Math Department 2007-2008

Course Descriptions 2007-2008

MATHEMATICS 1
Math 1 is a traditional Algebra course that takes students through the fundamentals of Algebra including: definitions, properties, order of operations, factoring quadratic equations, graphing, applications, systems of linear equations, exponents, and radical and rational expressions. Students' progress toward master of the concepts is measured through their test scores, homework, note taking, and class participation. Prerequisite: Completion of 8th grade math course. Text: Algebra 1, Foerster. Calculator requirement: scientific calculator.
(Year Course - 1 credit)

MATHEMATICS 1A (Accelerated)
This is the first course in the four-year sequence that takes students through first-semester college calculus. The course is designed for students who have had some study in Algebra 1 but are not yet ready for the rigors of the Honors course. The curriculum covers the traditional Algebra 1 syllabus through quadratics and provides additional topics of study and more challenging problem sets. Students' progress toward mastery of the concepts is measured through their test scores, homework, note taking, semester exams, and class participation. Prerequisite: Some study of Algebra 1, teacher recommendation, and appropriate performance on the placement test given the preceding spring. Text: Beginning Algebra, Lial, Hornsby, McGinnis. Calculator requirement: scientific calculator.
(Year Course - 1 credit)

MATHEMATICS 1H (Honors)
This is the first course in the four-year sequence that takes students through first-year college calculus. It starts with the algebra of straight line graphs. The material covered consists of most topics of second-year algebra and includes an introduction to trigonometry. Evaluation is by means of quizzes, tests, and exams. Prerequisite: One year of algebra and successful performance on the placement test given the preceding spring. Text: Algebra and Trigonometry, Foerster. Calculator requirement: TI 83/TI 83 Plus or TI 84/TI 84 Plus. (The TI 85/TI 86 calculators do not support the applications needed for this course.)
(Year Course - 1 credit)

MATHEMATICS 2
In this course students are introduced to the theorems of geometry and learn how to use them to write logical arguments called proofs. Topics studied include: inductive and deductive reasoning, area, volume, the Pythagorean Theorem, similarity, congruence, and the properties of lines, angles, triangle, polygons, circles and geometric solids. In addition students will use a compass and protractor to construct geometric figures and as tools to develop geometric concepts. Prerequisite: Math 1. Evaluation is by means of homework sets, quizzes, tests, and semester exams. Text: Geometry, Jacobs. Calculator requirement: scientific calculator.
(Year Course - 1 credit)

MATHEMATICS 2A (Accelerated)
This is the second course in the four-year sequence that takes students through first semester college calculus. This proof based course is designed for students who are prepared for a more rigorous and expansive geometry experience. The curriculum will include all the traditional topics in the geometry canon but with more challenging proofs and extension problems. Evaluation is by means of quizzes, tests and exams. Prerequisites: Successful completion of Math 1A and the recommendation of the teacher; or successful completion of Math 1H; or previous geometry experience. Texts: Geometry, Harold R. Jacobs and A Course in Geometry, Weeks and Adkins. Calculator requirement: scientific calculator.
(Year Course - 1 credit)

MATHEMATICS 2H (Honors)
This is the second course in the four-year sequence that takes students through first-year college calculus. It is a course in geometries: plane, solid, and analytic. Evaluation is by means of quizzes, tests, and exams. Admission is by departmental approval only. Texts: Geometry, Harold R. Jacobs and Course in Geometry Plane and Solid, Weeks and Adkins. Calculator requirement: TI 83/TI 83 Plus or TI 84/TI 84 Plus. (The TI 85/TI 86 calculators do not support the applications needed for this course.)
(Year Course - 1 credit)

MATHEMATICS 3
This course begins with a review of first-year algebra, focusing on equations, inequalities, and functions. Students then study systems of linear equations, matrices, quadratic functions, polynomials, powers and radical expressions, exponential and logarithmic functions, rational equations, conic sections, and an introduction to trigonometry. Learning to use a graphing calculator is an integral part of the course. Evaluation is by means of homework sets, quizzes, tests, and semester exams. Prerequisites: Math 1 and Math 2. Text: Algebra 2, Larson, Boswell, Kanold, and Stiff. Calculator requirement: TI 83/TI 83 Plus or TI 84/TI 84 Plus. (The TI 85/TI 86 calculators do not support the applications needed for this course.)
(Year Course - 1 credit)

MATHEMATICS 3A (Accelerated)
This is the third course in the four-year sequence that takes students through first-semester college calculus. It is a course for juniors with above-average mathematics ability who are not in the Honors program. Topics include those covered in Mathematics 3 with extensive coverage of trigonometry and analytic geometry. Evaluation is by means of quizzes, tests, and exams. Prerequisite: Math 2A and the recommendation of the teacher, Math 2H, or a year grade of 85 or above in both Math 1 and Math 2. Text: Algebra and Trigonometry with Analytic Geometry, Swokowski. Calculator requirement: TI 83/TI 83 Plus or TI 84/TI 84 Plus. (The TI 85/TI 86 calculators do not support the applications needed for this course.)
(Year Course - 1 credit)

MATHEMATICS 3H (Honors)
This is the third course in the four-year sequence that takes students through first-year college calculus. The course includes the study of series and sequences, mathematical induction, functions, trigonometry, analytic geometry, problem solving, limits, continuity, and calculus through rules of differentiation. Evaluation is by means of quizzes, tests, and exams. Admission is by departmental approval only. Texts: Algebra and Trigonometry with Analytic Geometry, Swokowski, and The Calculus 7 of a Single Variable, Leithold. Calculator requirement: TI 83/TI 83 Plus or TI 84/TI 84 Plus. (The TI 85/TI 86 calculators do not support the applications needed for this course.)
(Year Course - 1 credit)

MATHEMATICAL MODELING / DISCRETE MATHEMATICS AND STATISTICS
This course is a senior-level class that is divided into two separate semesters. The first semester concentrates on the use of technology to model real-world applications using functions, regression, parametric equations, difference equations, and matrices. The second semester explores a variety of discrete math topics such as graph theory, game theory, and cryptography, and then moves on to a study of the major concepts of statistics including sampling, the normal distribution, confidence intervals, and hypothesis testing. Texts: Mathematical Modeling Packet (compiled by Mr. Reeder), and For All Practical Purposes. Calculator requirement: TI 83/TI 83 Plus or TI 84/TI 84 Plus. (The TI 85/TI 86 calculators do not support the applications needed for this course.)
(Year Course - 1 credit)

PRE-CALCULUS WITH STATISTICS
The course is designed for students who have completed Math 3 or Math 3a in their junior year and who plan to continue in college with the traditional calculus sequence. A rigorous pre-calculus syllabus together with a statistics unit will be studied. Evaluation is by means of quizzes, tests, and exams. Text: Precalculus with Trigonometry, Concepts and Applications, Foerster. Calculator requirement: TI 83/TI 83 Plus or TI 84/TI 84 Plus. (The TI 85/TI 86 calculators do not support the applications needed for this course.)
(Year Course - 1 credit)

FINANCIAL MODELING
This rigorous, fast-paced class is for students who are interested in the application of mathematics to real-world business scenarios. Students learn the terminology, techniques, and applications of financial modeling. Case studies help students connect the concepts and techniques learned with actual business problems. In addition, guest speakers provide insight into solving the challenges faced by 21st century entrepreneurs.
Utilizing Harvard Business School cases, students begin the course by tackling the strategic challenges faced by actual businesses as they compete in the real world. A large part of the year is devoted to learning the language of business - accounting - with an emphasis on the underlying mathematics. Students study the balance sheet, income statement, financial ratios, return on investment, contribution margin, cash flow, sensitivity analysis, and related topics. Students explore various modeling techniques using Microsoft Excel to simulate and optimize a range of business scenarios.
Throughout the year, students compete in teams using a realistic online business simulation called Titan. During the simulation, teams determine their product's pricing, production levels, marketing campaigns, and other key factors. The computer simulates a dynamic marketplace and teams compete against each other to "win" the most market share and highest profits. The class competes against other high schools that also use the Titan business simulation. In the spring, the top US students compete in a regional competition. The regional winners move on to a national competition.
Evaluation is by tests, papers, presentations, and student participation in class discussion. This course is open to sophomores, juniors, and seniors. However, this course is not intended to replace the traditional math sequence. Interested students must be concurrently enrolled in another math course and must receive approval of the financial modeling instructor before registering for this course. Text: Management Accounting, Mackey and Thomas. Calculator Requirement: TI 83/TI 83 Plus or TI 84/TI 84 Plus. (The TI 85/TI 86 calculators do not support the applications needed for this course.)
(Year course - 1 credit)

CALCULUS AB - ADVANCED PLACEMENT
This is the final course in the four-year sequence that takes students through first-semester college calculus. The course covers the material listed in the College Entrance Examination Board syllabus for Calculus AB. It consists of a study of limits, differentiation and applications thereof, and simple integration and applications. Satisfactory performance on the Advanced Placement exam (AB) may earn one semester of college credit. Evaluation is by means of periodic quizzes, tests, and exams. Prerequisite: Successful completion of Math 3A and teacher recommendation. Text: Calculus: Graphical, Numerical, Algebraic, Finney, Demana, Waits, Kennedy. Calculator requirement: TI 83/TI 83 Plus or TI 84/TI 84 Plus. (The TI 85/TI 86 calculators do not support the applications needed for this course.) To learn the prerequisite for this course, please see the Advanced Placement statement on Page 1.
(Year Course - 1 credit)

CALCULUS BC - ADVANCED PLACEMENT
This is the final course in the four-year sequence that takes students through first-year college calculus. The course covers the material of the AB course and goes beyond it to differential equations, infinite series, and other topics, with an emphasis on theory. Satisfactory performance on the Advanced Placement exam (BC) may earn two semesters of college credit. Evaluation is by means of quizzes, tests and exams. Admission is by departmental recommendation only. Prerequisite: Math 3H. Text: Calculus: Graphical, Numerical, Algebraic, Finney, Demana, Waits, Kennedy. Calculator requirement: TI 83/TI 83 Plus or TI 84/TI 84 Plus. (The TI 85/TI 86 calculators do not support the applications needed for this course.) To learn the prerequisite for this course, please see the Advanced Placement statement on Page 1.
(Year Course - 1 credit)

AP STATISTICS
The first semester and part of the second semester of the course will prepare the students for the AP Statistics examination to be taken in May. Students enrolled in the course will be expected to take this examination. The remainder of the course will investigate topics in discrete mathematics such as graph theory, game theory, and cryptology. Class will be open to qualified sophomore, junior and senior students who have at least a B average in Math IH, Math 2H, Math 3A, or Math 3H. Interested students must receive the approval of the Math Department Chair before registering for this course. Please note that this course is not intended to replace the traditional precalculus/calculus sequence. Calculator requirement: TI 83/TI 83 Plus or TI 84/TI 84 Plus.
(Year Course - 1 credit)

COMPUTER SKILLS / STUDY SKILLS
This freshman requirement is designed to form the foundation for continuous learning and to be applicable to ever-changing innovations. A one-quarter course, it includes hands-on teaching of computer/technology skills by incorporating needs-based lessons drawn from the ninth grade curriculum. Proficiency is not an end in itself, but lays a foundation for adapting to high school learning. These skills become building blocks with which to meet the challenges of their personal and school lives.
Freshmen will get a jump-start by learning to adapt to the US network, master advanced Microsoft Office applications for writing papers, creating spreadsheets and databases, and doing research thoughtfully and critically. Using Adobe Creative Suite applications of InDesign, Photoshop, Photoshop Elements, and Acrobat, they will have the opportunity to use presentation, graphic, layout, and design software. Their new skills will enable them to move seamlessly into their required and elective coursework and into a variety of extracurricular activities where creativity is of foremost importance. Goals:

1. Help students develop confidence in their own ability to achieve academic success
2. Spend time on schoolwork more effectively
3. Ensure that students are equipped with the proper tools to do their work
4. Learn to strive for excellence
5. Develop a thirst for learning
6. Creative discovery
7. Prepare students to become involved in the life of the School
8. Prepare students for life after University School

COMPUTER PROGRAMMING (BASIC)
This course introduces a novice (or near novice) to computer programming with the BASIC language. First semester topics include real and string variables, loops, single-subscripted real and string arrays, and debugging techniques. The second semester introduces more sophisticated programming techniques: sorting, multidimensional real and string arrays, subroutines, error checking, graphics, sequential files, and number systems (base 2, 8, 16). The course concludes with an introduction to Java, the designated language of the Advanced Placement computer exam. Evaluation will be based on quizzes, tests, and programming assignments. Text: Microsoft Quick BASIC, Bent and Sethares.
(Year Course - 1 credit)

COMPUTER SCIENCE - ADVANCED PLACEMENT
This course will present material typically covered in a one-year introductory computer course at the college level. Starting in 2003-2004, the course's language will be Java. Students will learn to code fluently in Java, to design object-oriented programs, to use classic data structures and algorithms, and to understand a large case study in the target language. Completion of BASIC PROGRAMMING or an equivalent amount of programming experience (as determined by the instructor) is prerequisite. Evaluation is based on tests, programming assignments, and some homework exercises. Students must take the Advanced Placement Examination in May. Prerequisite: BASIC PROGRAMMIING or permission of the instructor. Text: Java, An Introduction to Computer Science and Programming, Savitch, Java Methods AB, Litvin and Litvin. To learn the prerequisite for this course, please see the Advanced Placement statement on Page 1.
(Year Course - 1 credit)

Sequence of Math Courses

Calculator Policy

• Math 1
• Math 1A
• Math 2
• Math 2A

• Math 1H
• Math 2H
• Math 3
• Math 3A
• Math 3H
• Mathematical Modeling
• Precalculus
• Financial Modeling
• AP Statistics
• AB and BC Advanced Placement Calculus
• Advanced Topics

SAT II Recommendations

• Mathematics Level IC
• Test questions are on the following topics.
• Algebra
• Geometry (plan Euclidean, coordinate, three-dimensional)
• Basic trigonometry
• Algebraic functions
• Elementary statistics, including probability, counting problems, data interpretation, and mean, median and mode
• Miscellaneous topics, including logic, elementary number theory, and arithmetic and geometric sequences
• Recommended Preparation: it is assumed that you have taken three years of college-preparatory mathematics (two years of algebar and one year of geometry).
• Calculator needed for about 40% of the problems.
• Mathematics Level IIC
• Test questions are on the following topics.
• Algebra
• Geometry (coordinate, three-dimensional)
• Trigonometry
• Functions
• Statistics including probability, permutations and combinations
• Miscellaneous topics, including logic and proof, elementary number theory, sequences and limits
• Recommended Preparation: it is assumed that you have taken more than three years of college-preparatory mathematics (two years of algebar, one year of geometry, and elementary functions [precalculus and/or trigonometry]).
• Calculator needed for about 60% of the questions.