Courses

Algebra I - Year

This course is an introduction to algebra. Extensive attention is given to developing algebraic and graphical problem-solving skills. The coordinate geometry of lines and parabolas, fractions, rational expressions and integral exponentials, and linear and quadratic equations through the quadratic formula are included with aneye toward developing confidence and agility in problem solving. TI-83 or TI-84 calculators are required at this level.

Algebra I Enhanced - Year

This course is designed for students who have already been exposed to some or all of the topics of Algebra I. Students are placed in this course in consultation with the Chair of the Math Department if there is concern that skills and confidence needfurther reinforcement to support higher levels of study. The Algebra I syllabus is used for this course; as time permits, topics are embellished and others added. TI-83 or TI-84 calculators are required at this level.

Geometry - Year

This course pursues a deepening of the students’ understanding of plane and solid geometrical figures and a building of their abilities to analyze and communicate mathematically. Much attention is given to logical structure and the writing of mathematical arguments as well as to geometrical problem solving.

Algebra II - Year

This course reviews, then extends, the study of algebra with greater attention toward function. Topics include linear andquadratic functions and relations, polynomial functions, rational expressions, exponents, and logarithms and elementary trigonometry. Students are expected to broaden their problem-solving skills and techniques. Increased attention is given to multiple representations with graphs and charts used to illustrate and enhance algebraic manipulation. TI-83 or TI-84 calculators are required.

Honors Algebra II - Year

This is an accelerated course in algebra in which topics are pursued in greater depth as well as at greater speed. Students are expected to have strong intuition and motivation for the studyof mathematics. Extensive work with trigonometric functions is usually encountered, reaching beyond the topics of Algebra II. (Prerequisites: teacher recommendation, placement test, and departmental permission.)

Statistics, Functions and Trigonometry

This yearlong course is for students who have completed Algebra II. It will include an introduction to the basic concepts of statistics, a review of linear, quadratic, exponential and logarithmic functions and a study of trigonometry. Modeling data using the functions and using statistics to verify the validity of the model will be an emphasis. There will be extensive use of the software program Fathom. Topics include: descriptive statistics, correlation, quadratic, exponential, logarithmic regression, circular trigonometry, sequences and series. This course will not be sufficient preparation for students to take a Calculus course at St. Mark’s. (Prerequisite: completion of Algebra II. Students cannot take this if they have completed Functions.)

Topics in Discrete Mathematics - Fall

This semester-long course offers students a chance to explore a variety of topics in discrete mathematics. Graphing calculators and computers are used in the study of matrices, recursion, counting methods, sequences, series and their application to such topics as fair division and apportionment, voting methods, probability, and population growth. Particular emphasis is placed on logical argument in presenting both verbal and written solutions to problems. (Prerequisite: completion of Algebra II. May be taken concurrently with Functions or Calculus.)

History of Mathematics - Spring

This semester-long course invites students to explore a variety of episodes from the history of mathematics. Learning about the development of mathematical concepts- and of humankind’s struggle with them-fosters a deeper understanding of the subject. The course begins by considering the relationship between the numeration systems of ancient civilizations and the development of mathematics in these cultures. Using the mathematical techniques of different times and places enables students to ask and answer questions of the type: Who is Euclid and why is his work so revered today? Who discovered zero? Who invented Calculus? What are complex numbers? The course considers both pure and applied mathematics. (Prerequisite: completion of the math requirement and departmental permission. May be taken concurrently with Functions or Calculus.)

Note: These semester-long courses offer an alternative or an enhancement to calculus. Students can elect to take one or both.

Precalculus - Year

Extensive discussion of polynomial, rational, exponential, logarithmic, and trigonometric functions and their properties and applications is encountered. Sequences, series, and limits are also introduced. A graphic scientific calculator is required atthis level for its aid in visualization and calculation. Students gain skill in analyzing functions and drawing connections between symbolic, graphic, and numerical representations. This course is primarily designed as a final preparation for the study of calculus.

Honors Precalculus - Year

This is an accelerated course in the elementary functions which includes an introduction to the study of calculus during the second half of the year. Students are expected to have exceptional intuition and motivation for the study of mathematics. (Prerequisites: one full term of analytical trigonometry from Honors Algebra II and departmental permission.)

Calculus - Year

This is an introduction to calculus designed for students who want to study calculus before college, but who do not yet feel prepared for the pace or depth of an Advanced Placement course. Students who have not already done so are encouraged to consider MA42/43 as an alternative unless they expect calculus to be a required part of their future studies. (Prerequisites: MA50 and departmental permission.)

Advanced Placement AB Calculus - Year

This course prepares the students for the AB Advanced Placement Examination. Graphing calculators are used to help the students visualize critical concepts. Applications and techniques of differential and integral calculus are illuminated. Successful completion of this course is roughly equivalent to one-half year of college calculus. (Prerequisites: MA50 and departmental permission.)

Advanced Placement BC Calculus - Year

This course prepares the student for the BC Advanced Placement Examination. Successful completion of this course is roughly equivalent to a full year of college calculus. It is a more thorough and rigorous course than AB Calculus, with a more extensivesyllabus, including an introduction to power series expansions, vector calculus, and the calculus of polar curves. (Prerequisites: M5A0 and departmental permission.)

Topics in Advanced Mathematics - Year

This course is redesigned annually to reflect the needs of our advanced students. (Prerequisite: completion of AB or BC Calculus and departmental permission.)

Advanced Placement Statistics - Year

This course introduces the basic concepts of statistics while preparing students for the Advanced Placement Examination in Statistics. Every student will become familiar with the use of the statistical functions found in the more useful graphing calculators. Computer statistical applications are studied using one which is commonly available and well recognized. By completing the course, a student will also be prepared to use statistics in the various pursuits which draw on this mathematical process to study and analyze data. (Prerequisites: MA50 or an Honors grade in MA40 and departmental permission.)