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Math Placement Test Practice: Elementary

Operations with (Evaluate each .)

1. | 7| | | 2. −7 3. | 7|

4. 2− −+ 1 5 6 5. ( 3) 6( 2) 4 ( 8) ( ) 6. 32− −÷ 5− 3− (−2) − − 2 7. 3 12 ÷−3 2 +∙ −2 15 ÷ 3 − ∙ ∙ Operations with Fractions (Evaluate each expression.)

( ) 8. 4 6−1 2 3 −9 9. 3 2 −8 2 2 10. 2 +−3 + 4 3 2 11. 5 ÷ 10 3 2 2 5 1 12. 5 + 3 ∙ ÷3 ∙ 3 1 2 8 1 23 + 6�5 5� 7− �2 ∙ � 13. 2 14. (2 5∙ �)4÷−4 � 2 15. − + 3 1 3 2 16. �2 − 52� ÷ + 1 4 3 �3 − � �− 9 2�

Percentages, Decimals, and Fractions

17. Order from least to greatest: , , , , , 1 1 3 3 4 8 18. Write as a decimal. 3 4 4 5 6 10 3 19. Write 8120% as a simplified fraction. 20. 4 is 25% of what ? 21. 15 is what percent of 40? 22. What is 84% of 600?

Geometric Computations

23. Find the area and perimeter of a rectangle that is 6 by 9 .

24. Find the exact area and of a with𝑓𝑓𝑓𝑓 a 𝑓𝑓𝑓𝑓 of 8 . Also compute the approximate values to the nearest thousandth. 𝑐𝑐𝑐𝑐 25. Find the area of the triangle shown 5 cm 5 cm 4 cm

6 cm

Operations with Algebraic Expressions

Simplify each expression

26. (4 + 6 + 9 8) (6 9 7 + 3) ( 3 ) 2 ( ) 4 2 27. 5 𝑥𝑥 + 3𝑥𝑥 𝑥𝑥+− +−8(6𝑥𝑥 −) 𝑥𝑥 − 𝑥𝑥 (2 ) 2 28. 6𝑎𝑎 13 +− 𝑎𝑎 𝑎𝑎 − 𝑎𝑎 ( ) 29. 4− 11𝑐𝑐 𝑓𝑓 6 + 25 30. (3𝑥𝑥 − + 7𝑥𝑥 − 2)( + 6) 2 31. (9𝑥𝑥 + 3)(𝑥𝑥9− 3𝑥𝑥) 32. ( 𝑎𝑎+ 3 ) 𝑎𝑎 − 2 33. Evaluate𝑎𝑎 𝑏𝑏 2 for = 3 and = 4 2 𝑥𝑥 − 𝑦𝑦 𝑥𝑥 − 𝑦𝑦 −

Operations with Exponents and Roots

34. Write 54,900,000 in scientific notation? 35. What is 1,200,000 ÷ 3,000 0.0000002 in scientific notation?

36. If = 3, then what is x? ∙ 37. If √𝑥𝑥 = 2, then what is x? 3 38. Simplify√𝑥𝑥 3 + 3 39. Simplify √4 7 +√3 7 40. Simplify 2√11 √7 11 41. Simplify √13 −2 √ ( ) 42. Simplify √using∙ only√ positive exponents ( ) ( ) 4 −3 2 2 2 5 0 𝑥𝑥𝑦𝑦 𝑥𝑥 𝑦𝑦 𝑥𝑥 𝑦𝑦 43. Simplify using only positive exponents 3 −2 9𝑥𝑥 𝑦𝑦 2 −1 2 �4𝑥𝑥 𝑦𝑦 𝑧𝑧 � 44. Perform the ; write the product as a sum of terms: 3 2 15𝑥𝑥 +6𝑥𝑥 −9𝑥𝑥 2 −3𝑥𝑥

Factoring

45. 50 18 3 46. 𝑥𝑥 16− 𝑥𝑥 4 47. 6𝑥𝑥 − 15 + 8 20 3 2 48. 𝑥𝑥 +− 5 +𝑥𝑥 6 𝑥𝑥 − 2 49. –𝑥𝑥 + 3𝑥𝑥 + 18 2 50. 4𝑥𝑥 20𝑥𝑥 + 25 2 51. 6𝑥𝑥 −+ 7 𝑥𝑥+ 2 2 52. 𝑥𝑥 + 𝑥𝑥 12 2 2 𝑥𝑥 𝑥𝑥𝑥𝑥 − 𝑦𝑦 Operations with Rational Expressions

53. 2 𝑥𝑥 −5𝑥𝑥+4 −18𝑥𝑥 2 9 ÷ ∙ 𝑥𝑥 −8𝑥𝑥+16 54. 2 𝑥𝑥 −16 𝑥𝑥+4 𝑥𝑥+2 ÷ 6𝑥𝑥+12 55. 2 2 𝑥𝑥 −8𝑥𝑥 𝑥𝑥 −16𝑥𝑥+64 3 7 2 56. 𝑥𝑥−+1 𝑥𝑥 −1 𝑦𝑦 5𝑦𝑦 5 57. 𝑥𝑥 𝑥𝑥 − 4𝑥𝑥 3 58. 𝑥𝑥−1 − 1−𝑥𝑥 1 𝑥𝑥−1 2 59. 𝑥𝑥2+4 −+𝑥𝑥 +4𝑥𝑥 +4 1 4 − 𝑥𝑥 𝑥𝑥−3 60. 2 6𝑥𝑥 + 7𝑥𝑥+2 1+2𝑥𝑥 61. 𝑥𝑥2+𝑥𝑥 𝑥𝑥2+𝑥𝑥−12 4𝑥𝑥+4 𝑥𝑥2−6𝑥𝑥+9

Solving and Inequalities

62. 12 + = 4 6 2( + 5) + 3 = 20 5 63. 𝑥𝑥 𝑥𝑥 − 64. 𝑥𝑥+ 4 > 7 𝑥𝑥 − 𝑥𝑥 𝑥𝑥 65. −26 + 9 5

66. 𝑥𝑥 ≤+ 𝑥𝑥 = + 2 1 1 1 1 67. 32−+�3 𝑥𝑥 3�= 6+ 2 𝑥𝑥 1 2 5 68. 𝑥𝑥 3 𝑥𝑥 − 5 =𝑥𝑥 2 3 4 1 69. 2𝑥𝑥−10+− 3𝑥𝑥=−15 10 4 2 3𝑥𝑥+12 2 70. 𝑥𝑥+3+ 7𝑥𝑥+1= 18𝑥𝑥 +4𝑥𝑥+3 2 71. (𝑥𝑥 3)𝑥𝑥 =25 2 72. 𝑥𝑥 −5 = 4 3 73. 𝑥𝑥 − + 𝑥𝑥−3= 𝑥𝑥 1 1 𝑥𝑥+11 𝑥𝑥+5 𝑥𝑥+11

Solving Systems of Equations

Solve each system. Tell the number of solutions. Also, describe the lines as intersection, parallel or same line. 3 = 12 74. 2 + 6 = 18 𝑥𝑥 − 𝑦𝑦 � 5 = 6 75. −4 𝑥𝑥 3 𝑦𝑦= 10− 𝑦𝑦 − 𝑥𝑥 � 2 + 3 = 9 76. 6𝑥𝑥 − 9𝑦𝑦 = 27 −2 𝑥𝑥+ 3 𝑦𝑦= 8 77. � 3𝑥𝑥 −+ 4𝑦𝑦 =−13 𝑣𝑣 𝑤𝑤 � 𝑣𝑣 𝑤𝑤 Linear Functions and Their Graphs

78. On the line 2 + 3 = 10, find the missing coordinates for the points (3, __) and (__, 2).

79. Find the x-intercept𝑦𝑦 𝑥𝑥 and y-intercept of 3 6 = 12. Use the intercepts to graph the− line. 80. Write the line 3 + 5 + 10 = 0 in slope𝑥𝑥 intercept− 𝑦𝑦 form. Identify the slope and y-intercept and use them to graph𝑥𝑥 the𝑦𝑦 line. 81. Graph the solution to the linear inequality 4 2 > 6

𝑥𝑥 − 𝑦𝑦 − 82. Find the of the line in slope-intercept form through the points (3, 2) and (9,2).

83. Find the equation of a line perpendicular to 4 + = 3 through the point (−8,6) 𝑥𝑥 𝑦𝑦 Applications

84. Write the algebraic expression for this phrase: The quotient of 9 and the quantity of a number increased by three. 85. Write the algebraic expression for this phrase: Three times the quantity 8 less than a number.

For each problem write and solve an algebraic equation or system of equations.

86. One less than the product of negative seven and a number is equal to twenty-seven. Find the number. 87. You buy two pairs of shoes for $145. One pairs costs four times the other pair. Find the price of each pair of shoes. 88. The length of a rectangle is 5 less than twice its width. The perimeter is 26 cm. What are the dimensions of the rectangle? 89. If it takes Roadrunner 5 minutes to mow a lawn and it takes Wily Coyote 30 minutes, how long does it take the two of them to mow the lawn if they work together? 90. A dark chocolate of 55% is made by mixing an 85% dark chocolate and a 47.5% dark chocolate. If ten pounds of the 55% mixture is desired, how many pounds of 85% and 47.5% must be mixed. 91. A truck travels 150 miles on 12 gallons of gasoline. How many gallons of gasoline are needed to travel 500 miles? 92. A school has a policy that two adults must accompany every 15 students on school trips. Not counting the bus drivers, how many seats are needed for a school trip with 180 students?

Solve the following

93. Find the diagonal length of an eight-inch by ten-inch piece of paper. 94. The number of math students is currently 4235. A year ago there were 4380. Find the percent change in the number of math students. 95. Four people are in line to purchase concert tickets which cost $12.50 each. While in line, they discover that they can purchase 5 tickets for $55. How much could each person save if the found a fifth person to share the cost? 96. John went to the store and bought 3 pounds of pork, 2.75 pounds of chicken, pounds of 1 7 cheese and 3 pounds of beef. How many2 total pounds did John buy at the store?12 (Write your answer as a mixed number.) 97. The sales tax rate in Denver is 7%. A new laptop is sold for $505.00? What will the total cost of the purchase be? 98. Justin’s math class has four 100-point chapter tests and a 200-point final exam. On the four class tests he got 90, 77, 65 and 72. What must he score on the final exam to earn a final grade of 80% Report your answer as both points and percent? 99. There are 32 students in a classroom. 37.5% of the class earned a B or better on the last exam. How many students did NOT earn a B or better? 100. Joe earned an average of 84 in his math class. All his test scores combined added up to 588 total points. How many tests were given in his math class? 101. A family spent $208 one month on food. This was 26% of its income. What was its income? 102. On a test with 88 questions, a student got 77 correct. What percent of the items were correct? 103. Tim missed 12 questions on his biology test and his score was 84%. How many questions were on the test?

Answers

1. 7 2. 7 3. -7 4. 33 5. 19 6. -16 7. 5 8. Undefined 9. 0 10. 53 11. 30 4 12. 25 3 13. -36 − 4 14. 23 15. − 4 301 16. 100 30 17. −, 19, , , , 1 1 3 4 3 4 18. 40.3753 5 6 4 5 19. 6 20. 516 21. 37.5% 22. 504 23. = 54 ; = 30 24. = 16 2 50.265 ; = 8 25.133 𝐴𝐴 𝑓𝑓𝑓𝑓 𝑃𝑃 𝑓𝑓𝑓𝑓 25. 12 2 2 𝐴𝐴 𝜋𝜋 𝑐𝑐𝑐𝑐 ≈ 𝑐𝑐𝑐𝑐 𝐶𝐶 𝜋𝜋 𝑐𝑐𝑐𝑐 ≈ 𝑐𝑐𝑐𝑐 26. 6 +2 4 + 15 + 16 11 𝑐𝑐𝑐𝑐 27. 4 4 9 +363 2 − 𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑥𝑥 − 28. 782 6 𝑎𝑎 − 𝑎𝑎 29. 7 + 31 − 𝑐𝑐 − 𝑓𝑓 30. 3 + 25 + 40 12 − 𝑥𝑥 31. 813 9 2 𝑥𝑥 𝑥𝑥 𝑥𝑥 − 32. +2 6 + 9 𝑎𝑎 − 33. 222 2 𝑎𝑎 𝑎𝑎𝑎𝑎 𝑏𝑏 34. 5.49 10 35. 8.0 10 7 𝑥𝑥 36. = 9 −5 𝑥𝑥 37. = 8 𝑥𝑥 38. 2 3 𝑥𝑥 √ 39. 7 7 40. 5 11 √ 41. 26 − √ 42. √𝑥𝑥 8 𝑦𝑦 43. 4 16𝑧𝑧 2 4 44. 815𝑥𝑥 𝑦𝑦 2 + 3 45. 2 (5 3)(5 + 3) − 𝑥𝑥 − 𝑥𝑥 46. ( + 4)( + 2)( 2) 𝑥𝑥 𝑥𝑥 − 𝑥𝑥 47. (32 + 4)(2 5) 𝑥𝑥 𝑥𝑥 𝑥𝑥 − 48. ( +2 2)( + 3) 𝑥𝑥 𝑥𝑥 − 49. ( 6)( + 3) 𝑥𝑥 𝑥𝑥 50. (2 5) − 𝑥𝑥 − 𝑥𝑥 51. (2 + 1)(23 + 2) 𝑥𝑥 − 52. ( + 4 )( 3 ) 𝑥𝑥 ( ) 𝑥𝑥 53. 𝑥𝑥2𝑥𝑥 𝑥𝑥−𝑦𝑦1 𝑥𝑥 − 𝑦𝑦 54. 6( 4) − 𝑥𝑥−4 ( ) 55. 𝑥𝑥 − 𝑥𝑥 𝑥𝑥+1 56. 𝑥𝑥−8 8𝑦𝑦−7𝑥𝑥 57. 5𝑥𝑥 4𝑥𝑥+3 58. (𝑥𝑥−1 )( ) 𝑥𝑥+8 2 59. 𝑥𝑥+4 𝑥𝑥+2 2( ) 2𝑥𝑥 −3𝑥𝑥+3 60. 3𝑥𝑥 𝑥𝑥+−32 ( ) 61. (𝑥𝑥 ) 𝑥𝑥 𝑥𝑥−3 62. 4 𝑥𝑥=+46 63. = 1 𝑥𝑥 64. < 18 𝑥𝑥 65. 3 𝑥𝑥 − 66. = 𝑥𝑥 ≥ 1 67. 𝑥𝑥 = 5 87 68. 𝑥𝑥 = 40 20 69. 𝑥𝑥 = 3 2 70. = 9, 2 𝑥𝑥 3 71. = 2,8 𝑥𝑥 − 72. = , 2 𝑥𝑥 6− 73. = 3, 2 𝑥𝑥 5 74. , 𝑥𝑥 − − 𝑁𝑁𝑁𝑁 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 75. (4,2), 76. , 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 77. = 7, = 2, 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 3, , 2 78. 𝑣𝑣 𝑤𝑤 − 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑖𝑖 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 1 14 79. x-intercept: (4,0); y-intercept: (0, 2) � 2� 𝑎𝑎𝑎𝑎𝑎𝑎 � 3 − � −

80. = 2, = , = 2 3 3 𝑦𝑦 − 5 𝑥𝑥 − 𝑚𝑚 − 5 𝑏𝑏 −

81. Graph of the linear inequality

82. = 4 2 83. 𝑦𝑦 = 3 𝑥𝑥 −+ 4 1 84. 9 ÷ ( + 3) 𝑦𝑦 4 𝑥𝑥 85. 3 ( 8) 𝑥𝑥 86. 7 1 = 27; = 4 ∙ 𝑥𝑥 − 87. + = 145; = 4 ; = 29; = 116 − 𝑥𝑥 − 𝑥𝑥 − 88. 2 + 2 = 26; = 2 5; = 6 ; = 7 𝑥𝑥 𝑦𝑦 𝑥𝑥 𝑦𝑦 𝑦𝑦 𝑥𝑥 89. + = ; = min 4.29 1 𝐿𝐿 1 𝑊𝑊1 30𝐿𝐿 𝑊𝑊 − 𝑊𝑊 𝑐𝑐𝑐𝑐 𝐿𝐿 𝑐𝑐𝑐𝑐 90. + = 10; 0.85 + 0.475 = 0.55(10); = 2 85%; = 8 47.5% 5 30 𝑥𝑥 𝑥𝑥 7 ≈ 𝑚𝑚𝑚𝑚𝑚𝑚 91. = ; = 40 𝑥𝑥12 𝑦𝑦 𝑥𝑥 𝑥𝑥 𝑦𝑦 𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙 𝑜𝑜𝑜𝑜 𝑦𝑦 𝑙𝑙𝑙𝑙𝑙𝑙 𝑜𝑜𝑜𝑜 92. 150= 500; 𝑥𝑥= 24 𝑔𝑔𝑔𝑔𝑔𝑔 ; = 204 2 𝑥𝑥 164 = 2 41 12.81 93. 15 18 𝑥𝑥 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 94. 3.31% √ 𝑖𝑖𝑖𝑖 √ 𝑖𝑖𝑖𝑖 ≈ 𝑖𝑖𝑖𝑖 95. $1.50/ticket ≈ − 96. 9 5 97. $540.35 6 𝑙𝑙𝑙𝑙 98. 176 points, which is 88% 99. 20 100. 7 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 101. $800 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 102. 87.5% 103. 75

𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞