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The overall goal of the Mathematics Department at North Shore Hebrew Academy High School is to develop students’ abilities to think quickly and analytically. The skills to take in information, process it, and prepare an intelligent response in all life situations are enhanced through the study of mathematics. Not all mathematics students go on to become engineers or physicists, but all students will grow up to encounter in their lives situations in which the ability to think on their feet makes the difference between success and failure. We further aim to prepare students fully for the experiences they will have in college mathematics courses, because we recognize that many of the professional fields our students will eventually pursue are math driven.

To achieve our goals, we have implemented a very strong program in the fundamentals of mathematics. Students at the school are expected to be able to think and apply mathematical concepts. Word problems are used throughout the curriculum to enhance the students’ abilities to apply mathematical concepts to real world situations. Calculators are used as tools and not as full-time crutches. Students are encouraged to build on their arithmetic abilities and develop the attitude that there is an advantage to having a strong math background.

Class lessons are student driven. Teachers are constantly modifying their presentations based on student feedback. Lessons may involve lecture, question and answer, demonstration by both teacher and student, and frequent assessment. Regular homework is a feature of every class. It is an important part of the learning process. Homework is collected after a thorough review, so that students have every opportunity to learn from their mistakes and correct their work.

Our curriculum is made up of the following courses whose syllabi will follow: Algebra, Geometry, Algebra 2 and Trigonometry, Pre-Calculus AB and BC, and AP Calculus AB and BC. An integral part of all grades is standardized testing readiness. Instruction is given to prepare students for the SAT I and II exams in mathematics, typically taken in the eleventh grade.

We will assess the achievement of the students by exams, projects, quizzes, homework, and classwork. There will be a final departmental exam at the end of the first semester, which will cover the material presented in the fall, and a departmental final given in June covering the second semester material.

Senior Pre-Calculus meets 5 times per week and ends when work study begins in February. All other classes meet 5 times per week for the entire year.

This foundation course is for students in the ninth grade who have had little or no experience with algebra. It introduces students to the skills involved in dealing with variables. Students learn about integers and rational numbers, equations and inequalities, exponents and polynomials, graphs and systems of equations, rational and radical expressions, relations and functions, and are introduced to probability and statistics. Students are encouraged to develop skills and work habits that will last throughout their academic careers.

Students in the ninth grade take this course if they have successfully completed an algebra course or an equivalent in middle school. Students learn the fundamentals of geometry; how to deal with geometrical figures and to apply deductive reasoning in the creation of formal proofs. Topics include: logic, geometric building blocks, deductive reasoning, parallel lines, congruence, triangles, quadrilaterals, inequalities, similarity, circles, constructions, loci, areas, volumes, coordinate geometry, and transformations.

Tenth grade students take this course after successful completion of ninth grade algebra. Students learn the fundamentals of geometry; how to deal with geometrical figures and to apply deductive reasoning in the creation of formal proofs. Topics include: logic, geometric building blocks, deductive reasoning, parallel lines, congruence, triangles, quadrilaterals, inequalities, similarity, circles, constructions, loci, areas, volumes, coordinate geometry, and transformations.

This course is given to tenth grade students who have completed geometry in ninth grade. Students enhance their algebraic skills and develop an understanding and mastery of trigonometric concepts. Topics include higher level examination of real numbers, equations and inequalities, functions, systems of equations, polynomials, rational expressions, complex numbers, quadratic equations, transformations, second degree equations, polynomial functions, exponential and logarithmic functions, matrices, sequences and series, probability, statistics, trigonometric functions, graphs, identities, and equations.

This course is given to eleventh grade students who have completed geometry. Students enhance their algebraic skills and develop an understanding and mastery of trigonometric concepts. Topics include higher level examination of real numbers, equations and inequalities, functions, systems of equations, polynomials, rational expressions, complex numbers, quadratic equations, transformations, second degree equations, polynomial functions, exponential and logarithmic functions, matrices, sequences and series, probability, statistics, trigonometric functions, graphs, identities, and equations.

This course is given to eleventh grade students who have completed Algebra II with Trigonometry. Students further develop the algebraic and trigonometric skills that are necessary for success in AP Calculus AB. Topics include linear and quadratic functions, polynomial functions, inequalities, functions, exponents and logarithms, analytic geometry and conic sections, trigonometric functions, trigonometric equations, triangle trigonometry, trigonometric addition formulas, and introduction to limits.

This course is given to eleventh grade students who have completed Algebra II with Trigonometry. Students further develop the algebraic and trigonometric skills that are necessary for success in AP Calculus BC. Topics include linear and quadratic functions, polynomial functions, inequalities, functions, exponents and logarithms, analytic geometry and conic sections, trigonometric functions, trigonometric equations, triangle trigonometry, trigonometric addition formulas, polar coordinates and complex numbers, vectors and determinants, sequences and series, matrices, limits, continuity, definition of the derivative, techniques of differentiation, derivatives of trigonometric functions, the chain rule, implicit differentiation, and related rates.

This course is open to seniors who have completed Algebra II with Trigonometry and elect to further their mathematics studies. Topics include linear and quadratic functions, polynomial functions, inequalities, functions, exponents and logarithms, analytic geometry, trigonometric functions, trigonometric equations, triangle trigonometry, and trigonometric addition formulas.

This course is offered to seniors who have completed Pre-Calculus AB. Topics include properties of functions, graphing functions including using the TI-84 graphing calculator, lines, families of functions, limits, continuity, definition of the derivative, techniques of differentiation, derivatives of trigonometric functions, the chain rule, implicit differentiation, related rates, local linear approximation and differentials, inverse functions, derivatives of exponential and logarithmic functions, inverse trig functions and their derivatives, L’Hopital’s rule, using calculus to graph functions, rectilinear motion, applied maximum and minimum problems, Newton’s method, Rolle’s theorem and the mean value theorem, the indefinite integral, slope fields, the definite integral, the fundamental theorems of calculus, average value, applications of the definite integral including area and volume, integration by parts, first order separable differential equations.

Open to seniors who have completed Pre-Calculus BC, this course covers uses of the TI-84 graphing calculator, local linear approximation and differentials, inverse functions, derivatives of exponential and logarithmic functions, inverse trigonometric functions and their derivatives, L’Hopital’s rule, using calculus to graph functions, rectilinear motion, applied maximum and minimum problems, Newton’s method, Rolle’s theorem and the mean value theorem, the indefinite integral, slope fields, the definite integral, the fundamental theorems of calculus, average value, applications of the definite integral including area and volume, length of a plane curve, work, integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, Simpson’s rule, improper integrals, first order separable differential equations, Maclaurin and Taylor series, convergence tests for series, polar coordinates, area in polar coordinates, and calculus on vector equations.