SYLLABUSAlgebra 2

INSTRUCTOR: ____Kintz__________________ SCHOOL YEAR: ____15/16___ PERIOD: __2,3,5,6,8___ COURSE NUMBER: 318

COURSE DESCRIPTIONThis is the third course in the college preparatory mathematics sequence. Units of study include a review of Algebra 1 topics, matrices, quadratic functions, polynomials and polynomial functions, rational functions, exponential and logarithmic functions, radical equations and functions, conic sections, and probability and statistics. Technological tools, such as the TI graphing calculator, will be used for both discovery and problem solving. Classroom sets of graphing calculators will be provided. Students will be expected to bring a TI-30X IIS scientific calculator to class on a daily basis.

ENDURING UNDERSTANDINGS - After successfully completing this course, the student will understand that:1. Functions are mathematical models of real-world applications. 2. The graphs of different types of functions have specific shapes. 3. The roots of functions have specific meaning in the real world.

CREDIT: 1 credit LEVEL: 11 – Regular

PREREQUISITESThis course is open to juniors and seniors, who have passed both semesters of Algebra 1 and have passed both semesters of Geometry.

AREAS OF STUDYFirst Semester Second SemesterReview Linear Functions and Systems of Equations Trigonometric Ratios and FunctionsQuadratics Exponential and Logarithmic FunctionsPolynomials Probability and StatisticsPowers, Roots, and Radicals

Semester 1

UNIT 1: Review Linear Functions and Systems of Equations(4 Weeks)

Enduring Understanding: ???

Essential Questions: ???

Knowledge and Skills1. Students will be able to solve multi-step equations

2. Students will be able to solve multi-step inequalities

3. Students will be able to solve word problems using equations and inequalities

4. Students will be able to solve absolute value equations

5. Students will be able to solve literal equations for a specified variable

6. Students will be able to graph linear equations

7. Students will be able to find the slope/rate of change of a linear function

8. Students will be able to write equations of lines

9. Students will be able to graph absolute value functions

10. Students will be able to solve systems of equations graphically using a calculator

11. Students will be able to solve systems of equations algebraically

12. Students will be able to use matrices on the calculator to solve systems of equations (two and three variable systems)

13. Students will be able to solve word problems using systems of equations

OPTIONAL: Students will be able to solve word problems using linear programming

UNIT 2: Quadratics(4Weeks)

Enduring Understanding: ???

Essential Questions ???

Knowledge and Skills14. Students will know that x-intercepts, zeroes, and solutions are synonymous

terms

15. Students will be able to solve quadratic equations algebraically

a. By factoring

b. Using square roots

c. By completing the square

16. Students will be able to perform operations (addition, subtraction, multiplication, and division) with complex numbers

17. Students will be able to solve quadratic equations with complex solutions

18. Students will be able to solve rational equations that become quadratic with cross-multiplication and/or simplification

19. Students will be able to solve quadratic equations graphically using a calculator

20. Students will be able to convert quadratic equations from/to standard form to/from vertex form

21. Students will be able to graph parabolas and describe the transformation from the parent function

22. Students will be able to find the focus and directrix of a parabola given its quadratic equation and write the quadratic equation of a parabola given its focus and directrix.

UNIT 3: Polynomials(4 Weeks)

Enduring Understanding: ???

Essential Questions: ???

Knowledge and Skills23. Students will be able to factor polynomial expressions, including sums and

differences of cubes

24. Students will be able to divide polynomials using

a. Long division

b. Synthetic division

25. Students will be able to solve polynomial equations by factoring

26. Students will be able to find the solutions of a polynomial equation given a zero or a factor

27. Students will be able to solve polynomial equations graphically using a calculator

28. Students will be able to analyze graphs of polynomial functions and describe

a. The relative minimum and relative maximum

b. Periods that are increasing or decreasing

c. The average rate of change in a specified interval

d. End behavior

UNIT 4: Powers, Roots, and Radicals(4Weeks)

Enduring Understanding: ???

Essential Questions: ???

Knowledge and Skills29. Students will be able to simplify numeric expressions with nth roots

30. Students will be able to use properties of exponents and radicals

31. Students will be able to simplify algebraic expressions with rational exponents

32. Students will be able to simplify algebraic expressions with radicals

33. Students will be able to graph square root and cube root functions and describe the transformation from the parent function

34. Students will be able to solve equations with rational exponents

35. Students will be able to solve equations with radicals

Semester 2

UNIT 5: Trigonometric Ratios and Functions(6 Weeks) Enduring Understandings: ???

Essential Questions: ???

Knowledge and Skills:1. Students will be able to convert from/to degrees to/from radians

2. Students will be able to find the value of the six trigonometric functions (sine, cosine, tangent, cosine, cosecant, cotangent) given an angle measure on the unit circle

3. Students will be able to find the value of the remaining trigonometric functions given the quadrant of the angle and the ratio of one trigonometric function

4. Students will be able to graph sine and cosine functions and describe

a. The amplitude

b. The frequency

c. The midline

5. Students will be able to model real-world situations using sine and cosine functions

6. Students will use the Law of Sines and the Law of Cosines to find missing measurements of a triangle.

UNIT 6: Exponential and Logarithmic Functions (6 Weeks)

Enduring Understandings: ???

Essential Questions: ???

Knowledge and Skills7. Students will be able to determine if a set of data represents

exponential growth, exponential decay, or neither

8. Students will be able to solve word problems using exponential growth and decay functions

9. Students will know that the number e is a constant used for modeling exponential growth and decay

10. Students will be able to convert from/to exponential form to/from logarithmic form

11. Students will be able to use properties of logarithms to condense logarithmic expressions

12. Students will be able to solve exponential equations

13. Students will be able to solve logarithmic equations

14. Students will be able to graph exponential and logarithmic functions using a calculator

15. Students will be able to solve real-world problems using exponential and logarithmic functions

UNIT 7: Probability and Statistics(6 Weeks)

Enduring Understandings: ???

Essential Questions: ???

Knowledge and Skills16. Students will be able to find the mean and standard deviation for a

data set to fit the data to a normal curve

17. Students will be able to estimate the are under a curve or a portion of a curve and explain the significance of the area

18. Students will be able to use a calculator to find the function of best fit (linear, quadratic, etc) for a scatter plot of data

19. Students will be able to analyze a data set and find outliers in the data

20. Students will be able to calculate a sample mean of population from a data set

21. Students will be able to find the probability of independent and dependent events

22. Students will be able to find the probability of compound (and, or) events

23. Students will be able to apply counting principle in the context of a probability problem