MATHEMATICS DEPARTMENT

MATHEMATICS DEPARTMENT

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 assessments will be viewed as a means to strengthen the students ’ mathematical skills. Additionally, there is a mandatory summer assignment for all students entering any level of algebra, geometry, algebra II, or calculus. There will be a diagnostic assessment on the material during the first week of classes. 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.

304 INTRODUCTION TO ENGINEERING I (Semester Course) 1/2 Credit

Grade: 9

Prerequisite: Student currently enrolled in 314Algebra I or above or approval of department chair

The course begins with the study of what it means to be an engineer, the different concentrations of engineering, societal impacts of engineering, and the connection engineering has to math and science. The major focus of the course is to expose students to the engineering design and reporting processes. This will be achieved through hands-on collaborative projects. Projects may include but are not limited to: Egg Drop, PaperAirplane, Circuits, House Design, Hurricane Tower, and Rubber Band Cars.

309 FOUNDATIONS INALGEBRA

Grade: 9

Prerequisite: Placement & Proficiency Test Scores 1 Credit

This course focuses on number sense in preparation for algebra. Concepts covered are real numbers, decimals, fractions, percents, ratios, proportions, prime and composite numbers, negatives and absolute value; analyzing tables, pictographs, charts; factors, multiples, exponents; area, perimeter, volume; relationships, functions, coordinate plane, graphing points; terms, and operations with terms.

312 MODERNALGEBRAI

Grade: 9

Prerequisite: Placement & Proficiency Test Scores 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.

314 ALGEBRAI

Grade: 9

Prerequisite: Placement & Proficiency Test Scores 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.

316 HONORSALGEBRAI

Grade: 9

Prerequisite: Placement & Proficiency Test Scores 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 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.

322 PLANE GEOMETRY

Grade: 10

Prerequisite: ModernAlgebra I orAlgebra I 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.

324 GEOMETRY

Grade: 10

Prerequisite: Algebra I 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.

326 HONORS GEOMETRY

Grade: 10

Prerequisite: Algebra I 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, with emphasis on deductive reasoning, constructions and proofs. The student will gain a knowledge and ability to use both the terms and the tools of geometry.

332 MODERNALGEBRAII

Grade: 11, 12

Prerequisite: Plane Geometry or Geometry 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 algebraic concepts 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.

334 ALGEBRAII

Grade: 11

Prerequisite: Geometry 1 Credit

Whenever possible, topics will be covered algebraically, graphically, numerically, and verbally with an emphasis on applications in modern contexts. Topics covered include properties of real numbers, linear functions quadratic functions, polynomial functions, rational functions, radical functions, complex numbers, exponential and logarithmic functions, conic sections, matrices, and basic probabilities. The graphing calculator will play an integral role in this course.

336 HONORSALGEBRAII/TRIGONOMETRY (Dual Credit)

Grade: 11

Prerequisite: Geometry 1 Credit

Whenever possible, topics will be covered algebraically, graphically, numerically, and verbally with an emphasis on applications in modern contexts. There will be a brief review of linear functions, quadratic functions, systems of equations, and exponents. Topics covered include polynomial functions, rational functions, radical functions, complex numbers, exponential and logarithmic functions, conic sections, matrices, trigonometric functions, trigonometric identities, sequences and series, basic probabilities and statistics. The graphing calculator will play an integral role in this course. In addition, students may apply to earn dual credit to receive college credit through Lewis University for an advanced mathematics course.

342 MODERN MATHEMATICS

Grade: 12

Prerequisite: ModernAlgebra II orAlgebra II 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 an entry-level college mathematics course. Topics covered include: inductive reasoning, estimation, problem solving, logic, number theory and the real number system, 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.

343 ALGEBRAIII WITH STATISTICS

Grade: 11, 12

Prerequisite: ModernAlgebra II orAlgebra IIAND Teacher Recommendation 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 quadratics), rational functions, exponential functions, and logarithmic functions with 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.

344 STATISTICSAND PROBABILITY/TRIGONOMETRY

Grade: 11, 12

Prerequisite: ModernAlgebra II orAlgebra II 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.

354 ANALYSISAND PRE-CALCULUS

Grade: 11, 12

Prerequisite: HonorsAlgebra II orAlgebra II and Teacher Recommendation 1 Credit

Whenever possible, topics will be covered algebraically, graphically, numerically, and verbally with an emphasis on applications in modern contexts. This course is designed for above-average students of mathematics who intend to continue with advanced mathematics. Topics covered include linear, quadratic, polynomial and rational equations and functions; exponential and logarithmic functions; solving systems of equations; trigonometric equations, graphs and identities; and permutations.

356 HONORSANALYSISAND PRE-CALCULUS

Grade: 11, 12

Prerequisite: HonorsAlgebra II orAlgebra II and Teacher Recommendation 1 Credit

Whenever possible, topics will be covered algebraically, graphically, numerically, and verbally with an emphasis on applications in modern contexts. This course is designed for above-average students of mathematics who are not yet ready for Calculus. Topics covered include linear, quadratic, polynomial and rational equations and functions; exponential and logarithmic functions; solving systems of equations; trigonometric equations, graphs and identities; parametric and polar functions; matrices and vectors; sequences and series; combinations, permutations, and probability; curve fitting, statistics and if time permits iterated functions and limits

358 ADVANCED PLACEMENT CALCULUSAB

Grade: 11, 12

Prerequisite: 3.7 GPAand HonorsAlgebra II/Trigonometry 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 functions, 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.

368 ADVANCED PLACEMENT CALCULUS BC

Grade: 12

Prerequisite: Calculus 358 1 Credit

This course is a continuation of Calculus 358. 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 slope fields, Euler’s method, exponential and logistic growth; sequences and series including convergence, Taylor and Maclaurin 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.

378 MULTIVARIABLE CALCULUS (Dual Credit)

Grade: 12

Prerequisite: Calculus 368 & teacher approval 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; Stoke’s theorem; and divergence and the divergence theorem. In addition, students may apply to earn dual credit to receive college credit through Lewis University for Calculus III.

388 ADVANCED PLACEMENT STATISTICS

Grade 11 or 12

Prerequisite: HonorsAlgebra II 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 variation), sampling and experimentation, anticipate patterns by exploring random phenomena using probability and simulation, and statistical inference (estimating population parameters and testing hypotheses).