Algebra II expands on the mathematical content of Algebra I and Geometry. Many new concepts and techniques are introduced that will be basic to more advanced courses in mathematics and the sciences. In general terms, the emphasis is on abstract thinking skills, the function concepts, and the algebraic solution of problems in various content areas.
Textbook: Algebra 2. Larson; Boswell; Kanold; Stiff. McDougal Littell ©2007
Topics Covered:
Linear Equations, Inequalities, Functions, Systems (Ch 1, 2, 3)
· Equations and Inequalities
· Linear Equations and Functions
· Linear Systems
Quadratic, Polynomial, and Radical Functions (Ch 4, 5, 6)
· Quadratic functions
· Factoring
· Graphing polynomial functions
· Operations on polynomials
· Rational Exponents
· Radical equations
Other Nonlinear Functions and Relations (Ch 7, 8, 9)
· Exponential functions
· Logarithmic functions
· Rational functions
· Distance/midpoint formulas
· Conic sections
· Systems of quadratics
Probability, Data Analysis, and Discrete Math (Ch 10, 11, 12)
· Counting Methods
· Probability
· Statistics
· Measures of central tendency
· Normal distributions
· Sequences and Series
Trigonometry (Ch 13, 14)
· Trigonometric Ratios
· Law of Sines/Cosines
· Graphs
· Solving Trigonometric Equations
Goals:
1. Students solve equations and inequalities involving absolute value.
2. Students solve systems of linear equations and inequalities (in two or three variables) by graphing, substitution, and linear combination.
3. Students are adept at operations on polynomials, including long division.
4. Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.
5. Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically.
6. Students add, subtract, multiply, and divide complex numbers.
7. Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator.
8. Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems.
9. Students demonstrate and explain the effect that changing a coefficient has on a graph of quadratic functions.
10. Students graph quadratic functions and determine the maxima, minima, and zeroes of the function.
11. Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
12. Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.
13. Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.
14. Students demonstrate and explain how the geometry of the graph of a conic section (asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it.
15. Given a quadratic equation of the form , students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation.
16. Students use fundamental counting principles to compute combinations and permutations.
17. Students use combinations and permutations to compute probabilities.
18. Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers.
19. Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.
20. Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series.
21. Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.
22. Students compute the mean, median, mode and 1st, 2nd, 3rd quartile of a distribution of data.
23. Students compute the standard deviation of a distribution of data.
24. Students organize and describe distributions of data by using the number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, and box-and-whisker plots.
Grading:
First semester
Tests/quizzes 40%
Homework 40%
Final 20%
Second semester
Tests/quizzes 40%
Homework 40%
Final 20%
This year I am requiring that you have a separate notebook for your assignments. You will write the notes in one book and your assignments in one book. The assignment book is to be labeled with the date and the section from the text that the assignment is from.
All work done in the assignment book will be done in pencil.
There will be no food allowed during class time. Come to class on time and prepared to be engaged in the material.
If absent, it is expected that you work through the assignment and be prepared for class the next day. If the absence is unexcused you will be given a zero for that days work.
I wish you all the best in this course! If you need to ask questions outside of class time please arrange a time that is suitable for both of us. I am willing and happy to meet with you but the responsibility is on you.
1
hismathdepartment.yolasite.com