The symbol is read as a. is less than or equal to c. is equal to e. is greater than b. is less than d. is greater or equal to Let N = the set of natural numbers W = the set of whole numbers Z = the set of integers Q = the set of rational numbers R = the set of real numbers Which of the following statements are correct? Read the symbol as "is a subset of". a. N R b. Q W c. Z N d. W R e. Z Q 3 Select all natural numbers from the following list of numbers. a. c. 0 e. 0. g. 9 b. 4 d. 0 f. 4 Select the whole numbers from the following list of numbers. a. 9 c. 0 e. g. 8 3 b. 0 d. 0.5 f. 5 Select all rational numbers from the following list of numbers. a. b. 7 c. 0. d. 6 e. 5 f. 0 0 6 Select the prime numbers from the following list of numbers. a. 7 c. 8 e. 4 g. b. 0 d. 0 f. 0 7 Select the odd integers from the following list of numbers. a. 9 b. 0 c. 8 d. 0.5 e. 0 f. PAGE
8 How many natural numbers are between 0.5 and 6.5 on the number line? a. 0 b. 7 c. 9 d. 7 e. 6 9 How many composite numbers are from 5 to? a. 5 b. c. 8 d. 0 e. 5 0 How many prime numbers are between 4 and 0 on the number line? a. 3 b. 0 c. 3 d. 0 e. 9 f. 8 How many even integers are between 3.5 and 5.5 on the number line? a. 6 b. 3 c. 5 d. 4 e. 7 How many odd integers are between 8 and 4 on the number line? a. 8 b. 5 c. 0 d. 7 e. 6 3 Write the inequality x > 6 using interval notation. a. ( 6, ) b. (, 6 ) c. ( 6, 6 ) d. [ 6, ) 4 Select the correct representation of the inequality in interval notation. x 4 a. [ 4, ) b. (, 4 ] c. (, 4 ) d. [, 4 ] PAGE
5 Select the correct representation in interval notation of the following inequality. 0 x < 0 a. (, 0 ] c. [ 0, 0 ) e. [ 0, ) b. ( 0, 0 ) d. [ 0, 0 ] 6 Select the correct union of intervals for the inequality. x 9 or x > 3 a. (, 9 ) ( 3, ) c. (, 9 ) [ 3, ) b. (, 9 ] ( 3, ) d. (, 9 ] [ 3, ) 7 Write the expression without using absolute value symbols. 9 a. 0 b. 9 c. 9 d. 8 Write the expression without using absolute value symbols. 9 a. 9 b. c. 0 d. 9 9 Write the expression without using absolute value symbols. x 6 and x < 9 a. ( x 6) b. ( x + 6) c. x 6 d. x + 6 0 Select the correct distance between the following two points on the number line. 3 and 7 a. 3 b. 4 c. 7 d. 39 e. 40 Write the number 0 without using exponents. a. 00 b. 0 c. 90 PAGE 3
Write the expression 0yyyy using exponents. a. 0y 4 b. 0y 3 c. 0y 3 d. 0y 4 3 Simplify the expression x 5 x a. x 0 b. x 6 c. x 7 4 Simplify the expression (x 3 ) 9 a. x 3 b. x 9 c. x 7 d. x 5 Simplify the expression (x 3 ) (x 4 ) 3 a. x 9 b. x c. x 8 PAGE 4
6 Simplify the expression. x 3 y 8 Express the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined. y 4 x x 6 y 0 x 4 y 6 x 4 y 6 7 Simplify the expression ( 8x) 0 Write the answer without using exponents. a. 8 b. c. d. 8 8 Simplify the expression x 7 Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined. a. x 7 b. x 8 c. x 7 PAGE 5
9 Simplify the expression x 6 x 4 x 3 x Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined. a. x 7 b. x 8 c. x 4 d. x 6 30 Simplify the expression x 4 x ( x ) 5 Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined. a. x 8 b. x 0 c. x 8 3 Simplify the expression a b 4 Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined. b 8 b a. b. c. a 8 a a b 8 PAGE 6
3 Simplify the expression r 5 r r 6 r 6 3 Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined. a. r 8 b. r 3 c. r 33 Simplify the expression ( 8 z y ) ( 5 y 3 z 4 ) 3 ( 5 y z 4 ) Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined. 8 z 9 0 9 64 z 5 y a. b. c. 5 y 0 5 y 9 64 z 0 34 Simplify the expression 7 [ + ( 85 9 ) ] 8 ( 4 5 ) a. 70 b. 68 c. 70 35 Let x = 4, y = 0, z = 4 and evaluate the expression. ( x z 3 ) z y a. 56 b. 0 c. 64 PAGE 7
36 Express the number 80000000 in scientific notation. a..8 0 8 b. 8 0 9 c..8 0 9 d..8 0 7 37 Express the number 0.00057 in scientific notation. a. 5.7 0 3 b. 0.57 0 3 c. 5.7 0 4 d. 57 0 5 38 8.58 0 5 Express the number in standard notation. a. 85800 b. 0.00008580 c. 858000 39 Calculate the expression ( 0.000044 ) ( 5000 ) 0.000076 Write the answer in scientific notation. a. 0.88 0 5 b. 8.8 0 5 c. 8.6 0 3 d. 8.8 0 4 40 Calculate the volume of a box that has dimensions of 5000, 900, 5600 millimeters. a..548 0 0 mm 3 b..548 0 mm 3 c..98 0 mm 3 4 Simplify the expression. 6 8 /4 a. b. 0 c. d. 3 5 7 PAGE 8
4 Simplify the expression. ( 7 ) /3 a. 30 b. 3 c. 7 d. 3 43 Simplify the expression. (9y ) / a. 3 y b. 3 y c. 9 y d. 3y e. 3 y 44 Simplify the expression 43x 5 3y 5 /5 a. 3x 3 b. 3x 4 c. 3x 3 d. y y y 3x 3 y 45 Simplify the expression. 6 3/ a. 67 b. 8 c. 9 d. 64 e. 66 46 Simplify the expression. 5 8 /3 4 4 5 8 5 4 50 5 PAGE 9
47 Simplify the expression. Assume that all variables represent positive numbers. ( 400s 0 ) / a. 0s 5 b. 0s 0 c. 30s 5 d. 400s 5 48 Simplify the expression. a 4/5 a /5 a 3/5 Write all answers without using negative exponents. Assume that all variables represent positive numbers. a. a /5 b. a 5/5 c. a /0 d. a 8/5 e. a /8 49 Simplify the radical expression. 4 6 a. 5 b. c. 3 d. 3 e. 50 Simplify the radical expression. 4 43 768 875 3 3 4 7 48 3 4 5 Simplify the expression. 80 5 a. 7 b. 6 c. 5 d. 4 5 PAGE 0
5 Simplify the expression. Assume that all variables represent positive numbers, so that no absolute value symbols are needed. 0y 3 49y 3 00y 9 a. 9y 5 b. y 50y 4 c. y 50y 5 d. y 50y 4 3 y 53 Simplify the expression. Assume that all variables represent positive numbers, so that no absolute value symbols are needed. 4 xy 5 + y 4 5xy 4 xy 5 a. 4y xy b. y xy c. 4y 4xy d. 8y 3xy 54 Rationalize the denominator and simplify. 5 a. 5 0 6 6 b. 5 5 6 c. 7 d. 6 e. 9 55 Rationalize the numerator and simplify. 3 e. 5 3 4 8 4 7 4 3 56 Simplify the expression. 4 8 4 5 4 3 3 4 5 57 Rationalize each denominator and simplify. 3 t 54 3 t 8 + 3 t 04 5 3 4t 5 3 4t 5 3 t 5 4 48 4 48 3 t PAGE
58 Simplify the radical expression. 6 5 a. 3 3 3 500 b. 6 5 c. 5 d. 5 e. 5 59 We can often multiply and divide radicals with different indexes. For example: 3 3 5 = 6 7 6 5 = 6 (7)(5) = 6 675 Use this idea to write the following expression as a single radical. 3 a. 6 3 6 6 b. 6 3 c. 3 d. e. 3 60 We can often multiply and divide radicals with different indexes. For example: 3 3 5 = 6 7 6 5 = 6 (7)(5) = 6 675 Use this idea to write the following expression as a single radical. 6 5 6 6 7 6 a. 080 b. 080 c. 080 d. 5 6 6 6 080 6 Give the degree of the polynomial. 5x 9 + 4x 978 + 3 a. 978 b. No defined degree c. 0 d. 9 6 Give the degree of the polynomial. 79 a. This is not a polynomial b. 0 c. No defined degree 63 Perform the operations and simplify. (9x 3 3x ) + (8x 3 5x) a. 9x 3 b. 7x 3x 5x 3 c. 7x 3 3x 5x d. 0 PAGE
64 Perform the operation and simplify. a (a + ) + 0a(a 5) a (a + 7) a. 0 b. 7a + 9a 4 50 c. 7a 3 9a 50 d. 7a 3 9a 50a 65 Perform the operation and simplify. (a 3) a. a 6a + 9 b. a 3a + 9 c. a 9 d. a + 6a + 9 e. a + 9 66 Perform the operation and simplify. (9r 0s) (4r 5rs 5s ) a. 36r 3 85r s + 3rs + 50s 3 c. 36r 3 + 85r s 3r s + 50s 3 b. 36r 3 + 85r s 3s 4 36s 3 d. 36r 3 + 85r s 3s 4 + 36s 3 67 Perform the operations and simplify (a / + b 7/ )(a / b 7/ ) a. (a b) 9 b. a 4 b 34 c. a b 7 d. (a + b) 68 Perform the operation and simplify (x / + y / ) a. x + y b. x x y + y c. x + x / y / + y d. x + x y + y 69 Rationalize the denominator 5 3 a. 5 + 5 b. 5 + 5 c. 5 5 d. 5 PAGE 3
70 Rationalize the denominator 3 5 a. 5 3 5 + 33 4 c. b. 5 3 5 + 33 + 4 d. 5 3 5 33 + 4 5 3 5 + 33 4 7 Rationalize the numerator. 7 5 5 3 7 + 4 7 4 7 + 4 3 7 4 7 Rationalize the numerator. x 6 x + x x 6 x + 66 6 x 6 x + 66 x 6 x 66 73 Perform the division and write the answer without using negative exponents 5a b 3 5ab 6 3a b 3 3ab 3 3 a. b. c. ab 3 d. 3a b 3 PAGE 4
74 Perform the division and write the answer without using negative exponents 3r s 5 t 3 40r 6 s t 8 4s 3 3 5 3 4s 4s 4s a. ` b. c. d. e. 5r 4 t 5 r 4 t 5 5r 4 t 6 5r 4 t 5 4 4s 5r 4 t 5 75 Perform division and write the answer without using negative exponents. 56x 6 y 4 z 9 4x 9 y 6 z 0 4z 9 4 9 4z 4z x 3 y x 3 y x 3 y 6 9 4z x 3 y 76 Perform the division and write the answer without using negative exponents. 360x 5 y 7 6x y 5 + 7xy 9x 5 y 4 a. 4y 3 4y + 7 x 3 x 4 y 9 c. b. 40y 3 4y + 8 x 3 x 4 y 3 d. 3 40y 40y + x 4 3 4y 40y + x 3 7 x 4 y 3 7 x 4 y 3 77 Perform the division. x + 3 3x 5x 7 a. 3x 4 b. 3x 4 c. 3x 3 d. 3 4x 78 Perform the division. x + x x 3 x 4x + 3 a. x 3 b. x 3 c. x 8 d. 8 x PAGE 5
79 Perform the division. x 3 x 3 0x 33x + 60 a. x b. x 0 c. 0 x d. x 0 80 Perform the division. x 5 43 x 3 a. x 4 + 3x 3 + 9x + 7x b. x 4 + 9x + 7x + 8 c. x 4 + 8 d. x 4 + 3x 3 +9x + 7x + 8 8 Complete the factoring formula. ax + bx = a. x + a + b b. x(a + b) c. xa + b d. x(a b) 8 Complete the factoring formula. x + xy + y a. (x + y) b. (x + x) c. (x + y) d. (x + y) 83 Factor the expression completely. 9x 8 a. 9(x + ) b. 9x + c. 9x d. 9(x ) 84 Factor the expression completely. 0x + 5x 3 a. 5x (3 + x) b. 5x ( + x ) c. 5x ( + x) d. 5x ( x) PAGE 6
85 Factor the expression completely. 4x 3 y 3 z 3 + 6x y z 64xyz a. 4xyz (x y z + 4xyz 6) c. 4xyz (x y z 4xyz + 6) b. 6xyz (x y z + 4xyz 6) d. 6xyz (x y z + 4xyz 4) 86 Factor the expression completely. 6x 3 + 6x 3x 3 a. (x + ) (3 6x ) b. (x + ) (6x 3) c. (x ) (6x +3) d. ( x) (6x 3) 87 Factor the expression completely. 8ax + 4ay 5bx 5by a. (x + 3y) (8a 5b) b. (3y x) (8a 5b) c. (x 3y) (8a + 5b) d. (x + 3y) (5b 8a) 88 Factor the expression completely. 64z 5 a. (8 z + 5) (8 z + 5) b. (8 z 5) (8 z 5) c. (8 z + 5) (5 8 z) d. (8 z + 5) (8 z 5) 89 Factor the expression completely. 5x 4 + a. (5x + ) b. (5x ) c. The expression is prime d. (5x + ) (5x ) PAGE 7
90 Factor the expression completely. z 4 a. (z + ) (z ) b. (z 4 + )(z )(z + ) c. (z 4 )(z )(z + ) d. (z + ) (z ) 9 Factor the expression completely. 9z + 30z + 5 a. (3z + 5) (3z 5) b. 5 (3 z + 5) c. (3z + 5) d. (3z 5) 9 Factor the expression completely. x + 7x + 6 a. (x + ) (x 6) b. (x + ) (x + 6) c. (x ) (x 6) d. (x + ) (x + ) 93 Factor the expression completely. 4x 3xy 40y a. (7x 8y) (5x + 6y) b. (7x 8y) (6x + 5y) c. (5x 8y) (6x + 7y) d. (7x + 8y) (6x 5y) 94 Factor the expression completely. 6r 36rs 70s a. (r 7s) (0r + 8s) b. (r 7s) (8r + 0s) c. (r + 7s) (8r 0s) d. (7r s) (8r + 0s) 95 Factor the expression completely. x + x 6 8 a. (x 6 4) (x 6 + ) b. (x 6 + ) (x 6 ) c. (x + 4) (x ) d. (x 6 + 4) (x 6 ) PAGE 8
96 Factor the expression completely. 36y n 5z 8n a. (6y n 5z 4 n ) (5y n + 6z 4 n ) c. (6y n 5z 4 n ) (6y n + 5z 4 n ) b. (5z 4 n 6y n ) (6y n + 5z 4 n ) d. (6y 4 n 5z n ) (6y 4 n + 5z n ) 97 Factor the expression completely. (x + y) 3 8 a. (x + y + ) (x xy + 4+ y + x + y) c. (x + y ) (x + xy + 4 + y + x + y) b. (x + y ) (x xy + 4 + y + x + y) d. (x + y ) (x + xy 4 + y + x + y) 98 Factor the expression completely. z + 4z + 4 36y a. (z + 9y) (z 9y) c. (z + 9y) (z + + 9y) b. (z + + 9y) (z + 9y) d. (z + 9 + y) (z + 9 y) 99 Factor the expression completely. (a + b) (a + b) 8 a. (a + b 4) (a + b + ) c. (a b 4) (a b + ) b. (a b + 4) (a + b + ) d. (a + b 4) (a + b ) PAGE 9
00 Factor the expression completely. 4x 4 + + 3x a. (x + x + ) (x x ) c. (x + x + ) (x x + ) b. (x + x ) (x x + ) d. (x x + ) (x x + ) 0 What fraction 6x 5y is equal to? 8xyz 4x a. ab b. c. c 36y x 0y 0 Perform the operations and simplify 3a 3 3b Assume that no denominators are 0. 3 43a a. b. c. 69b 3a b3 PAGE 0
03 Simplify the fraction 5x 5 x 5 Assume that denominator is not 0. 5 x x x 5 x 5 x + 5 5 x + 5 04 Simplify the fraction xy + 3x + 7y + x 3 + 343 Assume that denominator is not 0. y 3 y + 3 y + 7 a. x b. 7x 49 x c. 7x + 49 x d. 7x + 49 y 3 x 7x + 49 05 Perform the operations and simplify x 8 x x x + 8x + 8 Assume that no denominators are 0. x + 9x x + 9x x a. b. c. 9x d. x 9 x 8 x + 8 x 9x x + 9 PAGE
06 Perform the operations and simplify x + 7x x 7 x 49 x + 5 Assume that no denominators are 0. a. x 3 + 4x + 49x c. x + 5 x + 4x + 49 x + 5 x 3 4x b. + 49x d. x 5 x 3 + 4x x + 5 4x 07 Perform the operations and simplify x + 6x 7 x 4x + 49 x x 49 Assume that denominators are not 0. ( x + 7 ) a. c. x ( ) ( x + 7 ) ( x + ) b. d. x ( ) ( x 7 ) ( x 7 ) x + ( ) ( x + 7) ( x + 7 ) x + ( ) ( x 7 ) 08 Perform the operations and simplify ax + 5bx + 7a + 35b a + 0ab + 5b x 49 x 4x + 49 Assume that no denominators are 0. x 7 x 5 x + 7 a 5b a + 7b a + 5b x 7 a + 5b PAGE
09 Perform the operations and simplify x 3 + 6 x 4 x + 3x + 4 x + x x + 4x x 6x + 36 Assume that no denominators are 0. x + 7x x + 6x x a. b. c. 6x d. x + 6 x + 7 x + 7 x + 6x x 7 0 Simplify the expression 9 x + 6 + 8x + 6 x + 6 Assume that denominator is not 0. 8x + 5 8x 5 8x + 5 x 6 x + 6 x + 6 8x + 6 x + 5 Perform the operations and simplify 3x x 5 5 x 5 Assume that denominator is not 0. a. 3 b. 5 c. 5 d. 3 PAGE 3
Perform the operations and simplify x + 8 x + 4x + 48 + x x 36 Assume that no denominators are 0. x 6 x 36 x 6 a. x b. 36 x c. 6 x d. + 36 x + 6 x 36 3 Perform the operations and simplify 5x x 5 5 x + 5 Assume that no denominators are 0. 5 5 5 a. x b. + 5 x c. 5 x d. 5 5 x 5 4 Perform the operations and simplify x 5 + 3 x + 5 3x 5 x 5 Assume that no denominators are 0. 5 x + 5 x 5 x + 5 x + 5 PAGE 4
5 Perform the operations and simplify x 9y + x 9z 8z 8y ( x 9y )( x 9z ) Assume that no denominators are 0. 8z 8y a. 0 b. c. d. ( x 9y )( 9z x ) x 9y x 9z 6 Simplify the complex fraction. 5x y 5 0x 3 z 4 y 4 Assume that the denominators are not 0. x 5 4 y z x y 4 z x 4 a. b. c. y z d. x 4 y 3 z 4 7 Simplify the complex fraction. x 5x + 54 4x y x 8 4x y Assume that no denominators are 0. x 6 x + 6 x + 6 x + 9 x + 9 x 9 x 9 x 6 PAGE 5
8 Simplify each complex fraction x + 35 x x + + 35 x Assume that no denominators are 0. x 7 x + 5 x 5 x + 7 x 5 x + 5 x + 7 x 7 9 Write the expression without using negative exponents, and simplify the resulting complex fraction. Assume that denominator is not 0. y 4x + y x x x y + 4x 4y + x 4y + x x 4y x 0 Write the expression ( x + 0) + ( x ) ( x + 0 ) without using negative exponents, and simplify the resulting complex fraction. Assume that no denominators are 0. x + 9 x 9 x + 9 x x + x 0 9x + 9 x + PAGE 6
ANSWER KEY. d 6. b 3. c 46. b 6. a 76. b 9. c 06. a. a,d,e 7. b 3. c 47. a 6. b 77. b 9. b 07. d 3. f,g 8. a 33. b 48. a 63. c 78. a 93. b 08. d 4. b,f,g 9. a 34. c 49. b 64. d 79. b 94. b 09. b 5. a,c,d,e,f 0. e 35. c 50. d 65. a 80. d 95. d 0. c 6. a,g. a 36. a 5. c 66. a 8. b 96. c. d 7. a,f. a 37. c 5. b 67. c 8. d 97. c. a 8. e 3. c 38. c 53. a 68. c 83. d 98. b 3. b 9. e 4. c 39. d 54. a 69. b 84. c 99. a 4. a 0. f 5. c 40. b 55. e 70. a 85. a 00. c 5. a. d 6. d 4. a 56. c 7. c 86. b 0. c 6. c. e 7. b 4. d 57. b 7. c 87. a 0. b 7. a 3. a 8. c 43. a 58. c 73. a 88. d 03. d 8. c 4. b 9. d 44. d 59. c 74. a 89. c 04. b 9. c 5. c 30. c 45. d 60. c 75. a 90. b 05. d 0. a PAGE