WHITTIER UNION HIGH SCHOOL DISTRICT Whittier, California. July, 1984 COURSE OF STUDY COURSE DESCRIPTION

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1 WHITTIER UNION HIGH SCHOOL DISTRICT Whittier, California July, 1984 COURSE OF STUDY Course Title: Department: MATH ANALYSIS - HONORS MATHEMATICS Grade Levels: COURSE DESCRIPTION This semester is a study of elementary functions, analytical geometry, and related topics that will provide students with a mathematics preparation necessary for college mathematics. Math Analysis - Honors is differentiated from regular Math Analysis by the greater coverage of topics in both scope and depth and consequent need for greater intellectual concentration by the student. Length: One year Prerequisite for Enrollment: C or better grade in both semesters of Algebra 2 - Honors or approval of Mathematics Department Chairperson Recommendations for Enrollment: None Type of Course: Elective I. COURSE COMPETENCIES The Student Will: A. Conics M 1. Define a conic in terms of a locus of points M 2. Write the equation of a conic in standard form M 3. Graph a conic from the equation in standard form D 4. Write the equation of a conic given pertinent information D 5. Graph a conic given pertinent information D 6. Identify an equation as degenerate or the equation of a conic B. Functions 1

2 M 1. Identify relations that are functions M 2. Determine the domain and range of a function M 3. Find the zeros of a function M 4. Identify a function as a constant function, identify function, linear function, absolute value function or step function M 5. Graph a function D 6. Perform certain algebraic operations on two functions D 7. Determine the composition of two functions D 8. Find the inverse of a function D 9. Graph a function and its inverse A 10. Identify a function as increasing, non-increasing, decreasing, non-decreasing or a combination C. Graphing Techniques M 1. Classify the graph of a relation as symmetric with respect to the x axis, the y axis, the origin, or the line y+z M 2. Identify a relation as even or odd M 3. Find the intercepts of a relation M 4. Determine the excluded regions of a relation D 5. Determine any vertical, horizontal, or slant asymptotes of a relation D 6. Determine the approximate shape of the graph of a relation near the origin D 7. Sketch the curve of a relation D 8. Graph a relation by considering equations of translation and equations of rotation A 9. Graph a relation by considering a dilation and/or a reflection A 10. Determine the continuity of a function D 11. Identify a discontinuity at a point, as a jump or as an infinite discontinuity D. Induction D 1. Prove statements by using mathematical induction E. Parametric Equations D 1. Formulate parametric equations D 2. Solve by eliminating the parameter D 3. Graph parametric equations F. Polar Coordinates M 1. Transform from rectangular coordinates to polar coordinates and polar coordinates to rectangular coordinates D 2. Graph polar equations G. Polynomial Functions M 1. Identify a polynomial function D 2. Understand the characteristics of the graph of a polynomial function D 3. Sketch the graphs of a polynomial function A 4. Use synthetic substitution to find zeros and other characteristics of polynomial functions 2

3 H. Rational Functions D 1. Understand the unique properties of a rational function D 2. Sketch the graph of a relational function and asymptotes I. Vectors in a Plane M 1. Understand the vector concept M 2. Perform basic operations (i.e., addition, subtraction, and scalar multiplication) M 3. Determine the resultant of two or more vectors D 4. Find the dot product of two vectors D 5. Understand the properties of dot product J. Vectors in Space M 1. Understand a three dimensional coordinate system D 2. Perform and apply cross product of vectors A 3. Find equations of lines and planes in three dimensional vector space K. Limits M 1. Use the theorems on limits to find the limits of the constant function, the sum, the product, or quotient of functions M 2. Determine the limit of a sequence and series D 3. Use the properties of the limit of a function to establish the non-existence of a limit and the limit of certain functions involving infinity A 4. Understand the epsilon-delta definition of the limit of a function A 5. Use L'Hospital's rule to find limits of functions in quotient indeterminant form L. The Derivative M 1. State and apply the definition of the derivative M 2. Find the derivatives of elementary functions, composite functions, sums, products, and quotients using the power rule, the product rule, the quotient rule, and the chain rule D 3. Find derivatives of higher order D 4. Find derivatives of implicitly defined functions A 5. Find derivatives of inverse functions (including inverse trigonometric functions) M. Applications of the Derivative M 1. Find the slope of the tangent line to a curve, the equation of the tangent lines and normal lines to a curve D 2. Sketch graphs of functions using the first and second derivative tests. Find relative and absolute maximum and minimum points, concavity, increasing and decreasing intervals, and points of inflection A 3. Solve applied problems involving maxima and minima A 4. Solve applied problems involving velocity and acceleration of a particle moving along a line N. Antiderivatives 3

4 M 1. Find the antiderivative of simple functions D 2. Solve applied problems to find distance traveled and the velocity of an object given the acceleration of the object and some initial conditions O. The Definite Integral M 1. Approximate definite integrals using rectangles M 2. Understand the concept of a definite integral as an area D 3. Approximate definite integrals using upper and lower sums, the trapezoidal rule, and Simpson's rule D 4. Use the definition of the definite integral as the limit of a sum A 5. Understand the properties of the definite integral A 6. Evaluate definite integrals using the Fundamental Theorem of Calculus II. COURSE OUTLINE A. Conics B. Functions C. Graphing Techniques D. Induction E. Parametric Equations F. Polar Coordinates G. Polynomial Functions H. Rational Functions I. Vectors in a Plane J. Vectors in Space III. INSTRUCTIONAL METHODS A. Class lecture and demonstration B. Question - answer C. Small group activities D. Individualized instruction IV. EVALUATION/GRADING OF STUDENT WORK A. Objective tests B. Quizzes C. Homework assignments D. Classwork and participation E. Comprehensive final V. INSTRUCTIONAL MATERIALS A. Basic Texts See Board Approved List 4

5 B. Supplemental Materials See Board Approved List 5