Algebra II, Semester 2, Final Exam Review Part 1 – Constructed Response

1. Identify the asymptotes, domain & range, then graph y = 23

5+

+x

Vertical Asymptote: __________________ Horizontal Asymptote:________________

Domain:_______________

Range: ________________

2. Consider the graph of 1416

22

=+yx .

a) Describe the effects on the graph of changing the denominator of the y2 term from 4 to 16. b) Describe the effect on the graph of changing the denominator of the x2 term from 16 to 2. 3. A piece of equipment costs $75,000 new but depreciates 12% per year in each succeeding year. a.) Write the formula for its value after x years. b.) Find its value after 8 years. c.) In how many years will the equipment be worth only $15,000? 4. Use the formula If $1600 is deposited in an account at the bank and earns 14% annual interest, compounded continuously, what is the amount in the account, rounded to the nearest dollar, after 10 years?

5. Graph the function. Then state the domain and range. 43)( +−−= xxh Starting Value: ____________ Domain: ___________ Range: ____________

y

x

6. List the possible rational zeros f(x) = x3 + 7x - 12 of the function using the rational zeros theorem. 7. Find all zeros of the polynomial function. f(x) = x3 – x2 – 11x + 3 8. A soccer tournament has 32 teams participating. In the first round, 16 games are played. In each successive round, the number of games decreased by one half. A.) Write a rule for the number of games played in the nth round. B.) If 5 rounds are played, find the total number of games played.

2 – Selected Response - Graphing Calculator allowed

1. What is the simplified form of1273011

629

2

22

+++−

÷+−

xxxx

xx ?

2. What is the simplified form of 65

146

312

2 −+−

+−

−+

xxxxx

3. Solve the equation 22

252 −+

+xx

x = 1

3−x

4. Solve the equation 14

42

12 −=−

−− xx

.

5. Let and . What is the value of 65)( −= xxf 1)( 2 −= xxg ( )( )2fg ?

6. If 54)( 31+= xxf and 3

132)( xxxg += , what is )()( xfxg − ?

7. If the endpoints of the diameter of a circle are (2, -9) and (-3, 5), what are the coordinates of its center? 8. What are the foci of the ellipse given by 4x2 + 3y2 = 24? 9. Write each expression in simplest form: a. b. c. d. 10. Simplify the expression: 11. Condense the expression. yx 555 log4log316log −+ 12. Use the change-of-base formula to evaluate the expression. 13. Solve the equation. Check for extraneous solutions: ( ) 23log 4 =+x

14. Change the following to exponential form 315log125 =

15. Solve for x. 123

421 +

+

=⎟⎠⎞

⎜⎝⎛ x

x

16. Solve the equation. Check for extraneous solutions: 17. Write an exponential function whose graph passes through the points (0, 1) and xaby = (6, 64). 18. Write a power function whose graph passes through the points (1, 3) and (2, 24). baxy =

19. Simplify the expression 53

1+−

20. Which expression is the simplest form of 33 81816 − ? 21. Which expression is the simplest form of 3 53 23 44 xyyx • ? 22. Solve the following radical problem, eliminate extraneous solutions: 6124 =+x 23. Solve the following radical problem, eliminate extraneous solutions: 44 +=+ xx 24. Multiply: (-4x - 2y)2

25. Divide: 4

322 2

−−+

xxx

26. Use synthetic substitution to evaluate f(k) =3k3 - 2k2 – k + 9 when k = 3. 27. Find all solutions of the equation. x4 – 10x2 + 25 = 0 28. Determine where has its local maximum and minimum. 132)( 23 +−+= xxxxf 29. Write an equation for the cubic function whose roots/x-intercepts/zeros are (-2,0), (3, 0) & (1, 0) and goes through the ordered pair (0, 8). 30. The zeros/x intercepts/roots of the function )2)(7)(13(3)( −−+−−= xxxxf are: 31. What is the end behavior of the function: ? 362)( 27 −+−= xxxxf

32. Evaluate.

33. Find the sum of the first 12 terms of the arithmetic series. 8 + 15 + 22 + 29 + . . . 34. Find the sum of the first 10 terms of the arithmetic series. 5 + 14 + 23 + 32 + . . . 36. Find the sum of the first 10 terms of the arithmetic sequence where the first term is 6 and the common difference is -10. 37. Find the first four terms of the geometric sequence 321 =−= randa 38. Find the first four terms of the sequence ( )15 −= nnan 39. Find the 5th, 6th, and 7th terms of the following sequence nan 245 −= 40. Find the common ratio of the geometric sequence. Then write a rule for the nth term.

Part 3 – Selected Response – NO Calculator 1. The equations of the horizontal and vertical asymptotes of the graph with the equation,

g(x) = 24

120−+−

xx , are:

2. Identify the horizontal asymptotes for the following graphs. [a]

52

−+

=xxy [b]

53

+−

=xxy

3. What is the domain for the following equations?

[a] 62

+−

=xxy [b]

6−=

xxy

4. What is the standard from of the parabola with directrix x = -3 and vertex (0, 0)? 5. What is the equation of an ellipse with a vertex of (0, 4) and a co-vertex of (-3, 0)? 6. What are the asymptotes of the hyperbola y2 – 4x2 – 64 = 0 7. What is the standard form equation for a circle? 8. What is the standard form equation for a hyperbola?

9. Rewrite using radical exponents.

a. ( )27 x b. 9 2e 10. Graph 11 .Graph the function:

2. Write an equation for the following graph.

3. Evaluate the expression: (64

xxf 23)( ⋅= xy 2log=

1

) 32

1 .

4. Write as a fraction and simplify: 2-4.

15. Use the laws of exponents to simplify:

1

53

54

4

4 .

72

76

⎟⎟⎠

⎞⎜⎜⎝

⎛y 16. Simplify

17. State th omain & range of the following:

1−x +e d

a. ⋅=y b ⋅= xy 24 . 235