# MATHEMATICS

The Mathematics program at Montini Catholic High School is designed to provide each student with the opportunity to develop his or her mathematical talents to the fullest. Accordingly, daily assignments and frequent examinations will be viewed as a means to strengthen the students' mathematical skills. The department feels the student is best served by ability-level grouping; it has a special program for the slow learner and an accelerated program for the mathematically gifted. Registration for all courses is subject to department approval.

#### MODERN ALGEBRA I

Grade: 9

Course: 312

1 Credit

This course reinforces the computational skills of arithmetic while covering topics of modern algebra. The course covers the critical components of properties of real numbers, expressions, polynomials, solve equations and inequalities, solve systems of equations and inequalities, properties of exponents (both rational and irrational), functions, linear models, exponential models, quadratic models, properties of rational and irrational numbers, single variable statistics, and two variable statistics.

Prerequisite: Placement Test Scores

#### ALGEBRA I

Grade: 9

Course: 314

1 Credit

This is a complete course in the concepts and skills of Algebra I. All topics will be covered algebraically, graphically, numerically, and verbally with an emphasis on applications in modern contexts. Topics covered include properties of real numbers, expressions, polynomials, solve equations and inequalities, solve systems of equations and inequalities, properties of exponents (both rational and irrational), functions, linear models, exponential models, quadratic models, properties of rational and irrational numbers, single variable statistics, and two variable statistics. The graphing calculator will play an integral role in this course.

Prerequisite: Placement Test Scores

#### HONORS ALGEBRA I

Grade: 9

Course: 316

1 Credit

This course is for students who have had some Algebra I and have achieved an appropriate score on the entrance exam. All topics will be covered algebraically, graphically, numerically, and verbally with an mphasis on applications in modern contexts. Topics covered include properties of real numbers, expressions, polynomials, solve equations and inequalities, solve systems of equations and inequalities, properties of exponents (both rational and irrational), functions, linear models, exponential models, quadratic models, properties of rational and irrational numbers, single variable statistics, and two variable statistics. The graphing calculator will play an integral role in this course.

Prerequisite: Placement Test Scores and Approval of Department Chair

#### PLANE GEOMETRY

Grade: 10

Course: 322

1 Credit

The course covers the critical components of line and angle properties, triangle and polygon properties, circles, area and volume formulas, the Pythagorean Theorem, similarity, and deductive reasoning. The student will gain a knowledge and ability to use both the terms and the tools of geometry.

Prerequisite: Modern Algebra I or Algebra I

#### GEOMETRY

Grade: 10 (9 with Department Chair Approval)

Course: 324

1 Credit

This is a first course in geometry with an emphasis on Euclidean approaches and applications. Topics covered include: line and angle properties, triangle and polygon properties, circles, area and volume formulas, the Pythagorean Theorem, similarity, and deductive reasoning. The student will gain a knowledge and ability to use both the terms and the tools of geometry.

Prerequisite: Algebra I

#### HONORS GEOMETRY

Grade: 10 (9 with Department Chair Approval)

Course: 326

1 Credit

This course emphasizes proof and deductive reasoning. Topics covered include: point, line, plane, angles, parallel lines, congruent triangles, polygons, similarity, right triangles, circles, constructions, area and volume.

Prerequisite: Algebra I

#### MODERN ALGEBRA II

Grade: 11

Course: 332

1 Credit

Students who have taken Plane Geometry or who have had difficulty in regular Geometry and who want to build a stronger foundation in mathematics for college should take this course. It includes a study of equations, linear functions, systems of linear equations, quadratic functions, polynomial functions, rational functions, radical functions, complex numbers, exponential and logarithmic functions, conic sections, and matrices.

Prerequisite: Plane Geometry or Geometry

#### ALGEBRA II

Grade: 11 (10 with Department Chair Approval)

Course: 334

1 Credit

This course covers a brief review of linear and quadratic functions, systems of open sentences, polynomial and rational expressions, radicals, and irrational numbers. It also consists of function analysis including polynomial, rational, radical, exponential and logarithmic functions, conic sections, matrices, sequences and series, and, if time permits, trigonometric functions.

Prerequisite: Geometry

#### HONORS ALGEBRA II/TRIGONOMETRY

Grade: 9, 10, 11

Course: 336

1 Credit

This course covers a brief review of properties of real numbers, linear and quadratic functions, systems of open sentences, polynomial and rational expressions, radicals, and irrational numbers. It also consists of algebraic proof, function analysis including polynomial, rational, radical, exponential and logarithmic functions, conic sections, determinants, sequences and series, trigonometric functions and their graphs, trigonometric identities, inverses of periodic functions and their graphs, basic statistics and probability, and, if time permits, polar coordinates, and vectors.

Prerequisite: Geometry and Approval of Department Chair

#### MODERN MATHEMATICS

Grade: 12

Course: 342

1 Credit

This course is for those students who wish to take a fourth year of mathematics and want to move at a slower pace. The course is especially for college bound students who would like preparation for a college mathematics course. Topics covered include: inductive reasoning, estimation, problem solving, logic, number theory and the real number system, algebra graphs, functions, systems of linear equations, systems of linear inequalities, percent loans, simple interest, compound interest, installment buying, buying a house with a mortgage, probability and statistics.

Prerequisite: Modern Algebra II or Algebra II

#### ALGEBRA II WITH STATISTICS

Grade: 11, 12

Course: 343

1 Credit

This course is for those students who need a more in-depth study of algebra and an introduction to statistics. The course will stress the numerical and graphical relationships of radical functions, polynomial functions (including quadratic equations), rational functions, exponential functions, and logarithmic functions with a special emphasis on real world applications and statistical analysis (graphs, charts, regressions, measures of central tendency, and measures of variation). The graphing calculator will play an integral role in this course.

Prerequisite: Modern Algebra II or Algebra II and Teacher Recommendation

#### STATISTICS AND PROBABILITY/TRIGONOMETRY

Grade: 11, 12

Course: 344

1 Credit

This course is for those students who have completed Modern Algebra II with a grade of A or for those students who have completed Algebra II but are not taking Pre-Calculus. It serves as a preparation for first year college courses. The first semester covers right triangle trigonometry, radian measure, graphs of trigonometric functions, inverse functions, solving trigonometric equations, trigonometric laws, formulas, and identities, and real-world applications. Second semester covers experimental design, various graphs, charts, and plots to display data, measures of central tendency, measures of variation, regression, basic probability, probability distribution, normal distribution, central limit theorem, and hypothesis testing. Both semesters utilize the graphing calculator extensively.

Prerequisite: Algebra II

#### ANALYSIS AND PRE-CALCULUS

Grade: 11, 12

Course: 354

1 Credit

This course is designed for above-average students of mathematics who intend to continue in advanced mathematics. Topics covered include linear, quadratic, polynomial and rational equations and functions; graphing of exponential and logarithmic functions; solving systems of equations; trigonometric equations, graphs and identities; and permutations.

Prerequisite: Honors Algebra II or Algebra II and Teacher Recommendation

#### HONORS ANALYSIS AND PRE-CALCULUS

Grade: 11, 12

Course: 356

1 Credit

This course covers linear functions, linear programming, quadratic functions, polynomial and rational functions, parametric equations, exponential functions, logarithmic functions, financial and scientific applications, trigonometric functions, trigonometric identities, trigonometric applications, polar coordinates, complex numbers, vectors, matrices, Gaussian Elimination, determinants, sequences, series, combinatorics, probability, curve fitting, statistics, calculator programming, several projects, and, if time permits, iterated functions and limits.

Prerequisite: Honors Algebra II or Algebra II and Approval of Department Chair

#### ADVANCED PLACEMENT CALCULUS AB

Grade: 10, 11, 12

Course: 358

1 Credit

College credit may be earned. The student will be prepared to take the Advanced Placement AB test in May to earn one semester of college credit. Whenever possible, topics will be covered algebraically, graphically, numerically, and verbally. This course includes function, graphs, limits, continuity, differentiation, applications of derivatives, integration, applications of integration, techniques of antidifferentiation, numerical approximations to definite integrals, and variable separable differential equations including slopefields. The graphing calculator will play an integral role in this course.

Prerequisite: Honors Algebra II/Trigonometry and Approval of Department Chair

#### ADVANCED PLACEMENT CALCULUS BC

Grade: 11, 12

Course: 368

1 Credit

This course is a continuation of Calculus 358 – Advanced Placement Calculus AB. The student will be prepared to take the Advanced Placement BC test in May in order to earn two semesters of college credit. Whenever possible, topics will be covered algebraically, graphically, numerically, and verbally. In addition to all AB topics, this course covers techniques of antidifferentiation including parts, partial fractions, trigonometric substitution, and improper integrals; differential equations including slopefields, Euler's method, exponential and logistic growth; sequences and series including convergence, Taylor and Mac Laurin series and error bounds; and parametric, polar, and vector functions, their derivatives, antiderivatives, and applications. The graphing calculator will play an integral role in this course.

Prerequisite: Calculus 358 and Approval of Department Chair

#### MULTIVARIABLE CALCULUS

Grade: 12

Course: 378

1 Credit

This course covers vectors in the plane and in space; vector algebra; planes and quadric surfaces; other coordinate systems; curves in 3-space and differentiation, arc length, speed and curvature, functions of several variables and their limits; partial derivatives and tangent planes; directional derivatives and the gradient; chain rules; max-min problems; LaGrange multipliers; multiple and iterated integrals; double integrals over general regions, triple integrals; polar, cylindrical and spherical change of variables; vector fields and line integrals; fundamental theorem for line integrals; parametric surfaces and surface integrals; surface integrals of vector fields; Greene’s theorem; Stokes theorem; and divergence and the divergence theorem.

Prerequisite:Calculus 368 and Approval of Department Chair

#### ADVANCED PLACEMENT STATISTICS

Grade: 11, 12

Course: 388

1 Credit

This course covers the major concepts for collecting, analyzing, and drawing conclusions from data. Students will study four themes: explore data (including patterns and variations), sampling and experimentation, anticipate patterns by exploring random phenomena using probability and simulation, and statistical inference (estimating population parameters and testing hypotheses.)

Prerequisite: Honors Algebra II and Approval of Department Chair