Mathematics at Carroll /

A student is assigned to a Mathematics program that best fits his/her ability level and considers previous Mathematics experiences and future needs in each student's STEM Education.  Algebra I, Geometry, Algebra II, and Pre-Calculus are offered at several levels, all of which provide college preparatory work.  Levels will differ in degree of abstraction, pace of instruction, and the degree to which a student is expected to work on their own.

Calculators, software, and other technology are necessary for Mathematics education today.  They make important mathematical ideas available to students at earlier ages, make possible the use of real-life numbers and graphs in realistic problem situations, and facilitate open-ended problem exploration.  Graphing calculators introduce students to the technology used by professional mathematicians, scientists, and engineers.  They enable students to visualize complex mathematical functions.  Graphing calculators may be used by students taking the SAT, ACT, AP, and other standardized tests.  In addition to learning to use graphing calculators, students may have the opportunity to use technological tools such as Geometer’s Sketch Pad, Infinity software and hardware, and FANUC industrial robots and programming software. These technology tools are used to strengthen the comprehension of mathematical foundations and encourage critical thinking for solving problems in a variety of STEM Education applications.

Algebra IA 101/102

First semester topics include solving equations in one variable, solving inequalities in one variable, and basics of functions (notation, function language, graphing, etc.).  Second semester topics include the study of functions, systems of linear equations and inequalities, and polynomial expressions and functions.

Algebra IB 101/102

First semester topics include quadratic functions, radical expressions and radical equations. Second semester topics include exponential functions and equations and statistical modeling.

Algebra I 101/102

This course emphasizes the underlying structure of the Real Number System and the understanding and application of Algebraic concepts.  Topics to be studied include signed numbers, solution of linear equations in one variable, polynomials, factoring, rational expressions, rectangular coordinate system and graphing, and systems of linear equations.

Geometry 201/202

This course introduces the basic concepts and relationships of geometry.  Students learn to use deductive and inductive reasoning and apply postulates and theorems to geometric figures.  Topics to be studied include properties of angles, lines, polygons, ratio and proportion, circles, area, perimeter, coordinate geometry, and volume.  Algebra skills are reinforced throughout the course.

Algebra II/Trigonometry 301/302

This course extends concepts and skills learned in first year Algebra, especially equation solving and graphing.  Topics to be studied include linear equations, quadratic and higher order polynomials, complex numbers, systems of equations, graphing, conic sections, and trigonometry.

Pre-calculus 401/402

Students will review and extend their understanding and application of Algebra I and Algebra II/Trigonometry concepts.  In addition, polynomial, trigonometric, and logarithmic functions will be discussed.  The conic sections will be explored.  As time permits, polar coordinates, sequences, series, and the concept of limits may be discussed.

Scholarship Track

Scholarship Algebra I 101/102

Prerequisite: Recommendation from the Guidance Department

The first semester of this course covers properties of real numbers, functions, solutions of linear equations in one variable, and the Cartesian coordinate system, along with graphing.  Many types of problems are explored, with emphasis on developing equations to express relationships between variable quantities, performing correct solution procedures, and clearly expressing conclusions.  The second semester covers linear inequalities, systems of linear equations and inequalities, rational exponents, polynomials and factoring, and radical expressions. Statistics and probability topics will be included, as time permits.

Scholarship Geometry 201/202

Prerequisite: Scholarship Algebra I or teacher recommendation

The first semester of this course includes the study of angles, lines, and polygons.  Students are led to an appreciation of the need for mathematical proof and will learn to construct original proofs of various types. Second semester topics include circles, right triangles, ratio and proportion, area, perimeter, volume, and coordinate geometry.

Scholarship Algebra II/Trigonometry 301/302

Prerequisite: Scholarship Algebra I and Scholarship Geometry with a 2.0 or above or teacher recommendation

This course extends concepts and skills learned in first year algebra, especially equation-solving and graphing. First semester topics include linear equations and linear systems, matrices, quadratics and higher order polynomials, complex numbers, and rational exponents.  Second semester two topics include right triangle trigonometry, the unit circle, and graphing trigonometric functions.  Additionally, logarithmic and exponential functions are explored.

Scholarship Pre-calculus 401/402

Prerequisite: 2.0 or above in Scholarship Algebra II/Trigonometry or teacher recommendation

This course prepares students for the study of calculus.  Algebra and geometry are integrated with new topics by an approach which stresses analytic geometry, the concept of function, and the axiomatic structure of algebra.  Students are introduced to the standard language and symbols of college math.  First semester topics include real and complex number fields, plane analytic geometry, algebra of functions, graphing techniques, and periodic functions.  Second semester topics include trigonometry, polynomials, exponential and logarithmic functions, vectors, polar coordinates, and sequences and series with an introduction to limits.

Honors Calculus 501/502

Prerequisite: Scholarship Pre-Calculus or teacher recommendation

This course will cover an introduction to differential calculus.  First semester topics include limits, derivatives, and applications of differentiation.  Second semester topics will focus on integration and applications of integration.

Honors Track

Honors Algebra 101/102

This challenging course covers the solution of linear equations and inequalities in one variable.  Problems of many types are explored with emphasis on collection and analysis of data, choice of efficient solution procedures, and clear presentation of results.  Topics to be studied include the real number system, matrices, introductory set theory, statistics, formulas, analytic geometry, quadratic equations and graphs, functions, systems of equations and inequalities, exponents and radicals, polynomials and factoring, proportion, and rational expressions. Rectangular coordinate system and graphing are stressed throughout the course.

Honors Geometry 201/202

This challenging course covers mathematical reasoning and proof, angles, polygons, reflections, transformations, congruence, and area and perimeter.  Algebra is integrated with geometry.  Coordinates and transformations are used in both two and three dimensions.  Other topics covered include surface area, volume, coordinate geometry, similarity, indirect proof, introductory trigonometry, and circles.  Applications and problem solving are stressed.

Honors Algebra II/Trigonometry 301/302

This fast-paced course stresses algebraic computational techniques and problem-solving skills. Topics to be studied include linear equations and inequalities, relations and functions, graphing, systems of equations and inequalities, polynomials, factoring, rational expressions, complex and irrational numbers, quadratic equations and functions, conic sections, exponential and logarithmic equations, sequences and series, and matrices. Trigonometry topics include angle measure, circular functions, trig graphs, identities, and solution of triangles. Students in this class, as well as all honors classes, are expected to work at a sophisticated level and to demonstrate a high degree of self-motivation. Honors course materials and activities demand a high level of comprehension and proficiency in mathematical communication, problem-solving, and other basic skills.

AP Pre-calculus 401/402

Advanced Placement Precalculus involves the exploration of everyday situations using mathematical tools and lenses. Students will develop an understanding of modeling and functions, and examine scenarios through multiple representations. The course framework outlines content and skills needed for mathematics, physics, biology, health science, social science, and data science careers. AP Precalculus is equivalent to a college pre-calculus course or a college algebra with trigonometry course. In the first semester, students will study polynomial, rational, exponential, and logarithmic functions. Second semester topics include trigonometric and polar functions, as well as functions involving parameters, vectors, and matrices. Students will prepare for the College Board AP Precalculus exam.

Advanced Placement Calculus AB 401/402

This course covers the normal content of a first-year college course in calculus, stressing both traditional techniques and technology intensive problem-solving methods. Students will prepare for the Advanced Placement test in Mathematics of the College Entrance Examination Board (CEEB). After a review of functions, graphing, and analytic geometry, the student studies limits, slope of a curve, and the formal definition of derivative. First semester topics include differentiation formulas, implicit differentiation, applications of the derivative including related rates and optimization problems, curve sketching, and the indefinite integral. Practical applications to physics, biology and economics are included. The second semester covers the definite and indefinite integral, applications of integration, differentiation and integration of trigonometric, exponential, and logarithmic functions.

Honor Calculs II Independent Study

This course covers second-year calculus topics, including parametrically defined curves, polar curves, and vector-valued functions, as well as infinite sequences and series. Additionally, students will review important concepts, methods and applications of differential and integral calculus involving improper integrals, Euler’s method, logistic models, and arc length. Students will prepare for and have the opportunity to take the College Board AP Calculus BC Exam. Final Semester grade only will be awarded on pass/fail scale.

Electives

Finite Math 401/402

This course will explore various applications of mathematics in the social, finance, health, environmental, ext. fields with emphasis on developing informational, technological, logical, and visual reasoning skills. Topics from numeracy, probability and statistics, finance, mathematical modeling with linear, statistical, and exponential functions, and other areas of mathematics will be covered. This course will also incorporate hands-on technological experiences with mathematical correlations to real world situations

Honors Engineering and Robotics Topics

This STEM course will introduce students to robotics and engineering topics.  The focus of this course is to introduce students to actual industrial equipment and control devices to give them a better idea of what robotics entails.  This course will also provide the opportunity to practice research, modeling, and communication.  The scientific and engineering methods for problem solving will be taught.  Students will work both in groups and on their own to complete course objectives.

AP Computer Science Principals

This STEM course will capture important aspects of the work that a computer scientist engages in at the level of competence expected of the AP Computer Science Principles student.  The students will develop computational artifacts and analyze data, information, and knowledge represented for computational use.  Students will learn to collaborate to build computation artifacts and communicate their purpose.  By the end of the course, the students will create one of the two required performance tasks, which require students to create computations artifacts though programming.  This course will prepare students for the AP Computer Science Principles Test.

Scholarship Statistics and Probability 101/102

Prerequisite: Successful completion (2.0 or better) of Scholarship Algebra II/Trigonometry or above

Students will study the mathematics of probability; they will collect, analyze and interpret data; and they will hone skills in communication and presentation of data-driven results.  Students will develop critical thinking skills as they encounter real-world data in this Information Age.  This course aims to equip students with the skills to make important insights and to make good decisions as consumers and world citizens.  First semester topics of study include basic data analysis such as graphical displays, summary statistics, lines of best fit, use of the Normal curve, exponential and power models. Second semester topics of study include data collection such as sampling, polls, surveys, observational studies, experiments and simulations; probability basics such as counting strategies, probability rules, Venn and tree diagrams, expected value and binomial probability and inference concepts.

Advanced Placement Statistics

Prerequisite: Unweighted 2.5 or above in Honors Statistics

This course is a continuation of Statistics.  Graphical and numerical techniques will be employed to analyze patterns and departure from patterns.  Using statistical inference, well-developed plans will be synthesized to obtain valid information on a conjecture and to select appropriate models for study.  Probability will be used as a tool for anticipating what the distribution of data will look like for a given model.