Georgia Online Formative Assessment Resource (GOFAR) 8th Grade Number and Operations Review
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1 8th Grade Number and Operations Review Name: Date: Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 15 )
2 1. Use the given values of x and y to answer each part. Is x a rational number? Is y a rational number? Explain your answers. What fraction represents the sum of x and y? Show your work. Is work. greater than, less than, or between the values of x and y? Explain your answer or show your 2. The word micronis an abbreviated term for micrometer, or of one meter. Write an expression in scientific notation that is equivalent to Show your work. Find the area, in square microns, of a rectangular object with a width of 6,000 microns and a length of 2,000,000 microns. Show your work and write your final answer in scientific notation. The area of a different figure can be expressed as square microns. What is this area in square meters? Show your work and write your final answer in scientific notation. Part D The length of a virus is 0.4 microns. How many times the length of the virus is a 40-meter plastic tube? Show your work. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (2 of 15 )
3 3. Use these two equations to answer the questions in Parts A through D. The point answer. The point answer. lies on the graph of Equation 1. What is the value of k? Show your work or explain your lies on the graph of Equation 2. What is the value of j? Show your work or explain your Which of the equations, if either, represents a linear function? Explain your answer. Part D Does the graph of Equation 2 intersect the y -axis? Explain your answer. 4. A right triangle has legs 5 units and 8 units in length and hypotenuse x units in length. What is the exact value of x? Leave your answer in terms of a square root. Between what two consecutive whole numbers is the value of x? Explain your answer. The side length of another right triangle is Show your work and explain your answer. units. Determine the length of this side to the nearest tenth. Create a right triangle with a side length of units and a hypotenuse length of whole number units. Label all three side lengths of the right triangle. Use algebra to prove that the sides you chose form a right triangle. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (3 of 15 )
4 5. The table shows the population estimates for 3 countries in scientific notation. What number, written in scientific notation, represents the combined total population of countries P and Q? Show your work or explain your answer. How many times greater is the population of Q than the population of R? Show your work or explain your answer. The population of P is predicted to increase by 10% during the next 20 years. What number, written in scientific notation, represents the predicted total population of P? Show your work. Part D The population of R is twice the population it was 40 years ago. What was the average gain per year in population during this time period? Show your work. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (4 of 15 )
5 6. The cube shown has an edge length of x inches. The equation can be used to determine the length, in inches, of each edge of the cube. What is the value of x? Explain your answer or show your work. Convert the value of xfrom inches to feet. Write your answer in the form of integers. Show your work. where y and n are both The expression shown can be used to determine the volume of the cube when the length of each edge of the cube is tripled. Let a represent the length of each edge of the cube. Determine the value of b in the expression. Part D Using your answer from or to represent a and the value you found for b, rewrite the expression Part E Evaluate the expression you wrote in Part D. Label your answer with the correct units. 7. The square shown in the diagram has a side of length s units. The area is at least 15 square units and at Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (5 of 15 )
6 most 50 square units. What exact interval contains all possible values of s? Show your work or explain your answer. On a number line, plot points that represent the greatest and least values of s. Be as precise as possible. What is the approximate unit distance between the two points that you plotted? Explain your answer. 8. Television manufacturers often use the term dynamic contrast ratio to make claims about the quality of the picture on the screen. Company X claims their television has a 500,000 to 1 dynamic contrast ratio. Company Y claims their television has a 9,000,000 to 1 dynamic contrast ratio. Write the numbers 500,000 and 9,000,000 in scientific notation. Using your answers in, how many times greater is the dynamic contrast ratio of television Y than the dynamic contrast ratio of television X? Show your work. Company Z claims their television has a dynamic contrast ratio that is 50% of the dynamic contrast ratio of television Y. Write the dynamic contrast ratio of television Z in scientific notation. Part D Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (6 of 15 )
7 What percentage is the dynamic contrast ratio of television Z in comparison to television X? Show your work. 9. Which expression equals(4xy2z3)2? A)4x2y4z6 B)8x2y4z6 C)16x2y4z6 D)16x3y4z5 10. What does equal? A) B) C) D) 11. What is another way to express 4? A) Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (7 of 15 )
8 B) C) D) 12. Joanne has 2a3 number of animals. Ronnie has 3a3 number of animals. Odessa has a4 number of animals. How many animals do Joanne, Ronnie, and Odessa have altogether? A)5a10 B)6a 10 C)5a3 + a4 D)6a3 + a4 13. If what is the value of x? A)2 B)4 C)6 D)8 14. If what does equal? A)10x B) C) D) 15. Find the value of 3x-2x2 when x = -3. A)-27 B)-18 Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (8 of 15 )
9 C)0 D)9 16. A square-shaped playground has an area of 290 ft2. Approximately, how long is one side of the playground? A)12 ft B)17 ft C)36 ft D)73 ft 17. Why is one of the square roots of any positive number less than zero? A)because a negative number times a negative number is a positive number B)because a negative number times a negative number is a negative number C)because a negative number times a positive number is a negative number D)because a negative number times a positive number is a positive number 18. Jordan drove a3 miles per hour for a5 hours. How far did Jordan drive? A)a2 miles B)a8 miles C)a12 miles D)a15 miles 19. Which of the following best represents? A number between A)3 and 4 B)6 and 7 C)7 and 8 D)8 and Write.063 x 10-6 in scientific notation. A)6.3 x 10-4 B)6.3 x 10-8 C)63,000 D) Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (9 of 15 )
10 Alyssa estimated that there are five hundred twenty billion grains of sand on a beach. How is this number written in scientific notation? A) B) C) D) China has a population of approximately 1.3 x 109 people. The United states has a population of approximately 3 x 108 people. How many more people live in China than in the United States? A)107 people B)108 people C)109 people D)1010 people 23. A water tower holds 2,340,000 gallons of water. Express this number in correct scientific notation. A) B) C) D) Which expression below represents in scientific notation? A) B) C) D) Argentina has a population of approximately people, and Switzerland has a population of approximately people. How many times greater is Argentina s population than Switzerland s? A)2 B)4 C)5 D)7 Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (10 of 15 )
11 26. Which expression is equivalent to A) B) C) D) 27. The diameter of Earth is approximately 13,000 kilometers. The diameter of a grain of sand is approximately millimeter. If the grain of sand is spherical, what would its volume be in cubic millimeters? Use 3 to approximate write your answer in scientific notation. The number of millimeters equal to 13,000 kilometers is How many times greater is the diameter of Earth than the diameter of the grain of sand? Show your work, and write your answer in scientific notation. The diameter of a volleyball is approximately 21.5 centimeters, or kilometers. To the nearest whole number, how many volleyballs, placed side by side, would be needed to equal the length of the diameter of Earth? Show your work. and Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (11 of 15 )
12 28. The number of stars in the Milky Way is estimated to be The number of stars in a different galaxy, Abell 2029, is estimated to be Very large numbers, such as the number of stars in a galaxy, are often written in exponential form to make them easier to multiply or divide. Explain how to apply the laws of exponents when multiplying and dividing numbers with the same base but different exponents. How many times the number of stars in the Milky Way galaxy is in the Abell 2029 galaxy? Express your answer in scientific notation. Show your work. 29. A warehouse stores goods in cube-shaped boxes, each with a volume of cubic feet. If the volume of a single box is 216 cubic centimeters, what is the value of x? Explain your answer. In one room, the boxes are arranged together to form a rectangular solid measuring feet high, feet long, and feet wide. How many boxes are arranged together in this room? Explain your answer. In a second room, boxes are arranged together in a straight line. What is the total volume of all the boxes in the second room in terms of x? Explain your answer. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (12 of 15 )
13 30. The diameter of an atom is centimeters. The diameter of the nucleus of the atom is centimeters. How many times longer is the diameter of the atom than the diameter of its nucleus? Show your work. To convert a length from centimeters to nanometers, the quantity is multiplied by of the nucleus, in nanometers? Show your work. What is the diameter 31. One of Anna s homework problems is to evaluate the expression shown. Anna knows is irrational. Should she expect the expression to be rational or irrational? Explain your answer. Show a sequence of steps Anna could use to determine the two consecutive numbers, counting by tenths, that the value of falls between. Show your work or explain your answer. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (13 of 15 )
14 32. The number of members of an online music company grew at a constant rate per year from 2006 to The table shows the numbers of members during the first and last years. In 2006, each member paid $15 to join. How much money did the company receive from these members? Write your answer in scientific notation and show your work. How many times greater was the number of members in 2008 than the number of members in 2006? Explain your answer. What was the yearly rate of increase in the number of members? Write your answer in standard notation and explain your reasoning. Part D If the yearly rate you found in remains the same, how many members will there be in 2015? Write your answer in scientific notation. 33. Tracey needs to convert to a fraction in lowest terms. Her work is shown. Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (14 of 15 )
15 Tracey made at least one error. Explain any errors that Tracey made. What is the correct fraction in lowest terms? Show or explain your work. Explain whether number. is rational or irrational in terms of the decimal form and the fraction form of the Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (15 of 15 )
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