REVIEW for Fall 2014 Semester Exam _____ Class: _____ Date: _____ ID: A 1 REVIEW for Fall 2014...
Transcript of REVIEW for Fall 2014 Semester Exam _____ Class: _____ Date: _____ ID: A 1 REVIEW for Fall 2014...
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
ÔÔÔÔÔÔÔÔÔÔ
57. y = −4x + 8
−8x − 2y = −16
Ï
ÌÓ
ÔÔÔÔÔÔÔÔÔÔ
58. −21x − 3y = −3
y = −7x + 2
Ï
ÌÓ
ÔÔÔÔÔÔÔÔÔÔ
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
ÔÔÔÔÔÔÔÔÔÔ
62. 7x + 2y = −13
4x − 3y = 5
Ï
ÌÓ
ÔÔÔÔÔÔÔÔÔÔ
63. −3x + 2y = −3
3x − 2y = 3
Ï
ÌÓ
ÔÔÔÔÔÔÔÔÔÔ
Solve the system of inequalities by graphing.
64. y ≤ −4x − 1
y > 4x − 2
Ï
ÌÓ
ÔÔÔÔÔÔÔÔÔÔ
65. x ≥ −2
y > 1
Ï
ÌÓ
ÔÔÔÔÔÔÔÔÔÔ
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
DIF: L2 REF: 1-1 Properties of Real Numbers 3. ANS:
rational numbers, real numbers
DIF: L2 REF: 1-1 Properties of Real Numbers 4. ANS:
−43
, 34
DIF: L2 REF: 1-1 Properties of Real Numbers 5. ANS:
Distributive Property
DIF: L2 REF: 1-1 Properties of Real Numbers 6. ANS:
Associative Property of Multiplication
DIF: L2 REF: 1-1 Properties of Real Numbers 7. ANS:
Commutative Property of Addition
DIF: L2 REF: 1-1 Properties of Real Numbers 8. ANS:
–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
DIF: L2 REF: 1-3 Solving Equations 13. ANS:
x = 5 or x = −1
DIF: L2 REF: 1-5 Absolute Value Equations and Inequalities 14. ANS:
t = S5r4
DIF: L2 REF: 1-3 Solving Equations 15. ANS:
8.8 cm by 26.3 cm
DIF: L2 REF: 1-3 Solving Equations 16. ANS:
12 cm, 16 cm, and 20 cm
DIF: L2 REF: 1-3 Solving Equations 17. ANS:
55 mi/h and 65 mi/h
DIF: L3 REF: 1-3 Solving Equations 18. ANS:
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
DIF: L2 REF: 1-4 Solving Inequalities 21. ANS:
x < –1 or x > 0
DIF: L2 REF: 1-4 Solving Inequalities 22. ANS:
1 ≤ x < 4
DIF: L3 REF: 1-4 Solving Inequalities 23. ANS:
x ≤ −4 or x ≥ 3
DIF: L2 REF: 1-5 Absolute Value Equations and Inequalities 24. ANS:
–13 < x < 4
DIF: L2 REF: 1-5 Absolute Value Equations and Inequalities 25. ANS:
14
DIF: L2 REF: 2-1 Relations and Functions
ID: A
4
26. ANS:
DIF: L2 REF: 2-2 Linear Equations 27. ANS:
152
DIF: L2 REF: 2-2 Linear Equations 28. ANS:
9x + y = 4
DIF: L2 REF: 2-2 Linear Equations 29. ANS:
83
x + y = −323
DIF: L3 REF: 2-2 Linear Equations 30. ANS:
−43
DIF: L2 REF: 2-2 Linear Equations 31. ANS:
12
DIF: L2 REF: 2-2 Linear Equations 32. ANS:
1
DIF: L2 REF: 2-2 Linear Equations
ID: A
5
33. ANS: y = 4x − 29
DIF: L2 REF: 2-2 Linear Equations 34. ANS:
y = 14
x + 354
DIF: L2 REF: 2-2 Linear Equations 35. ANS:
x = 5
DIF: L2 REF: 2-2 Linear Equations 36. ANS:
yes; k = 7; y =7x
DIF: L2 REF: 2-3 Direct Variation 37. ANS:
yes; 45
DIF: L2 REF: 2-3 Direct Variation 38. ANS:
no
DIF: L2 REF: 2-3 Direct Variation 39. ANS:
77
DIF: L2 REF: 2-3 Direct Variation 40. ANS:
110.4 mi
DIF: L2 REF: 2-3 Direct Variation 41. ANS:
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:
DIF: L2 REF: 2-5 Absolute Value Functions and Graphs 45. ANS:
(32
, –5)
DIF: L3 REF: 2-5 Absolute Value Functions and Graphs 46. ANS:
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
DIF: L2 REF: 2-6 Families of Functions 49. ANS:
y = 14
x| | − 18
DIF: L3 REF: 2-6 Families of Functions 50. ANS:
y = x + 2| |
DIF: L2 REF: 2-6 Families of Functions 51. ANS:
y = x + 1| | − 7
DIF: L2 REF: 2-6 Families of Functions 52. ANS:
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
DIF: L2 REF: 3-1 Graphing Systems of Equations 57. ANS:
dependent
DIF: L2 REF: 3-1 Graphing Systems of Equations 58. ANS:
inconsistent
DIF: L2 REF: 3-1 Graphing Systems of Equations 59. ANS:
(–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)
DIF: L2 REF: 3-2 Solving Systems Algebraically 62. ANS:
(–1, –3)
DIF: L2 REF: 3-2 Solving Systems Algebraically
ID: A
10
63. ANS: infinite solutions
DIF: L2 REF: 3-2 Solving Systems Algebraically 64. ANS:
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