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Review of Algebra I

Review Test

Table of Contents

Further Reading

1. Which of the following is a solution set to x 2 - 12 = 5x + 2 ?

2. Solve for y in 2y + 5 = - 3y - 10 .

3. Which property is illustrated in the following:
y = 5x and 5x = 3 . Thus, y = 3 .

4. Meredith and Molly go shopping. Meredith buys a shirt for $10 and two pairs of pants for $10 each. She has $15 left over. Molly buys a dress for $50 and two packs of cards. If Molly started with $20 more than Meredith, and if Molly spent all her money, how much does one pack of cards cost?

5. Tobin rows 2 miles per hour faster than her opponent. If it takes Tobin 30 minutes to finish a race, and it takes her opponent 45 minutes to finish the same race, how fast does Tobin row?

6. Greg receives the following scores on his math tests: {90, 83, 78, 95} . What is the minimum score he needs on the last math test in order to get an 85 average in the class?

7. Solve for x in 3x + 2≤ - x - 2 .

8. What inequality does the following graph represent?

9. Solve for y in - y + 6 < - 4y .

10. Name all the members of set A :

11. If P = {2, 3, 0, 8, 7, -1} and Q = {0, 1, 6, 8, -3, -2} , what is QP ?

12. What inequality does the following graph represent?

13. Compute 3×| 4 - 5|×| 15| - | - 2| .

14. Solve for x in -4| x - 3| = - 16 .

15. Solve for y in 6 - | - 3y + 1| = 8 .

16. If Marsha grabs one shirt from a drawer containing 2 white shirts, 6 black shirts, and 8 striped shirts, what is the probability that she will grab a black shirt?

17. What is the probability of an event if the probability of its complement is ?

18. The mean of {5, 6x - 1, 12, and - 2} is 8 . What is x ?

19. The median of {2, 3, 6, x, 11, -2} is 4.5 . Which of the following numbers could be a value of x ?

20. The mode of {2, 8, 9, 8, 4, 4, 8, x} is 8. Which of the following could not be a value of x ?

21. Which of the following ordered pairs (x, y) is a solution to xy = 3x - 9 ?

22. Which of the following could be a graph of y - 3 = 2x ?

23. What is the x -intercept of y - 6 = 3(x + 2) ?

24. What is the slope of the line that passes through (- 2, 4) and (7, 1) ?

25. What is the slope of the line given by the equation 6y - 3x = 12 ?

26. Which equation describes the following graph?

27. What is y - 4 = (x - 2) in general linear form?

28. What is 4x - 3y = 8 in slope-intercept from?

29. If y varies directly as x , and y = 6 when x = 9 , which of the following equations describes this variation?

30. If y varies directly as x , and y = 7 when x = 14 , what is x when y = 18 ?

31. If y varies inversely as x , and y = 4 when x = 2 , which of the following equations describes the variation?

32. Solve the following system of equations for (x, y) :

x + y = 5  
2x - 3y = -5  

33. Solve the following system of equations for (x, y) :

4x + y = 0  
-2x + 5y = 22  

34. Which statement is true about the system:

4y - 5x = 16  
y = + 4  

35. Which of the following is an inconsistent system?

36. Simplify and rationalize the denominator:

37. Simplify and rationalize the denominator: ×

38. Simplify .

39. Simplify (x 2)(4x) + (- 6x 2)3 - .

40. Write the answer in scientific notation: 4.5×1017 - 5.6×1016

41. Write the answer in scientific notation: (3.0×105)×(1.5×10-9)

42. Write the answer in scientific notation: (7.5×10-6)÷(2.5×10-3)

43. What is the degree of the polynomial -5x 6 y 2 +2x 7 +3x 2 + xyz 5 ?

44. Simplify 5x 2 y(- 3x - 2xy + x 2 y) .

45. Multiply and simplify: (4x - 3)(- 2x + 1)

46. Factor x 2 - 10x - 24 .

47. Solve for x in x 2 + 6x + 9 = 0 .

48. Solve for x in 12x 2 - x - 2 = 0 .

49. How many times does the graph of y = - 5x 2 + 6x - 2 cross the x -axis?

50. Complete the square in the equation y = 8x 2 + 8x + 1 .