Math

Algebra 1

Teacher: Alex. Weir

Text: UCSMP: Algebra (2nd edition), McConnell, Brown, Usiskin, Senk, et al. Prentice Hall, 2002.

Algebra is the branch of mathematics concerned with representing numbers and ideas with symbols. Students have been using symbols for many years, but this is the first course that is entirely about algebra. All year, students will create and solve equations using many methods: trial-and-error, algebraic manipulation, tables, graphs and technology (computers and calculators). Students learn many new concepts but will focus on linear equations, quadratic equations, polynomials, systems of linear equations, exponential equations, and probability distributions. Many “real-world” examples are used, so that students can see how the math applies to jobs, science, and other academic subjects; this course starts to prepare students for these areas of study. Graphing calculators will be used in the classroom, but students are not expected to purchase one.

Algebra 2

Teacher: Alex Weir

Text: UCSMP Advanced Algebra, 2nd edition, Senk, Thompson, Viktora, Usiskin et al. Prentice Hall, 2002.

In Advanced Algebra, students become better at understanding the concepts of algebra. Mostly, students study functions: Linear equations in one variable; Systems of linear equations in several variables; Matrices; Quadratic functions; Power functions; Root functions; Exponential functions; Logarithms and logarithmic functions; Trigonometric functions; And polynomials. Conic sections (circles, ellipses, hyperbolas…) are also studied. Arithmetic and geometric series are introduced in this course, and statistics are studied in more detail than before.

Technology is integrated throughout the curriculum. Graphing calculators are used extensively as visualization tools, and as symbolic manipulators to expedite algebraic computations, or to check answers arrived at by paper-and-pencil means. There will be many problems that students cannot solve without graphing calculators (like problems involving matrices). Students are required to own a graphing calculator because they are used so much.

Applied Mathematics

Teacher: Alex Weir

Text: Applied Mathematics 12 Source Book, 1^st edition, Pearson Addison Wesley / Applied Mathematics 12, Project Book, 1^st edition, Pearson Addison Wesley

Applied Mathematics helps students to develop mathematically by engaging them in hands-on, open-ended, context-rich explorations that incorporate authentic data and the use of real-worlds tools, particularly the tools of technology. Through study mathematics from an applied perspective, students learn to see mathematics as a powerful set of processes, models and skills that can be used to solve non-routine problems, both in and out of the classroom. Students are asked to take the initiative and are given the latitude to explore.

Geometry

Teacher: Matthew Kaun

Text:  Geometry, by Burger et al; Published by Holt, 2012

Software:  Geogebra -   www.geogebra.org

Graphing Calculators:  Helpful, but not required in this course.  (TI-84 plus Silver Edition is recommended.)

In this course, we will use traditional methods and interactive, electronic resources like Geogebra to learn about the geometry of plane figures.  Initial topics that will be covered will include parallel and perpendicular lines, triangles (congruent and otherwise), and other types of polygons.  Students will be introduced to inductive reasoning using Geogebra, then they will learn to formalize their findings using deductive logic and formal proof.  Geogebra will continue to be an especially powerful tool to help us examine the geometries of similarity and transformations – reflections, rotations, translations, dilations, and compositions.  Lastly, we will learn about the geometry of 3-Dimensional figures (Surface Area and Volume), as well as the geometry of lines and angles in circles.

Pre-Calculus

Teacher: Matthew Kaun

Text:  Precalculus, by  David Cohen et al; Brooks/Cole/Centgage, 2012

Software:  Geogebra   www.geogebra.org

Graphing Calculator:  A graphing calculator is required for this course.  (TI-84 plus Silver Edition is recommended.)

Precalculus is a course designed to prepare students for the further study of calculus in general, and specifically for AP Calculus AB.  About half of the course consists of a further study of functions, including polynomial, rational, power, and exponential functions, as well as their inverses, including logarithmic functions.  The other half of the course will consist of a further study of trigonometry, including trigonometric identities, relationships, and graphs of the six trigonometric functions and their inverses.   Graphing calculators, interactive Geogebra drawings, and other electronic resources will be used in most class sessions to deepen students’ understandings of these topics, including function transformations, domain and range, end-behavior, asymptotic behavior, increasing and decreasing intervals, maxima and minima, and real-world problems applying these ideas.  Other topics to be addressed are the Binomial Theorem, Synthetic Division & the Rational Root Theorem, elementary matrix and vector operations, parametric equations, and polar coordinates. Some calculus topics will be introduced throughout the year (but not mastered), including limits, continuity, and the average change function.

AP Calculus

Teacher: Matthew Kaun

Text:  Calculus, by Paul Foerster.  Key Curriculum Press, 2010

Software:  Geogebra  - www.geogebra.org

Graphing Calculators:  A graphing calculator is required for this course.  (TI-84 plus Silver Edition is recommended.)

AP Calculus is a course designed to introduce students to differential and integral calculus, and to prepare students for the culminating AP Calculus Exam given the following month of May.  The course can be broken into three sections:  Limits, Differential Calculus, and Integral Calculus.  To begin, students will formally learn about limits, and limiting situations.  This will culminate in several forms of the limit-definition of the derivative.  In the Differential Calculus section of the course, students will learn about a multitude of differentiating techniques (including the product rule, quotient rule, chain rule, and implicit derivatives) for a multitude of familiar and unfamiliar functions (including polynomial, rational, power, trigonometric, exponential, and combination functions).  Calculus techniques will be used to work on real-world applications, including kinematic problems (position, velocity, and acceleration), problems involving related rates, problems involving maxima and minima, and other applications.  In the Integral Calculus section of the course, we will learn about a multitude of anti-differentiation techniques with, again, numerous familiar and unfamiliar functions.  Applications of the integral will be introduced as well.  Ideally, we will finish the AP Calculus AB syllabus near the end of March, so that we have 4-6 weeks to review topics before the AP Calculus Exam in early in the month of May.  After the AP Calculus Exam, we will examine a few other topics and applications of calculus.