The introductory course in the St. Anselm's mathematics sequence. Over the year, students will build confidence in understanding and applying the fundamentals of advanced arithmetic and basic geometry. Topics to be studied include: Fractions, decimals, rational
and irrational numbers, probability, combinations and permutations, areas, and
volumes.
Course Length: All Year
Registration Policy: Required for Form A
This course finalizes students’ foundation in arithmetic and provides an introduction to Algebra. Topics covered include: introduction to signed numbers, arithmetic operations, introduction to variables, simple one-variable equations, simple geometric figures and their measurements, ratio, percent and probability.
Course Length:
All Year
Registration Policy:
Required for Form I
This course, which covers the full Algebra I textbook, will help students to become comfortable with symbol manipulation and the idea of a quantity without a fixed value. Topics covered over the year include: variables, fundamental and distributive properties, exponents, adding, subtracting, multiplying and
dividing polynomials, factoring, linear and quadratic equations, word problems,
inequalities, and systems.
Course Length: All Year
Registration Policy: Required for Form II
A continuation of the students' study of algebra which begins to explore higher-order equations and the concept of complex numbers. Topics covered over the year include: division of polynomials, factoring to solve third-degree and higher polynomials, irrational and complex
numbers, algebraic fractions, trigonometric functions, exponential and
logarithmic functions, sequences and series, statistics and probability.
Course Length: All Year
Registration Policy: Required for Form III
This course exposes students to the principles and applications of common geometric operations in two and three dimensions. Students embrace an intuitive and axiomatic approach to the material, studying truth tables and symbolic and syllogistic arguments. The focus of the course will be on traditional Euclidean geometry, including theorems on lines and planes, angles, constructions, areas and volumes, coordinate geometry and trigonometry. The course concludes with a section in preparation for pre-calculus, including sequences and series, matrix algebra, probability theory, and analytic geometry.
Course Length:
All Year
Registration Policy:
Required for Form IV
This is a course in algebra designed to introduce and develop those topics that are used in higher math and includes limits, the analysis of rational and polynomial functions, transcendental functions including the exponential, logarithmic, trigonometric and complex. Considerable attention will be placed on the trigonometric functions including the derivation of the laws of sines and cosines and an introduction to vectors. Systems of equations will be studied including both equalities and inequalities. Matrix methods will be developed for the solution of the systems. Finally, there will be an in-depth study building on previous study of sequences, series, probability and analytic geometry.
Course Length:
All Year
Registration Policy:
Mathematics option for Form V
This course is identical to the (AB) course except that it will be taught in one semester. In the second semester students will take the first year college course in differential calculus.
Course Length:
Fall Semester
Registration Policy:
Mathematics option for Form V
This course covers the material found in the first year of basic college calculus. It includes the theory of the derivative and its uses in finding the maximum and minimum of functions, the tangents to curves, how the change of one function is related to the change in another function and includes application to the sciences. In the second semester the integral is developed and is applied to the problems of finding areas, length of curves, volumes and surface areas. Other topics include:
Limits, continuity, derivatives, mean value theorem, related rates, min-max, inflection points, derivative tests, applications to geometric systems, optimizing, graphing, integrals, areas, volumes, techniques of integration, separable differential equations, improper integrals.
Course Length:
All Year
Registration Policy:
Mathematics option for Form VI
A second-semester follow-up to the students' course in Pre-Calculus (BC). In this fast-paced course, students will become fluent in the vocabulary, principles, and procedures of introductory calculus. Topics to be covered include: Limits, continuity, derivatives, mean value theorem, related rates, min-max, inflection points, derivative tests, introduction of the integral.
Course Length:
Spring Semester
Registration Policy:
Prerequisite: Pre-calculus (BC); Mathematics option for Form V
This is a continuation of the Calculus (BC) I which was begun in the second semester of Form V. The theory of the integral and its use to calculate averages of continuous functions, areas, length of curves, volumes, and surface areas are discussed. Other topics include theory of integration, methods of integration in Cartesian and polar coordinates, geometric and scientific applications of integrals, parametric equations, improper integrals, differential equations, numerical methods, infinite series, Taylor’s theorem, harmonic, geometric, alternating, power, and convergence in integrals.
Course Length:
All Year
Registration Policy:
Prerequisite: AP Calculus I (BC);
Mathematics option for Form VI