Pattern & Algebra Practice Problems

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1 Pattern & Algebra Practice Problems Solve Linear Inequalities 1. Solve for x. A. x > -3 B. x > 0 C. x < 0 D. x < -3 4x < x Symbolize Problem Situations 2. Scott is draining his swimming pool. The pool contains 14,000 gallons of water. It can be drained at a rate of 8 gallons per minute. If x represents the number of minutes the pool has been draining, and y represents the amount of water in the pool, which of the following is correct about the y-intercept of the graph relative to this situation? A. The y-intercept represents the rate at which the pool can be drained. B. The y-intercept represents the amount of water in the pool after it has been drained. C. The y-intercept represents the amount of water in the pool before it has been drained. D. The y-intercept represents the number of minutes it takes to drain the pool. Solve Linear Equations 3. Given the formula below, solve for m. y = mx + b A. m = xy + b B. m = C. m = b - y x x y - b

2 D. m = y - b x Solve Linear Inequalities 4. Solve for x. A. x > 5 B. x < 5 C. x > 6 D. x < 6 7x > 35 Evaluate Expressions 5. If a = 1, b = 4, and c = 3, what is the value of the following expression? (a + b) c 3 A. 30 B. 19 C. 27 D. 51 Graphing on Number Lines Which inequality is graphed on the number line? A. x > 1 B. x < 1 C. x > 1 D. x < 1

3 Evaluate Expressions 7. If a = 12, b = 20, and c = 2, what is the value of the following expression? A. -41 B. 14 C. -39 D. 2 Symbolize Problem Situations 8. A company sells snack bags that contain a mixture of almonds and walnuts. There are 12 almonds per bag and 8 walnuts per bag. If x represents the number of snack bags the company sells, which of the following equations can be used to find the total number of nuts needed to fill the snack bags? A. y = 12x + 8 B. y = 8x + 12 C. y = x + 20 D. y = 20x Solve Linear Equations 9. Which value for x makes the sentence true? 2(x - 1) = 6 A. 3 1 / 2 B. 2 C. 4 D. 6 Properties of Arithmetic 10. Which of the following shows the Inverse Property of Multiplication?

4 A. B. C. ( ) D. Patterns 11. What are the first four terms of the sequence defined by the following equation? A. 12, 36, 108, B. 4, 12, 36, C. 12, 144, 1,728, 20, D. 4, 12, 144, 1, Patterns 12. The following rule describes an arithmetic sequence where the first term is 11. Which of the following is the tenth term? A. 7 B. 6 C D. 6.5 NEXT = NOW Properties of Arithmetic 13. If a = b, then which of the following expressions is equivalent to a + c? A. b + c

5 B. b - c C. a b D. a + b Translate Expressions, Equations, & Inequalities N / 8 = 7 Which of the following sentences represents the equation above? Two decreased by the quotient of a number and 8 is 7. A. Two increased by the product of a number and 8 is 7. B. Two increased by the quotient of a number and 8 is 7. C. Eight increased by the quotient of a number and 2 is 7. D. Translate Expressions, Equations, & Inequalities 15. Which of the following expressions represents the statement below? A. 5 - N 2 B. 5 + N 2 five minus the square of a number C. D. (5 - N) 2 Properties of Arithmetic 16. Which property is illustrated by the following statements?

6 A. multiplicative inverse property B. multiplication property of inequalities C. multiplicative identity property D. associative property of multiplication Change in Variable 17. The Hydro water department has a monthly service charge of $13.30 and a volume charge of $1.66 for every 100 cubic feet of water. The total monthly cost is equal to the service charge plus the charge for the volume used during the month. If we let x represent the number of cubic feet of water (in hundreds) and y represent the total monthly cost, then we have: total monthly cost = volume charge + service charge y = 1.66x If the Johnson family used 200 ft 3 less water this month than last month, then they can expect A. a decrease in their water bill of $3.32. B. a decrease in their water bill of $ C. an increase in their water bill of $ D. an increase in their water bill of $3.32. Graph Functions 18. Which of the following equations matches the graph below? A. B. C. D. y 3x 2 y 3x 2 1 y x y x 2 3

7 Translate Expressions, Equations, & Inequalities 19. Translate the following written equation into a mathematical equation. "The sum of one-fourth of m and the square root of n is less than the square of the sum of m and n." A. B. C. D. Change in Variable 20. A Spruce tree was measured three years after sprouting at a height of 3.87 feet. After its sixth year, the tree reached a height of 7.74 feet. Assuming a constant rate of growth, which of the following statements applies? An additional year is associated with an additional 3.87 feet of growth. A. An additional 3.87 years is associated with an additional foot of growth. B. An additional 1.29 years is associated with an additional foot of growth. C. An additional year is associated with an additional 1.29 feet of growth. D. Solve Linear Inequalities 21. Solve for x. A. x > 0 B. x > 3 C. x < 3-2x > -6

8 D. x < 0 Solve Linear Inequalities 22. Solve for x. A. x < 4 B. x > 4 C. x > 6 D. x < 6-4x > -24 Solve Linear Inequalities 23. Solve for x. A. x < -4 B. x > -3 C. x < -3 D. x > x < -2 Graphing on Number Lines Which inequality is graphed on the number line? A. x < 3 B. x > 3 C. x > 3 D. x < 3 Simplify Expressions

9 25. Simplify the following expression. A. 4a - 5 B. 15a + 35 C. 15a - 35 D. 4a a - 7(a + 5) Solve Linear Equations 26. Which value for x makes the sentence true? A. x = 2 B. x = 3 C. x = 8 D. x = 12 3x - 2 = 7 Simplify Expressions 27. Simplify the following expression. (-4x - 4y) + (3x - 4y) A. -x B. -3x C. -x - 8y D. -9x - 10y Change in Variable 28. In the graph, as x increases by 1, y

10 Decreases by 2 A. Increases by 2 B. C. Increases by 1 2 D. Decreases by 1 2 Graphing on Number Lines Which inequality is graphed on the number line? A. x > 2 B. x > 2 C. x < 2 D. x < 2 Properties of Arithmetic 30. The statement below is justified by the.

11 If 8 < b, then 8 + c < b + c. A. identity property B. distributive property C. associative property D. addition property Graph Functions 31. The cost of a long-distance telephone call is given by the function C(m) = 0.1m where m is the length of the call in minutes. What does the slope represent? A. cost of having a phone line B. cost per minute C. connection cost D. length of call Solve Linear Equations 32. Which value for x makes the sentence true? 6(x - 1) = 24 A. 3 B. 4 1 / 6 C. 5 D. 6 Graphing on Number Lines Which inequality is graphed on the number line? A. x < 5

12 B. x > 5 C. x > 5 D. x < 5 Graph Functions 34. At which point does the line above cross the y-axis? A. (0,2) B. (0,-2) C. (2,0) D. (-2,0) Simplify Expressions 35. Simplify the following expression. A. 16a + 8 B. 6a - 2 C. 6a - 8 D. 6a a - 4(a + 2)

13 Translate Expressions, Equations, & Inequalities 36. Which of the following equations matches the statement below? The quotient of 16 and 4, plus 19, is (4 + 19) = 23 A = 23 B = 23 C. (16-4) + 19 = 23 D. Graph Functions 37. y = -1 / 2 x + 2 Which of the following graphs represents the equation above? W. X. Y. Z. A. X B. Y C. Z D. W Symbolize Problem Situations

14 38. Billie Sue's BBQ had their grand opening this year. The first month they did not turn a profit. However, each month thereafter, they have had steady profits of $1,600 per month. If x represents the number of months they have profited, which of the following equations represents the amount of profits after x months? A. y = 1,600x B. y = 1,600 - x C. y = 1,600x + x D. y = x + 1,600 Patterns 39. The half-life of a certain material is second. Approximately how much of a 14-gram sample will be left after second? A. 12 grams B. 3.5 grams C gram D. 7 grams Patterns 40. What is the rule for this sequence? 48, 45, 42, 39, 36 Each number in the sequence is 3 less than the previous number. A. The sequence decreases by multiples of 3: first by 3, then 6, then 9, then 12. B. The sequence decreases by multiples of 4: first by 4, then 8, then 12, then 16. C. Each number in the sequence is 4 less than the previous number. D. Translate Expressions, Equations, & Inequalities 41. Translate the following written expression into a mathematical expression. "The sum of c and d squared times the square root of the difference of e and f"

15 A. B. C. D. Solve Linear Equations 42. Which value for x makes the sentence true? 7x = 5x + 12 A. 14 B. 6 C. 1 D. 10 Graph Functions 43.

16 Which of the following equations represents the line graphed above? A. y = 2 / 3 B. y = 2 / 3 x C. y = 4 / 5 x - 3 D. y = 5 / 4 x + 3 Evaluate Expressions 44. If a = 2 and b = 6, what is the value of the following expression? 3(a + 5b) - 8 A. 96 B. 72 C. 88 D. 28 Evaluate Expressions 45. Nelson invested $ in a certificate of deposit that pays 3% simple interest when it matures according to the formula below. I = Prt In the formula, I represents interest, P represents the money invested, or principal amount, r is the simple interest rate, and t represents the time, in years, that the money is invested. If Nelson will earn $66.00 in interest when the certificate of deposit matures, how long will it take to mature? A. 4 years B. 8 years C. 3 years D. 0.4 years Simplify Expressions 46. Simplify the following expression. 10a - 7(a + 3)

17 A. 3a - 3 B. 13a + 21 C. 3a + 21 D. 3a - 21 Patterns 47. What is the rule for this sequence? 18, 20, 22, 24, 26 Each number in the sequence is 2 more than the previous number. A. The sequence increases by multiples of 2: first by 2, then 4, then 6, then 8. B. The sequence increases by multiples of 3: first by 3, then 6, then 9, then 12. C. Each number in the sequence is 3 more than the previous number. D. Symbolize Problem Situations 48. The number of students enrolled in a school district triples each year. Which formula models the number of students enrolled in the school district the next year during this period of time? A. NEXT = NOW 3 B. NEXT = 3 NOW C. NEXT = NOW + 3 D. NEXT = (NOW) 3 Solve Linear Inequalities 49. Solve for x. A. x < 4 B. x > 4 C. x < 5 7x > 28

18 D. x > 5 Solve Linear Equations 50. Solve for x. A. x = 6 B. x = 2 C. x = 4 D. x = 0 3x - 2 = 4 Evaluate Expressions 51. If a = 16, b = 36, and c = 4, what is the value of the following expression? ( 3a - 2b c) 2 A. 36 B. 16 C. -36 D. 12 Solve Linear Equations 52. Grace makes and sells hair bows. The graph below shows the relationship between the time she spends making the hair bows and the number of hair bows she completes.

19 When she has made 40 hair bows, how many hours did she work? A. 7 B. 6 C. 5 D. 4 Change in Variable 53. A relationship is shown.

20 How does the value of y change as the value of x increases from 0 to 1? A. The value of y increases by 1. B. The value of y increases by 2. C. The value of y decreases by 1. D. The value of y decreases by 2. Patterns 54. Which graph matches the rule 1 more than twice a number? W. X. A. X B. W Y. Z.

21 C. Y D. Z Evaluate Expressions 55. If a = 3 and b = 6, what is the value of the following expression? a b 5 A. 129 B. 142 C. 123 D. 147 Graphing on Number Lines Which inequality is graphed on the number line? A. x > 3 B. x < 3 C. x > 3 D. x < 3 Translate Expressions, Equations, & Inequalities 57. Which of the following equations matches the statement below? 3 times the difference of a number and 3 is 75. A. 3(x / 3 ) = 75 3(x - 3) = 75 B. 3x - 3 = 75 C.

22 3x = 75 D. Solve Linear Equations 58. Which value for x makes the sentence true? 3x = -3x + 12 A. 6 B. 1 C. 2 D. 0 Graph Functions 59. Determine the slope of the line above. 5 A. 2 B. C

23 D. 2 5 Evaluate Expressions 60. If a = 6, b = 1, and c = 4, what is the value of the following expression? (5 + a) 2 + (b 2 - c - 5) A. 14 B. 113 C. 10 D. 165 Change in Variable 61. Marissa noticed that the price of chocolate milk at her school has increased at a constant rate since she was in first grade. Which of the following graphs accurately represents this situation? W. X. Y. Z. A. X B. Y C. W D. Z

24 Simplify Expressions 62. Simplify the following expression. A. 10y B. 16y C. 16y - 36z D. 10y - 64z 8(2y + 4z) - 32z Patterns 63. What is the missing number in this sequence? 36, 37, 39,, 46 A. 39 B. 43 C. 45 D. 42 Symbolize Problem Situations 64. Roni recently bought a car for $44,000. Her research shows the car will depreciate an average of $1,200 per year. If x represents the number of years Roni owns the car, which of the following equations represents the value of the car after x years? A. y = 44,000-1,200x B. y = 1,200x - 44,000 C. y = 44, ,200x D. y = 44,000x - 1,200 Change in Variable 65. A landowner wanted to determine the change in the water levels of his pond over time. First, he filled the pond to a water level of five feet. After two weeks, the water level was at 3.4 feet. If the water level continues to change at that same rate, which of the following statements applies?

25 For each week that passes, the water level decreases by -0.8 foot. A. For each week that passes, the water level decreases by -1.6 feet. B. For each week that passes, the water level decreases by 1.6 feet. C. For each week that passes, the water level decreases by 0.8 foot. D. Solve Linear Inequalities 66. Solve for x. A. x < 10 B. x < 0 C. x > 0 D. x > 10 x - 5 < 5 Patterns 67. Gigi bought a loaf of bread that was cut into 18 slices. The number of slices left each day for five days is shown by the sequence in the table below. Day Slices Left If Gigi continues to use the same number of slices each day, how many days will the loaf of bread last? A. 9 B. 4

26 C. 10 D. 8 Evaluate Expressions 68. If x = -3, what is the value of x 3 + x - 5? A. -35 B. 19 C. -29 D. 25 Translate Expressions, Equations, & Inequalities 69. Which equation represents the following sentence? A number is equal to the product of seven and another number, decreased by four. A. y + 7x = 4 B. y = 7x - 4 C. y = 7(x - 4) D. y - 4 = 7x Graph Functions 70. The graph of y = x is shown below. Which of the following shows the graph of y x 2?

27 W. X. Y. Z. A. X B. Y C. Z D. W Simplify Expressions 71. Simplify the following expression. 5x(5y - 4z) + 3xy A. 28xy - 20xz B. 28xy - 20z C. 28xy - 4xz D. 8xyz Simplify Expressions 72. Simplify the following expression. 4y(3x + 2y) - 2x(3y - 4x) A. 8x 2 + 6xy + 8y 2 B. -8x 2 + 6xy + 8y 2 C. 4x 2 + 6xy + 2y 2 D. 8x + 6xy + 8y

28 Graphing on Number Lines Which inequality is graphed on the number line? A. x > 2 B. x < 2 C. x > 2 D. x < 2 Simplify Expressions 74. Simplify the following expression. 3(6x) + (8x 2-6x + 3) - 7(x 2 + 3x - 4) A. x x + 31 B. x 2-9x - 25 C. x 2-9x + 31 D. x 2 + 3x + 31 Symbolize Problem Situations 75. Mike's Bike Shop needs to purchase some supplies. He needs 12 tires which cost $9 each and several water bottle holders which cost $6 each. He does not want to spend more than $358 for the 12 tires and the bottle holders. Which of the following inequalities could be used to solve for w, the number of water bottle holders he can order? A. $108 + $6w < $358 B. $12 + w < $358 C. $15w < $358 D. $108 + $15w < $358

29 Change in Variable 76. Chris draws a triangle with a height of 7 inches and a base of 8 inches. If he wants to draw another triangle with half the base of the first triangle, but with the same area of the first triangle, then what will the height of the new triangle be? A. 12 inches B. 28 inches C. 14 inches D. 16 inches Graph Functions 77. y = 1 / 2 x - 1 Which of the following graphs represents the equation above? W. X. Y. Z. A. Y B. Z C. W D. X Graphing on Number Lines

30 Which inequality is graphed on the number line? A. x > 1 B. x < 1 C. x > 1 D. x < 1 Graph Functions 79. Which term below best describes the linear relationship shown in the graph above? A. decreasing B. constant C. increasing Properties of Arithmetic 80. The statement below is justified by the. If 7(6x - 12) < 13y, then 42x - 84 < 13y. A. associative property B. commutative property C. identity property D. distributive property Symbolize Problem Situations 81. Pete's Putt-Putt Golf charges $7 per person for their first round of golf. Each extra round is $4 per person. Rick and his 3 friends have $84 to spend on putt-putt.

31 Which of the following inequalities could be used to solve for r, the number of extra rounds of putt-putt they can play? A. $28 + $16r < $84 B. $44r < $84 C. $11 + $4r < $84 D. $21 + $12r < $84 Properties of Arithmetic 82. If a = b, then which of the following expressions is equivalent to a c? A. b + c B. b c C. a b D. a + b Symbolize Problem Situations 83. Serenity Spa charges $56 for a one hour massage. They charge $0.75 for each additional minute over an hour. If x represents the number of minutes over one hour, which of the following equations represents the cost of a massage? A. y = -0.75x + 56 B. y = 0.75x + 56 C. y = 0.75x D. y = 56.75x Properties of Arithmetic 84.

32 Which of the following can be added to the number indicated on the number line above to sum to 0? 2 A. 3 B. C. D Graphing on Number Lines Which inequality is graphed on the number line? A. x < 1 B. x < 1 C. x > 1 D. x > 1 Translate Expressions, Equations, & Inequalities 86. Translate the following mathematical expression into a written expression. (c 2 + d 2 ) A. "the difference of c squared and d squared" B. "the product of c squared and d squared" C. "the square of c squared and d squared" D. "the sum of c squared and d squared"

33 Properties of Arithmetic 87. Which uses the distributive property to simplify the following? a (b + c) A. (a b) + c B. a + b + c C. (a b) + (a c) D. a b c E. (a b) (a c) Patterns 88. x y Which of the following describes the sequence represented by the table above? A. each term is 4 times the previous term B. each term is 4 times the x-value plus one C. each term is 3 times the x-value plus one D. each term is 3 times the previous term plus 1 Translate Expressions, Equations, & Inequalities 89. Which equation represents the following sentence? Four sevenths less than a number is the opposite of negative twenty-four.

34 A. n - 4 / 7 = 24 B. n - 4 / 7 = -24 C. n = 4 / 7-24 D. 4 / 7 - n = 24 Solve Linear Inequalities 90. Solve for x. A. x < -5 B. x > -2 C. x < -2 D. x > x < -2 Patterns 91. What is the missing number in this sequence? 61, 59, 55,, 41 A. 47 B. 49 C. 52 D. 50 Change in Variable 92. A relationship is shown.

35 As the value of x decreases, what happens to the value of y? A. The value of y increases. B. The value of y decreases. C. The value of y increases and decreases. D. The value of y stays the same. Evaluate Expressions 93. If x = 3, what is the value of 13x + 12? A. 75 B. 27 C. 195 D. 51 Symbolize Problem Situations 94. Jarrod helped his teachers pack textbooks into boxes for the summer. He packed 6 boxes of science textbooks with 14 books per box. He also packed math textbooks with 12 books per box. If x represents the total number of boxes he packed, which of the following equations can be used to find the total number of books that Jarrod packed into boxes?

36 A. y = 12(x - 6) + 84 B. y = 12x + 84 C. y = 84(x - 6) + 12 D. y = 84x + 12 Change in Variable 95. In the graph, as x increases by 1, y. Decreases by 1 A. Increases by ½ B. Decreases by ½ C. Increases by 1 D. Graphing on Number Lines Which inequality is graphed on the number line?

37 A. x > 2 B. x < 2 C. x < 2 D. x > 2 Properties of Arithmetic 97. Which of the following shows the sum of the number indicated on the number line above and? A. B. C. D. Simplify Expressions 98. Simplify the following expression. A. 12y - 16z 3(4y + 4z) - 12z

38 B. 7y - 24z C. 12y D. 7y Solve Linear Inequalities 99. Solve for x. A. x < -4 B. x > -4 C. x < -6 D. x > x < 7 Solve Linear Equations 100. In the linear function graphed below, when y = 3, what is the value of x? A. 4 B. 3 C. 0 D. 1

39 Answers 1. D 2. C 3. D 4. A 5. C 6. B 7. C 8. D 9. C 10. D 11. B 12. D 13. A 14. C 15. A 16. B 17. A 18. A 19. A 20. D 21. C 22. D 23. A 24. D 25. D 26. B 27. C 28. A 29. C 30. D 31. B 32. C 33. C 34. B 35. C 36. B 37. D 38. A 39. B 40. A 41. C 42. B 43. B

40 44. C 45. A 46. D 47. A 48. B 49. B 50. B 51. A 52. B 53. A 54. B 55. D 56. C 57. B 58. C 59. D 60. B 61. A 62. B 63. D 64. A 65. D 66. A 67. C 68. A 69. B 70. D 71. A 72. A 73. A 74. C 75. A 76. C 77. C 78. C 79. A 80. D 81. A 82. B 83. B 84. A 85. C 86. D 87. C 88. A 89. A

41 90. A 91. B 92. A 93. D 94. A 95. D 96. B 97. A 98. C 99. B 100. A

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