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Math Dept Course Offerings

Algebra I - 45310

Students learn to manipulate algebraic expressions and use them to model real world phenomena in Algebra 1. An emphasis is placed on representing problems both graphically and algebraically.

1st Semester Topics: Properties of Equality, Substitution and Distribution, Signed Numbers, Algorithms for Solving Linear Equations and Inequalities, Linear Graphing

2nd Semester Topics: Formulas, Functions, Systems of Equations, Exponents, Radicals, Polynomials, Proportions

Prerequisites: None

Geometry - 45410

Investigation, justification and proof are themes repeated throughout this course. With Geometer's Sketchpad students investigate geometric situations and are taught to justify their conjectures using a variety of methods. Whenever possible, paper folding and other "hands on" methods are used to introduce concepts.

1st Semester Topics: Habits of Mind, Congruence, Area

2nd Semester Topics: Similarity, Coordinates, Vectors, Optimization

Prerequisite: Algebra 1

Algebra 2 AB - 45210

This course covers some material from Algebra 1 in greater depth and introduces new topics, such as logarithms and exponentials, to be extended in Pre-Calculus. The use of graphing calculators as a tool for investigation is emphasized.

1st semester topics: Linear Graphs, Functions, Systems of Equations, Quadratics

2nd semester topics: Exponentials, Logarithms, Polynomials, Rational Expressions, Right Triangle Trigonometry

Prerequisites: Algebra 1 and Geometry

Algebra 2 BC - 45010

The ideas of Algebra 1 are extended here, particularly in the first semester. Trigonometry is integrated throughout the course, including a study of the unit circle, as well as the law of sines and cosines. Problem solving is emphasized. Basic statistical ideas are reviewed, and connections are made to Combinatorics and the Binomial Theorem.

1st semester topics: The Real Number System, Combinatorics, Linear Equations and Inequalities, Systems of Equations, Exponents, Factoring

2nd semester topics: Advanced Factoring, Rational Expressions, Radicals, Quadratics, Exponentials, Logarithms

Prerequisites: Algebra 1, Geometry and Teacher Recommendation

Pre-Calculus AB - 46813

All of the functions that are necessary to take a full Calculus course are studied here. Polynomial, rational, exponential and logarithmic functions are studied at a greater depth than in Algebra 2; similarly, the triangle trigonometry introduced in Geometry is extended to the unit circle, along with graphing in the coordinate plane and manipulations using identities. Sequences and series are studied at a level appropriate for students intending to take the Advanced Placement AB exam. As in all courses at Payton, students learn to move fluidly between graphic, numeric and symbolic representations of these functions.

1st Semester Topics: Polynomials, Exponentials, Logarithms, Trigonometry

2nd Semester Topics: Further Trigonometry, Sequences and Series, Discrete Mathematics

Prerequisites: Algebra 2

Pre-Calculus BC - 45710

The central strands of Precalculus BC are functions (both general and specific), trigonometry, and mathematical modeling. In the first semester, students are introduced to the algebra of functions from three perspectives used throughout the course: graphical, numeric, and symbolic. We have two goals: first, students should be able to solve complicated equations and manipulate complex expressions; second, they should also understand and be able to apply the properties of these functions in a wide variety of contexts. Students learn to write and read proofs about algebraic concepts. Students become proficient at creating and using statistical models for modeling variation and spread using Fathom software; as they gain algebraic fluency over the year, we introduce computerized symbol manipulators such as the TI-89 calculator and Mathematica software.

1st Semester Topics: Polynomial, Rational, Radical, Exponential and Logarithmic Functions, Graphs of Trigonometric Functions

2nd Semester Topics: Trigonometric Identities, Vectors, Polar Coordinates, Complex Numbers, Sequences and Series

Prerequisites: Algebra 2 BC and Teacher Recommendation

AP AB Calculus - 47210

Students will learn Calculus through multiple representations-numeric, graphic and symbolic. The graphing calculator will be used to develop conceptual understanding, but traditional paper manipulation will also be emphasized. The outline for this course, AP Statistics and AB Calculus is available through the College Board's website (collegeboard.com). All students will be expected to take the AP exam in May, for which many colleges will grant one semester of Calculus credit.

1st Semester Topics: Continuity, Limits, Derivatives with Applications

2nd Semester Topics: Integrals, The Fundamental Theorem of Calculus, Polynomial Approximation and Series

Prerequisite: Pre-Calculus

AP BC Calculus - 47110

All of the topics in AB Calculus are included in BC; additional topics include Taylor Series, Parametrics and Polar Equations, Vectors, L'Hopital's Rule, Euler's Method and Improper Integrals. The outline for this course, AP Statistics and AB Calculus is available through the College Board's website (collegeboard.com). All students will be expected to take the AP exam in May, for which many colleges will grant two semesters of Calculus credit.

1st Semester Topics: Continuity, Limits, Derivatives with Applications, Integrals, The Fundamental Theorem of Calculus

2nd Semester Topics: Approximation and Series, Taylor Series, Improper Integrals, Vector Calculus, Calculus in Polar Coordinates

Prerequisites: BC Pre-Calculus and Teacher recommendation

AP Statistics - 47410

The Advanced Placement course in statistics will introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students will be exposed to four broad conceptual themes: (1) exploring data: observing patterns and departures from patterns; (2) planning a study: deciding what and how to measure; (3) anticipating patterns: producing models using probability theory and simulation; and (4) statistical inference: confirming models and using sample data to make inferences about the entire population. Students will learn to use statistics software both on the computer and on the TI-83 calculator, and the course will not emphasize rote computation, but rather interpretation of the computed output. All students will be expected to take the AP exam in May, for which many colleges will grant credit and placement for freshman statistics.

Prerequisites: Must have taken or be enrolled in Algebra 2 and Teacher Recommendation

Kaleidoscopic Advanced Mathematics I - 40310

Students enrolled in Pre-Calculus or beyond are eligible to take this course with a teacher recommendation. The intention of KAM is to expose possible college math and science majors to a survey of college level math topics. KAM I will include study of a variety of advanced Geometry. We will begin the first quarter with Euclidean topics beyond the standard Geometry curriculum: Ceva’s theorem, advanced constructions, the Fermat Point, the Nine Point Circle, etc. This section will be followed by an in depth look at synthetic inversion. In the second quarter we will go on to study non-Euclidean Geometry, including Taxicab, Spherical, and Hyperbolic. The second semester of KAM I will involve a thorough introduction to iteration, fractals, and chaos. Julia sets and the Mandelbrot sets will be studied at the conclusion of the course.

1st Semester topics: Advanced Euclidean geometry, Inversion, Taxicab Geometry, Absolute, Spherical, and Hyperbolic geometry

2nd Semester Topics: Iteration, Fractals, Chaos, including the chaos game, fractional dimension, Julia sets, and the Mandelbrot set.

Prerequisites: Algebra 2/BC and Teacher Recommendation

Kaleidoscopic Advanced Mathematics II - 40320

Kaleidoscopic Advanced Mathematics is an in-depth look at the axioms and major theorems of the real numbers. The course begins with an introduction to number theory, and continues with rigorous definitions of limits, convergence, continuity, derivatives, and integrals. The course will conclude with an investigation of one of several possible topics, including the construction of the real number system or the theory of computation, according to student interest. Class time will consist primarily of student presentations of proofs of the lemmas and theorems derived in the course, and student solutions to other problems. The course is roughly equivalent to an advanced, Honors Calculus sequence for college mathematics majors.

Prerequisites: Enrollment in AP Calculus, or beyond, and Teacher Recommendation.

* The letters "AB" and "BC" relate to the Advanced Placement Calculus Exams; AB Calculus and BC Calculus. The Algebra 2 and Pre Calculus BC courses are required for students intending to take the Advanced Placement BC Calculus course. Many colleges offer two semesters of credit for students receiving a passing grade on the BC Advanced Placement exam; students passing the AB exam typically receive only one semester of credit.