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Course
Catalog > Mathematics
Mathematics
The Cushing Mathematics Department strives to meet all students at their ability level and to engage and stretch them as far as they can go in mathematics. The department’s curriculum is, therefore, composed of a variety of topics and levels. It offers a traditional college prep course sequence: Algebra I, Geometry, Algebra II, Precalculus, and Calculus. An honors section is offered in Geometry, Algebra II, Precalculus, Calculus, and Independent Study and an AP section is offered in Calculus and in Probability for those students who have demonstrated agility, confidence and skill in their previous study of math. Likewise, modified sections for those students who require a slower pace and more individualized attention are offered in all courses. In each course, students are exposed to both the principles and applications of the mathematics being taught. Students make connections to topics they have previously learned and to other disciplines they have studied, such as biology and physics. In addition to acquiring traditional skills in algebra and geometry, students analyze data, work with statistics and numerical patterns, and read graphs and charts. They learn to draw conclusions from their observations and state them persuasively and logically. All students make regular use of TI-83 or TI-83 Plus graphing calculators and course-specific software on their laptops in order to better understand and gain insights to topics presented in the classroom.
Here you will find courses offered at Cushing by discipline. Please note that some changes are made to our programs each year - for the complete listing of courses for the 2008-2009 academic year as distributed to students and listed in our viewbooks, please view the PDF file. If you have questions about the curriculum at Cushing Academy, you may contact Susie Kendall Carlisle, Dean of Academic Affairs.
Mathematics Department Course Offerings
Topics in Algebra I
Algebra I
Honors Algebra I
Geometry
Honors Geometry
Topics in Geometry
Algebra II
Honors Algebra II
Algebra II Modified-A
Algebra II Modified-B
Introduction to Precalculus
Precalculus
Honors Precalculus
Probability and Statistics
Calculus
Advanced Placement Calculus AB
Advanced Placement Calculus BC
Advanced Placement Statistics
Discrete Mathematics
Independent Study in Mathematics
Topics in Algebra I
Students in Topics in Algebra I improve their knowledge of the Real Number System. This course emphasizes: variables, problem solving, equations, functions, order of operations, exponents, and the use of tables and graphs. Both skills and concepts are stressed. Students learn concrete, informal, and formal methods of solving linear equations. Students apply algebraic methods to solve a variety of real-world problems. Offered: Full Year
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Algebra I
Most students entering the ninth grade take Algebra I unless they have previously completed it. This is the first course in Cushing’s mathematics sequence. Topics in this course include linear statements, lines and distances, slopes and lines, exponents and powers, and quadratic functions. Offered: Full Year
Offered: Full Year
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Honors Algebra I
Honors Algebra I is an alternative to Algebra I for talented and highly-motivated mathematics students. This course covers all topics in Algebra I, most in greater detail. Additional topics include systems of linear equations, inequalities, rational and irrational numbers, and quadratic functions. Prerequisite: departmental permission. Offered: Full Year
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Geometry
Students in Geometry improve their knowledge of the properties of two- and three-dimensional figures, work with better visual perception of two- and three-dimensional figures, and develop the skills of using inductive and deductive reasoning as problem-solving tools. Topics covered in this course include parallel lines and planes, properties of triangles, quadrilaterals and circles, congruent and similar triangles, areas of polygons, circles, and an introduction to trigonometry. Prerequisite: Algebra I; freshmen who have already taken Algebra I must take a competency test. Day students may take it over the summer; all others will take it on the first day of class. Offered: Full Year
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Honors Geometry
Honors Geometry is an alternative to Geometry for talented and highly motivated mathematics students. This course covers all topics in Geometry, most in greater detail. Additional topics include coordinate geometry and three-dimensional geometry. Prerequisite: B in Algebra I, departmental permission. Offered: Full Year
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Topics in Geometry
Topics in Geometry is a course designed specifically for those students who need more time and individual attention in order to become proficient with the concepts of Geometry. Material is generally introduced at a slower rate and is reviewed in greater depth. Topics include lines, planes, angles, deductive reasoning, triangles, quadrilaterals, polygons and circles. Prerequisite: Algebra I, departmental permission. Offered: Full Year
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Algebra II
Topics investigated in this course include linear relations, polynomials, quadratic functions, rational expressions, irrational and complete numbers, exponents, and an introduction to trigonometry. Prerequisites: Geometry, departmental permission. Offered: Full Year
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Honors Algebra II
Honors Algebra II is an alternative to Algebra II for talented and highly motivated mathematics students. This course is taught from the same text as the Algebra II course. However, additional topics are covered in greater detail, including graphs of trigonometric functions, statistics, and probability.
Prerequisites: B in Honors Geometry, departmental permission. Students wishing to enroll in Honors Algebra II need to demonstrate both strong skills and performance in previous math classes. Students are strongly encouraged to enroll in Honors Algebra II only if they feel confident that they can meet the rigors of the honors level for a full year. Students are discouraged from changing placement tracks in the middle of the year. Offered: Full Year
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Algebra II Modified-A
Algebra II Modified-A is the first part of a two-year course sequence that is designed specifically for those students who need more time and individual attention in order to become proficient with the concepts of Algebra. Material is generally introduced at a slower rate and reviewed in greater depth. A strong emphasis is placed on ensuring that students have mastered the concepts learned in previous mathematics courses. Topics include equations, inequalities, functions, graphs, systems, polynomials and rational expressions. Prerequisites: Geometry, departmental permission. Offered: Full Year
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Algebra II Modified-B
Algebra II Modified-B is the second course in this two-year sequence. This course completes the regular Algebra II curriculum and begins an investigation of some advanced topics, such as trigonometric functions. Prerequisites: Algebra II Modified-A. Offered: Full Year
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Introduction to Precalculus
Introduction to Precalculus is a course for students who have successfully completed Algebra II but are not ready for the rigors of regular Precalculus. In Fall Term, fundamental and advanced topics from algebra and geometry are reviewed and solidified. In the winter and spring, trigonometry is explored in great detail, with a concentration on its applications. Prerequisites: Algebra II. Offered: Full Year
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Precalculus
Precalculus is a course that draws heavily from the topics introduced in previous algebra courses and which lays the foundation for the study of calculus. In addition to learning a variety of new topics, students come to understand how all previously-learned mathematics concepts fit together. Topics covered in this course include linear, polynomial, rational, expo-nential, trigonometric, and logarithmic functions, as well as graphs, relations, conic sections, and systems of equations. Prerequisites: Algebra II. Offered: Full Year
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Honors Precalculus
Honors Precalculus is an alternative to Precalculus for talented and highly motivated mathematics students. Most students who plan to take Advanced Placement Calculus as a senior will elect this course for their junior year. This course covers all topics covered in Precalculus, most in greater detail. Additional topics include sequences and series, limits and the derivative. Prerequisites: B in Honors Algebra II, departmental permission. Offered: Full Year
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Probability and Statistics
This course is designed for students who have completed Introduction to Precalculus or Precalculus. Topics covered in this course include descriptive and inferential statistics, curve fitting, and mathematical models, combinations, and probability. Prerequisites: Introduction to Precalculus or Precalculus, depart-mental permission. Offered: Full Year
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Calculus
Calculus is a course designed for students who wish to take calculus but not the Advanced Placement exam. Students in this class refine their problem-solving skills and are exposed to introductory calculus. Topics include a review of topics in algebra, exponential and logarithmic functions, the derivative, differentiation rules, applications of the derivative, the integral and volumes. Prerequisites: B in Precalculus, departmental permission Offered: Full Year
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Advanced Placement Calculus AB
Advanced Placement Calculus AB follows the curriculum set forth by the College Board. Students who have maintained a strong honors average in Honors Precalculus should select this course. Calculus AB is worth one semester of college credit upon successful completion of the Advanced Placement test offered in May. Students enrolled in this course are required to take this test. Topics covered include functions and graphs, limits of functions, the derivative, examining extrema, antiderivatives, the definite integral, applications of the definite integral, and logarithmic, exponential and trigonometric functions. Prerequisites: B in Honors Precalculus, departmental permission. Offered: Full Year
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Advanced Placement Calculus BC
Advanced Placement Calculus BC follows the curriculum set forth by the College Board. Students who have maintained a high honors average in Honors Precalculus should select this course. Calculus BC is worth two semesters of college credit upon successful completion of the Advanced Placement test in May. Students enrolled in this course are required to take this test. Topics covered include functions and graphs, limits of functions, the derivative, examining extrema, anti-derivatives, the definite integral, applications of the definite integral, logarithmic, exponential and trigonometric functions, techniques of integration, indeterminate forms, improper integrals, infinite series and sequences. Prerequisites: A- in Honors Precalculus, departmental permission. Offered: Full Year
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Advanced Placement Statistics
Advanced Placement Statistics follows the curriculum set forth by the College Board. Students who have maintained a high honors average in Calculus or who have completed AB Calculus should select this course. AP Statistics is worth two semesters of college credit upon successful completion of the Advanced Placement test in May. Students enrolled in this course are required to take this test. Topics covered include data organization (patterns and departure from patterns), normal distributions, density curves, Z-scores, scatterplots, correlation, least-square regression, exponential and power regressions, relations in categorical data, sampling, probability, and simulation. Prerequisites: B in Honors Precalculus or Calculus, departmental permission. Offered: Full Year
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Discrete Mathematics
This course is open to students who have successfully achieved a minimum of 3 on the AP exam or a B+ in AP Calculus BC. Whenever possible, examples will be selected from AP Calculus curriculum to illustrate the theoretical concepts. All the topics will be complemented with computer laboratory projects.
Fall Term: Logic - The study of reasoning will include truth tables, proofs using binary logic, and tautologies. Set Theory: Algebra of Sets, Relations: Partial Orders, Linear Orders, Equivalence Relations and Classes, The construction of Rational Numbers. Functions: Injection, Surjection, Bijection, Inverses
Winter Term: Elementary Number Theory - Divisibility, Euclidian Algorithm, Greatest Common Divisors, Perfect Numbers, Congruences, Fermat's Little Theorem, Euler's Theorem, The Chinese Remainder Theorem, the Law of Quadratic Reciprocities, The Moebius Function, The Euler Function, Fibonacci Numbers
Spring Term: Linear Algebra - Systems of Linear Equations, Vector Spaces, Linear Transformations, Eigenvector and Eigenvalues
Prerequisite: B+ in BC Calculus, departmental permission. Offered: Full Year
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Independent Study in Mathematics
For students at an advanced level, independent study is available. Prerequisite: B+ in BC Calculus, departmental permission. Offered: Full Year
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