HONORS PRE-CALCULUS, B (formerly called Analytic Geometry)
HONORS PRE-CALCULUS, B (formerly called Analytic Geometry)
COURSE DESCRIPTION: Analytic geometry is a course designed to prepare the student for the study of calculus and linear algebra. The past decade has witnessed important changes in the study of algebra, geometry, and trigonometry and this course is designed to reflect the changes in the spirit and content of those changes. This is a one semester course that should deepen and extend the student’s interest in the subject and its applications.
COURSE GOALS: To provide the student with a course to prepare him for the rigors of calculus and to ascertain that he has learned all the previous mathematics he has taken in the past, especially the algebraic procedures in simplification and in solving equations. It also provides the student with more applications of mathematics in problem solving.
COURSE OBJECTIVES: The student will be able to
Distinguish between the conic sections
Use the coordinate system
Recognize equations for the various conic sections
Write equations for the conic sections and transcendental functions
Manipulate equations
Graph polar equations
Identify the relationship between rectangular and polar coordinates
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Chapter |
Competencies |
Assessment |
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Chapter 1 Fundamental Concepts |
The student is introduced to the notation and terminology to be used throughout the course. In particular, concepts from geometry, coordinate geometry, analytic proofs, functions and relations, and writing equations for given graphs are reviewed. |
Homework Class discussion Overhead presentations Team Problems Quizzes Tests |
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Chapter 2 The Straight Line and the Circle |
The student is re-introduced to the straight line and the circle. This is done by investigating the relationship between first-degree equations in x and y and line in the coordinate plane, writing equations for lines in different forms, investigating the correspondence between circles and second-degree equations, studying families of circles, and working with the translation of axes for lines and circles. |
Homework Class discussion Overhead presentations Team problems Graphing calculators Quizzes Tests |
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Chapter 3 Conics |
The student is introduced to the conic sections by using locus definitions of the parabola, the ellipse, and the hyperbola to write equations for and to graph these conic sections. Then the student will be able to write second- degree equations for these conic sections, graph these conic sections, and give important data about these conic sections. |
Homework Class discussion Overhead presentation Team problems Graphing calculators Quizzes Tests |
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Chapter 4 Simplification of Equations |
Students will learn how to simplify second-degree equations by translation of axes, by rotation of axes, by combining rotation and translation of axes, and to determine whether the graph of a given second-degree equation is an ellipse, a parabola, or a hyperbola. |
Homework Class discussion Overhead presentations Team problems Graphing calculators Quizzes Tests |
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Chapter 5 Algebraic Curves |
Students return to the algebraic curves to use x-intercepts, symmetry, and signs of y-values between intercepts as aids in graphing polynomial functions of higher degree. The students also analyze and graph rational and irrational functions, graphing equations in factored form, and find the intersection of graphs of two equations. |
Homework Class discussion Overhead presentations Graphing calculators Quizzes Tests |
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Chapter 6 Transcendental Functions |
Students are led through a pretty thorough study of trigonometric functions, exponential and hyperbolic functions, logarithmic functions, and inverse functions. These functions are used to solve applied problems. Students also use addition of ordinates to graph functions. |
Homework Class discussions Overhead presentations Quizzes Tests |
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Chapter 7 Polar Coordinates |
Students are re-introduced to the polar coordinate system. Relationships between the polar and rectangular coordinates are reviewed, DeMoivre's Theorem is used to find roots of complex numbers, and solving trigonometric equations are done again. New is the solving of polar equations. |
Homework Class discussions Overhead presentations Quizzes Tests |
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Chapter 8 Parametric Equations |
Students are introduced to parametric equations ! how to change parametric equations to rectangular equations and vice versa, how to graph parametric equations, and how to use parametric equations to solve applied problems. |
Homework Class discussion Overhead presentations Graphing calculators Quizzes Tests |
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Chapter 9 Space Coordinates and Surfaces |
Students will be introduced to a 3-dimensional coordinate system and will learn to locate points in that system, find the distance between points in that system, and graph equations in that system. |
Homework Class Discussion Overhead Presentations Quizzes Tests |
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Chapter 10 Vectors, Planes and Lines |
Students will learn to perform addition, subtraction, and scalar multiplication of vectors. The students will also study the vectors in 2 and 3-dimensional planes, the dot product, the cross product, and the use of vectors to solve applied problems. |
Homework Class Discussion Overhead Presentations Quizzes Tests |
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Chapter 11 Curve Fitting |
Students will learn to use the method of least squares to find the line of best fit for a set of data that can be modeled by a linear equation. The students will also learn to use natural logarithms to obtain an exponential equation to model data involving exponential growth or decay. |
Homework Class Discussion Overhead Presentations Quizzes Tests |