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Name ——————————————————————— 8 Chapter Test A For use after Chapter 8 Simplify the expression. Write your answer using exponents. 1. 52 p 57 (22)10 2. } (22)3 3. 6 1 }38 2 5. ( y 4)5 1 6. }6 p w15 w 7. At the end of 2005, the national debt for the U.S. was about 10 trillion dollars, and the population of the U.S. was about 108. About how much was the per capita (per person) debt? 3. 4. 5. 6. Evaluate the expression. 8. 322 1. 2. Simplify the expression. 4. x 3 p x5 Answers 9. 224 p 2 522 10. } 523 Simplify the expression. Write your answer using only positive exponents. 1 12. } 7t23 7. 8. 9. (6m22n3)0 10. 14. One of the shortest electromagnetic wavelengths comes from 11. 11. p25 13. X rays, and one of the longest electromagnetic wavelengths comes from radio waves. The wavelength of an X ray is 10212 meter and is 1016 times shorter than the wavelength of a radio wave. What is the wavelength of a radio wave? 16. 6421/3 275/3 17. } 274/3 Write the number in scientific notation. 18. 56,000 19. 0.00351 20. 90,000,000 22. 5.71 3 1022 15. 16. 17. 18. Write the number in standard form. 21. 3.2 3 103 13. 14. Evaluate the expression. 15. 251/2 12. 23. 9.3 3 109 24. The distance from the sun to Earth is about 1.5 3 108 kilometers. 19. 20. 5 If the speed of light is 3 3 10 kilometers per second, how many seconds does it take the light from the sun to reach Earth? Use d 5 rt. 21. 22. 23. 24. 152 Algebra 1 Chapter 8 Assessment Book Copyright © Holt McDougal. All rights reserved. CHAPTER Date ———————————— Name ——————————————————————— Chapter Test A CHAPTER 8 For use after Chapter 8 Date ———————————— continued In Exercises 25–27, use the function y 5 3x. Answers 25. Complete the table for the function. 25. See left. 26. See left. x 22 21 0 1 2 y 27. 26. Graph the function. y 28. 9 29. 3 1 21 30. x 31. 27. Identify the domain and range of the function. 32. In Exercises 28 and 29, use the following information. You deposit $200 in a savings account that earns 5% annual interest compounded yearly. You do not make any other deposits or withdrawals. 33. See left. 34. See left. 28. Write a function that models the balance in the account over time. 29. Find the balance in the account after 3 years. Copyright © Holt McDougal. All rights reserved. Match the function with its graph. 30. y 5 (0.4) x A. 1 32. y 5 } (0.4) x 2 31. y 5 5(0.4) x B. y C. y y 5 5 5 3 3 3 1 1 21 3 x 21 1 x 23 21 1 x Tell whether the sequence is arithmetic or geometric. Then graph the sequence. 33. 2, 4, 8, 16, ... 34. –2, 0, 2, 4, ... Y Y / X / X Algebra 1 Chapter 8 Assessment Book 153 Name ——————————————————————— CHAPTER 8 Date ———————————— Chapter Test B For use after Chapter 8 Simplify the expression. Write your answer using exponents. 1. (27)9(27)2 2. 12 p 12 3. } 123 2 (53)8 4 Answers 1. 2. In Exercises 4 and 5, use the table. 3. Unit tera giga mega kilo hecto deka Meters 1012 109 106 103 102 101 4. 5. 4. How many hectometers are there in 1 gigameter? 6. 5. How many kilometers are there in 1 terameter? 7. Simplify the expression. 6. x4 p x 7. (9pq)2 8. 5 1 9. } p y11 y 10. (25m6)2 p m3 8. 8 4 1 2}1t 2 11. a 1} 2b 2 9. 12. Write and simplify an expression for the area of the triangle. 10. 11. x2 12. Simplify the expression. Write your answer using only positive exponents. 13. 2w27 1 15. } 10 26 8c d 14. (5g)23 94/3•9 18. } 91/3 17. 6424/3 16. 17. Complete the statement using <, >, or 5. 19. 9.27 3 1024 ? 0.00927 14. 15. Evaluate the expression. 16. 165/2 13. 20. 527,000,000 ? 5.27 3 108 Evaluate the expression. Write your answer in scientific notation. 9.3 3 1012 21. (4 3 108)3 22. (4 3 1013) (5 3 1029) 23. } 3.1 3 1023 24. In a recent year, 6.5 3 108 metric tons of wheat were produced in the world. One metric ton is equivalent to 1000 kilograms. A grain of wheat weighs about 0.000008 kilogram. Find the number of grains of wheat that were produced in the world. 18. 19. 20. 21. 22. 23. 24. 154 Algebra 1 Chapter 8 Assessment Book Copyright © Holt McDougal. All rights reserved. 6x 4 Name ——————————————————————— Chapter Test B CHAPTER 8 For use after Chapter 8 25. Write a rule for the function. Date ———————————— continued Answers x 22 21 0 1 2 y 1 } 8 } 1 2 2 8 32 25. 26. In Exercises 26–29, use the following information. 27. A house was bought 20 years ago for $160,000. Due to inflation, its value has increased about 5% each year. 28. 26. Write a function that models the value of the home over time. 29. See left. 27. Identify the initial value, the growth factor, and the growth rate. 28. What is the home worth today? y 1 1 x 29. Graph the function y 5 25 } and 3 1 2 1 21 21 1 x compare it to the graph of y 5 1 }3 2 . 5 x 23 Then identify its domain and range. 25 Tell whether the graph represents exponential growth or exponential decay. Then write a rule for the function. Copyright © Holt McDougal. All rights reserved. 30. 31. y 12 (1, 12) 10 10 (0, 8) 6 (0, 4) 1 21 30. 6 2 23 y 12 3 x 23 (1, 3.6) 2 1 21 3 x Tell whether the sequence is arithmetic or geometric. Then graph the sequence. 32. 192, 48, 12, 3, ... 31. 32. 33. –4, 2, 8, 14, ... See left. Y Y 33. See left. X X Algebra 1 Chapter 8 Assessment Book 155 Name ——————————————————————— Date ———————————— Chapter Test C CHAPTER 8 For use after Chapter 8 Simplify the expression. Write your answer using exponents. 7 p7 1. } 72 3 8 (26a7b4)(3a3b5) 4. 3 2. 1 }18 2 5. [(k 1 2)2]8 p 85 3 3 2w 1} v 2 Answers 1 6w 1. 6. 58 p 5 p 511 2. 3. p }3 3. In Exercises 7–9, use the following information. Draw an equilateral triangle with side lengths that are 1 unit long. Divide it into 3 new triangles by connecting the midpoints of the sides of the triangle, as shown in Step 1. 4. 5. 6. 7. Step 2 8. 7. Complete the table that shows the number of new shaded triangles 9. Step 0 Step 1 See left. and the side lengths of the new triangles for Steps 1–4. 10. Step Number of new triangles Side length of new triangle 1 3 13. 4 14. 8. Write and simplify an expression to find by how many times the number of new triangles increased from Step 2 to Step 7. 9. Write and simplify an expression to find the perimeter of a triangle 15. 16. formed in Step 6. 17. Simplify the expression. 18. 10. 024 324 11. } 327 13. 23(3f 21g 3)22 14. 1 1 2 6 12. 422 }0 11 22c4d 24 4 3c d } 21 22 2 15. 1 }q5 2 2 22 Evaluate the expression. 16. 16923/2 18. (21255)(212521/3)(212524) Algebra 1 Chapter 8 Assessment Book 2164\3 17. 21625/3 • } 21621/3 Copyright © Holt McDougal. All rights reserved. 12. 2 156 11. Name ——————————————————————— CHAPTER 8 Chapter Test C For use after Chapter 8 Date ———————————— continued 19. Order the numbers from least to greatest: Answers 0.0000284; 0.00020079; 3.4 3 1025; 4.07 3 1026; 0.00004 19. Evaluate the expression. Write your answer in scientific notation. (2,000,000,000)3(0.00009) 20. }} 600,000,000 1.2 3 1029 21. } 4 3 1027 20. 3 22. The radius of Earth is about 6.38 3 10 kilometers and the radius of a grain of sand is about 1 3 1023 meter. Assume Earth and a grain of sand are spheres. Find the ratio of the volume of Earth to the volume of a grain of sand. Round your answer to the nearest hundredth. What does the ratio tell you? 21. 22. Graph the function. Compare the graph with the graph of y 5 2x. Then identify its domain and range. 1 24. y 5 } p 2x 3 23. y 5 24 p 2x y 3 23. See left. 24. See left. y 1 25 23 21 21 1 1 x 25 23 1 21 21 x 23 Copyright © Holt McDougal. All rights reserved. 23 In Exercises 25–27, use the following information. A ball is dropped from a height of 64 feet. It rebounds three-fourths of the height from which it falls every time it hits the ground. 25. Identify the initial height, the decay factor, 64 ft and the decay rate. 26. Write a function that models the height of Not drawn to scale 25. the ball over time. 27. Find the height of the ball after it hits the ground three times. 26. 28. Tell whether the sequence 27. 1164, 1081.5, 999, 916.5, 834, ... is arithmetic or geometric. Then graph the sequence. Y 28. See left. X Algebra 1 Chapter 8 Assessment Book 157 Chapter 7, continued Passing plays ANSWERS b. y 100 80 60 40 20 0 c. (72, 36); yes 5. 6. y y 7 7 5 5 3 3 (72, 36) 0 40 120 x 80 Running plays 1 23 d. 72 running plays e. 21 1 23 x 21 1 3 x y 7. y 5 80,000(1.05)x; $107,208 40 20 8. geometric; x 20 40 60 Y 120 f. Sample answer: (50, 30); (70, 25); (30, 50) g. x > y h. 3 y / X 40 Chapter Test A x 20 40 60 120 36 1. 59 2. (22)7 3. }6 4. x8 5. y 20 6. w 9 8 t3 1 1 1 7. $100,000 8. } 9. } 10. 5 11. }5 12. } 7 9 8 p Chapter 8 Quiz 1 1. 85 2. (23)6 3. 615 4. (22)10 5. 164 p 74 6. 49 7. 97 8. 212 9. x10 10. 2x14 11. 3x13 x20 12. 72x9 13. x15 14. } 16 1 13. 1 14. 10,000 meters 15. 5 16. } 17. 3 4 18. 5.6 3 104 19. 3.51 3 1023 20. 9 3 107 21. 3200 22. 0.0571 23. 9,300,000,000 24. 500 sec Quiz 2 y6 x3 2 1 1. } 2. } 3. } 4. 9x2 5. 9 6. } 5 3 8 343 xy 16x8 25. 7. 64 8. 625 9. 930,000 10. 70,400 11. 0.00562 12. 0.000004209 13. 9.3 3 107mi x 22 21 0 1 2 y } 1 9 } 1 3 1 3 9 26. y 9 Quiz 3 3 1. 2. y 7 7 5 5 3 3 1 23 21 y 1 21 1 3 23 x 21 1 3 x 1 x 27. The domain is all real numbers and the range is all positive real numbers. 28. y 5 200(1.05)x 29. $231.53 30. B 31. A 32. C 33. geometric; 34. arithmetic; Y 3. 4. y Y y 7 7 5 5 3 A20 21 Algebra 1 Assessment Book X X Chapter Test B 1. (27)11 2. 524 3. 123 4. 107 5. 109 6. x 5 1 23 1 3 x 23 21 1 3 x 1 7. 81p 2q 2 8. 25m15 9. y 10 10. 2}5 t Copyright © Holt McDougal. All rights reserved. 20 Chapter 8, continued 1 a32 11. }4 12. } x 2(6x4); 3x 6 square units 2 16b d6 2 1 1 13. }7 14. }3 15. } 16. 1024 17. } 256 w 125g 8c10 Step Number of new triangles Side length of new triangle 1 3 } 2 9 } 3 27 } 4 81 } 1 2 25 20. 5 21. 6.4 3 10 22. 2 3 105 23. 3 3 1015 24. 8.125 3 1016 25. y 5 2 p 4x 26. y 5 160,000(1.05)t 1 4 1 8 27. $160,000; 1.05; 0.05 28. $424,528 29. The graph is a vertical stretch and reflection 1 x in the x-axis of the graph of y 5 }3 ; The domain 1 2 is all real numbers and the range is all negative real numbers. y 1 21 21 1 5 x 23 ANSWERS 18. 81 19. , 7. 1 16 37 3 1 6 8. }2 5 35 5 243 9. 3 } 5 } 10. undefined 2 64 3 f2 3 16c 20 25 11. 27 12. } 13. 2}6 14. } 15. }4 8 8 3g 81d q 1 2 1 16. } 17. 1 18. 225 2197 19. 4.07 3 1026; 0.0000284; 3.4 3 1025; 25 31. exponential decay; y 5 4 p (0.9)x 0.00004; 0.00020079 20. 1.2 3 1015 21. 3 3 1023 22. 2.60 3 1029; The number of grains of sand that equal the volume of Earth. 32. geometric; 23. 30. exponential growth; y 5 8 p (1.5)x y Y 1 25 21 21 1 x Copyright © Holt McDougal. All rights reserved. / X 33. arithmetic; The graph is a vertical stretch and reflection in the x-axis of the graph of y 5 2x. The domain is all real numbers and the range is all negative real numbers. y 24. Y 3 1 23 / 21 21 1 3 x 23 X Chapter Test C 4w 6 1. 79 2. 82 3. } 4. 218a 10b 9 5. (k 1 2)16 3 3v 6. 520 The graph is a vertical shrink of the graph of y 5 2x. The domain is all real numbers and the range is all positive real numbers. 25. 64 ft; 0.75; 0.25 26. y 5 64(0.75)t Y 27. 27 ft 28. arithmetic X Algebra 1 Assessment Book A21