EASTERN ARIZONA COLLEGE Precalculus

Transcription

1 EASTERN ARIZONA COLLEGE Precalculus Course Design Course Information Division Mathematics Course Number MAT 187 Title Precalculus Credits 5 Developed by Adam Stinchcombe Lecture/Lab Ratio 5 Lecture/0 Lab Transfer Status ASU NAU UA MAT 170 (3) & Elective Credit (2), Mathematics (MA) MAT Departmental Elective --and-- MAT 125 also satisfies: Foundation Requirement [FNRQ] MATH 120R --and-- MATH Departmental Elective Activity Course No CIP Code Assessment Mode Pre/Post Test (20 Questions/100 Points) Semester Taught Fall and Spring GE Category Mathematics Separate Lab No Awareness Course No Intensive Writing Course No Prerequisites MAT 120 with a grade of "B" or higher or placement test score as established by District policy and ENG 091 with a grade of C or higher or reading placement test score as established by District policy Educational Value This course is designed to prepare students to be successful in Calculus. Description Topics from college algebra and trigonometry essential to the study of calculus. Includes linear, quadratic, polynomial, rational, exponential, trigonometric functions, conic sections, and analytic trigonometry. Additional topics may include partial fraction decomposition, nonlinear systems of equations, matrices, DeMoivre s Theorem, and polar coordinates. May receive credit for only one of the following: MAT 154 or MAT 187. EASTERN ARIZONA COLLEGE Precalculus

2 Supplies Scientific calculator; TI-83 or TI-84 recommended Competencies and 1. Understand functions and graphs. a. Distinguish between functions and relations, and use function notation. b. Determine the domain and range of functions. c. Graph basic functions including square, square root, cube, cube root, absolute value, and piecewise defined functions. d. Identify properties of functions including increasing, decreasing, constant, maximum, minimum, etc. e. Perform transformations of functions. f. Combine functions using arithmetic operations and composition of functions. g. Find the inverse of a one-to-one function. h. Solve basic nonlinear systems. o You can demonstrate the ability to distinguish between functions and relations, and use function notation o You can demonstrate the ability to determine the domain and range of functions o You can demonstrate the ability to solve and graph quadratic equations o You can demonstrate the ability to graph basic functions including square, square root, cube, cube root, absolute value, and piecewise defined functions o You can demonstrate the ability to identify properties of functions including increasing, decreasing, constant, maximum, minimum, etc. o You can demonstrate the ability to perform transformations of functions o You can demonstrate the ability to combine functions using arithmetic operations and composition of functions o You can demonstrate the ability to find the inverse of a one-to-one function o You can demonstrate the ability to solve basic nonlinear systems 2. Analyze polynomial and rational functions. a. Solve and graph quadratic equations including vertex, axis of symmetry, and intercepts. b. Solve and graph quadratic inequalities. EASTERN ARIZONA COLLEGE Precalculus

3 c. Define complex numbers and perform arithmetic operations with complex numbers. d. Use synthetic division to help factor polynomials. e. Use the rational zeros theorem to help find all the zeros of a polynomial function. f. Graph polynomial functions including the end behavior and behavior at zeros. g. Find the domain of a rational function. h. Graph rational functions including vertical asymptotes, horizontal asymptotes, skew asymptotes and x and y intercepts. o You can demonstrate the ability to solve and graph quadratic equations including vertex, axis of symmetry, and intercepts o You can demonstrate the ability to solve and graph quadratic inequalities o You can demonstrate the ability to define complex numbers and perform arithmetic operations with complex numbers o You can demonstrate the ability to use the synthetic division to help factor polynomials o You can demonstrate the ability to use the rational zeros theorem to help find all the zeros of a polynomial function o You can demonstrate the ability to graph polynomial functions including the end behavior and behavior at zeros o You can demonstrate the ability to find the domain of a rational function o You can demonstrate the ability to Graph rational functions including vertical asymptotes, horizontal asymptotes, skew asymptotes and x and y intercepts 3. Know exponential and logarithmic functions and their graphs. a. Find the domain and range of exponential function. b. Graph exponential functions with different bases. c. Use the exponential function base e. d. Find the domain and range of the logarithm function. e. Graph logarithm functions with different bases. f. Use the properties of exponents and the properties of logarithms. g. Solve exponential and logarithmic equations. EASTERN ARIZONA COLLEGE Precalculus

4 o You can demonstrate the ability to find the domain and range of exponential function o You can demonstrate the ability to graph exponential functions with different bases o You can demonstrate the ability to use the exponential function base e o You can demonstrate the ability to find the domain and range of the logarithm function o You can demonstrate the ability to graph logarithm functions with different bases o You can demonstrate the ability to use the properties of exponents and the properties of logarithms o You can demonstrate the ability to solve exponential and logarithmic equations 4. Describe trigonometric functions and their graphs. a. Know the parts of an angle and how to measure an angle in degrees and radians. b. Define the trigonometric functions in terms of the unit circle. c. Determine the exact values of the trigonometric functions for 0, 30, 45, 60, 90 angles. d. Graph sine and cosine including period, amplitude, phase shift, and vertical translation. e. Graph other trigonometric functions as ratios of sine and cosine. f. Find domain and range for inverse sine, inverse cosine, and inverse tangent functions. g. Solve right triangles and right triangle applications. o You can demonstrate you know the parts of an angle and how to measure an angle in degrees and radians o You can demonstrate the ability to define the trigonometric functions in terms of the unit circle o You can demonstrate the ability to determine the exact values of the trigonometric functions for 0, 30, 45, 60, 90 angles o You can demonstrate the ability to graph sine and cosine including period, amplitude, phase shift, and vertical translation o You can demonstrate the ability to graph other trigonometric functions as ratios of sine and cosine o You can demonstrate the ability to find domain and range for inverse sine, inverse cosine and inverse tangent functions o You can demonstrate the ability to solve right triangles and right triangle applications EASTERN ARIZONA COLLEGE Precalculus

5 5. Prove trigonometric identities. a. Verify trigonometric identities. b. Identify and apply the sum and difference identities. c. Identify and apply the double angle and half angle identities. d. Identify and apply the product-to-sum and sum-to-product identities. e. Solve trigonometric equations. o You can demonstrate the ability to verify trigonometric identities o You can demonstrate the ability to apply sum and difference identities o You can demonstrate the ability to apply double and half angle identities o You can demonstrate the ability to apply product-to-sum and sum-to-product identities o You can demonstrate the ability to solve trigonometric equations 6. Apply trigonometry. a. Know when to use and how to apply the Law of Sines. b. Know when to use and how to apply the Law of Cosines. c. Graph in polar coordinates. d. Convert between polar and rectangular coordinates. e. Write complex numbers in polar form. f. Apply DeMoivre s theorem. o You can demonstrate the ability to use the Law of Sines o You can demonstrate the ability to use the Law of Cosines o You can demonstrate the ability to graph in polar coordinates o You can demonstrate the ability to convert between polar and rectangular coordinates o You can demonstrate the ability to write complex numbers in polar form o You can demonstrate the ability to use DeMoivre s theorem EASTERN ARIZONA COLLEGE Precalculus

6 7. Graph conic sections. a. Graph and find the parts of vertical and horizontal parabolas including vertex, directrix, axis of symmetry, and focus. b. Graph and find the parts of vertical and horizontal ellipses including center, vertices, axis, and foci. c. Graph and find the parts of vertical and horizontal hyperbolas including center, vertices, axis, asymptotes and foci. o You can graph parabolas, including the vertex, directrix, axis of symmetry, and focus o You can graph ellipses, including the center, the vertices, the axis and the foci o You can graph hyperbolas, including the center, the vertices, the axis of symmetry, the asymptotes, and the foci 8. Use algebra to solve linear and nonlinear problems. a. Perform partial fraction decomposition. b. Use of matrices. c. Use of parametric equations. o You can perform partial fraction decomposition o You can solve systems using matrices o You can perform operations with vectors o You can graph parametric equations EASTERN ARIZONA COLLEGE Precalculus

7 Types of Instruction Classroom Presentation Grading Information Grading Rationale Each instructor has the flexibility to develop evaluative procedures within the following parameters. 1. Written exams must represent at least 60% of the final course grade. 2. Final exam must represent at least 20% of the final course grade. 3. The Post Test is to be embedded in the final exam and must represent at least 10% of the final course grade. 4. Other activities may represent at most 20% of the final course grade. Grading Scale A 90%-100% B 80%-89% C 70%-79% D 60%-69% F Below 60% EASTERN ARIZONA COLLEGE Precalculus