Elizabethtown Area School District Algebra III/Trigonometry Name of Course

Transcription

1 Algebra III/Trigonometry Name of Course Course Number: 247 Grade Level: Length of Course: 1 Semester Total Clock Hours: 120 hours Length of Period: 80 minutes Date Written: 8/3 8/4/05 Periods per Week/Cycle: 5 Weighting: 1.0 Written By: John Haldeman Karen Muckenthaler Credits (if app.): 1 Prerequisite: Algebra II and Geometry Course Description: This course is designed for students who plan to attend a post-secondary institution, but not necessarily in pursuit of a career in mathematics or science. Algebra and geometry concepts will be reinforced and utilized in a more practical setting. A variety of problem-solving techniques and assessment strategies will be emphasized to better prepare students for college board exams as well as other standardized tests. AlgebraIII/Trigonometry encompasses a multitude of mathematical concepts that will include advanced algebra, trigonometry, and math analysis, which will be useful in future college courses. A scientific calculator or graphing calculator will be required for this course. (A TI-83 or TI-84 is the recommended calculator.) page 1

2 I. Overall Course/Grade Level s Students will KNOW and be able TO DO the following as a result of taking this course. A. Use the properties of real numbers, powers, and roots. B. Set up, solve, and graph algebraic equations/inequalities in a variety of settings. C. Factor polynomials and recognize the special cases of factoring. D. Simplify rational expressions and solve rational equations. E. Analyze polynomial functions algebraically and graphically. F. Execute calculations involving trigonometry and various geometric shapes, specifically the triangle. G. Graph and name the characteristics of the sine and cosine functions. H. Perform calculations involving arithmetic/geometric sequences and series. I. Describe formulas and notations associated with arithmetic/geometric sequences and series. J. Know the characteristics of exponential and logarithmic functions. K. Execute calculations and graph equations involving exponential and logarithmic functions. L. Identify various formulas and identities associated with trigonometry. M. Know how to calculate permutations and combinations. N. Know how to calculate the probability of simple and compound events. O. Use a variety of strategies to solve SAT questions. page 2

3 II. Content Major Areas of Study List all units of study below: Unit Estimated Time 1. Basic Concepts of Algebra 2 Weeks Textbook and 2. Sequences/Series/Combinatorics 2 Weeks Textbook and 3. SAT prep. 3 Weeks Textbook and 4. Trigonometric Functions 3-4 Weeks Textbook and 5. Applications of Trigonometry 3 Weeks Textbook and 6. Trigonometric Identities and Equations 2 Weeks Textbook and 7. Properites of Polynomial Functions 2 Weeks Textbook and

4 Name of Course: Advanced Math Name of Unit: Basic Concepts of Algebra Essential Question for the Unit: What are the properties of the real number system and how are they used to simplify expressions and solve algebraic equations? Priority Aligned to Course Aligned to PA A. What are the properties of real numbers? C A 2.1 B. How do we simplify expressions with integer I A 2.8 exponents? C. What is the Order of Operations and how is it used C A 2.2 to simplify expressions? D. How do we add, subtract, and multiply E A 2.8 polynomials? E. How do we identify and factor out the greatest E C 2.8 common factor? F. What are the special products of polynomials and E C 2.8 how are they factored? G. How do we determine the domain of a rational I D 2.8 expression? H. How do we simplify, add, subtract, and multiply E D 2.8 rational expressions? I. How do we simplify complex rational expressions? E D 2.8 J. How do we simplify radical expressions? E A 2.8 K. How do we convert between exponential and radical notation? L. How do we simplify expressions with rational exponents? I A 2.8 I A 2.8

5 Name of Course: Advanced Math Name of Unit: Sequences, Series, and Combinations Essential Question for the Unit: What are the differences between an arithmetic sequence and a geometric sequence? A. How do we find the nth term of an arithmetic or geometric series? B. How do we find the sum of an arithmetic or geometric series? C. How do we express a series of terms in sigma notation? D. How do we know if the sum of an infinite geometric series exists and if so, how do we find the sum? E. How do we evaluate permutation and combination notation? F. How do we expand a power of a binomial using Pascal s Triangle? How do we expand a power using factorial notation? G. How do we find a specific term of a binomial expansion? H. How do we compute the probability of a simple event? Priority Aligned to Course Aligned to PA E H, I 2.7 E H, I 2.7 E I 2.7 E H 2.7 I M 2.7 I M 2.8 I M 2.8 C N 2.7 I. J.

6 Name of Course: Advanced Math Name of Unit: SAT Preparation Essential Question for the Unit: What are key strategies used to solve SAT problems? A. What is the plugging-in strategy and how is it used to solve SAT questions? B. What is the backsolving strategy and how is it used to solve SAT questions? C. What are the strategies used to solve Roman Numeral answer SAT questions? D. What are the key geometry concepts we know in order to allow us to successfully answer SAT geometry questions? E. How do we correctly fill-in a fraction grid-in answer? How do we correctly fill-in a decimal grid-in answer? F. What are the strategies used to solve SAT questions involving arithmetic? G. What are the strategies used to solve SAT questions involving algebra topics? Priority Aligned to Course Aligned to PA E O 2.4, 2.5 E O 2.4, 2.5 C O 2.4, 2.5 E O 2.4, 2.5 E O 2.4, 2.5 I O 2.4, 2.5 I O 2.4, 2.5 H. I. J.

7 Name of Course: Advanced Math Name of Unit: Trigonometric Functions Essential Question for the Unit: What are the relationships between solving right triangles and trigonometric functions? A. What are the six trigonometric ratios for a given acute angle of a right triangle? Priority Aligned to Course Aligned to PA I F, L 2.10 B. How do we solve right triangles? E F, L 2.10 C. How do we solve applied problems involving right triangles and trigonometric functions? D. How do we find angles that are coterminal, supplementary, and complementary to a given angle? E. How do we determine the six trigonometric function values for any angle in standard position? F. How do we find the function value for any angle whose terminal side lies on an axis or makes an angle of 30, 45, or 60 degrees with the x-axis? G. How do we convert from radian to degree measure? How do we convert from degree to radian measure? H. What are the characteristics of the basic sine function? What are the charactersitics of the basic cosine function? I. How do determine the amplitude, period, and phase shift of the graphs of sine and cosine? E F, L 2.10 C F, L 2.10 I F, L 2.10 E F, L 2.10 I F, L 2.10 E G 2.10 E G 2.10

8 Name of Course: Advanced Math Name of Unit: Applications of Trigonometry Essential Questionfor the Unit: How are trigonometric functions used to solve oblique triangle application problems? A. How do we use the Law of Sines to solve triangles? B. How do we find the area of a triangle using trigonometry? C. How do we use the Law of Cosines to solve triangles? D. How do we determine whether the Law of Sines or Cosines would be used to solve triangle application problems? E. How do we determine whether two vectors are equivalent? F. How do we find the sum, or resultant, of two vectors? G. How do we resolve a vector into its horizontal and vertical components? H. How do we solve applied problems involving vectors? Priority Aligned to Course Aligned to PA E F, L 2.10 C F, L 2.10 E F, L 2.10 E F, L 2.10 I F, L 2.10 I F, L 2.10 I F, L 2.10 E F, L 2.10 I. J.

9 Name of Course: Advanced Math Name of Unit: Trigonometric Identities and Equations Essential Question for the Unit: How are inverse trigonometric functions used to solve trigonometric equations? A. What are the values of inverse trigonometric functions? Priority Aligned to Course Aligned to PA C L 2.10 B. How do we solve trigonometric equations? E L 2.10 C. D. E. F. G, H. I. J.

10 ority andard Elizabethtown Area Name of Course: Advanced Math Name of Unit: Properties of Functions Essential Question for the Unit: What do the zeros of a polynomial function represent? A. How do we perform operations involving the composition and inverse of functions? B. How do we graph linear equations and inequalities in one and two variables? C. How do we determine properties and relationships of linear functions? D. How do we graph non-linear functions and find their zeros? E. How do we determine the minimum and maximum value of a quadratic function? E A, E 2.8 C B 2.8 I E 2.8 I B, E 2.8 E E, J, K 2.8 F. G, H. I. J.

11 III. Course Assessments Check types of assessments to be used in the teaching of the course. (Provide examples of each type.) _X Objective Tests/Quizzes Constructed Responses _ X_ Essays Reports Projects Portfolios _X_ Presentations 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). 1. Pre and Post Test 2. Final Exam Name of Common Assessment When given? Beginning and end of Each Semester End of Semester page 5

12 IV. Expected levels of achievement Current grading scale: A B C D 65-0 F 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