2nd Semester Final Review Algebra 2 2011

1.  Simplify:

2. Simplify:

3. Simplify:

4. Solve for x:

5. Solve for x:

6. A 3 person committee is chosen at random from a group of 22 people. How many different committees are possible?

7. A menu consists of 8 different kinds of entrees, 4 different kinds of soup and 5 different drinks. How many choices are there for ordering an entree, a bowl of soup, and a drink?

8. 15 people entered a race. If there are no ties, in how many ways can the first three places come out?

9. A bag contains 3 white marbles and 5 red marbles. One marble is drawn at random. What is the probability that the first marble is red.

10. Find the standard deviation for the data set:

3, 8, 5, 8, 6

11. Solve for x:

12. Evaluate:

13. Use the change of base formula to evaluate the expression .

14. Condense the expression:

15. Expand:

16. Solve for x: 2x+1=15

17. Solve for x:

18. Find the inverse of .

19. The rate of decay of a particular sample can be modeled by the equation: , where y represents the units existing after a specified amount of time, t. How many units will be left after 900 days?

20. If there are initially 400 bacteria in a culture, and the number of bacteria increase by 80% each hour, how many bacteria will be present after 4 hours?

21. Write an exponential function to model the following situation. A population of 100 butterflies decreases at an annual rate of 18.5%. How many butterflies will be left after 3 years?

22. Find the sum of the first 20 terms of the series:

–4 + 0 + 4 + 8 . . .

23. Find the 21st term of the sequence:

-1, 3, 7, 11, 15, ……

24. Find the sum of the infinite series:

25. For the series 3, 9, 27, 81, …. what is the sum of the first 15 terms?

26. Evaluate:

27. Write the first five terms of the sequence defined by

and d = 2

28. Write the first five terms of the sequence defined by

and r =

29. What is the coefficient of the x5y5 term in the expansion of (3x - y)10?

30. Expand

31. Change the equation to vertex form:

32. Write the equation of a circle with center at (-3, 0) with a radius of 4.

33. What conic shape does the graph of represent?

34. What conic shape does the graph of represent ?

35. Find the exact value of the Sin 240º.

36. Find the exact value of the cos radians.

37. Convert 20º to radians

38. Convert radians to degrees

39. Find the measure of an angle between that is coterminal with

40. Evaluate the three trig functions of the following triangle.

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