ACADEMIC KNOWLEDGE AND SKILLS FOR PRECALCULUS. (If submission is not a book, cite appropriate location(s)) A Trigonometry

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1 A Trigonometry Apply circle and angle relationships SE/TE: , 240-Area of Sector, , 325, 328-The SAS Area Formula, 331-Problem 2, 792. TR: Lesson Master and Answer Master 4-1, Teaching Aids 32, 35. TECH: 235-above Example 3. Apply special right triangle relationships SE/TE: , , 356. TR: Lesson Masters and Answer Masters 4-4, 5-1, 5-2, 5-3, 5-4, Teaching Aids 33, 39, 46, 48, 49, Assessment Sourcebook: Quiz for Lessons 5-1 through 5-3. TECH: 312-middle of page, 313-Example 3, 321-top of page, 330-Examples 1-2, Explorations 4-4, 5-3,

2 Develop, graph and apply the six trigonometric functions SE/TE: , , , , , , TR: Lesson Masters and Answer Masters 4-3, 4-6, 4-7, 4-8, 4-9, 4-10, 5-1, 5-3, 5-5, 5-6, 13-1, Teaching Aids 32, 33, 34, 37, 38, 41, 42, 43, 44, 46, 47, 48, 50, 51, 112, 115, 116, Assessment Sourcebook: Quiz for Lessons 4-1 through 4-3, Quiz for Lessons 4-4 through 4-7, Quiz for Lessons 5-1 through 5-3, Quiz for Lessons 5-4 through 5-6. TECH: 264, 268-Checks 1, 2, 273-Technology, 274-Check, 278-Check, 289- Solution 1, 312-above Example 2, 313-example 3, 321-first paragraph, 324-Activity 3 Technology, 334-middle of page, 336- Example 2, 337-Check, 338-Problem 22, 343-Problems 10-12, 344- problem 29, 806-Example 1, 807-Example 2, 810-Problems 18 & 30, Exploration 4-3, 4-10, 5-3, Technology Sourcebook: Computer Masters 5, 6, Calculator Masters 4, 5. Apply laws of sines and cosines SE/TE: , TR: Lesson Masters and Answer Masters 5-2, 5-4, Teaching Aids 46, 49. TECH: Exploration 5-4. Explore and apply properties of circular functions SE/TE: TR: Lesson Masters and Answer Masters 4-6, 4-7, 4-8, 4-9, 4-10, Teaching Aids 33, 34, 42, 43, 44, Assessment Sourcebook, Quiz for Lessons 4-4 through 4-7. TECH: , 268-Check, 273- Technology, 274-Check, 278-Check, 280-Activity, 283-problem 15a, 289- Solution 1, Explorations 4-7, 4-8, 4-10, Technology Sourcebook, Computer Masters 5, 6. Represent complex numbers in trigonometric form SE/TE: TR: Lesson Masters 13-7, 13-8, Teaching Aids 114, 124,

3 Solve trigonometric equations and verify trigonometric identities SE/TE: , , TR: Lesson Masters and Answer Masters 4-4, 5-7, 13-2, Teaching Aids 33, 39, 47, 112, 117. TECH: 345, 348-Check 2, 350-Check 2, 815-problems 10-13, Explorations 4-4, Technology Sourcebook : Calculator Master 10. Graph and model circular functions SE/TE: TR: Lesson Master and Answer Master 4-6, Teaching Aids 33, 34, 41, 42, 43. TECH: 268-Check 2, Technology Sourcebook: Computer Masters 5, 6. Apply transformations to graphs of circular functions SE/TE: TR: Lesson Masters and Answer Masters 4-7, 4-8, 4-9, Teaching Aids 33, 34, 44, Assessment Sourcebook: Quiz for Lessons 4-4 through 4-7. TECH: 272-Example 1c, 273-Technology, 274-Check, 278-Check, 280- Activity, Explorations 4-7,

4 Graph and evaluate trigonometric inverses SE/TE: , TR: Lesson Masters and Answer Masters 5-3, 5-5, 5-6, Teaching Aids 46, 47, 48, 50, 51, Assessment Sourcebook: Quiz for Lessons 5-4 through 5-6. TECH: 321-first paragraph, 334-second paragraph, 336-Check, 337-Check, 338-Problems 12-14, Exploration 5-3, Technology Sourcebook: Calculator Masters 4, 5. Represent coordinates in trigonometric and polar form SE/TE: TR: Lesson Master and Answer Master 13-5, Teaching Aids 113, 120, 121, 122. TECH: 829-Rose Curves, 832-problem 21, Exploration B Statistics Fit and model linear and nonlinear curves to data SE/TE: 42-Projected U.S. Population, , , , , , , , TR: Lesson Masters and Answer Masters 2-2, 2-3, 2-5, 2-6, 2-8, 2-9, 3-3, 3-6, 4-10, 6-7, Teaching Aids 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 26, 27, 34, 56, Assessment Sourcebook: Quiz for Lessons 2-1 through 2-3, Quiz for Lessons 3-4 through 3-6. TECH: Explorations 2-2, 2-5, 2-6, 3-3, Technology Sourcebook: Computer Masters 2, 3, 7, Calculator Master 2. 4

5 C Functions and Relations Translate among tabular, symbolic and graphical representation of functions Develop algorithms and analyze functions using the Fundamental Theorem of Algebra SE/TE: , , , , , , TR: Lesson Masters and Answer Masters 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7, 2-8, 2-9, 3-2, 3-7, 3-8, 6-1, 6-2, 9-2, 9-5, 9-7, 12-2, 12-3, 12-4, Teaching Aids 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 53, 57, 79, 80, 81, 82, 84, 103, 104, 107, 108, 109, Assessment Sourcebook: Quiz for Lessons 2-1 through 2-3, Quiz for Lessons 2-4 through 2-6, Quiz for Lessons 9-4 through 9-7, Quiz for Lessons 12-1 through TECH: 122-Check, 373-Example 2, 377-Solution 3, 130-Activity 1, 131- Activity 2, 377-Activity 1, 379, 565-Activity 1, 761-Explorations 2-2, 2-5, 2-6, 12-2, 12-3, 12-4, Technology Sourcebook: Computer Masters 2, 13, Calculator Masters 1, 2, 3, 8. SE/TE: TR: Lesson Master and Answer Master 9-7, Teaching Aids 81, 84, Assessment Sourcebook: Quiz for Lessons 9-4 through 9-7. Find and graph compositions of functions SE/TE: TR: Lesson Master and Answer Master 3-7, Teaching Aid 27. TECH: Exploration 3-7, Technology Sourcebook: Computer Master 4. 5

6 Find and graph inverses of functions SE/TE: , , , 379-Example 3, 386-top of page. TR: Lesson Masters and Answer Masters 3-8, 5-3, 5-5, 5-6, Teaching Aids 28, 46, 47, 48, 50, 51, Assessment Sourcebook: Quiz for Lessons 5-4 through 5-6. TECH: 321, 323-Check, Exploration 5-3, 334, 336-Check, 337-problem 4, 338-problems & 22, Technology Sourcebook: Calculator Masters 4, 5. Graph and model exponential and logarithmic functions SE/TE: , TR: Lesson Masters and Answer Masters 6-3, 6-4, 6-6, Teaching Aids 54, 58, 59, Assessment Sourcebook: Quiz for Lessons 6-1 through 6-3, Quiz for Lessons 6-4 through 6-6. TECH: Explorations 6-3, 6-4, 6-6. Graph and model piecewise functions Identify domain and range for algebraic and transcendental functions SE/TE: 82-87, 204-example 4, TR: Lesson Masters and Answer Masters 2-1, 4-6, 4-7, 4-8,4-9, Teaching Aids 14, 17, 33, 34, 41, 42, 43, 44, Assessment Sourcebook: Quiz for Lessons 4-4 through 4-7. TECH: , 268-Check 1, 273-Technology, 274-Check, 278-Check, 289-Solution 1, Explorations 4-7, 4-8, Technology Sourcebook: Computer Masters 5, 6. Graph and analyze both linear and nonlinear systems SE/TE: 702-problem 26, 735-top of page, 736-problems 15 &

7 Perform operations with complex numbers SE/TE: , 599-Conjugate Zeroes Theorem, TR: Lesson Masters and Answer Masters 9-6, 13-6, 13-7, 13-8, Teaching Aids 80, 83, 113, 114, 123, 124, 125. TECH: Exploration D Discrete Mathematics Develop and investigate axiomatic systems Use mathematical induction E Underpinnings of Calculus Analyze curves with respect to intervals of increase/decrease, end behavior and horizontal, vertical and oblique asymptotes SE/TE: , , , TR: Lesson Masters and Answer Masters 2-6, 2-7, 8-2, 8-5, 9-2, Teaching Aids 15, 16, 21, 22, 71, 72, 74, 75, 79, 82, Assessment Sourcebook: Quiz for Lessons 2-4 through 2-6. TECH: 497-Technology, 519-top of page, 568-problem 16, Explorations 8-2, 8-5, Technology Sourcebook: Calculator Master 8. 7

8 F Geometry from an Algebraic Perspective Identify and compare conic sections and sketch their graphs SE/TE: , , 766-Problem 14, 766-problems 17-19, , , 786-after Activity 2. TR: Lesson Masters and Answer Masters 2-6, 12-1, 12-2, 12-3, 12-4, 12-5, 12-6, Teaching Aids 15, 21, 22, 103, 104, 105, 106, 107, 109, 110, 111, Assessment Sourcebook: Quiz for Lessons 2-4 through 2-6. TECH: 122-Check, 764-Using Technology, 766-Problem 16, Explorations 12-1, 12-2, Perform vector operations algebraically and geometrically Graph and perform two- and three-dimensional vector computations G Patterns and Functions 8

9 Apply sums, products and determinants of matrices SE/TE: , 720-Problem 26, 735-top of page, 736-Problem 15 & TR: Lesson Master and Answer Master 11-1, Teaching Aid 95. Apply special right triangle relationships SE/TE: , , 356. TR: Lesson Masters and Answer Masters 4-4, 5-1, 5-2, 5-3, 5-4, Teaching Aids 33, 39, 46, 48, 49, Assessment Sourcebook: Quiz for Lessons 5-1 through 5-3. TECH: 312-middle of page, 313-Example 3, 321-top of page, 330-Examples 1-2, Explorations 4-4, 5-3, 5-4. Explore sine, cosine and tangent functions in right triangles SE/TE: TR: Lesson Master and Answer Master 5-1, Teaching Aid 46. TECH: 313-middle of page. 9

Syllabus ENGR 190 Introductory Calculus (QR)

Syllabus ENGR 190 Introductory Calculus (QR) Catalog Data: ENGR 190 Introductory Calculus (4 credit hours). Note: This course may not be used for credit toward the J.B. Speed School of Engineering B. S.