Mathematics Department

Radnor’s mathematics curriculum has been developed to accommodate the various levels of a student’s mathematical abilities and skills. Although traditional math skills will be taught in all courses, the goal of the mathematics curriculum will be to develop thinking skills through emphasis on mathematical concepts. Use of problems requiring critical thinking will be employed to better prepare the student for a world which is becoming more technologically dependent. Students should follow teacher recommendations when deciding which sequence of courses to select.
Seminar level courses are intended for the highly motivated math students and are designed to challenge the most mathematically capable students. The courses will involve rigorous pacing and workload with teacher expectations intended to challenge the student. The course will require more independent and self guided learning (with an emphasis on writing explanations) than all other courses.
Honors level courses are intended for the motivated math student who is very good with mathematics but needs more teacher guidance to assist in the mastery of the material. The course will involve accelerated pacing and a demanding workload with some written explanations expected. Students on this level will be prepared to take AP Calculus AB.
Advanced level courses will feature a more challenging pacing and workload with teacher guidance to assist in the mastery of the material. Students enrolled on this level should be seeking to satisfy college requirements/expectations of mathematics course but not necessarily have an interest in pursuing math related college majors. Any student who wishes to advance in math and to be eligible to take Calculus in High School can do so by taking Algebra II and Geometry concurrently, or by taking an approved Geometry summer school course at the expense of the parent(s)/guardians. The student must also take the RHS Geometry.
College Prep level courses will feature a moderate pace and workload and a higher degree of teacherguidance to assist in the mastery of the material. These courses will cover material necessary to prepare students for the Keystone Exams as well as prepare the student to take the SAT test if post secondary education is desired.
Students interested in pursuing college majors in the science, engineering, medical, and mathematics fields should enroll in the Honors level courses.

The mathematics curriculum is intended to meet the needs of all students. To aid each student in determining his/her appropriate course of study in mathematics, the classroom teacher evaluates the progress of each individual at course selection time and recommends a specific course for the following year. This personal evaluation takes into account attitude, mathematical background, future plans, and current achievement. As a result, a student may be recommended to move from one level to another. Students should pay careful attention to these recommendations, as well as to the prerequisites, before electing a course.The mathematics department believes that the very nature of the mathematics curriculum must be changed to meet the needs of our students as they prepare for their future. Mathematics problems and the methods used to solve them have changed with technological advances. The understanding and competent use of technological tools are important to all our students. The department requires that each student have his/her own calculator. A scientific calculator, such as the TI34 is sufficient for courses up to and including Geometry. For all courses at the Algebra 2 Level and beyond, a graphing calculator such as the TI84 PLUS is required. More sophisticated graphing calculators are optional for honors courses. Classroom instruction includes demonstrations on the TI84 PLUS calculator. Since graphing calculators are allowed on the SATs, we encourage all students to be proficient in their use. The department realizes that graphing calculators are expensive. If financial considerations are a problem, please notify the teacher or the department chairperson.
PreAlgebra Courses

Introduction to Algebra I (05040412)
1.0 Credit; Unweighted
Length: Year; Format: Meets Daily
Grade(s): 9
Prerequisite(s): 8th grade Intensive Math or Teacher Recommendation
This course is designed to be the first year of a twoyear study of Algebra I and will provide students with a foundation in the algebraic strand of mathematics, which includes understanding patterns, relations, and functions, representing and analyzing mathematical situations and structures using algebraic symbols, using mathematical models to represent and understand quantitative relationships, and analyzing change in various contexts. Mathematics itself is looked at not just as calculation but also as a modeling language, as a process for logical thought, and as a field of study. This approach to Algebra I is organized around families of functions, with special emphasis on linear functions. Students will learn about each family of functions, how to represent them in multiple ways: as verbal descriptions, equations, tables, and graphs. They also will learn to model realworld situations using functions in order to solve problems arising from those situations. Course pacing and structure will allow for important skills to be honed through additional practice time. Students at this level complete Algebra I in two years and will take the Algebra I Keystone Exam upon completion of the second course.
Algebra 1 Courses

Algebra 1 A (05040414)
1.0 Credit; Unweighted
Length: Year; Format: Meets Daily
Grade(s): 9, 10
Prerequisite(s): Teacher RecommendationThe goal of this course is to develop algebraic skills and concepts and to enhance problem solving ability. Topics include: polynomial expressions and equations, quadratic functions, irrational numbers, coordinate graphing, graphing linear and quadratic functions, basic statistics, determining and analyzing the slope of lines, and factoring polynomial expressions. Algebra skills and concepts needed to solve equations, inequalities, and systems of equations/inequalities are developed. Algebraic problem solving techniques are employed to solve relevant applications.

Algebra 1 CP (05040416)
1.0 Credit; Unweighted
Length: Year; Format: Meets Daily
Grade(s): 9
Prerequisite(s): 8th grade intensive math or Teacher RecommendationAlgebra concepts and skills and problem solving techniques will be developed at a moderate pace and an appropriate difficulty level. Topics will include the basic skills in working with integers, exploring patterns, and solving equations and inequalities with one or two variables. Applications of these skills will be used to enhance problem solving ability. Additional topics including functions, data analysis, graphing techniques, polynomials, factoring, quadratics, and systems of equations will be introduced. The course is designed to help students meet the Pennsylvania State Standards in mathematics.
Geometry Courses

Seminar Geometry H (05040420)
1.0 Credit; Weighted
Length: Year; Format: Meets Daily
Grade(s): 9
Prerequisite(s): 8th grade Algebra with a Grade of “A” or Teacher RecommendationThis course is a challenging, rigorous, proofbased approach to Geometry. Students in Seminar Geometry analyze geometric figures using deductive reasoning, make conjectures and formulate hypotheses, draw conclusions, make connections with other mathematical concepts, and model situations geometrically as a problem solving strategy. Algebraic and geometric skills and interactive computer software may be integrated throughout the curriculum.

Geometry H (05040422)
1.0 Credit; Weighted
Length: Year; Format: Meets Daily
Grade(s): 9, 10
Prerequisite(s): 8th grade Algebra 1 with a “B” and Teacher RecommendationNote(s): Students with a grade of “C”or lower in Algebra 1 are strongly encouraged to enroll in Algebra 1 A (0414) or take Algebra 1 in a summer school program before taking the course. This course uses a disciplined approach to traditional Geometry, integrating the concepts and skills previously developed in Algebra 1. Students in Geometry H apply geometric concepts to solve problems, use twocolumn proofs to establish relationships among triangles and parts of triangles, apply similarity theorems to geometric figures, relateknowledge of parallel and perpendicular lines to solve practical problems, combine algebraic and geometric skills to solve perimeter, area and volume problems, and apply skills involving trigonometry and transformational geometry. Interactive computer software may be integrated throughout the curriculum.

Geometry A (05040424)
1.0 Credit; Unweighted
Length: Year; Format: Meets Daily
Grade(s): 9, 10, 11
Prerequisite(s): Algebra 1 A or a “B” in 8th grade Algebra 1
Note(s): Students with a grade of a “C” or lower in Algebra 1 are
strongly encouraged to enroll in Algebra 1 A (0414) or take Algebra 1 in a summer school program before taking this course.This class is a conceptbased approach to traditional Geometry designed to reinforce and extend previous algebra skills while integrating new geometric concepts. Students in Geometry derive and use formulas for perimeter, circumference, area, surface area, and volume of many types of figures, use the Pythagorean Theorem, use congruence and similarity in describing relationships between figures, and analyze geometric figures. Some computer lab work may be performed during the year. Throughout the course, algebra skills will be reviewed and reinforced through the application of geometry concepts.

Geometry CP (05040426)
1.0 Credit; Unweighted
Length: Year; Format: Meets Daily
Grade(s): 9, 10, 11
Prerequisite(s): Algebra 1 CP or Teacher RecommendationThe course will cover the basic concepts of geometry at a moderate pace and an appropriate difficulty level. Topics will include the definitions and properties of geometric shapes. The concepts of congruence and similarity will be applied to appropriate figures and problem solving situations. Perimeter, area and volume formulas will be used for various geometric shapes. Pythagorean Theorem and the right triangle trigonometric ratios will be introduced. Throughout the course, algebra skills will be reviewed and reinforced through applications of geometric concepts. The course is designed to help students meet the Pennsylvania State Standards in mathematics.
Algebra 2 Courses

Seminar Algebra 2 H (05040430)
1.0 Credit; Weighted
Length: Year; Format: Meets Daily
Grade(s): 10
Prerequisite(s): Seminar Geometry H with a grade of “B” or Teacher Recommendation
Seminar Algebra 2 H is an enriched and extended study of the topics of Algebra 2 H (0453). In addition, it includes an indepth study of exponential and logarithmic functions, quadratic relations (conics), sequences and series, probability, matrix algebra and the graphs of rational functions. This course uses an exploration/discovery approach to develop course content. There is a heavy emphasis on realworld applications. Written explanations are a part of assessment. Students are required, on a regular basis, to make connections within and between mathematical concepts. 
Algebra 2 H (05040432)
1.0 Credit; Weighted
Length: Year; Format: Meets Daily
Grade(s): 10, 11
Prerequisite(s): 8th grade Algebra 1 with a “B” and Geometry H with a “B”, Seminar Geometry with a “B”
This course reviews and extends the number system, formulas, equations and graphs. Subject matter includes quadratics, radicals, exponents, and complex numbers. An emphasis is placed on both the development of the concept of function and graphing functions using a transformational approach. Logarithms, exponential functions, theory of equations and sequences and series are introduced during the course. Students are challenged to apply skills to new problems and to connect skills and concepts. Students are expected to handle a demanding workload. 
Algebra 2 A (05040434)
1.0 Credit; Unweighted
Length: Year; Format: Meets Daily
Grade(s): 11, 12
Prerequisite(s): Geometry A with a “C”
Note(s): This course cannot be used as a prerequisite for Precalculus H (0443). A graphing calculator is required.
This course reviews and extends an understanding of the number system, formulas, equations and graphs. Subject matter includes quadratics, radicals, exponents, complex numbers and the mathematical concept of function. Logarithms, exponential functions and theory of equations are introduced during the course. This course involves the use of a graphing calculator to develop and practice concepts, rather than the theoretical approach used in Algebra 2 H. Students are expected to handle an appropriate workload at a moderate pace. 
Algebra 2 CP (05040436)
1.0 Credit; Unweighted
Length: Year; Format: Meets Daily
Grade(s): 11, 12
Prerequisite(s): Algebra 1 CP and Geometry CP
The course reinforces and extends the skills and concepts from previous algebra courses. Topics include, but are not limited to, solutions of linear equations and inequalities, solutions of quadratic equations, rules for exponents, radicals and rational expressions, and graphs of linear, absolute value, and quadratic functions. Where appropriate, applications using geometric concepts are included.
Algebra 3 Courses

Algebra 3 and Trigonometry CP (05040446)
1.0 Credit; Unweighted
Length: Year; Format: Meets Daily
Grade(s): 11, 12
Prerequisite(s): Algebra 2 CP
Algebra 3 is intended to complete the topics of Algebra not developed in Algebra 2. In addition, the course will review, reinforce and strengthen the concepts and skills studied in Algebra 2 with emphasis on equation and inequality solving. The new topics will include but not be limited to complex numbers, exponential and logarithmic functions, and sequences and series. Trigonometry will be introduced through right triangles and extended to include the circular functions.
Advanced Mathematics & Calculus Courses

Seminar Precalculus H (05040440)
1.0 Credit; Weighted
Length: Year; Format: Meets Daily
Grade(s): 11
Prerequisite(s): Seminar Algebra 2 H with a Grade of “B” or Teacher Recommendation
Students who successfully complete this course are prepared for Advanced Placement Calculus AB or BC. Explorations and discovery methods are emphasized in developing course content. Students are expected to make connections and to explain understanding of mathematical concepts through written and oral presentations. Students apply knowledge to math modeling. Topics include: right triangle and circular trigonometry, graphing trigonometric functions using advanced techniques, inverse trigonometric functions, identities and equations, math induction, laws of sines and cosines, polar functions, polar conics, parametric functions, DeMoivre’s Theorem, sequences and series, polynomial, rational, exponential and logarithmic functions, limits, operations of functions, and rates of change. 
Precalculus H (05040441)
1.0 Credit; Weighted
Length: Year; Format: Meets Daily
Grade(s): 11, 12
Prerequisite(s): Algebra 2 H with a Grade of “B” or Trigonometry/Discrete Math A with a "B” or Teacher Recommendation
This course prepares students to take a college level Calculus or Advanced Placement Calculus AB course. Emphasis is on making connections and indepth explanations of mathematical processes that demonstrate an understanding of concepts. Real world applications are used to enhance mastery. Topics covered are linear, polynomial, rational, exponential, logarithmic, trigonometric, piecewise, quadratic, polar and inverse functions, sequences and series, math induction, laws of sines and cosines, trigonometric identities and equations. 
Precalculus A (05040448)
1.0 Credit; Unweighted
Length: Year; Format: Meets Daily
Grade(s): 12
Prerequisite(s): Algebra 2 A
The goal of this course is to examine trigonometric concepts and application and explore appropriate discrete topics. Trigonometry is taught using both a right triangle and unit circle approach. Exponential and logarithmic functions, sequences and series, and as time allows, other topics in discrete math are introduced. Many of these topics have applications in engineering, management, and the social sciences. Algebra skills necessary for success in subsequent mathematics courses will be reviewed throughout the year. 
Advanced Placement Calculus AB (05040450)
1.0 Credit; Weighted
Length: Year; Format: Meets Daily
Grade(s): 12
Prerequisite(s): Precalculus H with a “B” or Teacher Recommendation
Note(s): This collegelevel course prepares students to successfully take the Calculus AB Advanced Placement Exam and receive 1 or 2 semesters of college credit and/or placement as a result.Students electing this course engage in a thorough study of: limits and continuity, differentiation, integration, and differential equations as well as appropriate applications. The functions studied in previous mathematics courses will be used to develop these themes. This is a PLTW + AP Pathway course.

Advanced Placement Calculus BC (05040460)
1.0 Credit; Weighted
Length: Year; Format: Meets Daily
Grade(s): 12
Prerequisite(s): Recommended by Department
Note(s): This collegelevel course prepares students to successfully take the Calculus BC Advanced Placement Exam and receive 2 or 3 semesters of college credit and/or placement as a result.In addition to the topics listed under Advanced Placement Calculus AB, students electing this course engage in a thorough study of: L’Hopital’s Rule for evaluating some limits, use of derivatives to analyze polar, parametric, and vector functions, integration techniques and applications, numerical solutions to differential equations using Euler’s Method, and sequences and series, including the use of tests for convergence and the development of Maclaurin and Taylor polynomials and their convergence. This is a PLTW + AP Pathway course.

Calculus 1 A (05040452)
1.0 Credit; Unweighted
Length: Year; Format: Meets Daily
Grade(s): 12
Prerequisite(s): Precalculus H or Trigonometry/Discrete Math A with a “B” or Teacher RecommendationTraditionally, calculus has been the mathematics course taken by college freshmen. There is currently a growing realization that students also need to be prepared in the areas of linear algebra, probability and statistics, logic, and other discrete mathematics topics. This need arises because of the everincreasing role of computing in all disciplines and the importance of discrete mathematics in computing. The objective of this course is to provide an introduction to traditional first semester calculus and to introduce students to the many topics in discrete mathematics – both of which have important applications in engineering, management, and the social sciences.

Linear Algebra H (05040480)
1.0 Credit; Weighted
Length: Year; Format: Meets Daily
Grade(s): 11, 12
Prerequisite(s): AP Calculus AB, AP Calculus BC, or teacher recommendationThis college level course is designed to prepare the student for eventual courses in multivariable calculus and modern algebra. Students will study systems of equations, vectors and vector spaces, linear transformations and matrix representations, determinants, eigenvectors and eigenvalues and a variety of applications. Linear algebra is used in abstract algebra, functional analysis and has extensive applications to both natural sciences and social sciences. This is dual enrollment course.

Note: Multivariable Calculus will be offered on alternating years beginning in 20172018. Multivariable Calculus will not be offered again until 20192020.
Multivariable Calculus H (05040500)
1.0 Credit; Weighted
Length: Year; Format: Meets Daily
Grade(s): 11, 12
Prerequisite(s): AP Calculus BC with a B or better.
This college level course is designed to prepare the student for eventual courses in differential equations. Students electing to take this course will review polar and parametric curves as well as infinite series. They will study vectors and the geometry of space, vector functions, vector calculus, partial derivatives, multiple integrals, and second order differential equations.
Statistics

Advanced Placement Statistics (05040470)
1.0 Credit; Weighted
Length: Year; Format: Meets Daily
Grade(s): 11, 12
Prerequisite(s): Seminar Algebra 2 with a Grade of "C" or Algebra 2 H with a Grade of a "B" or Teacher Recommendation
AP Statistics introduces students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad concepts: exploring data for patterns and departures from patterns, sampling and experimentation in planning and conducting a study, anticipating patterns while exploring random phenomena using probability and simulation, and statistical inference during estimating population parameters and testing hypotheses. Students who successfully complete this course and the College Board AP Statistics examination may receive advanced credit for one semester of introductory college statistics. 
Statistics A (05040472)
1.0 Credit; Unweighted
Length: Year; Format: Meets Daily
Grade(s): 11, 12
Prerequisite(s): Algebra 2 A or Algebra 2 CP
The four major themes of statistics of describing data through graphical means, sampling and experimentation, anticipating patterns, and statistical inference are explored along with the basic concepts of probability. Various computer and statistical projects are given to complement the course throughout the year.
Computer Science Courses

Advanced Placement Computer Science A (05040490)
1.0 Credit; Weighted
Length: Year; Format: Meets Daily
Grade(s): 1012
Prerequisite(s): Introduction to Computer Science or with a Teacher Recommendation (This prerequisite begins in the 20182019 school year)Students electing this course engage in a study computer science and will design and implement solutions to problems by writing, running and debugging computer programs. Use and implement commonly used algorithms and data structures. Develop and select appropriate algorithms and data structures to solve problems. Develop code fluently in an objectoriented paradigm using the programming language Java. Recognize the ethical and social implications of computer use. Read and understand a large program consisting of several classes and interacting objects. Read and understand a description of design and developmental process leading to such a program. This is a PLTW + AP Pathway course.