught using discovery methods through simulations, activities, and projects. This course is designed for students who have completed Trig and Analysis. It may be taken concurrently with Precalculus.