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Worksheet 1.1-1.4 name: Algebra 2 Evaluate each expression if a = 4, b = -3, c = ½ , d = -2, e = 5, f = -6, g = 0 : 1. a+b.d–e 2. d – f + ac 5. bd 2 - b3 c 6. ge 2 + ab d 3. 7. 2b2 4. (2b)2 ( f + d)2 - a3 bc 8. abc eg - g 2 Choose the correct answer: 9. Decimals that terminate are ________________________ numbers. a) 10. rational 12. irrational c) whole d) not real d) not real Decimals that repeat are ________________________ numbers. a) 11. b) rational b) irrational c) whole Decimals that are non-repeating and non-terminating are ________________________ numbers. a) rational b) irrational c) whole Fill in: Rational numbers can be expressed as a ratio d) not real a , where a and b are both _____________________ and b b is not _______________. (see page 11 in your textbook) Name the sets of numbers to which each number belongs. There may be more than one answer: (Choose from: natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, not real) 13. -2.54 14. 0 18. 33.3 19. 0 23. -8 24. 6 29. 62.5 28. 13 62 Simplify the expressions: 15. 7 0 184.005 16. -5 17. π 22. -9 -8.26 27. 65,000 62.516 32. - 3 20. 2 21. - 36 25. 81 49 26. 30. 62.5 31. 4 33. 36. 1 (4j 5 + 2k + 6j – 7k) æa bö 12 ç - ÷ è3 4ø 34. 4(20 – 4p) – 37. ö 1 5æ3 ç x +12y ÷ - ( 2x -12y) ø 4 6è5 3 4 (4 – 16p) 35. 2(4z – 2x + y) – 4(5z + x – y) 38. a2 – a + 4a – 3a2 + 1 Find the additive inverse and multiplicative inverse for each number: 39. - 2 9 40. 1.4 Name the property illustrated by each equation (see 1.2 notes and 1.3 notes for properties) 41. 3a + 0 = 3a 42. (6m + 8m) + 7m = (8m + 6m) + 7m 44. æ1ö 5y ç ÷ = 1 è 5y ø 47. If p = -5 and -5 = q, then p=q. 45. ( ) 5 x + 5 = 5x + 5 48. If x – 5 = 13, then x = 18. 43. (6m + 8m) + 7m = 6m + (8m + 7m) 46. If 14 = -7x, then -7x = 14 49. If 1 3 x = 9, then x = 27. Write an algebraic expression to represent each verbal expression: 50. 8 less than the product of 5 and a number 51. 15 increased by the cube of a number 52. 4 more than the quotient of a number and 3 53. 6 decreased by twice the square of a number Write a verbal sentence to represent each equation: 54. 55. 2(c– 1) = 3c x 4 + 8 = -16 Solve the equations: 56. 4n + 20 = 68 – 2n 57. -3b + 7 = -18 + 2b 58. 100 = 20 – 5r 59. 62. 6y – 15 = -3(2y – 7) 63. 7– 1 2 x=3 Solve the equations: 60. a- 2a =3 5 61. Solve for the specified variable: 64. a = 3b – c, for b 67. 65. A= x + y , for y 2 66. 3x – 24 = -5x H = vt – gt2, for v (Draw a picture, and use algebra to solve this problem) Robert’s father is five years older than three times Robert’s age. If the sum of their ages is 53, find the age of Robert’s father. 69. - 12 n = 85 The length of a rectangle is 10 cm longer than its width. If the total perimeter of the rectangle is 44 cm, find the dimensions. 68. 3 4 (Use algebra to solve this problem) Jason started with d dollars in his piggy bank. One week later, Jason had doubled the amount in his piggy bank. Another week later, Jason was able to add $20 to his piggy bank. At this point the piggy bank has $50 in it. What amount did Jason start with? (Use algebra to solve this problem) Evaluate each expression if w = -4, x = 2, y = 70. |22y + z| + |yz| 71. 1 2 and z = -6: 3|wx| + 1 4 |4x + 8y| 72. 10 – |wy| + |z + x| Solve each equation. Check your solutions: 73. |x + 15| = 37 74. |y – 13| = -24 77. |4a + 3| = 15 – 2b 75. |8d – 2| – 5 = 13 78. |5b + 9| + 16 = 2 76. 79. -2|7 – 3y| – 6 = -14 |8 + p| = 2p – 3 _________________________________________________________________________________________________________ ANSWERS: 1) 5 2) 6 3) 18 4) 36 5) 30 6) 6 7) 0 8) undefined 9) rational 10) rational 11) irrational 12) integers, zero 16) integer, rational, real 13) rational, real 15) rational, real 20) irrational, real 26) rational, real 27) natural, whole, integer, rational, real 30) rational, real 31) rational, real 36) 4a–3b 42) commutative prop 43) associative property 44) multiplicative inverse 45) 47) transitive property 48) 49) multipliation property 53) 6–2x2 60) a=5 68) 41 years old 75) d=5/2 or d=- 2 37) 21) rational, real 13y 38) 22) not real n=¼ addition property 62) 69) 76) 32) -2a2+3a+1 54) various answers 61) 17) irrational, real y=3 $15.00 55) 63) x=3 70) 8 y=1 or y=11/3 23) AI: 2/9 71) 77) b= rational, real 33) MI: -9/2 various answers 64) 18) rational, real whole, integer, rational, real 19) whole, integer, rational, real 24) not real 25) rational, real 28) natural, whole, integer, rational, real irrational, real 39) 14) a+c 3 27 a=2 or a=-9 2j–k 40) 56) n=8 65) 72) 34) 29) rational, real 77–4p 35) -8x+6y–12z AI: -1.4 or -7/5 MI: 5/7 distributive prop 50) 5x–8 57) b=5 y=2a–x 12 73) 78) 66) v= identity prop 46) symmetric property 51) 58) 41) 15+x3 52) r=–16 59) 67) H + gt 2 t x/3 + 4 x=8 6 cm x 16cm x=22 or x=-52 74) no solution no solution 79) p=11