Copyright 2015 Edmentum - All rights reserved Picture is not drawn to scale.

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1 Study Island Copyright 2015 Edmentum - All rights reserved. Generation Date: 05/26/2015 Generated By: Matthew Beyranevand Students Entering Grade 8 Part 2 Questions and Answers Compute with Rational Numbers 4. Simplify the following expression Scale Drawings 5. Picture is not drawn to scale. The dimensions of triangle A are twice the dimensions of triangle The area of triangle A is 32 cm 2. What is the area of triangle B? 8 cm 2 16 cm 2 64 cm 2 32 cm 2

2 Compute with Rational Numbers 6. Simplify the following complex fraction. Scale Drawings 8. Above are two different models of the same triangular-shaped garden. If the height of the model on the left is 11 cm, what is the height of the model on the right? 22 cm 18.5 cm 16 cm 13 cm

3 Probability 11. Kasey is ordering prints of some digital photos. She needs to decide the size, finish, and color for her prints. The photo options are shown below. Size Finish Color 4 in 6 in (1) matte (M) color (C) 5 in 7 in (2) glossy (G) black and white (B) 8 in 10 in (3) 11 in 14 in (4) Which of the following lists all the possible outcomes for choosing a size, finish, and color for the prints? 1, M, C 2, M, C 3, M, C 4, M, C 1, M, B 2, M, B 3, M, B 4, M, B 1, G, C 2, G, C 3, G, C 4, B, C 1, G, B 2, G, B 3, G, B 4, C, B 1, M, C 2, M, C 3, M, C 4, M, C 1, M, B 2, M, B 3, M, B 4, M, B 1, G, C 2, G, C 3, G, C 4, G, C 1, G, B 2, G, B 3, G, B 4, G, B W. X. 1, M, C 2, M, C 3, G, C 4, M, C 1, M, B 2, M, B 3, G, B 4, M, B 1, G, C 2, G, C 3, G, C 4, G, C 1, G, B 2, G, B 3, G, B 4, G, B 1, M, C 2, M, C 3, M, C 4, M, G 1, M, B 2, M, B 3, M, B 4, M, B 1, G, C 2, G, C 3, G, C 4, G, M 1, G, B 2, G, B 3, G, B 4, G, B Y Z X W Y. Z. Compute with Rational Numbers 12. Simplify the following expression

4 Compute with Rational Numbers 13. Simplify the following expression (-8) Compute with Rational Numbers 14. Simplify the following expression (-10) Compute with Rational Numbers 15. Simplify the following expression Compute with Rational Numbers 16. Simplify the following expression.

5 Compute with Rational Numbers 17. Simplify the following expression Compute with Rational Numbers 18. Simplify the following expression Scale Drawings 20. Picture is not drawn to scale. The dimensions of triangle A are three times the dimensions of triangle The area of triangle A is 54 cm 2. What is the area of triangle B? 6 cm cm 2 18 cm 2 9 cm 2

6 Compute with Rational Numbers 21. Simplify the following expression. Scale Drawings 22. Picture is not drawn to scale. The dimensions of rectangle B are twice the dimensions of rectangle The area of rectangle A is 72 cm 2. What is the area of rectangle B? 216 cm cm 2 36 cm cm 2 Compute with Rational Numbers 24. Simplify the following expression (-6)

7 Compute with Rational Numbers 25. Simplify the following expression (-28) Probability 26. Audra rolled a six-sided number cube with sides numbered 1 through 6 multiple times. Her results are shown below. Number Cube Rolls Number of Side Times Rolled Based on the data, what is the experimental probability that the next time Audra rolls the number cube, she will roll a 2?

8 Probability 27. Fred is going to flip one coin four times and record whether it lands on heads or tails for each flip. The list below shows the possible outcomes for each of the four flips. H H H H H H H T H H T T H T T T T H H H T T H H T T T H T T T T H T H T T H T H T H H T H T T H H H T H T T H T T H T T H T H H What is the probability of flipping two tails and two heads? Scale Drawings 29. Picture is not drawn to scale. The dimensions of rectangle A are three times the dimensions of rectangle The area of rectangle B is 32 cm 2. What is the area of rectangle A? 288 cm 2 96 cm 2 16 cm cm 2

9 Scale Drawings 30. Above are two different models of the same television. If the screen in the model on the left has a 10-cm diagonal, what is the diagonal of the screen in the model on the right? 20 cm 60 cm 30 cm 40 cm Probability 31. The probability of randomly selecting a female from a group of 25 elementary school teachers is. Which of the following describes the likelihood of selecting a female elementary school teacher? neither unlikely nor likely likely unlikely

10 Probability 32. Rolando tossed a coin 4 times. Which of the following is a list of all the possible outcomes with 2 or 3 heads? HHTT TTHH HHTT TTHH HHTT TTHH HHTT TTHH HTHT THHH HTHT THHH HTHT THHH HTHT THHH HTTH HTHH HTTH HTHT HTTH HTHH HTTH HTHH THHT HHTT THHT HHTH THHT HHTH THHT HHTH THTH HHHT THTH HHHT THTH HHHH THTH HHHT W. X. Y. Z. Z X W Y Compute with Rational Numbers 33. Simplify the following expression Scale Drawings Above are two different models of the same rectangular patio. If the area of the model on the left is 6 sq cm, what is the area of the model on the right? 60 sq cm 31 sq cm 30 sq cm 150 sq cm

11 Compute with Rational Numbers 37. Simplify the following expression (-15) Compute with Rational Numbers 38. Simplify the following expression Compute with Rational Numbers 40. Simplify the following expression.

12 Scale Drawings 41. Figure STUV and figure WXYZ, shown below, are similar figures. The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 39 mm and SV = 51 mm, what is the length of side WZ? 17 mm 13 mm 117 mm 153 mm 43. Scale Drawings Above are two different models of the same diamond-shaped platform. If the length of side a is 4 cm, what is the length of side b? 5.25 cm 10 cm 6 cm 5 cm

13 Scale Drawings 44. Picture is not drawn to scale. The dimensions of rectangle A are four times the dimensions of rectangle The area of rectangle B is 128 cm 2. What is the area of rectangle A? 1,024 cm 2 2,048 cm cm 2 64 cm 2 Scale Drawings 45. The image on a movie poster was shrunk to make the DVD cover art for the movie, so that the cover art is a scale image of the poster. The poster is 54 inches wide, and the DVD cover art is 6 inches wide. If the diagonal of the poster is 6.75 feet, what is the diagonal of the DVD cover art? 13.5 inches 9 inches 8 inches 0.75 inch

14 Scale Drawings 46. The following blueprint of a kitchen has dimensions of 8 inches by 8 inches. The island has been highlighted in red. The island's actual dimensions are feet by feet. If the scale of the blueprint is 1 inch = feet, what are the dimensions of the island on the blueprint? Scale Drawings 47. Picture is not drawn to scale. The dimensions of circle B are twice the dimensions of circle The area of circle A is 64 cm 2. What is the area of circle B? 64 cm cm 2 16 cm cm 2

15 Scale Drawings 48. Above are two different diagrams of the same backyard. If the length of the diagram on the left is 4 in, what is the length of the diagram on the right? 1.33 in 17 in 7 in 12 in Scale Drawings 49. Above are two different models of the same hexagon. If the side length of the model on the left is the corresponding side length of the model on the right? in, what is

16 Scale Drawings 51. Preston drew a blueprint of an additional room he is planning to add to his house. On the blueprint, 1 centimeter is equal to 4 feet in the actual room. If Preston wants the room to measure 12 feet by 16 feet, what are these dimensions on the blueprint? 4 cm by 6 cm 6 cm by 8 cm 3 cm by 4 cm 3 cm by 8 cm Probability 53. Katrina and Tara are pulling billiards, numbered 1 through 8, from a bag. Their results are listed below. Katrina Tara Pull Number 1 Pull Number 9 Pull Number Whose experimental probability is closer to the theoretical probability of pulling out a billiard with a prime number printed on it? They are the same. Tara Katrina Neither

17 55. Scale Drawings Above are two different models of a microchip. If the model of the microchip on the left measures 6 cm tall, how tall is the model of the microchip on the right? 12 cm 14 cm 16 cm 6 cm 56. Probability Maya drew one highlighter at a time from a container of highlighters. After each draw, the highlighter was replaced. Maya recorded the results of 20 draws in the table below. Draw Result Draw Result Draw Result Draw Result 1 blue 6 purple 11 orange 16 yellow 2 pink 7 orange 12 pink 17 purple 3 purple 8 blue 13 yellow 18 blue 4 orange 9 orange 14 purple 19 orange 5 blue 10 purple 15 orange 20 pink What is the experimental probability of drawing an orange highlighter?

18 Compute with Rational Numbers 58. Simplify the following expression. Scale Drawings 59. Picture is not drawn to scale. The dimensions of square A are three times the dimensions of square The area of square A is 1,296 cm 2. What is the area of square B? 432 cm 2 36 cm cm cm 2

19 Probability 60. Which of the following is a true statement? A probability near 0 indicates a likely event. A probability near 0 indicates an unlikely event. A probability near indicates a likely event. A probability near 1 indicates an unlikely event. 63. Scale Drawings Picture is not drawn to scale. The dimensions of triangle B are twice the dimensions of triangle The area of triangle A is 21 cm 2. What is the area of triangle B? 63 cm 2 42 cm 2 84 cm cm 2 Compute with Rational Numbers 65. Simplify the following expression

20 Probability 67. There are 10 contestants left in a television competition where the contestants complete weekly challenges. For the next challenge, each contestant will be paired with one of the other contestants. Which diagram shows all the possible combinations of the contestants? W. X. Y. Z. Z X W Y Probability 68. Fill in the blank. A probability near indicates an event that is neither unlikely nor likely. Scale Drawings 71. Above are two different models of the same rectangle. If the area of the model on the left is 81 sq cm, what is the area of the model on the right? 75 sq cm 27 sq cm 9 sq cm 243 sq cm

21 Compute with Rational Numbers 72. Simplify the following expression. Scale Drawings 73. The dimensions of an office conference room are 8 feet by 16 feet. If the conference room blueprint dimensions are 4 centimeters by 8 centimeters, what is the scale of the blueprint? 1 centimeter = 2 feet 1 centimeter = 6 feet 1 centimeter = 4 feet 1 centimeter = 8 feet Scale Drawings 74. Clarise drew the scale drawing below of a circular fish pond she plans to put in her backyard. If 1 centimeter on the scale drawing represents 2 feet, what will be the diameter of Clarise's fish pond? 62.8 feet 20 feet 157 feet 10 feet

22 Probability 75. The possible outcomes for rolling a pair of fair dice are shown below. What is the probability of rolling a sum that is a prime number? Compute with Rational Numbers 76. Simplify the following expression

23 77. Scale Drawings Above are two different models of the same triangular handkerchief. If the area of the model on the right is 72 sq cm, what is the area of the model on the left? 36 sq cm 8 sq cm 24 sq cm 18 sq cm Probability 78. Dorian has two bags. Each bag has the letters A, B, and C written on little pieces of paper inside of it. He draws one letter from each bag. What is the probability that he draws out a vowel and a consonant?

24 Compute with Rational Numbers 79. Simplify the following expression. Probability 80. James does an experiment in which he spins a spinner and rolls a die. The spinner has 7 sections, labeled 1 to 7, and the die has 6 sides, labeled 1 to 6. The results of James' experiment are recorded in the histogram below. Based on the information in the graph, what is the experimental probability that the next spin and roll will have a sum of 8 to 10? Compute with Rational Numbers 81. Simplify the following expression.

25 Probability 82. Fred has a spinner that is split into four equal sections: red, blue, green, and yellow. Fred spun the spinner 952 times. Which of the following would be a good estimate of the number of times the spinner lands on the green section? Scale Drawings 84. Figure KLMN and figure PQRS, shown below, are similar figures. If KN = 3 cm, MN = 7 cm, RS = 14 cm, and PS = 6 cm, what is the scale factor of figure KLMN to figure PQRS?

26 Probability 85. Noel is playing a game where he draws one playing card each out of two stacks of 5 cards. The table below shows all possible sums for the two numbers on the cards. Value of Card 2 Sum of Two Cards Value of Card Is Noel more likely to draw two cards with a sum that is a multiple of 3 or two cards with a sum that is greater than 13? Noel is more likely to draw two cards with a sum that is a multiple of 3, because. Noel is more likely to draw two cards with a sum that is greater than 13, because. Noel is more likely to draw two cards with a sum that is greater than 13, because. Both are equally likely, because. Scale Drawings 86. Above are two different models of the same triangle. If the area of the model on the right is 9 sq in, what is the area of the model on the left? 4.5 sq in 18 sq in 45 sq in 36 sq in

27 Compute with Rational Numbers 87. Simplify the following expression. Probability 88. If the spinner above is spun 80 times, predict the number of times the spinner would land on Section The spinner would land on Section C roughly 8 times, but probably not exactly 8 times. The spinner would land on Section C roughly 10 times. The spinner would land on Section C exactly 20 times. The spinner would land on Section C roughly 20 times, but probably not exactly 20 times.

28 Compute with Rational Numbers 89. Simplify the following expression. Compute with Rational Numbers 90. Simplify the following expression (-9)

29 Answers C 5. A 6. B A C 12. B 13. C 14. B 15. C 16. D 17. B 18. D A 21. D 22. B A 25. C 26. A 27. B A 30. C 31. B 32. A 33. A D 37. C 38. B D 41. A C 44. B 45. B 46. A 47. B 48. D 49. A

30 C B A 56. A D 59. D 60. B C A D 68. A C 72. D 73. A 74. B 75. A 76. C 77. B 78. B 79. C 80. A 81. B 82. C D 85. C 86. D 87. A 88. D 89. A 90. A