# 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

#### Solution Summary

Fifty algebra problems are solved and explained.