Elizabethtown Area School District Honors Algebra II

Transcription

1 Honors Algebra II Course Number: 222 Grade Level: 9-12 Length of Course: 1 Semester Total Clock Hours: 120 hours Length of Period: 80 minutes Date Written: Periods per Week/Cycle: 5 Credits (if app.): 1 Written By: Kay Baxter and John Haldeman Weighting: 1.10 Prerequisite: Algebra I and/or Honors Geometry Course Description: This weighted course is designed to give students who are interested in pursuing a career in math or science related fields a thorough understanding of advanced algebra concepts needed for their future. This course includes the study of real and complex numbers, techniques of algebra, concepts of functions (linear, quadratic, exponential, and logarithmic) and graphs, with emphasis on equation solving and its applications to the solutions of real-world problems. A graphing calculator wll be required for this course. (A TI-83 or TI-84 is the recommended calculator.) Honors and Advanced Criteria: Recommended minimum final average of 92% in Algebra I or recommended minimum final average of 83% in Honors Geometry. * Indicates Honors Algebra II Curriculum

2 page 1 Elizabethtown Area Overall Course/Grade Level s Students will KNOW and be able TO DO the following as a result of taking this course: A. Use function notation to express an equation in terms of the independent and dependent variables. B. Graph linear, quadratic, exponential, and logarithmic functions. C. Use the properties of powers and roots to simplify expressions and solve equations. D. Perform basic matrix operations. E. Factor polynomials. F. Use basic probability rules to find probabilities of compound events. G. Solve real world problems using a variety of algebraic techniques. Translate words into algebraic expressions and equations. Solve various types of algebraic equations and inequalities. Describe the characteristics/properties of various functions. K. Explain relationships between algebraic equations and their graphs. L. Discuss the complex number system. M. State the properties of a normal distribution. N. Identify the characteristics of relations, functions, inverses, and composites of functions. O. Recognize the relationship between careers and math concepts. P. Use several methods to summarize and organize data. page 2

3 I Content Major Areas of Study List all units of study below: Unit Estimated Time Materials 1. The Language of Algebra 7 8 days 2. Linear Equations and Functions 5-6 days 3. Systems of Linear Equations and Inequalities 5 6 days 4. Matrices and Determinants 5 6 days 5. Quadratic Functions days 6. Polynomials and Polynomial Functions 8 9 days 7. Powers, Roots, and Radicals 9 10 days 8. Exponential and Logarithmic Functions 7 8 days 9. Rational Equations and Functions 7 8 days 10. Probability and Statistics 8 9 days page 3

4 Name of Course: Algebra II Name of Unit: The Language of Algebra Essential Question for the Unit: How do you translate real-world situations to algebraic expressions or equations? A. How do you graph the different subsets of numbers on a number line? E H 2.1, 2.2 B. What is the order of operations? E H 2.1, 2.2 C. How does solving a linear equation differ from simplifying a linear equation? D. How do formulas help us solve real-world problems? E. How do you translate a verbal problem into an algebraic model? F. What is the difference between solving linear inequalities and solving linear equations? G. How do you solve absolute value equations and inequalities? * How do you rewrite common formulas with more than one variable? E G, H, I 2.1 E G, I, O 2.5 E H,O 2.5 E I 2.2, 2.5 E I 2.8 E I 2.8 * Honors Algebra II

5 Name of Course: Algebra II Name of Unit: Linear Equations and Functions Essential Question for the Unit: What is a linear function? A. When is a relation a function? E A, N 2.8 B. How can slope be used to classify lines and in realworld situations? C. How do you graph a line using the slope and y- intercept? D. Given information about a line, how do you write a linear equation? I B, G 2.8 I B, O 2.8 E K 2.8 E. What is a line of best fit? I G, O 2.6, 2.8 F. How do you draw a graph of a linear inequality in two variables? I B 2.8 G,

6 Name of Course: Algebra II Name of Unit: Systems of Linear Equations and Inequalities Essential Question for the Unit: What are the various methods used to solve systems of linear equations and inequalities? A. How do you use a graph to determine how many solutions there are for a system of linear equations? B. How are algebraic methods used to solve linear systems in two variables? C. What is the procedure to graph a system of linear inequalities? D. How are algebraic methods used to solve linear systems in three variables? E B, J 2.8 I I 2.8 E I 2.8 I I 2.8 E. F. G,

7 Name of Course: Algebra II Name of Unit: Matrices and Determinants Essential Question for the Unit: What are matrices and how are they used? A. What are the components of a matrix? E D 2.2, 2.8 B. How do you perform basic matrix operations? E D 2.2, 2.8 C. How do you find the determinant of a 2 x 2 matrix? D How are a square matrix, its identity and the inverse matrix related? C D 2.2, 2.8 C D 2.2, 2.8 E. F. G,

8 Name of Course: Algebra II Name of Unit: Quadratic Functions Essential Question for the Unit: How do quadratic functions differ from linear functions and how are they used? A. Given a specific form of a quadratic equation, how do you graph it? B. What must be true about a quadratic equation before you can solve it using the Zero Product Property? C. How do you simplify the square root of a number that is not a perfect square? D. How do you solve a quadratic equation using properties of square roots? E. What is the difference between a complex number and a real number and how are the basic operations performed? F. How do you solve quadratic equations by completing the square? G. How is the discriminant related to the quadratic formula and the number of solutions to a quadratic equation? * How do you graph quadratic inequalities in two variables? E A, B, J, K 2.8 E I 2.4, 2.8 I C 2.8 E I 2.8 E I, L 2.8 C I 2.8 E I 2.4, 2.8 I B 2.8 * Honors Algebra II

9 Name of Course: Algebra II Name of Unit: Polynomials and Polynomial Functions Essential Question for the Unit: What is a polynomial function and how is it used? A. What are the properties of exponents and how are they used to simplify expressions? B. How is synthetic substitution used to evaluate polynomials? C. How are the basic operations performed with polynomials? E C 2.2 I C 2.2 E C 2.2 D. How do you factor polynomials? E E 2.8 E. How can synthetic division be used to perform polynomial division? E C 2.8 F. How do you find the zeroes of a function? E E, G, I, O 2.8 G. * How do you find the rational zeroes of a polynomial function? I E, G, I 2.2 * Honors Algebra II

10 Name of Course: Algebra II Name of Unit: Powers, Roots, and Radicals Essential Question for the Unit: What are power functions and how are they used? A. What is the relationship between a root and a rational exponent? B. How do you simplify radical and exponential expressions? E C 2.2 E C 2.2 C. What is a composition of functions? E A, C, N 2.8 D. How do you find the inverse of a function? I A, C, N 2.8 E. How do you solve equations containing radicals? E C, I 2.2, 2.8 F. * How do you use square root and cube root functions to solve real-world problems? C A, C 2.2, 2.8 G, * Honors Algebra II

11 Name of Course: Algebra II Name of Unit: Exponential and Logarthmic Functions Essential Question for the Unit: What is the relationship between exponential and logarithmic functions? A. How do you graph exponential growth functions? E B, J 2.8 B. How do you graph exponential decay functions? E B, J 2.8 C. How do you use the number e as the base of E B, J 2.4, 2.8 exponential functions? D. How do you evaluate logarithmic functions? E B, J 2.8 E. What are the properties of logarithms? E C, J 2.4, 2.8 F. How do you solve exponential equations? E C, J, I, O 2.4, 2.8 G.* How do you model data with exponential functions? * How do you evaluate and graph logistic growth functions? C C, J, I, O 2.4, 2.8 C C, J, O 2.4, 2.8 Honors Algebra II

12 Name of Course: Algebra II Name of Unit: Rational Equations and Functions Essential Question for the Unit: How do you use inverse variation and joint variation in everyday life? A. How do you write and use joint variation models? E C, I 2.2, 2.4, 2.8 B.* How do you use the graph of a rational function I C, I 2.2, 2.8 to solve real life problems? C.* How can you use rational expressions to model I C, E, I 2.5, 2.8 real life situations? D.* How do you simplify complex fractions? I C, E 2.8 E.* When simplified, how do you solve rational equations? F. I C, E, F 2.8 G. Honors Algebra II

13 ority andard Elizabethtown Area Name of Course: Algebra II Name of Unit: Probability and Statistics Essential Question for the Unit: How are probability and statistics used in everyday life? A. What is the fundamental counting principle? E F, O 2.7 B. How are permutations and combinations used? E F 2.7 C. What is the difference between theoretical and E F, G, O 2.7 experimental probability? D. How do you find the probability of compound E F, G 2.7 events? E. How do you find the probability of independent E F, G 2.7 and dependent events? F. How can data be represented in graphs and tables? E F, G 2.6 G. How can the normal distribution be used to find probabilities? E P, O, M 2.6