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Algebra / Statistics (50 Problems) : Sets, Word Problems and Systems of Inequalities and Equations

1. Convert 0.58 to a fraction and write your answer in lowest terms.

2. Evaluate. | 16 | - | -11 |
A) -27
B) -5
C) 5
D) 27

3. Simplify: -(-(-27)).

4. Determine the maximum and minimum values for the following set.
5, -50, 30, 20, -18, -6

5. Express 76% as a fraction.

6. Subtract. 14.318 - 10.72

7. Find the opposite of 44.

8. List all the factors of 16.

9. Which property of the real numbers is illustrated by the following statement?
19 + 3 = 3 + 19
A) Commutative property of addition
B) Associative property of addition
C) Distributive property

10. Which of the following is not an expression?
A) a(t + 9)
B) a - ÷ t
C) t?a - 3
D) t + a + 6

11. Marcie gets paid $1.25 an hour to babysit her little brother. If she babysits for 3 hours, how much money do Marcie's parents owe her?
A) $3.25
B) $3.50
C) $3.75
D) $4.00

12. Evaluate b2 - 2bc + c2 if b = 3 and c = -2.
A) -7
B) 1
C) 17
D) 25

13. Multiply.
a6 a8

14. Use the distributive property to remove the parentheses in the following expression. Then simplify your result if possible.

A) 21
B) 9
C) 20
D) 10

15. Use the properties of addition and multiplication to complete the statement.
12 ? (17 + 4) = 12 ? ____ + 12 ? 4

16. Subtract. -20 - 18
A) 38
B) 2
C) -2
D) -38

17. Solve. 10x - 4 - 5x = 6 + 3x - 8

18. A home purchased for $300,000 depreciated 8% over a 1-year period. What was the value of the home after at the end of the year?
A) $272,000
B) $274,000
C) $276,000
D) $278,000

19. Find the mean and the median.
-7, -6, 1, 9, 10, 17

20. Solve. -6(x + 3) - 10 = 3(-2x - 5) - 13

21. Find the mean.
3, 5, 7, 12, 13

22. Solve. -5(x + 5) = -10

23. Solve for b. a = bc2

A)

B)

C)

D)

24. Solve. 6(2 - x) = 4x

25. The line graph below shows the number of trees in a certain seaside town.

(a) Which year had the fewest trees?
(b) Between which two years did the greatest increase in the number of trees occur?

26. If y varies directly with x, and y = 42 when x = 3, find the constant of variation k.

27. Find the slope of the line passing through the points (1, -3) and (-9, 0).
A)

B)

C)

D)

28. Graph 3x + 2y = 6.
A)

B)

C)

D)

29. Find the slope of the line passing through the points (8, 8) and (7, 7).

30. The following bar graph shows the enrollment at a community college.

How many people were enrolled in 1998?

31. The following bar graph shows the enrollment at a community college.

What was the increase in enrollment from 1999 to 2000?

32. Which of the ordered pairs is a solution for the equation 2x - 3y = 6?
A) (0, 2)
B) (-3, 0)
C) (-3, -2)
D) (0, -2)

33. Find the slope of the graphed line.

A) 4
B) -4
C)

D)

34. Graph f(x) = 4x + 1.

35. Rewrite the equation -x - 2y = 20 as a function of x.

36. Write the equation of the line that passes through point (2, -2) with a slope of 3.

37. Match the graph with one of the equations.

A) y = x

B) y = 3x
C) y =

D) y = x + 3

38. Write the equation of the line with slope -2 and y-intercept (0, 0). Then graph the line.
A) y = -2x

B) y = -2x

C) y = x - 2

D) y = x - 2

39. Graph the inequality.
x - y  2

40. Are the following lines parallel, perpendicular, or neither?
L1 through (-4, -7) and (1, 3)
L2 through (2, 6) and (4, 10)
A) Parallel
B) Perpendicular
C) Neither

41. Graph f(x) = -2x + 4.

42. Find the y-intercept.
-x - 9y = -9
A) (9, 0)
B) (0, 1)
C) (1, 0)
D) (0, 9)

43. Solve the system by graphing.
2x + y = 4
x + y = 3

44. Solve the system by graphing.
3x - y = 1
3x - y = 2

45. The difference of two numbers is 68. The second is 8 less than 5 times the first. What are the two numbers?

46. Solve the system by graphing.
x - y = -3
x - y = 4

47. Solve the system by graphing.
x - y = 2
3x - 3y = 6

48. Solve the system by substitution.
4x + 3y = 12
y = -x + 5

49. Solve the system by addition or substitution.
-10x + 5y = -36
y = 2x - 8

50. Solve the following system of linear inequalities by graphing.
3x - y < 2
x + y > 2

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Solution Summary

Fifty algebra problems are solved and explained.

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