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Review of Algebra II

Review Test

Table of Contents

Further Reading

1.

3 + x = ?    

2.

= ?    

3. The reduced row echelon form of

is    

4. Which of the following is the multiplicative inverse of

?    

5. Which of the following is a solution to

   

6. Which of the following is equal to x , if

   

7. How many different values of (x, y, z) satisfy the following system of equations?

   

8. Which of the following is a graph of 3x - y≥3 ?
Figure %: 3x - y≥3

9. Which of the following graphs represents the solution to the system of inequalities

   

Figure %: System of inequalities

10. Factor 15x 2 - x - 6 .

11. Factor 8x 3 - y 3 .

12. Factor 2x 3 +5x 2 - 18x - 45 .

13. How many real roots does f (x) = 4x 2 - 8x - 16 have?

14. + - = ?

15. × = ?

16. ÷ = ?

17. What is the solution set of + = ?

18. y is a function of x in all the following relations EXCEPT:

19. What is the domain of f (x) = ?

20. What is the range of f (x) = x 2 - 4 ?

21. If f (x) = 2x + 1 and g(x) = x 2 - 6x , what is 3f (x) + 2g(x) ?

22. If f (x) = 2x - 4 and g(x) = 5x + 3 , what is fg(x) ?

23. If f (x) = 3x - 7 and g(x) = x 2 - 1 , what is g o f (x) ?

24. What is the inverse of f (x) = + 5 ?

25. If g(x) is shifted up 3 units and right 4 units from f (x) , what is g(x) ?

26. If g(x) is stretched horizontally by a factor of 2 and shifted down 3 units from f (x) , what is g(x) ?

27. If g(x) is a reflection of f (x) = x 3 + x 2 - 4 over the y -axis, what is g(x) ?

28. Which of the following graph is symmetric with respect to the origin?
Figure %: Graphs

29. Name all the vertical asymptotes and holes in the graph of f (x) = ?

30. Which equation could describe the following graph?
Figure %: Graph

31. If 7 athletes are running a race, in how many different ways can they finish in first place, second place, and third place?

32. Which of the following is equivalent to C(15, 10) ?

33. A function is defined recursively by

   


What is f (4) ?

34. What are the next two number in the sequence 1, 1, 2, 3, 5, 8, 13, __, __ ?

35. What is ()- ?

36. If = 1 - 2x , what are all the possible values of x ?

37. Which equation could describe the following graph?
Figure %: Graph

38. log3 = ?

39. Simplify 3 log2 x + 2 log2(x - 2) - log2(x - 3) .

40. Solve for x : log2(x 2 -1) - log2(x + 1) = 3 .

41. Solve for x : 6x36x-1 = 216 .

42. If $700 is put into a bank account with an interest rate of 5%, compounded yearly, how much money is in the account after 6 years?

43. Simplify .

44. (2 - 3i)(5 + 7i) = ?

45. (4 + 3i)÷(5 + 3i) = ?

46. Which of the following is a factor of x 4 -22x 2 + 31x - 28 ?

47. What is the remainder when P(x) = 2x 5 -2x 4 -6x 3 +12x 2 + 4x + 16 is divided by x + 2 ?

48. Factor completely: 2x 4 +11x 3 +10x 2 - 11x - 12 .

49. If 2 - i is a zero of P(x) = x 3 -3x 2 + x + 5 , factor P(x) completely.

50. (x - 5y)4 = ?