Academy of the Holy Angels

Course Descriptions - Mathematics

Course Numbers: 3101 - 3424
Courses are: All courses are College Preparatory. College preparatory courses of a more rigorous nature are indicated by Honors (H), High Honors (HH), or Advanced Placement (AP).
Requirement: All students are required to take 3 years of a Mathematics course sequence.
All averages presented are unweighted, yearly averages, unless otherwise noted.
SAT Subject Tests: Students must consult with their Teacher and Counselor before testing, OR retesting.
Incoming Freshman: Must score 80% or above on the math section of the COOP Entrance Exam to
be eligible to sit for the Geometry Placement Exam.

High Honors Math Program GRADES 9, 10, 11, 12 4 YEARS
Courses: Plane and Solid Geometry-HH, Algebra II and Trigonometry-HH, Precalculus-HH, and Calculus-HH.
Prerequisites: To remain in High Honors Program, a student must maintain a minimum average of 85% in all math courses up to and including Precalculus, achieve a minimum grade of 80% on both semester exams and teacher recommendation.

Algebra I (3101) GRADE 9 YEAR
This course is a modern introduction to Algebra which leads to the understanding of the basic structure of algebra through an informal and intuitive approach. Students will be provided with an in-depth study of the language of Algebra. A substantial amount of time is spent on skills and concepts to enable students to make the transition from arithmetic to Algebra. Application of these skills and concepts is also enforced. The graphing calculator, TI-84, will be introduced when graphing is studied.
Prerequisites: A score between 70-79% National Percentile on the COOP Exam (Math). Consideration will also be given to their reading scores and math grades from previous years.

Algebra I - Honors (3102) GRADE 9 YEAR
This course is a modern introduction to Algebra which leads to the understanding of the basic structure of Algebra through an informal and intuitive approach. Appropriate emphasis is placed on mastering more rigorous skills, concepts and mathematical content. Students are encouraged to develop thinking and problem solving skills throughout the course, and applications of these skills will be of primary importance. The graphing calculator, TI-84, will be introduced when graphing is studied.
Prerequisites: A score between 80-89% National Percentile on the COOP Exam (Math). Consideration will also be given to their reading scores and math grades from previous years.

Algebra I - High Honors (3103) GRADE 9 YEAR
This accelerated course is a modern approach to algebra in which the concepts, principles and basic structure of algebra are explored. Emphasis will be placed on problem solving and real-life applications so that the students can be given a greater appreciation for the relevance of algebra in their lives and careers. Additional topics that will be covered beyond the scope of an Algebra I course include radical expressions, quadratics and an introduction to probability and statistics. The graphing calculator, TI-84, will be introduced when graphing is studied.
Prerequisites: Minimum of 90% National Percentile on the COOP Exam (Math). Consideration will also be given to reading scores and reports from previous years.

Eligibility for 2 Math Courses in 10th Grade:
1. If you have taken Algebra I:
- 93% average
- 85% on the midterm and final exam
- Minimum 82% national percentile (math) on NEDTs
- Teacher recommendation
Your two courses would be Geometry and Algebra II.

2. If you have taken Algebra I Honors:
- 93% average
- 85-90% on the midterm and final exam
- Minimum 85% national percentile (math) on NEDTs
- Teacher recommendation
Your two courses would be Plane & Solid Geometry Honors and Algebra II Honors.

3. If you have taken Algebra I High Honors there are 2 possibilities:
- 93% average
- 85% on the midterm and final exam
- Minimum 91% national percentile (math) on NEDTs
- Teacher recommendation
Your two courses would be Plane & Solid Geometry High Honors and Algebra II and Trigonometry High Honors.
OR
- 90 - 92% average
- 80% on the midterm and final exam
- Minimum 85 - 90% national percentile (math) on NEDTs
- Teacher recommendation
Your two courses would be Geometry Honors and Algebra II Honors.

Geometry (3201) GRADE 9, 10 YEAR
A modern approach to the basic principles of Geometry aims to develop a knowledge of geometric elements and their relationships in order to help the student grow in mathematical awareness and conceptual understanding. This course will cover all the basic ideas and terms of traditional geometry. A non-rigorous approach to the deductive method of proof will be presented to promote logical reasoning skills. The key concepts of Algebra will be re-enforced throughout the year. TI-84 Graphing Calculator is required for the 3rd quarter.
Prerequisites - Freshman: Minimum of 80% National Percentile in the COOP (Math), a full year course of Algebra I and successful completion of the Geometry Placement exam.

Plane and Solid Geometry - Honors (3202) GRADE 9, 10 YEAR
A modern approach to the basic principles of geometry aims to develop a knowledge of geometric elements and their relationships in order to help the student grow in the use of the deductive method of proof. Formal proofs will be explored in detail throughout the entire course. A study of three-dimensional solids including their lateral areas, surface areas and volumes will be studied during the fourth quarter. TI-84 Graphing Calculator is required for the 3rd quarter.
Prerequisites - Freshmen: Minimum of 80% National Percentile in the COOP (Math), a full year course of Algebra I and successful completion of the Geometry Placement exam.
Prerequisites - Sophomores: Minimum average of 80% in Algebra I – Honors, and 75% on both semester exams. Consideration will also be given to standardized test scores. Students in Algebra I must have a 93% average, 80% on both exams and NEDT math scores between 85-90%.

Plane and Solid Geometry - High Honors (3203) GRADE 9, 10 YEAR
This course provides an in-depth study of geometry with heavy emphasis on deductive proofs from the outset. All
of the traditional topics of Euclidean geometry will be studied in detail as well as coordinate geometry and an introduction to right triangle trigonometry. A study of three-dimensional solids including their lateral areas, surface areas and volumes will be studied during the fourth quarter as well as an introduction to geometric probability. TI– 84 Graphing Calculator is required for the 3rd quarter.
Prerequisites - Freshmen: Minimum of 92% National Percentile in the COOP (Math), a full year course of Algebra I and successful completion of the Geometry Placement exam.
Prerequisites - Sophomores: Minimum average of 88 % in Algebra I- HH, and receive 80% on both semester exams and minimum NEDT score of 91%.

Algebra II (3301) GRADE 10, 11 YEAR
A modern integrated course in Algebra consists of a thorough review of Algebra I . A complete study of quadratic equations, factoring, completing the square, the quadratic formula, graphing, problem solving, solving systems of equations and inequalities and polynomial equations will be provided. Additional topics will include operations on rational expressions and radicals. TI–84 Graphing Calculator is required.
Prerequisites: Successful completion of Algebra I and Geometry. Geometry may also be taken simultaneously with this course for those sophomores doubling up in math.
Note: Students are encouraged to take the June SAT Subject Test – Mathematics Level 1. Students must consult with their counselor and their teacher before taking this exam.

Algebra II - Honors (3302) GRADE 10, 11 YEAR
An extended study of the topics introduced in Algebra I is made. The real number system with emphasis on linear functions and relations, systems of equations and inequalities, rational expressions, radicals and irrational numbers, complex numbers, polynomial functions, conic sections, and exponential and logarithmic functions are included in the course of the year. Students review and expand their knowledge of problem solving.
Prerequisites: Acceptance will be based on earning a minimum average of 80% in Algebra I-H, Plane & Solid Geometry – H, 75% on both semester exams, standardized test scores and department approval. Students not meeting the requirements for Algebra II & Trig will also be placed in this course. Students entering this course from Geometry must have a 93% average, 80% on both exams and minimum of 500 on PSAT scores. TI–84 Graphing Calculator is required.
Note: Students are encouraged to take the June SAT Subject Test – Mathematics Level 1. Students must consult with their counselor and their teacher before taking this exam.

Algebra II & Trigonometry - High Honors (3303) GRADE 10, 11 YEAR
An extended study of the topics introduced in Algebra I is made. The real number system with emphasis on linear functions and relations, systems of equations and inequalities, rational expressions, radicals and irrational numbers, polynomial functions, conic sections, and exponential and logarithmic functions. The course is fast-paced and emphasis will be placed on higher order thinking and problem solving. After the completion of Algebra II, basic trigonometric and circular functions are introduced as preparation for the Precalculus-HH course the following year. TI–84 Graphing Calculator is required.
Prerequisites - Juniors: Minimum average of 90% in Algebra I - Honors, a 93% average in Plane & Solid Geometry- Honors and a minimum grade of 85% on both semester exams and teacher recommendation. We will pay special attention to the students’ Algebra I grade. Juniors entering this course from Plane & Solid Geometry –HH must have a minimum average of 85% and a minimum grade of 80% on both semester exams.
Prerequisites - Sophomores: Sophomores entering this course from Plane & Solid Geometry – H must have a 92% yearly average, a minimum grade of 85% on both semester exams, and teacher recommendation. Students entering this course from Plane and Solid Geometry HH must have an 85% average and a minimum grade of 80% on both semester exams.
Note: Students are encouraged to take the June SAT Subject Test– Mathematics Level 1. Students must consult with their counselor and their teacher before taking this exam.
Note: Any junior who has a 95% average in Algebra II & Trig – HH, and a score of 650 or above on the PSAT or SAT, may take Precalculus at an outside source. This will enable these students to enroll in Calculus HH or Calculus AB as seniors. They will be expected to pass the both semester exams for Precalculus- HH for Calculus AB, or Precalculus-H for Calculus HH.

Precalculus (3411) GRADE 11, 12 YEAR
This course is a continuation of Algebra II. Topics will include a complete study of trigonometry, conic sections,
exponential and logarithmic functions, probability, and sequences and series. TI–84 Graphing Calculator is required.
Prerequisites: Minimum average 85% in Algebra II as well as a 75% on both semester exams. Students not meeting the requirements for Precalculus-Honors will also be placed in this course.
Note: Students are encouraged to take the June SAT Subject Test– Mathematics Level 1. Students must consult with their counselor and their teacher before taking this exam.

Precalculus - Honors (3412) GRADE 11, 12 YEAR
This course is a preparation for Calculus. Topics will include a complete study of trigonometry, functions and their inverses, advanced graphing techniques, exponential and logarithmic functions, sequences and series, the binomial theorem and probability. Applications of these concepts will also be included. An introduction to limits and continuity may also be explored.
Prerequisites: Minimum average of 85% in Algebra II-Honors, as well as a minimum grade of 75% on both semester exams in Algebra II - Honors. Consideration will also be given to standardized test scores. TI–84 Graphing Calculator is required. Students who wish to enter this course from Algebra II must have a minimum yearly average of 95% and a minimum grade of 85 on both semester exams. In addition, they must enroll in a summer math course (21 hours) at Academy of the Holy Angels to study Conic Sections and Introduction to Logarithms. An assessment will be given at the end of the course. Students not meeting the requirements for Precalculus-HH will also be placed in this course.
Note: Students are encouraged to take the June SAT Subject Test – Mathematics Level 1 or Mathematics Level 2. Students must consult with their counselor and their teacher before taking this exam.

Precalculus - High Honors (3413) GRADE 11, 12 YEAR
This rigorous course will provide the students with a strong background for Calculus (AB) or Calculus HH. Additional topics in trigonometry as well as advanced graphing, polynomial functions, logarithm and exponential functions, sequences and series, complex numbers in polar form, polar graphing, limits, continuity, and probability will be studied in depth. An introduction to Differential Calculus will also be included. The course will also focus on the theoretical development of each of these topics, and emphasis will be placed on higher order thinking skills and challenging applications. Use of the graphing calculator will be essential to the course.
Prerequisites: A minimum yearly grade of 85% in all High Honors courses to date, a minimum grade of 80% on both semester exams and teacher recommendation. TI–84 Graphing Calculator is required. Students who wish to enroll in this course from Algebra II –Honors must have a 93% average, a minimum grade of 85 on both semester exams and teacher recommendation. They must also complete a Summer Mini Course (21 hours) at Academy of the Holy Angels to study selected topics in Trigonometry and Logarithms. An assessment will be given at the end of the course.
Note: Students are encouraged to take the June SAT Subject Test – Mathematics Level 2. Students must consult with their counselor and their teacher before taking this exam.

Calculus (3401) GRADE 12 YEAR / ELECTIVE
This course is open to Seniors who have successfully completed Precalculus. The course will include a study of limits, continuity, the basic rules of differentiation, as well as applications of differentiation to curve sketching and word problems involving related rates and optimization. The derivative of the exponential and logarithmic functions will also be studied. Techniques of integration will be introduced. Limits of trigonometric functions and differentiation and integration of trigonometric functions will not be studied in this course.
Prerequisites: Students entering this course must have a minimum average of 85% in Precalculus and a grade of 80% on the midterm and final exam. Students not meeting the requirements for Calculus (HH) will also be placed in this course. TI–84 Graphing Calculator is required.

Calculus - High Honors/Middle College Program (3403) GRADE 11, 12 YEAR / ELECTIVE
In this course, students will continue to study the concepts of limits and continuity. The basic concepts of the derivative with its applications to velocity, acceleration, curve sketching, related rates, and max-min problems will be studied in the first semester. The definite and indefinite integral will be introduced during second semester.
Techniques of differentiation and integration of the trigonometric functions, the natural logarithmic function, the exponential function and the inverse trigonometric functions will be studied. Integration will be applied to finding area and volume.
Prerequisites: Students entering this course from Precalculus-HH must have a minimum average of 80% and 75% on both semester exams. Students entering this course from Precalculus-H must have a minimum average of 85%, 80% on both semester exams and teacher recommendation. TI–84 Graphing Calculator is required. Students not meeting the requirements for Calculus-Advanced Placement will also be placed in this course.
Note: Students may earn college credit through the Middle College Program of Fairleigh Dickinson University upon successful completion of this course in Calculus.
Note: Students are encouraged to take the SAT II – Mathematics Level 1 or Mathematics Level 2. (if not already taken.) Students must consult with their counselor and their teacher before taking this exam.
Note: All students are required to complete a summer assignment as further preparation. This assignment is due the 1st week of school in September.

Calculus (AB) - Advanced Placement (3404) GRADE 11, 12 YEAR / ELECTIVE
Students will continue to study limits and continuity begun in Precalculus. An introduction to the basic concepts of differential and integral calculus with applications to velocity, acceleration, curve sketching, related rates and max-min problems will be given. Techniques of differentiation and integration will be studied and applied to areas, radioactive decay, and volumes and surface areas of revolution. The theoretical development of each of these topics will be stressed. The course concludes with the Advanced Placement Examination in May.
Prerequisites: A minimum cumulative average of 86% in all High Honors courses, a minimum grade of 80% on both semester exams in Precalculus-HH and teacher recommendation. TI–84 Graphing Calculator is required. Students in Precalculus- H may take Calculus (AB)-Advanced Placement if they have a 95% average in Precalculus-H and a minimum of a 90% on both semester exams.
Note: All students take the AP Exam in May.
Note: All students are required to complete a summer assignment as further preparation. This assignment is due the 1st week of school in September.

Probability and Statistics (3421) GRADE 11, 12 YEAR / ELECTIVE
This full-year mathematics course will cover basic concepts in statistics and probability. Emphasis will be placed on the collection, processing, analysis and interpretation of numerical data, as well as probability theory and combinatorics. This course will be highly beneficial not only to students planning to study mathematics and science but also to those who wish to pursue a career in the social sciences or business. TI-84 Graphing Calculator is required.
Prerequisites: This course is open to all seniors who wish to take a fourth year of mathematics and to those who wish to take two mathematics courses simultaneously. It is also open to juniors who are in honors math classes and would like to take an additional math course.

Statistics - Advanced Placement (3424) GRADE 11, 12 YEAR / ELECTIVE
This course is open to juniors and seniors who have successfully completed Precalculus-Honors or Precalculus-High Honors or who are taking either of these courses simultaneously with AP Statistics. The focus of this course is on problem solving. The course will introduce students to the major concepts and tools for collecting, analyzing and drawing inferences from data. Students will concentrate on the following topics: exploring data, planning a study, anticipating patterns and statistical inferences. TI-84 Graphing Calculator is required.
Prerequisites - Seniors: A minimum SAT score of 600 in Math and 600 in English, a minimum average of 88% in Precalculus-Honors, a minimum average of 85% in Precalculus-High Honors, a minimum grade of 80% on previous year’s midterm and final examination. A minimum grade of 80% must also be attained on the current midterm examination. Teacher recommendation is also required.
Prerequisites - Juniors: A minimum PSAT score of 550 in Math and 550 in English, a cumulative minimum average of 85% in High Honors Math courses or 88% in Honors Math courses. A minimum grade of 80% must also be attained on the current midterm examination. Precalculus must be taken simultaneously with this course.
Teacher recommendation is also required.
Note: All students take the AP Exam in May.