Math

Algebra I (9th grade)

In high school students will be exposed to yet another extension of numbers, when the real numbers are augmented by the imaginary numbers to form the complex numbers. With each extension of number, the meanings of addition, subtraction, multiplication, and division are extended. In each new number system – integers, rational numbers, real numbers, and complex numbers – the four operations stay the same in two important ways: they have the commutative, associative, and distributive properties, and their new meanings are consistent with their previous meanings. Topics covered in this class include: algebraic expressions, solving equations and inequalities, learning to graph, working with polynomials, factoring, rational expressions and equations, solving systems of equations, solving radical expressions and equations, and solving quadratic equations. (Please note: Only students who take the New York State Regents Exam in Algebra and score an 80% or better will be able to advance to Geometry in their Freshman year at Montfort. Students who take Algebra in the 8th grade but who do not take the Regents exam must take Algebra at Montfort unless they take a Montfort-supervised Regents exam.)

Geometry (9th or 10th grade)

Although there are many types of geometry, high school mathematics is devoted primarily to plane Euclidean geometry, which is studied both synthetically (without coordinates) and analytically (with coordinates). Euclidean geometry is characterized most importantly by the Parallel Postulate, that through a point not on a given line there is exactly one parallel line that exists. During high school, students begin to formalize their geometry experiences from elementary and middle school, using more precise definitions and developing careful, well thought out proofs of axioms and postulates. Later, in college, students are able to develop Euclidean and other geometries carefully from a small set of axioms. Topics covered in this class include: points, lines, and planes; angles and parallel lines; geometry of the triangle; congruence of the triangle; quadrilaterals; coordinate geometry; geometry of the circle; transformations on the coordinate plane; perimeter, area, surface area, and volume; locus; logic and proofs.

Algebra II/Trigonometry (10th or 11th grade)

Once students have mastered both Algebra I and Geometry, they are able to take on the challenges that
both higher level algebra and trigonometry present to the learner. Within this course, the number system
will be extended to include imaginary and complex numbers. The families of functions to be studied
will include polynomials, absolute value, radical, trigonometric, exponential, and logarithmic functions.
Problem situation involving direct and indirect variation will be solved. Problems resulting in systems
of equations will be solved graphically and algebraically. Algebraic techniques will be developed to
facilitate rewriting mathematical expressions into multiple equivalent forms. Data analysis will be
extended to include measures of dispersion and the analysis of regression that model functions studied
throughout this course. Associated correlation coefficients will be determined, using technology tools
and interpreted as a measure of strength of the relationship. Arithmetic and geometric sequences will be
expressed in multiple forms, and arithmetic and geometric series will be evaluated. Binomial
experiments will provide a basis for the study of probability theory and the normal probability
distribution will be analyzed and used as an approximation for these binomial experiments. Right
triangle trigonometry will be expanded to include the investigation of circular functions. Problem
situations requiring the use of trigonometric equations and identities will also be investigated.

Pre‐Calculus (11th or 12th grade)

Students will be exposed to some interesting topics that they may not otherwise see in any other math
class such as: working with vectors, matrices, and conic sections. Students will also be honing their
skills in all of the math concepts that they have been exposed to throughout their high school careers.
This course is structured so that students are ready to take a college level calculus course as freshmen in
college. Within this course students will also be exposed to how to take and apply derivatives of
functions. The course also offers students the opportunity to pick topics which they find interesting
within mathematics and spend some of their time and energy to dive deeper into math and create a
better understanding for themselves. Topics covered in this course include: polynomial and rational
functions, exponential and logarithmic functions, trigonometric functions of real numbers, trigonometric
functions of angles, analytical trigonometry, sequences and series, counting and probability, limits,
derivatives, and related rates.

Calculus and AP Calculus (12th grade)

This is an intensive course in the calculus of one variable including limits, differentiation, maxima
and minima, and the chain rule for polynomials, rational functions, trigonometric functions, and
exponential functions. It also introduces integration with applications to area and volumes of
revolution followed by further development of integration, inverse trigometric and logarithmic
functions, techniques of integrations, and applications which include work and pressure. Other
topics covered are infinite series, power series, Taylor’s formula, polar coordinates, parametric
equations, introduction to differential equations, and numerical methods. Select students will be able
to use this course as preparation for the AP Calculus AB examination.