MATHEMATICS DEPARTMENT

McQuaid Jesuit students are required to complete three years of mathematics: Algebra, Geometry and Algebra II/Trigonometry. Class sections are formed according to Mathematics ability levels. In the first ability grouping the student's relating of concepts requires mainly knowledge, comprehension and application. The ENRICHED ability grouping also requires the relating of concepts on the analysis and synthesis levels. The ADVANCED sections demand higher-level skills beyond memorization, requiring knowledge, comprehension and, especially, application, analysis, synthesis and evaluation. The amount of work, its intensity and difficulty, and the teacher’s expectations all increase with each successive ability level.

Placement in the ability groups is based upon performance and the department's recommendations.

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The first year of mathematics is ADVANCED Algebra or Algebra. These courses contain: introduction to algebra; working with real numbers; solving equations and problems; polynomials; factoring polynomials; fractions; applying fractions; introduction to functions; systems of linear equations; inequalities; rational and irrational numbers; quadratic functions.

The second year of mathematics is ADVANCED Geometry or Geometry. The course is designed to develop: (1) an understanding of geometric relationships in a plane and in space, (2) the ability to think creatively and critically, in both mathematical and nonmathematical situations, and (3) an understanding of the meaning and nature of proof. These courses contain: review of algebra; lines and angles; congruent triangles; parallel lines, angle sums and quadrilaterals; circles; proportions involving line segments and similar triangles; areas of polygons; regular polygons and the circle; inequalities; locus; coordinate geometry; constructions; solid geometry.

The third year of mathematics is ADVANCED Algebra II/Trigonometry or Algebra II/ Trigonometry. The course is designed to enhance problem solving skills and develop reasoning skills such as analyzing information, making conjectures and giving convincing arguments.
The Texas Instruments TI-83 or TI-84 calculator can be used for the course.

These courses contain: basic concepts of algebra; inequalities and proof; linear equations and functions; products and factors of polynomials; rational expressions; irrational and complex numbers; quadratic equations and functions; variation and polynomial equations; analytic geometry; exponential and logarithmic functions; sequences and series; triangle trigonometry; trigonometric graphs and identities; trigonometric applications; probability and statistics.

College Algebra This course is designed for the senior who does not intend to take Introductory Calculus and/or was in the first ability grouping of Algebra II/Trigonometry. The course requires the relating of concepts mainly on the comprehension, application and analysis levels. The course covers the following topics: algebra review; equations and inequalities; functions and graphs; polynomial and rational functions; exponential and logarithmic functions; topics in analytic geometry; systems of equations; matrices and determinants; sequences and series; probability; statistics. (NOTE: This course will be scheduled if a sufficient number of students enroll.)
The Texas Instruments TI-83 or TI-84 calculator can be used for the course.

Prerequisite: For placement into College Algebra the student should have an average of 80 or better in both Algebra II/Trigonometry and his overall average. Students with a Math PSAT score of 50 or greater will not be allowed to take College Algebra unless they are given permission by both their current Mathematics teacher and the Department Chair. In the opinion of the department the student must demonstrate ability to do the required work of the course. Approval rests with the Algebra II/Trigonometry teacher and the Department Chair.

Note : College Algebra may not be taken by students who have completed Introductory Calculus.

Statistics This course is designed for the junior or senior who has completed at least three years of math. Statistics will deal in the collection, processing, analysis and interpretation of numerical data. This course contains: frequency distributions and graphs; data description; counting techniques; probability and probability distributions; normal distribution; confidence intervals and sample size; hypothesis testing; testing the difference between means and proportions; correlation and regression; chi-square; the F-test and analysis of variance; nonparametric statistics; sampling and simulation; quality control.
The Texas Instruments TI-83 or TI-84 calculator can be used for the course.

For placement into Statistics the student should have an average of 80 or better in his overall average and in his previous math class (either Enriched or Advanced Algebra II/Trigonometry, College Algebra, or Introductory Calculus or Advanced Introductory Calculus). In the opinion of the department, the student must demonstrate ability to do the required work of the class. Approval rests with the teacher of the course and the Department Chair.

Introductory Calculus This course is designed for the junior or senior who has been in ENRICHED Algebra II/Trigonometry and intends to take Calculus at McQuaid Jesuit or in college. The student should have a comprehensive understanding of Algebra, Geometry and Algebra II/Trigonometry. The course requires the interrelating of concepts mainly on the application, analysis and synthesis levels. See ADVANCED Introductory Calculus for a listing of topics.
The Texas Instruments TI-83 or TI-84 calculator can be used for the course.

For placement into Introductory Calculus the student should have an average of 85 or better in both ENRICHED Algebra II/Trigonometry and his overall average. A minimum of 50 on the Mathematics portion of the PSAT is required. In the opinion of the department the student must demonstrate ability to do advanced work in mathematics. Approval rests with the ENRICHED Algebra II/Trigonometry teacher and the Department Chair.

Advanced Introductory Calculus This course is designed for the sophomore or junior who has been in the ADVANCED classes and/or who intends to take AP Calculus at McQuaid Jesuit. The course demands thinking skills beyond memorization. These higher-level thinking skills include application, analysis, synthesis and evaluation. ADVANCED Introductory Calculus extensively covers the following topics: real analysis; analytic geometry; sequences and series; limits; theory of polynomials; introduction to differential calculus; trigonometric functions, identities and applications; exponential and logarithmic functions; vectors; matrices; introduction to integral calculus; probability and statistics.
The Texas Instruments TI-83 or TI-84 calculator can be used for the course.

For placement into ADVANCED Introductory Calculus the student should have an average of 85 or better in both ADVANCED Algebra II/Trigonometry and his overall average. A minimum of 60 on the Mathematics portion of the PSAT is required. In the opinion of the department the student must demonstrate ability to do advanced work in mathematics. Approval rests with the ADVANCED Algebra II/Trigonometry teacher and the Department Chair.

Calculus The course is designed to prepare the student for a beginning college calculus program and it contains the major concepts of the AP Calculus AB, but not the depth. Students taking this course should take Calculus I in college. The course demands higher-level skills (application, analysis, synthesis and evaluation), a monumental amount of work both in class and out of class, and substantial amounts of time. (NOTE: This course will be scheduled if a sufficient number of students enroll.) The course will culminate with a May examination, which MUST be passed in order to graduate. The course includes all concepts of Introductory Calculus, analysis of limits and their properties, explicit and implicit differentiation, applications of differentiation, transcendental functions, and techniques of integration with applications.
The Texas Instruments TI-83 or TI-84 calculator can be used for the course.

Prerequisite: Successful completion of ADVANCED Introductory Calculus or Introductory Calculus with an average of 80 or better in both the course and overall average. Approval rests with the Introductory Calculus teacher and the Department Chair.

During the summer the student MUST REVIEW the entire Introductory Calculus course in preparation for a September examination. The course will culminate with the Advanced Placement examination that MUST be taken. The course includes all concepts of Introductory Calculus; analysis of limits and their properties, explicit and implicit differentiation, applications of differentiation, transcendental functions, and techniques of integration with applications.
The Texas Instruments TI-83 or TI-84 calculator can be used for the course.

Prerequisite: Successful completion of ADVANCED Introductory Calculus with an average of 80 or better in both the course and overall average or successful completion of Introductory Calculus with an average of 85 or better in both the course and overall average. Approval rests with the Introductory Calculus teacher and the Department Chair.

AP Calculus BC The course is designed for the student who has completed successfully the Advanced Placement Calculus AB program. This course is paramount in demanding higher-level skills (application, analysis, synthesis, and evaluation). Advanced Placement Calculus BC contains all AP Calculus AB topics. Some additional topics are: parametric, polar, and vector functions; slope fields; applications of integrals to physical, social, and economic models; improper integrals; logistic equations; and Taylor series.
The Texas Instruments TI-83 or TI-84 calculator can be used for the course.

Prerequisite: Successful completion of Advanced Placement Calculus AB and the approval of the calculus teacher.

AP Statistics The course is designed to prepare the student for the Advanced Placement Examination, which each student MUST take in May in order to receive credit for the course. The course concludes with a statistics research project in place of a June examination. Statistics will deal in the collection, processing, analysis and interpretation of data. This course contains: frequency distributions and graphs; data description; counting techniques; probability and probability distributions; normal distribution; confidence intervals and sample size; hypothesis testing; testing the difference between means and proportions; correlation and regression; analysis of variance.
The Texas Instruments TI-83 or TI-84 calculator can be used for the course.