REVIEW for Fall 2014 Semester Exam ___ Class: _ Date: ___ ID: A 1 REVIEW for Fall 2014 Semester Exam Short Answer To which sets of numbers does the number belong? 1. 73 2.

Name: ________________________ Class: ___________________ Date: __________ ID: A

1

REVIEW for Fall 2014 Semester Exam

Short Answer

To which sets of numbers does the number belong?

1. 73

2. 3

3. 0.5

Find the opposite and the reciprocal of the number.

4. 43

Name the property of real numbers illustrated by the equation.

5. 4(x + 6) = 4x + 24

6. 2 ⋅ 13 ⋅ 7Ê

ËÁÁÁ

ˆ

¯˜̃˜ = 2 ⋅ 13

Ê

ËÁÁÁ

ˆ

¯˜̃˜ ⋅ 7

7. π + 15 = 15 + π

Evaluate the expression for the given value of the variable(s).

8. −2x2 + 7x + 4; x = –2

Name: ________________________ ID: A

2

Simplify by combining like terms.

9. c − 2d + 7c − 4d 10. 2(4y − 2) + 2y

Solve the equation.

11. 4y − 13 = 8 + 9y

12. 2y + 14 = 6(y + 7)

13. x − 2| | = 3

Solve the equation or formula for the indicated variable.

14. S = 5r4t, for t

15. A rectangle is 3 times as long as it is wide. The perimeter is 70 cm. Find the dimensions of the rectangle. Round to the nearest tenth if necessary.

16. The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 48 cm?

17. Two cars leave Denver at the same time and travel in opposite directions. One car travels 10 mi/h faster than the other car. The cars are 240 mi apart in 2 h. How fast is each car traveling?

Solve the inequality. Graph the solution set.

18. –8 + 3k ≤ –2

19. 3r + 6 ≥ 13

20. 2(2y – 2) < 28

Name: ________________________ ID: A

3

Solve the compound inequality. Graph the solution set.

21. 5x – 6 < –11 or 4x + 5 > 5 22. −2 ≤ 2x − 4 < 4

Solve the inequality. Graph the solution.

23. 8x + 4| | ≥ 28

24. 2x + 9| | < 17

25. For f x( ) = 5x + 4, find f 2( ).

26. Graph the equation y =3

4x − 1.

Find the slope of the line through the pair of points.

27. (–6, 9) and (–8, –6)

Write in standard form an equation of the line passing through the given point with the given slope.

28. slope = –9; (1, –5)29. slope = −8

3; (–4, 0)

Find the slope of the line.

30. y = −43

x + 9

31. −2x + 4y = 5

Name: ________________________ ID: A

4

32.

Find an equation for the line:

33. through (8, 3) and perpendicular to y = −14

x – 1. 34. through (–3, 8) and parallel to y = 14

x – 4.

35. through (5, 6) and vertical.

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

36.

x y

5 35

20 140

80 560

320 2240

Name: ________________________ ID: A

5

Determine whether y varies directly with x. If so, find the constant of variation k.

37. 5y = 4x 38. 8y – 8x = –2

Find the value of y for a given value of x, if y varies directly with x.

39. If y = 43 when x = –129, what is y when x = –231?

40. The distance traveled at a constant speed is directly proportional to the time of travel. If Olivia traveled 56 miles in 3.5 hours, how many miles will Olivia travel in 6.9 hours at the same constant speed?

41. A 3-mi cab ride costs $6.70. A 7-mi cab ride costs $13.10. Find a linear equation that models cost c as a function of distance d.

42. A cannery processed 1570 pounds of strawberries in 6.5 hours. The cannery processed 2480 pounds in 10 hours.a. Write a linear equation to model the weight of strawberries S processed in T hours. b. How many pounds of strawberries can be processed in 11 hours?

Graph the absolute value equation.

43. y = x − 3| |

44. y = − 3x + 3| |

45. What is the vertex of the graph of the function y = 2x − 3| | − 5?

Name: ________________________ ID: A

6

46. Write the equation for the translation of y = x| | . 47. Compare the graphs of the pair of functions. Describe how the graph of the second function relates to the graph of the first function.y = −2 x| | and y = −2 x| | − 3

Write an equation for the vertical translation.

48. y =6

7x ; 2 units up

49. y =1

4x| | − 9; 9 units down

50. Write an equation for the horizontal translation of y = x| | .

51. Write the equation that is the translation of y = x| | left 1 unit and down 7 units.

Name: ________________________ ID: A

7

Graph the inequality.

52. –3x + 4y > 8 53. x + 4y ≥ 6

Graph the absolute value inequality.

54. y > |x – 5| + 3

Solve the system by graphing.

55. −x − y = 5

2x − y = −4

Ï

ÌÓ

ÔÔÔÔÔÔÔÔÔÔ

Without graphing, classify each system as independent, dependent, or inconsistent.

56. −5x − 3y = 12

2x − y = 4

Ï

ÌÓ


57. y = −4x + 8

−8x − 2y = −16

Ï

ÌÓ


58. −21x − 3y = −3

y = −7x + 2

Ï

ÌÓ


Solve the system by the substitution method.

59. −5x − 2y = −1

x − y = −4

Ï

ÌÓ

ÔÔÔÔÔÔÔÔÔÔ 60.

−2x − 2y + 3z = 4

x + 2y + z = −8

x − 2z = 4

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔ

Name: ________________________ ID: A

8

Use the elimination method to solve the system.

61. x − y = 2

x − 4y = 11

Ï

ÌÓ


62. 7x + 2y = −13

4x − 3y = 5

Ï

ÌÓ


63. −3x + 2y = −3

3x − 2y = 3

Ï

ÌÓ


Solve the system of inequalities by graphing.

64. y ≤ −4x − 1

y > 4x − 2

Ï

ÌÓ


65. x ≥ −2

y > 1

Ï

ÌÓ


Solve the system using either method of substitution or elimination.

66.

−x + y + 2z = −5

−2x − y + 4z = −4

−x − 2y + 2z = 0

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔ

ID: A

1

REVIEW for Fall 2014 Semester ExamAnswer Section

SHORT ANSWER

1. ANS: irrational numbers, real numbers

DIF: L2 REF: 1-1 Properties of Real Numbers 2. ANS:

natural numbers, whole numbers, integers, rational numbers, real numbers


rational numbers, real numbers


−43

, 34


Distributive Property


Associative Property of Multiplication


Commutative Property of Addition


–18

DIF: L2 REF: 1-2 Algebraic Expressions 9. ANS:

8c − 6d

DIF: L2 REF: 1-2 Algebraic Expressions 10. ANS:

10y − 4

DIF: L3 REF: 1-2 Algebraic Expressions

ID: A

2

11. ANS:

−415

DIF: L2 REF: 1-3 Solving Equations 12. ANS:

−7


x = 5 or x = −1

DIF: L2 REF: 1-5 Absolute Value Equations and Inequalities 14. ANS:

t = S5r4


8.8 cm by 26.3 cm


12 cm, 16 cm, and 20 cm


55 mi/h and 65 mi/h


k ≤ 2

DIF: L2 REF: 1-4 Solving Inequalities 19. ANS:

r ≥ 213

DIF: L2 REF: 1-4 Solving Inequalities

ID: A

3

20. ANS: y < 8


x < –1 or x > 0


1 ≤ x < 4


x ≤ −4 or x ≥ 3


–13 < x < 4


14

DIF: L2 REF: 2-1 Relations and Functions

ID: A

4

26. ANS:

DIF: L2 REF: 2-2 Linear Equations 27. ANS:

152


9x + y = 4


83

x + y = −323


−43


12


1

DIF: L2 REF: 2-2 Linear Equations

ID: A

5

33. ANS: y = 4x − 29


y = 14

x + 354


x = 5


yes; k = 7; y =7x

DIF: L2 REF: 2-3 Direct Variation 37. ANS:

yes; 45


no


77


110.4 mi


c = 1.60d + 1.90

DIF: L2 REF: 2-4 Using Linear Models 42. ANS:

S = 260T – 120; 2740 lb

DIF: L2 REF: 2-4 Using Linear Models

ID: A

6

43. ANS:

DIF: L2 REF: 2-5 Absolute Value Functions and Graphs 44. ANS:


(32

, –5)


y = x| | − 5

DIF: L2 REF: 2-6 Families of Functions 47. ANS:

The second function is the graph of y = −2 x| | moved down 3 units.

DIF: L2 REF: 2-6 Families of Functions

ID: A

7

48. ANS:

y = 67

x + 2


y = 14

x| | − 18


y = x + 2| |


y = x + 1| | − 7


DIF: L2 REF: 2-7 Two-Variable Inequalities

ID: A

8

53. ANS:

DIF: L2 REF: 2-7 Two-Variable Inequalities 54. ANS:

DIF: L2 REF: 2-7 Two-Variable Inequalities

ID: A

9

55. ANS:

(–3, –2)

DIF: L2 REF: 3-1 Graphing Systems of Equations 56. ANS:

independent


dependent


inconsistent


(–1, 3)

DIF: L2 REF: 3-2 Solving Systems Algebraically 60. ANS:

(4, –6, 0)

DIF: L2 REF: 3-6 Systems With Three Variables 61. ANS:

(–1, –3)


(–1, –3)

DIF: L2 REF: 3-2 Solving Systems Algebraically

ID: A

10

63. ANS: infinite solutions


DIF: L2 REF: 3-3 Systems of Inequalities 65. ANS:

DIF: L2 REF: 3-3 Systems of Inequalities 66. ANS:

no solution

DIF: L4 REF: 3-6 Systems With Three Variables

REVIEW for Fall 2014 Semester Exam _____ Class: _____ Date: _____ ID: A 1 REVIEW for Fall 2014 Semester Exam Short Answer To which sets of numbers does the number belong? 1. 73 2.

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REVIEW for Fall 2014 Semester Exam ___ Class: _ Date: ___ ID: A 1 REVIEW for Fall 2014 Semester Exam Short Answer To which sets of numbers does the number belong? 1. 73 2.