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# Mathematics Department

## Overview

The primary function of the Mathematics Department is to enhance the goals expressed in the Mission Statement of Bishop Hendricken High School and to implement the Mathematical Standards as set forth by the National Council of Teachers of Mathematics.  We accomplish this by helping the student to develop, through sequential programs, the necessary skills to understand and utilize the concepts of mathematics for logical thought and problem solving.  To enhance the student’s mathematical abilities in ways that will give a basis for using math as it serves the needs of everyday life and a point of departure for engaging in advanced studies in mathematics.

### 8th Grade SELECT Honors Institute

Algebra 1 –  Honors
Algebra 1 Honors is intended to build a foundation for all higher level math classes. This course will review algebraic expressions, integers, and mathematical properties that will lead to working with variables and linear equations. There will be an in-depth study of graphing, polynomials, quadratic equations, data analysis and systems of equations through direct class instruction, group work, homework, student projects and technology.

Algebra 2 –  Honors
This course is designed for students who have a solid understanding and application of algebraic concepts. After a brief review of the basics regarding equations, systems of linear equations, verbal problems and factoring, the course moves into an in depth consideration of relations, functions, irrational numbers, quadratic equations and systems, complex numbers, and polynomial functions. Progressions, binomial expansions, matrices and determinants, and probability are also explored. The course pace is rather fast and is intended to challenge those of superior ability.

### Freshman Year

Algebra 2/Analysis –  ERS
This course is designed for freshmen that have a talent in mathematics and have a near mastery in understanding and applying algebraic concepts. The course embraces the real number field; functions and their graphs; composition of functions and inverse functions; exponential and logarithmic functions; parametric equations; vectors on a plane; Analytical Geometry including circles parabolas, ellipses, hyperbolas; rotation and translation of axes; and an introduction to some key concepts appearing in Calculus.

Algebra 2  – Honors
This course is designed for freshmen who have a solid understanding and application of algebraic concepts. After a brief review of the basics regarding equations, systems of linear equations, verbal problems and factoring, the course moves into an in depth consideration of relations, functions, irrational numbers, quadratic equations and systems, complex numbers, and polynomial functions. Progressions, binomial expansions, matrices and determinants, and probability are also explored. The course pace is rather fast and is intended to challenge those of superior ability.

Algebra 1 –  Accelerated
This course is designed for those freshmen who have had some exposure to Algebra prior to high school. The course consists of the basics of Algebra including solutions to linear equations and inequalities, systems of equations, verbal problems, factoring, operations with polynomials, operations with rational equations, relations, functions, graphing linear equations and inequalities, and solving quadratic equations. The pace of this course is faster than that of Algebra I CP1 and a greater degree of mathematical rigor is required from the students.

Algebra 1 –  CP1
This course is designed for freshmen that have acquired a reasonable understanding of the concepts of Pre-algebra, but who have acquired little or no algebraic skills prior to high school. The course consists of basics of Algebra including solutions to linear equations and inequalities, systems of equations, verbal problems, factoring, operations with polynomials, operations with rational equations, relations, functions, graphing linear equations and inequalities, and solving quadratic equations.

Algebra 1 – CP
This course is designed for freshmen that have had little or no Algebra prior to high school and who have been identified as students whose background indicates a consistent weakness in the area of mathematics. The course proceeds at a slightly slower pace, covers a few less topics, and goes slightly less in depth than Algebra I CP1. The course will cover the language of algebra in verbal, tabular, graphical, and symbolic forms. Emphasis will be on the development of analytical thinking skills and the integration of algebra with statistics, data analysis, probability, and discrete mathematics.

### Sophomore Year

Geometry/Trigonometry – ERS
This course is designed for sophomores that have successfully completed the Algebra II / Analysis ERS course. The course covers theorems, proofs, the relationship between Geometry and Algebra, triangles, parallelograms, polygons, circles, areas and volumes. The Trigonometry includes periodic functions, identities, equations, graphs, inverse functions, solutions of triangles, and a host of applications. The course also looks at the logical underpinnings of mathematics, the philosophical reasons behind apparently arbitrary decisions in mathematics, and gives students the experience of developing mathematics.

Geometry  – Honors
This course is designed for sophomores who have successfully completed the Algebra II Honors course. The course will cover the geometric relationships in a plane and the meaning, nature, and use of proofs in both mathematical and non-mathematical situations. Emphasis will be on the development of analytical and creative thinking skills, the nature and structure of proof, and the integration of Geometry and Algebra. The depth of knowledge and rigor required of students is greater than the Geometry Accelerated course and may require the use of skills honed in Algebra II Honors.

Geometry  – Accelerated
This course is designed for sophomores who have successfully completed the Algebra I Accelerated course. The course will cover the geometric relationships in a plane and the meaning, nature, and use of proofs in both mathematical and non-mathematical situations. Emphasis will be on the development of analytical and creative thinking skills, the nature and structure of proof, and the integration of Geometry and Algebra. The pace of this course is faster than the Geometry CP1 course and should be a challenge for the student.

Geometry  – CP1
This course is designed for sophomores who have successfully completed the Algebra 1 CP1 course. The course will cover the geometric relationships in a plane and the meaning, nature, and use of proofs in both mathematical and non-mathematical situations. Emphasis will be on the development of analytical thinking skills and the integration of Geometry with Algebra.

Algebra 2  – CP
This course is designed for sophomores who generally struggle in mathematics and have successfully completed the Algebra I CP course. The course entails a thorough review of first year algebra, but often involves an increase in the difficulty and/or complexity of the problems. Topics include operations of real numbers, polynomials and algebraic expressions, postulates of the real number system, factoring, first degree equations and inequalities, systems on linear equations, verbal problem solving, linear functions, operations on algebraic expressions, real numbers and radicals, the systems of complex numbers, as well as quadratic equations, the graphs of quadratic functions, relations, equations and inequalities. The latter part of the course extends the laws of exponents to functions and logarithms.

### Junior Year

AP Statistics
The topics for AP Statistics are divided into four major themes: exploratory analysis, planning a study, probability, and statistical inference:

1. Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. In examining distributions of data, students should be able to detect important characteristics, such as shape, location, variability, and unusual values. From careful observations of patterns in data, students can generate conjectures about relationships among variables. The notion of how one variable may be associated with another permeates almost all of statistics, from simple comparisons of proportions through linear regression. The difference between association and causation must accompany this conceptual development throughout.
2. Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained. The plan must identify important variables related to the conjecture and specify how they are to be measured. From the data collection plan, a model can be formulated from which inferences can be drawn.
3. Probability is the tool used for anticipating what the distribution of data should look like under a given model. Random phenomena are not haphazard: they display an order that emerges only in the long run and is described by a distribution. The mathematical description of variation is central to statistics. The probability required for statistical inference is not primarily axiomatic or combinatorial, but is oriented toward describing data distributions.

Statistical inference guides the selection of appropriate models. Models and data interact in statistical work: models are used to draw conclusions from data, while the data are allowed to criticize and even falsify the model through inferential and diagnostic methods. Inference from data can be thought of as the process of selecting a reasonable model, including a statement in probability language of how confident one can be about the selection.

Pre-Calculus  – Honors
The purpose of this course is to prepare the student for a high level course in Calculus. The course embraces the real number field; functions and their graphs; composition of functions and inverse functions; exponential and logarithmic functions; Trigonometry; vectors on a plane; analytical Geometry, sequences and series, and an introduction to limits and the difference quotient. While similar in nature to Pre-Calculus Accelerated, it covers more material at a deeper level.

Algebra 2  – Accelerated
This course is designed for students of above average ability who have fulfilled the requirements of Algebra I Accelerated and Geometry Accelerated. The course entails a brief review of first year algebra, but often involves an increase in the difficulty and/or complexity of the problems. Topics include postulates of the real number system, advanced techniques of factoring, first degree equations and inequalities, matrices, the laws of exponents, logarithms, systems on linear equations, verbal problem solving, linear functions, operations on algebraic expressions, real numbers and radicals, the systems of complex numbers, as well as quadratic equations, the graphs of quadratic functions, relations, equations and inequalities.

Algebra 2 – CP1
This course is designed for students of average ability who have fulfilled the requirements of Algebra I CP1 and Geometry CP1. The course entails a thorough review of first year algebra, but often involves an increase in the difficulty and/or complexity of the problems. Topics include operations of real numbers, polynomials and algebraic expressions, postulates of the real number system, factoring, first degree equations and inequalities, systems on linear equations, verbal problem solving, linear functions, operations on algebraic expressions, real numbers and radicals, the systems of complex numbers, as well as quadratic equations, the graphs of quadratic functions, relations, equations and inequalities. The latter part of the course extends the laws of exponents to functions and logarithms.

Geometry  – CP
This course is for juniors who tend to struggle in mathematics and have successfully completed Algebra I CP and Algebra II CP. The course will cover the geometric relationships in a plane, theorems, triangles, parallelograms, polygons, circles, areas and volumes. Emphasis will be on the development of creative thinking skills and the integration of Geometry with Algebra.

### Senior Year

AP Calculus BC
Calculus BC is taught to be an equivalent course to the first two semesters of college calculus, providing both theoretical underpinnings with Calculus as well as experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. The connections among these representations are also important. Technology is used regularly by students to aid computation and understanding, but each topic also has concepts and problems that students will be expected to apply without the aid of technology. The overall themes that span the course and provide motivation for the development of the topics are the historical problems that faced mathematicians, the new mathematical concept of limits and its application to each of the three main areas of study (derivatives, integrals, and series), and Calculus’ unique historical and practical relationship with the subject of physics. To this end, students taking Calculus BC take it as part of a two-period course that teaches both AP Calculus and AP Physics together, reinforcing their relationship and strengthening the students’ understanding of both.

AP Calculus AB
Calculus AB is taught to be an equivalent course to the first one and a half semesters of college calculus, providing both theoretical underpinnings with Calculus as well as experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. The connections among these representations are also important. Technology is used regularly by students to aid computation and understanding, but each topic also has concepts and problems that students will be expected to apply without the aid of technology. The overall themes that span the course and provide motivation for the development of the topics are the historical problems that faced mathematicians, and the new mathematical concept of limits and its application to each of the two main areas of study (derivatives, and integrals). These themes serve to unify the course into a cohesive subject.

Pre-Calculus – Honors
The purpose of this course is to prepare the student for a high level course in Calculus. The course embraces the real number field; functions and their graphs; composition of functions and inverse functions; exponential and logarithmic functions; Trigonometry; vectors on a plane; analytical Geometry, sequences and series, and an introduction to limits and the difference quotient. While similar in nature to Pre-Calculus Accelerated, it covers more material at a deeper level.

Pre-Calculus –  Accelerated
The purpose of this course is to prepare the student for Calculus. The course embraces the real number field; functions and their graphs; composition of functions and inverse functions; exponential and logarithmic functions; a review of Trigonometry; vectors on a plane; and analytical Geometry.

Pre-Calculus – CP1
The purpose of this course is to solidify and expand a student’s understanding of Algebraic needed for a course in Calculus. The course embraces the real number field; functions and their graphs; composition of functions and inverse functions; exponential and logarithmic functions; Trigonometry. While similar in nature to Pre-Calculus Accelerated, this course covers the material in less depth and with less mathematical rigor.

Statistics Accelerated
This course is designed for students who have successfully completed Algebra II Accelerated or have achieved an outstanding understanding of Algebra II CP1. Students are introduced to the topics as described in Statistics AP, but are measured using evaluation methods more suitable to the students’ level.

Math Topics (2 Semester Courses)
This course is designed for those students that struggle in mathematics and have successfully completed Algebra I CP, Geometry CP, and Algebra II CP. The purpose of this course is to provide a strong preparation and solid foundation for these students as they begin to take college placement tests and prepare to take more advanced courses such as trigonometry, statistics, finite mathematics, and pre-calculus. This course presents the fundamentals of algebra needed for further work in mathematics. Due to the purpose the exact material covered in the course will vary from class to class, depending on the make-up of that particular class’s abilities. The course often includes a thorough review of arithmetic and algebraic concepts, such as linear equations, and inequalities. The course also often includes a review of Algebra II, with polynomial, quadratic, and rational functions. There is an attempt made to introduce students to types of mathematics that can be fresh and invigorating. These topics have included trigonometric ratios and equations, polar coordinates, mathematical applications, and logic.