Algebra II First Semester Assignment #5 (Review of Sections 1.1 through 1.8)

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1 Algebra II First Semester Assignment #5 (Review of Sections 1.1 through 1.8) Do not rely solely on this review to prepare for the test. These problems are meant only as a means to remind you of the types of problems we have discussed and the topics we have covered. To fully prepare for the test you need to take notes in class, be well-organized, do all your homework, ask questions when needed, and study from notes, homework assignments, and quizzes as well. You will not be allowed to use a calculator on the first test of the year. Simplify each expression ( 3) (6 ) [5 + ( 4) 4 ] 15 1 S 1 A s s i g n m e n t # 5

2 Simplify each expression. 4. ( ) 9 (5 6) Solve the equation. 7. 7p (3 4p) = 1p (p + 4) S 1 A s s i g n m e n t # 5

3 Solve each equation (1z 4) = 3 (4 16z) r + 4(r + 1) + 7r = r + 3(r + 6) (8z 1) = 1 (36z + 1) S 1 A s s i g n m e n t # 5

4 Solve each equation. 11. b 3(4b 6) = 10 3[4(b 5) + 4b] w = 4 15 w 4 S 1 A s s i g n m e n t # 5

5 Evaluate each expression if w = 6, x = 3, y = 10, and z = (y w) 3(y 3w) 14. 3y wx y 15. 4(y+x 8) 3w+ 16. y 3x w 5 S 1 A s s i g n m e n t # 5

6 Evaluate each expression if w = 6, x = 3, y = 10, and z =. 17. (x+w) y z x Classify each number according to all classifications that apply. (a) (b) 5 (c) (d) 3 (e) 0 (f) π S 1 A s s i g n m e n t # 5

7 0. Solve for x: a(x b) = c Write a simplified expression in terms of the given variable. 1. The width of a rectangle is 3 cm less than the length, which is L cm. What is the perimeter of the rectangle?. The number of nickels, dimes, and quarters in a bank are consecutive odd integers, in increasing order. If there are d dimes, what is the value of the money in cents? 3. What is the multiplicative identity? 4. What is the additive identity? 5. What is the additive inverse of 3 5? 6. What is the multiplicative inverse of 3 5? 7 S 1 A s s i g n m e n t # 5

8 7. Give the shorthand notation for each of the following sets of numbers. (a) Real numbers (b) Natural Numbers (c) Rational Numbers (d) Integers 8. Simplify: (5) Justify each step with the appropriate property. 1 x + ( 3) = 0 Given [ 1 x + ( 3)] + 3 = x + [( 3) + 3] = x + 0 = x = 3 3. ( 1 x) = ( 1 x) = 6 Substitution ( 1 ) x = x = x = S 1 A s s i g n m e n t # 5

9 Name the property that justifies each statement. Use the choices listed below. (A) Associative Property of Addition (B) Associative Property of Multiplication (C) Commutative Property of Addition (D) Commutative Property of Multiplication (E) Distributive Property (F) Additive Identity (Identity Property of Addition) (G) Multiplicative Identity (Identity Property of Multiplication) (H) Additive Inverse (Property of Opposites) (I) Multiplicative Inverse (Property of Reciprocals) (J) Subtraction Property of Equality (K) Addition Property of Equality (L) Multiplication Property of Equality (M) Transitive Property of Equality (N) Division Property of Equality (9 + 87) = (5 + 9) ( 1)( 1) = (3ab) = 9(3ba) (7 + ) = 15 + ( + 7) 41. ( 1 3 ) ( 3) = 1 4. If x = y, then x + 3 = y (x) = ( 5 )x 44. (17a)(13y) = (13y)(17a) 45. (0.5) = If a = 13, then a = (3) = 3(7) 48. 1y = 1y (w + yz) = 4(yz + w) 9 S 1 A s s i g n m e n t # 5

10 Name the property that justifies each statement. Use the choices listed below. 50. ( m) ( 1 ) = 1, m 0 m 51. 7(x + t) = (x + t)7 5. (cd) ( 1 ) = 1, cd 0 cd 53. z + ( z) = a + 0 = 5a 55. a + (b + 0) = (a + b) x + ( 16x) = ac = 14ac 58. (0.6s)t = t(.6s) ( + 4) = (11)() + (11)(4) 60. If a = b, then a = b. 61. If c + d =, then c + d = x + 9y = 9(x + y) 63. If a = 18, then a + 3 = S 1 A s s i g n m e n t # 5

11 Name the property that justifies each statement. Use the choices listed below. (A) Associative Property of Addition (B) Associative Property of Multiplication (C) Commutative Property of Addition (D) Commutative Property of Multiplication (E) Distributive Property (F) Additive Identity (Identity Property of Addition) (G) Multiplicative Identity (Identity Property of Multiplication) (H) Additive Inverse (Property of Opposites) (I) Multiplicative Inverse (Property of Reciprocals) (J) Subtraction Property of Equality (K) Addition Property of Equality (L) Multiplication Property of Equality (M) Transitive Property of Equality (N) Division Property of Equality x + 4x = (13 + 4)x = a = a 67. If a + b = c and c = d, then a + b = d ( 3 4 ) = m( 1) = ( 1)m 70. If 3 + b = c and c = 4, then 3 + b = x 46y = 3(x y) 7. Complete the statement to show an example of the Symmetric Property. If 3x + 9y = 1, then. 73. Complete the statement to show an example of the Reflexive Property. 5x + 3y 9 = 11 S 1 A s s i g n m e n t # 5

12 1 S 1 A s s i g n m e n t # 5

13 Answers 7. p = 1 8. z = 5 9. r = b = 1. w = (a) R, Q, Z, whole, N (b) R, irrational (c) R, Q (d) R, Q, Z (e) R, Q, Z, whole (f) R, irrational 0. x = c + b, a a 0 1. p = 4L 6. (40d + 40) cents (a) R (b) N (c) Q (d) Z Addition Property 30. Associative Property of Addition 31. Additive Inverse 3. Additive Identity 33. Multiplication Property of Equality 34. Associative Property of Multiplication 35. Multiplicative Inverse 36. Multiplicative Identity 13 S 1 A s s i g n m e n t # 5

14 37. A 38. I 39. D 40. C 41. I 4. K 43. B 44. D 45. I 46. L 47. D 48. F 49. C 50. I 51. D 5. I 53. H 54. F 55. A 56. H 57. F 58. D 59. E 60. N 61. J 6. E 63. K 64. E 65. I 66. G 67. M 68. H 69. D 70. M 71. E 7. 1 = 3x + 9y 73. 5x + 3y 9 14 S 1 A s s i g n m e n t # 5

15 15 S 1 A s s i g n m e n t # 5

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