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Pre-Algebra Practice Exam Semester One Remember! Take a deep breath and relax while you go through the problems Do not assume on the exam that if the answer is there it is automatically correct, check your work. Don’t forget PEMDAS Watch those darn negative signs! The procedure has not changed just because the problem is in the form of a story problem. Create an equation by breaking the problem into the bits and pieces. For that matter, the procedure hasn’t changed just because I use a fraction in an algebraic expression. I still multiply through and I still isolate the variable. Use the Glencoe Online Resources for practice in taking multiple choice tests. Log on to http://glencoe.mcgraw-hill.com/sites/0078885159/ and click on the Chapter Tests and Self-Check Quizzes. Personal Tutor and Vocabulary Review are also great helps. When reviewing problems from the textbook, the Hotmath Homework Help link found in the Glencoe Online Resources is another great help. Here you will find step-by-step solutions, with hints, to ALL odd-numbered problems in the text. Note!! A (***) indicates a repeating decimal 1. Write a numerical expression for the verbal phrase; the total number of gumballs if Joe has nineteen and Sue has thirteen. 1.1 19 + 13 2. Evaluate each expression: 1.1 4[(12 – 4) + 2] 40 3. 2 x 9 ÷ 3 6 4. 15 – 5 6–4 5 5. 16 ÷ 4 + 15 19 6. Translate into an algebraic expression; 1.2 1) the quotient of a number and three. 2) the difference of six and a number 3) 12 less than a number 4) a number less three n÷3 6-n n – 12 n–3 7. Amusement park Gold Reef City charges $25.00 for the first ticket and $7.00 for each additional ticket. Write an expression used to calculate the total price to enter the park. Then calculate the total for 13 people to have fun at the park. 1.2 25 + 7t 13 people would cost $109.00 8. Find each sum or difference and write in simplest form. 3.6 9 1 10 2 Solutions: 9 1 5 10 2 5 9 5 14 10 10 10 4 2 or 1 1 10 5 3 5 4 16 34 5 4 4 16 12 5 16 16 7 16 1 7 9. 7 2 2 10 11 4 3 15 12 7 3 15 6 7 2 35 15 2 6 5 14 15 30 30 29 30 3 1 5 16 12 4 4 3 5 15 4 12 5 16 15 60 60 31 60 11 1 14 6 Solutions: 4 4 5 6 5 48 13 21 10. Express the following ordered pairs as a table & give the domain and range 1.4 {(1,4), (2,8), (3,12), (4,16)} X 1 2 3 4 Y 4 8 12 16 D = {1, 2, 3, 4} R = {4, 8, 12, 16} 11. If one roll of quarters contains 40 quarters, then write an equation that can be used to find the number of quarters, q, in any number of rolls, r, of quarters. r = 40q 12. Simplify these algebraic expressions: 4.4 7y = 56 -3r = 12 n/-2 = -30 3r 12 3 3 7 y 56 7 7 y=8 (2) r = -4 n (30)(2) 2 n = 60 n 0 8 21 p 231 21 p 231 21 21 n (8) (0)(8) 8 n=0 p = 11 13. Number Sense: What type of relationship is shown on a graph that shows the following values? 1.6 As x increases, y decreases : negative As x decreases, y decreases : positive 14. Solve using the distributive property. 4.3 Sebastien had a bake sale to raise money for the French Club and made $16.25. If he sold 25 rice krispie bars for 25 cents and 20 muffins, how much did he charge for the muffins? (25)(.25) + 20x = $16.25 $6.25 + 20x = $16.25 -6.25 -6.25 20x = $10.00 ÷ 20 ÷ 20 x = $.50 15. Write an integer for each situation 2.1 4 inches less than normal -4 14 degrees above normal + 14 a loss of 15 yards - 15 16. Select the appropriate symbol to make the statements true, <, >, = 2.1 8 3 -3 0 -7 -3 -6 -6 < < < = 17. Evaluate each expression 2.1 | -5 | | 12 | 5 12 | -4 | - | -10 | | 20 | - | 10 | -6 10 if a = 4, b = 3, c = -3 | ac | - | b | |(4) (-3)| - 3, 12-3 = 9 18. Find each product. Write in simplest form. 3.3 3 1 4 4 Solutions: 3 16 2 3 4 12 20 3 100 6 1 48 8 p 1 19. 4 q 60 6 100 10 140 1 420 3 1 2 4x st 3 2 9u s 2 x 3st t 2 3us 9us 2x 1 2x 4x 2 Solutions: p 4q 14 10 15 28 1 20. Evaluate each expression if a= -2 ½, b= 3 , c = 2 ¾. Write the product in simplest form. 3 ab Solutions: 1 1 2 3 2 3 5 10 2 3 50 2 1 8 8 6 6 3 1 4 b 4 1 1 4 3 4 3 17 10 4 3 170 2 1 14 14 12 12 6 21. Evaluate each expression if a = 9, b = 4, c = 11 : 1.2 1 1 abc 9 1 1 3 1 1 2 3 2 2 3 4 9 10 5 10 11 9 2 3 4 100 25 50 110 5500 25 25 216 54 18 12 216 2c – 5 17 ab 6 6 45 - bc 3 4b + 3c – 5a 4 22. Find the sum 2.2 -4 + (-4) = 5 + (-4) = -34 + 17 = -10 + 8 + 10 = -1 -17 8 -8 23. Use the distributive property to write each expression as an equivalent expression. Then evaluate. 4.1 4(10 + 3) (-10 + 7) 3 4(10) + 4(3) 40 + 12 = 52 -10(3) + 7 (3) -30 + 21 = -9 24. -8 (u – 2) (b – 1) -4 -8u – (-16) -8u + 16 -4b – (-4) -4b + 4 (-8)(70 – 3) (1 -75) -2 -8(70) – (3)(-8) -560 – (-24) -560 + 24 = - 536 50(x + 1) 1(-2) – 75 (-2) (-2) – (-150) -2 + 150 = 148 -18 (-r – 5) 50x +50 -18r – (-18)(5) -18r + 90 25. Find the difference 2.3 -25 – (-30) -10 – (5) -22 – 33 8 – (-3) 5 -15 -55 11 26. if a = 6, b = 3, c = -1 a–9 6 – 9 = -3 c–b -1 – 3 = -4 b–a–c 3 – 6 – (-1) = -2 c–b+a -1 – 3 + 6 = 2 27. Find each product 2.4 0 (-5) -1 ( -40) -8 (-2)(-1) 0 40 -16 28. (-5) (9v) 24 (-27y) (-z) 29g (2)(-2)(0)(-3) 27yz 0 -45v (- 4)(-6) (-20m)(- 2)(-3n) -120mn 29. Name the property shown by the following statements; 1.3 56 + 6 = 6 + 56 Commutative Property of Addition (x + 4) + y = x + (4 + y) Associative Property of Addition (1) (mp) = mp Multiplicative Identity (7n) (0) = 0 Multiplicative Property of Zero 30. Find each quotient and write in simplest form. 3.4 1 1 2 10 3 3 8 9 5 31. 0 1 1/8 2x 1 3 9 ab b 8 a 6x 17 18 2 4 3 9 27 0 -21 ¾ 3st 4t r r 2x 4 y y a²/8 3s/4 -x/2 32. Evaluate each expression 2.5 If x = -4 and y = -8 6x ÷ y -4x 2 2x y 2xy ( y) 6(- 4) ÷ -8 = 3 -4 (- 4) = 8 2 2(- 4) = 1 -8 2(-4)(-8) = -8 -8 33. Write an expression for each problem and then solve Sebastien wants to buy an Ipod for $205.00 and he makes $5.00/week in allowance. If he already has $45.00, how long will it take him to save up the money to buy the Ipod? 5x + 45 = $205.00 5x = $160.00 x = 32 weeks let x = number of weeks 34. The temperature dropped 24 degrees over the course of 6 hours. What was the “mean” hourly drop? 24 ÷ 6 = an average of 4 degrees per hour 35. What is the mean number of video games the kids have? Sebastien had 16 video games Vanessa had 21 video games 16 + 21 + 24 + 20 = 20.25 games Zachary had 24 video games Liesel had 20 video games 36. Write each fraction as a decimal 3.1 3 5 1 8 0.6 9 11 0.125 0.81 -5 12 7 9 -0.416 0.7 1 3 -2 3 0.3 - 0. 37. Select the appropriate symbol to make the statements true, <, >, = 3.1 - 13 2 -6.4 < 6 7 5 6 -0.75 > - 15 20 = -3 8 - 0.40 > 38. Arrange the following in order of least to greatest. 3.1 - 8 - 8 - 0.80*** 9 , 10, -8 - 0.80 9, -8 10 39. List which of the following numbers ( -3, -1.60, 0, 45, ¾, 2.56***, 777) are 3.2 A natural number: 45, 777 A whole number: An Integer: 0, 45, 777 -3, 0, 45, 777 A rational number: -3, -1.60, 0, 45, ¾, 2.56***, 777 40. What would be an example of an irrational number? Pi, 1.313313331… 41. Solve each equation and check your solution: 5.2 14m = 18 + 12m -2h -16 =3h – 6 2y + 7 = y 14m = 18 + 12m -12m = -12m 2m = 18 ÷2 = ÷2 m=9 -2h -16 =3h – 6 +2h = +2h -16 = 5h -6 +6 = +6 -10 = 5h ÷5=÷5 2=h h = -2 2y + 7 = y -7 = y -7 2y = y -7 -y = -y y = -7 14(9) = 18 + 12(9) 126 = 18 + 108 126 = 126 -2(-2) -16 = {3(-2)} -6 4 – 16 = - 6 – (6) -12 = -12 2 (-7) + 7 =-7 -14 + 7 = -7 -7 = -7 42. Translate the verbal expression into an algebraic expression, then simplify: 1.3 The sum of three times a number and three added to ten times a number. 3n + 3 + 10n 13n + 3 The product of eight and four times a number multiplied by six. 6(8 x 4n) 6(32n) = 192n 43. Copy and complete a function table. Then state the domain and range of the function. 1.5 Each ticket to the Spring Musical costs $8.00 Number of Tickets Total Cost ($) Input Output answers: 32 56 72 96 D: {4, 7, 9, 12} R: {32, 56, 72, 96} 44. Write each number as a fraction. 3.2 -7 ½ 3¼ 2¾ -15/2 13/4 11/4 45. Find each quotient 2.5 -21 ÷ 21 80 ÷ (- 4) -64 ÷ (- 8) -1 -20 8 46. -100 -5 20 -49 ÷ 7 -7 90 -6 -72 9 215 5 -15 -8 43 47. Find the multiplicative inverse of each number: 3.4 - 6/7 10/20 -33 4¼ - 7/6 or – 1 1/6 20/10 or 2 - 1/33 4/17 48. Simplify these algebraic expressions: 4.2 & 4.3 h + 5h – 3 – 5h 9 – t -3(t + 3) -11x + 4 +8x -4 + 3x b – 2(b – 2) 6h – 3 – 5h 6h – 5h -3 = h – 3 9 – t -3t – 9 -4t +9 – 9 = -4t -11x + 4 + 11x -4 -11x + 11x + 4 – 4 = 0 b -2b – 4 -b – 4 49. z + 5 = 12 -5 = -5 z=7 r – 16 = -16 +16 = +16 r=0 50. Simplify each expression: 1.3 b(4 x 6) = 24b y – (-12) = 0 y + 12 = 0 -12 -12 y = -12 p – 21 = -2 +21 +21 p = 19 25 + (15 + s) = 40 + s (6 x r) x 5 = 30r 51. Simplify these algebraic expressions: 4.5 52. 5d – 9 = -24 +9 = +9 5d = - 15 ÷5=÷5 d = -3 w/2 – 16 = 5 + 16 = + 16 w/2 = 21 (2)(w/2) = 21(2) w = 42 n/5 + 4 = -11 - 4 = -4 n/5 = -15 (5)(n/5) = (-15)(5) n = -65 53. Find each sum or difference: chapter 0.3 25.72 + 18.67 = 25.54 + 36.7 = 44.39 4865.7 + 705.76 = 62.24 5571.46 54. 458.07 – 67.75 = 73.2 – 42.86 = 390.32 30.34 852 – 469.72 = 382.28 55. Find each sum or difference and write in simplest form. 3.5 5/10 – 3/10 3/10 2/9 - 6/9 2/10 = 1/5 -4/9 -7/9 -4/9 -8 7/10 + 2 -11/.9 = -1 2/9 -6 2/5 56. Find the product or quotient: 0.3 6.2 x 3.9 = 24.18 57. 92.4 ÷ 5.5 16.8 49 x 3.7 = 181.3 382.1565 ÷ 36.57 = 10.45 6.535 x 3.7 = 24.1795 6482.84 ÷ 46.22 140.2604933 58. Make the following conversions: 0.6 1 yd = ____ft. 4 ft = ____in. 3 ft. ____mm = 34 cm 48 in. 340mm 59. Number Sense: 0.2 The product of 2 consecutive even integers is 1088. What are the integers? This is meant to be a Guess and Check problem. The answer is 32 & 24 60. Find the perimeter and area for each figure described. 5.1 A square with a side = 5 cm A rectangle with side a = 6ft and b = 9 ft P = 5 + 5 + 5 + 5 = 20 cm P = 6 + 6 + 9 + 9 = 30 ft A = 5 x 5 = 25 cm² A = 6 x 9 = 54 ft² 61. A Right triangle where a is the height = 14, b is the base = 48, c = 50 cm P = 14 + 48 + 50 = 112 cm A = ½ (48) (14) = 24 x 14 = 336 cm² 62. Find the perimeter and area for each figure described. 5.1 A triangle where a is the height = 17, b is the base = 21, c = 23 ft P = 17 + 21 + 23 = 61 ft A = ½ (21) (17) = 10.5 x 17 = 178.5 63. Find the missing dimension: 5.1 A right triangle where a is the height is = 36 cm, b is the base = ?, c = 60cm and the area = 864cm² What is the measurement of the base? ½ (b) x 36 = 864 cm² ÷ 36 = ÷ 36 (1/2)b = 24 2/1) (1/2)b = 24 (2/1) b = 48 cm 64. Find the missing dimension: 5.1 A rectangle has side a = 14 ft and area = 68 ft², what is the measure of side b? A = (side a) (side b) 68 ft² = 14b ÷ 14 = ÷ 14 b = 17 ft 65. Define a variable and write an equation to find each number. Then solve. 5.2 Four times a number is 21 more than the number. What is the number Let x = a number 4x = 21 + x -x = -x 3x = 21 ÷3 = ÷3 x=7 4 (7) = 21 + 7 28 = 21 + 7 28 = 28 66. Define a variable and write an equation to find each number. Then solve. 5.2 Eight less than three times a number = that number. What is the number 3x – 8 = x +8 = +8 3x = 8 + x -x = -x 2x = 8 x=4 Let x = a number 3(4) – 8 = 4 12 – 8 = 4 4=4 67. Do Example 2, numbers 20-26 on page 28 in the Textbook 1.4 L (2,4) N (2,1) Q (3,7) S 68. Scatter Plots: 1.6 (5,0) Complete #11 on page 44 and Refer to the answers in the back of the book 69. Do the following problems in the textbook for 2.6 and 2.7, see your homework, quizzes or tests for additional problems. Page 98, numbers 20, 22, 24, 26 (only name the coordinate) 20. II 22. I 24. III 26. None 70. Page 105, numbers 10, 11, 12 10. Translation 5 units to the right 11. reflection over the x-axis 12. Translation 5 units to the left and 4 units down