Pre Calculus Course Number: 229 Grade Level: 10-12 Length of Course: 1 Semester Total Clock Hours: 120 Hrs. Length of Period: 80 Mins. Date Written: 10-17-06 Periods per Week/Cycle: 5 Written By: Dennis Brown Credits (if app.): 1.0 Weighting: 1.10 Prerequisite: Geometry and one of the following: Honors Algebra II, Algebra III/Trigonometry or teacher recommendation Honors and Advanced Criteria: Recommended minimum final average of 92% in Algebra II or recommended minimum final average of 83% in Honors Algebra II or recommended minimum final average of 92% in Algebra III/Trigonometry Course Description: This honors-level, weighted course is a rigorous study of advanced algebraic techniques with an emphasis on trigonometry. Topics will include vectors, polynomial functions, and trigonometric properties, complex numbers, parametric equations, conics, sequences, series, matrices, exponential and logarithmic functions, and analytic geometry. A graphing calculator will be required for this course. (A TI-83 or TI-84 is the recommended calculator.) page 1
Overall Course/Grade Level Standards Students will KNOW and be able TO DO the following as a result of taking this course. A. Solve equations or inequalities to determine specific answers. B. Given specific criteria, create an equation based upon given clues and prompts. C. Graph functions with or without the use of a graphing calculator. D. Analyze and interpret behavior of functions at specific locations. E. Apply problem solving techniques to solve applications. F. Contrast between different interpretations of concepts. (i.e. degree vs. radian, polar vs. rectangular) Visualize vector diagrams and concepts to solve problems. Interpret finite and infinite sequences and series. K. page 2
I Content Major Areas of Study List all units of study below: Unit Estimated Materials Time 1. Manipulation of Equations and Functions 2 weeks Textbook, Supplemental 2. Polynomial Equations & Rational Functions 2 weeks Textbook, Supplemental 3. Zeroes of a Function 1.5 weeks Textbook, Supplemental 4. Circular Functions and Their Applications 2 weeks Textbook, Supplemental 5. Graphs of Trigonometric Functions and Principal Values 2 weeks Textbook, Supplemental 6. Trigonometric Identities and Equations 1.5 weeks Textbook, Supplemental 7. Vectors and Parametric Equations 1 week Textbook, Supplemental 8. Conics 1.5 weeks Textbook, Supplemental 9. Exponential and Logarthmic Functions 1 week Textbook, Supplemental 10. Sequences 1 week Textbook, Supplemental 11. Polar Coordinates and Equations 1 week Textbook, Supplemental
page 3 Essential Questions A. What are the algebraic characteristics of a function? B. What are the characteristics of a function when it is graphed on a coordinate plane? C. What is the behavior of polynomial and rational functions when graphed on the coordinate plane? D. What are some practical uses of trigonometric functions when solving triangles? E. What are the characteristics of a trigonometric function when graphed on the coordinate plane? F. How are solving trigonometric identities different from solving trigonometric equations? Under what circumstances do you use parametric equations? What are the characteristics of both the equations and the graphs of conic? How are logarithmic functions different from exponential functions? What are the practical uses of arithmetic and geometric sequences? K. What are the characteristics of equations graphed in polar coordinates?
Name of Course: Pre Calculus Name of Unit: Manipulation of Equations and Functions Essential Question for the Unit: What are the algebraic characteristics of a function? Priority Aligned to Course Standard Aligned to PA Standard A. Is a particular relation a function? E F 2.8 B. Can you manipulate the function by using add, I B 2.5, 2.8 subtract, multiply, divide, or composition procedures? C. What is the domain and range of a specific E D 2.5, 2.11 function? D. What is the inverse of a specific function? E A 2.8 E. What is the slope, midpoint, distance and or equation in a selected linear function? F. Using the method of your choice what is the point of intersection of two lines? I D 2.8 E D 2.5, 2.8 G, page 4a
Name of Course: Pre Calculus Name of Unit: Polynomial Equations and Rational Functions Essential Question for the Unit: What are the algebraic characteristics of a function when it is graphed on the coordinate plane? Priority Aligned to Course Standard Aligned to PA Standard A. Is a particular relation a function? E F 2.8 B. How do you manipulate the function by using add, I B 2.5, 2.8 subtract, multiply, divide or composition procedures? C. What is the domain and range of a specific E D 2.5, 2.11 function? D. What is the inverse of a specific function? E A 2.8 E. What is the slope, midpoint, distance and or equation in a selected linear function? F. Using the method of your choice what is the point of intersection of two lines? I D 2.8 E D 2.5, 2.8 _
ority andard Name of Course: Pre Calculus Name of Unit: Zeroes of a Function Essential Question for the Unit: What is the behavior of polynomial and rational functions when graphed on the coordinate plane? A. How do you determine the number of roots of a polynomial equation? B. What is the procedure for completing the square in solving a quadratic equation? C. What is the procedure for finding specific roots of a polynomial equation? D. How do you solve rational equations and inequalities? E. How do you solve radical equations and inequalities? E E 2.8 E E 2.8 E C, D, E 2.8, 2.9 I E 2.8 I E 2.8 F
ority andard Name of Course: Pre Calculus Name of Unit: Circular Functions and Their Applications Essential Question for the Unit: What are some of the practical uses of trigonometric functions when solving triangles? A. Can you convert between radian and degree measures? B. Applying established formulas, what are the values for arc measure, arc length, and velocity? C. Using circular functions and their definitions, what are the values of sides or angles in right triangles? D. Can you solve a triangle by using Law of Cosines or Law of Sines? E. What is the area of a specific triangle, employing trigonometic principles? F. E F 2.3, 2.8 I A, F 2.8, 2.5 E B. F 2.5, 2.10 E B 2.5, 2.9, 2.10 E A, B, E, F 2.8, 2.9, 2.10
ority andard Name of Course: Pre Calculus Name of Unit: Graphs of Trigonometric Functions and Principal Values Essential Question for the Unit: What are the characteristics of a trigonometric function when graphed on the coordinate plane? A. Without the use of a graphing calculator, can you display a graph of a trig function that may include amplitude adjustments, period or phase shift changes? B. Can you determine specific values for any of the six inverse trig functions? E C 2.5, 2.8, 2.10, 2.11 E D 2.5, 2.10 C. Can you graph any of the six inverse trig functions? I C 2.8, 2.10 D. What is the equation of a graph of a specific problem involving harmonic motion? E. C B, E 2.8, 2.10, 2.11 F
ority andard Name of Course: Pre Calculus Name of Unit: Trigonometric Identities and Equations Essential Question for the Unit: How are solving trigonometric identities different from solving trigonometric equations? A. How do you integrate trigonometric rules with algebraic procedures to prove trigonometric identities? B. Using previously used trigonometric identities, what is the solution set to a trigonometric equation? E B, E 2.5, 2.8, 2.10 E A 2.5, 2.8, 2.10 C. D. E. F
ority andard Name of Course: Pre Calculus Name of Unit: Vectors and Parametric Equations Essential Question for the Unit: Under what circumstances do you use parametric equations? A. How do you represent a vector in ordered pair form E E 2.5, 2.9 or on the coordinate plane? B. How do you manipulate vectors by using addition, E E, G 2.5, 2.8, 2.9 subtraction, multiplication, or inner product of vectors? C. How do you solve a specific parametric equation? I B, E 2.5, 2.8 D. How do you represent vectors in 3-dimension? C E, G 2.5, 2.9 E. F
ority andard Name of Course: Pre Calculus Name of Unit: Conics Essential Question for the Unit: What are the characteristics of both the equations and graphs of conics? A. How do you graph a specific conic and identify any of the key points? B. Given specific clues about a conic, can you create an equation of the conic? C. What is the intersection point of two conics graphed simultaneously? D. E C,D 2.5, 2.8 E B 2.5, 2.8 C D 2.5, 2.8 E. F
ority andard Name of Course: Pre Calculus Name of Unit: Exponential and Logarthmic Functions Essential Question for the Unit: How are logarithmic functions different from exponential functions? A. How do you apply properties of exponents and logarithms to generate solutions? B. By applying properties of exponents and logarithms, can you solve equations? C. How do you graph exponential and logarithmic functions with or without a graphing calculator? D. E A 2.2, 2.5 E A 2.5, 2.8 E C 2.8, 2.10 E. F
ority andard Name of Course: Pre Calculus Name of Unit: Sequences Essential Question for the Unit: What are the practical uses of arithmetic and geometric sequences? A. How do you identify a sequence as arithmetic or E F, H 2.11 geometric? B. What is the nth term of a specific sequence? E A, E, H 2.8, 2.11 C. What is the sum of a specific sequence? E A, E, H 2.8, 2.11 D. How do you utilize sigma notation to signify a particular sequence? E. How do you use the binomial theory to generate a specific term of that sequence? F E B, H 2.5, 2.11 I A, H 2.5, 2.11
ority andard Name of Course: Pre Calculus Name of Unit: Polar Coordinates and Complex Numbers Essential Question for the Unit: What are the characteristics of equations graphed in polar coordinates? A. How do you plot points and graph equations in polar coordinates? B. How do you perform basic operations on complex numbers in both rectangular and polar form? C. C C, F 2.8, 2.10 C A, F 2.5, 2.8 D. E. F
II Course Assessments Check types of assessments to be used in the teaching of the course. (Provide examples of each type.) X_Objective Tests/Quizzes X_Constructed Responses Essays Reports Projects Portfolios Presentations _X Performance tasks Response Journals Logs Computer Simulations Research Papers X_Class Participation Notetaking X_Daily Assignments Writing Samples Provide copies of common assessments that will be utilized for all students taking this course. Overall course/grade level standards will be measured by a common course assessment. Unit objectives will be measured on an ongoing basis as needed by the classroom teacher to assess learning and plan for instruction. List common assessements below and recommended date/time frame for administration (at least quarterly). Name of Common Assessment When given? 1. Pre Test Beginning of Sequences 2. Post Test End of Semester 3. Final Exam End of Semester 4. 5. 6.
IV. Expected levels of achievement Current grading scale: 92 100% = 4 83 91% = 3 74 82% = 2 65 73% = 1 0 64% = 0 PA Proficiency Levels Advanced Proficient Basic Below Basic Attach rubrics, checklists, or other documentation noting how levels of proficiency will be determined for common assessments. The following scoring documents have been developed for this course:
page 6