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Name ——————————————————————— CHAPTER 1 Date ———————————— Chapter Test A For use after Chapter 1 Evaluate the expression. Answers 1. 12 2 q when q 5 8 2. 3x when x 5 9 3. w 3 when w 5 2 4. 24 t } when t 5 4 6. (2.6)3 7. n6 8. The height of a horse is often measured in hands. You can estimate the height (in inches) of a horse by using the expression 4h, where h is the number of hands. How tall is a horse that measures 14 hands? Evaluate the expression. 9. 15 2 7 p 2 2. 3. Write the power as a product. 5. 104 1. 4. 5. 6. 7. 10. 2 1 23 4 4 11. 5(32 2 4) 8. Translate the verbal phrase into an algebraic expression. 9. 12. The sum of a number x and 9 Write an equation or an inequality. 10. 11. 14. Three more than twice a number b is equal to 13. 12. 15. The product of 5 and a number k is less than 60. 13. Check whether the given number is a solution of the equation or the inequality. 14. 16. 10x 2 3 5 27; 3 17. 4y 2 1 ≥ 20; 4 15. 18. 2x 1 1 < 17; 8 19. 4a 2 7 5 3a 2 4; 3 16. 20. A bicycle travels at an average speed of 15 miles per hour. 17. How many miles does the bicycle travel in 1.5 hours? 18. Tell whether the statement is always, sometimes, or never true. 19. 21. For a given whole number x, the expression 10x represents an even 20. number. 22. For any positive number x, x2 < x 21. 22. 10 Algebra 1 Chapter 1 Assessment Book Copyright © Holt McDougal. All rights reserved. 13. The number of quarters in d dollars Name ——————————————————————— Chapter Test A CHAPTER 1 continued For use after Chapter 1 Tell whether the pairing is a function. 23. Date ———————————— Input Output 0 24. Answers 23. Input Output 3 1 12 24. 5 7 2 6 25. See left. 10 7 2 3 15 11 3 1.5 26. See left. 27. See left. Make a table for the function. Identify the range of the function. 25. y 5 2x 1 1 28. Domain: 0, 1, 2, 3 29. Input, x Output, y 26. y 5 20 2 3x Domain: 0, 2, 4, 6 Input, x 27. The table shows the height H (in feet) of an object as a function of the time t (in seconds) after being thrown vertically upward. Graph the function for the domain given in the table. Time elapsed, t 0 1 2 3 4 5 Height, H 6 23 28 24 18 13 Determine whether the graph represents a function. 28. 29. y 4 3 2 1 O Height (in feet) Copyright © Holt McDougal. All rights reserved. Output, y H 28 24 20 16 12 8 4 0 0 1 2 3 4 5 6 t Time (in seconds) y 4 3 2 1 1 2 3 4 x O 1 2 3 4 x Algebra 1 Chapter 1 Assessment Book 11 Name ——————————————————————— CHAPTER 1 Date ———————————— Chapter Test B For use after Chapter 1 Evaluate the expression. Answers 1. 34.5x when x 5 4 2. 9 10 1 3 } y when y 5 } 1. 2. Evaluate the power. 3. 54 4. 17 1 5 5. } 2 1 2 6. You can convert temperatures in degrees Fahrenheit to degrees 9 Celsius by using the expression } C 1 32, where C is the temperature 5 (in degrees Celsius). Convert 358C to degrees Fahrenheit. Evaluate the expression. 3. 4. 5. 6. 7. 8. 3[15 2 (23 2 6)2] 7. 16 4 (4 2 2) 2 3 8. Evaluate the expression for the given values of the variables. 9. 3m 2 n when m 5 5 and n 5 4 10. 2u2 1 v when u 5 3 and v 5 7 10. 11. A rectangular box is created by cutting out squares of equal sides 11. of lengths x from a piece of cardboard 10 inches by 15 inches and folding up the sides as shown in the figure. The volume of the box is given by V 5 x(10 2 2x)(15 2 2x). Find the volume of the box when the side length of the square is 3 inches. 10 in. x x x Write an algebraic expression, an equation, or an inequality. 12. The quotient of the square of a number t and 14 13. The product of 6 and the quantity 2 more than a number x is at least 45. 14. The sum of 4 and the quotient of a number k and 9 is 12. Check whether the given number is a solution of the equation or the inequality. r 15. 7z 1 8 > 20; 2 16. } 1 15 5 20; 25 5 16. Copyright © Holt McDougal. All rights reserved. 15. x Algebra 1 Chapter 1 Assessment Book 13. x x x 12. 14. 15 in. x 12 9. Name ——————————————————————— Chapter Test B CHAPTER 1 Date ———————————— continued For use after Chapter 1 17. A carpet outlet advertises a price of $470.40 to carpet a 12-foot by 16-foot room. If a customer was given a price of $725.20 for carpeting a room that is 16 feet wide, what is the length of the room? Answers 17. 18. Tell whether the statement is always, sometimes, or never true. 18. For a given whole number x, the expression 4x represents an even number. 19. 20. 19. For any positive number x, x2 > x – 1. 21. Write a rule for the function. 22. 20. Input, x 1 3 5 7 Output, y 2 6 10 14 See left. 23. 21. Input, x 12 15 18 21 Output, y 4 5 6 7 See left. Find the range of the function. Then graph the function. 24. 1 22. y 5 } x 1 3 2 25. 23. y 5 x 2 6 Copyright © Holt McDougal. All rights reserved. Domain: 0, 1, 2, 3, 4 Domain: 10, 12, 14, 16, 18 y y 16 6 5 4 3 2 1 ⫺4 ⫺3 ⫺2 O 14 1 2 3 12 10 8 6 4 2 4 x ⫺2 O 2 4 6 8 10 12 14 16 18 x Determine whether the graph represents a function. 24. 25. y 4 3 2 1 3 2 1 O y 4 1 2 3 4 x O 1 2 3 4 x Algebra 1 Chapter 1 Assessment Book 13 Name ——————————————————————— CHAPTER 1 Date ———————————— Chapter Test C For use after Chapter 1 Evaluate the expression. 1. 2 n3 when n 5 }3 Answers 2. x 1 2 } y when x 5 6 and y 5 } 3. You can estimate your distance (in miles) from a thunderstorm by t , where t is the number of seconds between using the expression } 4.8 seeing the lightning and hearing the thunder. How far away is the thunderstorm, if 24 seconds after you see the lightning you hear the thunder? 1. 2. 3. 4. 5. Evaluate the expression. 4. [15 1 (52 p 2)] 4 13 (37 2 26)2 2 6 5. }} 32 4 22 2 (42 2 13) Evaluate the expression for the given value of the variable. 6. 7. 8. 6. 8 1 4(q 2 3) 1 q when q 5 6 9. 7. 2m 2 n when m 5 5 and n 5 3 } m2 2 2n 1 2 10. 8. The formula for the area of a trapezoid is one-half the product of the sum of the bases times the height. Find the area of the trapezoid below. 11. 12. 6 cm 13. 5 cm 14 cm Write an equation or an inequality. 9. The product of 5 and the sum of a number n and 7 is less than the quotient of the number n and 2. 10. Three times the sum of 4 and a number y squared is the same as the difference of 14 and the number y. Tell whether the statement is always, sometimes, or never true. 11. For a given whole number x, the expression 13x 1 1 represents an odd number. 12. For any positive number x, 3x2 > 6x. Check whether the given number is a solution of the equation or inequality. x21 13. } 1 5 > x 1 1; 8 2 14 Algebra 1 Chapter 1 Assessment Book 14. 3(x 2 7) 5 19 2 x; 10 Copyright © Holt McDougal. All rights reserved. 14. Name ——————————————————————— Chapter Test C CHAPTER 1 Date ———————————— continued For use after Chapter 1 15. Your aunt wants to spend at most $800 on a video camera and video- tapes. She plans to buy the camera for $695 and tapes for $5.75 each. Can she buy 20 videotapes? 16. You invested $1500 in a bank account for 5 years and received $150 in interest. What was the annual simple interest rate for the account? Answers 15. 16. 17. 17. At a yard sale, you find a number of paperback books by your favor- Amount left (in dollars) ite author. You have $10 and each book is priced at $.75. Write a rule for the amount of money you have left as a function of the number of books you buy. Then use the grid below to graph the function. y 10 9 8 7 6 5 4 3 2 1 0 See left. 18. See left. See left. 19. 20. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 x Number of books Copyright © Holt McDougal. All rights reserved. Make a table for the function. Identify the range of the function. Then graph the function. 1 18. y 5 } x 21 3 y 9 8 7 6 5 4 Domain: 12, 15, 21, 30 Input, x Output, y 3 2 1 O 3 6 9 12 15 18 21 24 27 30 x Determine whether the graph represents a function. 19. y 4 20. 3 2 1 3 2 1 O y 4 1 2 3 4 x O 1 2 3 4 x Algebra 1 Chapter 1 Assessment Book 15 Name ——————————————————————— Date ———————————— Chapter Test A CHAPTER 2 For use after Chapter 2 Tell whether the number is a real number, a rational number, an irrational number, an integer, or a whole number. 5 1. 1 } 8 2. 210 3. 0.2 4. 7 1 5. Graph 23, }, 0, 22 on the number line. Then order the numbers 2 Answers 1. 2. from least to greatest. 3. 24 ⫺3 ⫺2 ⫺1 0 1 6. Let U be the set of integers from 0 to 9. Find A ø B and A ù B for 4. the sets A 5 {3, 5, 8} and B 5 {0, 1, 2, 8}. Identify the property being illustrated. 5. See left. 7. (22 1 3) 1 5 5 22 1 (3 1 5) 8. 7 1 (27) 5 0 6. 9. 2(x 1 3) 5 2x 1 6 10. 6 p (23) 5 23 p 6 Find the sum. 12. 8 1 (22) 13. 213 1 6 8. 14. In Alaska, the elevation of Mount McKinley is 45,514 feet higher than the Aleutian Trench, which is 25,194 feet below sea level. What is the elevation of Mount McKinley? 9. 10. Find the difference. 15. 11 2 (29) 11. 16. 27 2 5 17. 215 2 (28) 12. 13. 14. 15. 16. 17. 30 Algebra 1 Chapter 2 Assessment Book 30 Copyright © Holt McDougal. All rights reserved. 11. 24 1 (21) 7. Name ——————————————————————— Chapter Test A CHAPTER 2 Date ———————————— continued For use after Chapter 2 Tell whether the statement is true or false. If it is false, give a counterexample. Answers 18. 18. If a number is a negative integer, then the number is a whole number. 19. If a number is an integer, then the number is a real number. 19. 20. Find the change in temperature or elevation. 20. From 358F to 2128F 21. 21. From 2560 meters to 2240 meters 22. Evaluate the expression when x 5 7 and y 5 23. 23. 22. x 1 y 23. x 2 y 24. ⏐y⏐ 2 x Find the product or quotient. 24. 25. 25. 29(3) 26. 25 p 0 3 27. } (212) 4 26. 28. 218 4 (23) 29. 28 4 (27) 1 30. 215 4 } 2 27. 28. 31. Find the mean of the numbers 212, 29, 3, and 6. Evaluate the expression when x 5 22 and y 5 25. 33. 2x 1 2y 32. 2xy 2x 1 y 34. } 23 29. 30. Copyright © Holt McDougal. All rights reserved. 31. Simplify the expression. 32. 35. 9 1 7a 2 2 2 10a 33. 36. 3x 1 6(x 2 5) 37. 34. 14x 2 2 2 } 35. 38. Find the perimeter and the area of the rectangle with the given dimensions. 36. 37. 5 38. 2x + 14 39. Evaluate the expression. } 39. 6Ï 25 } 40. Ï 121 3 } 41. 2Î 1331 40. 41. Algebra 1 Chapter 2 Assessment Book 31 Name ——————————————————————— CHAPTER 2 Date ———————————— Chapter Test B For use after Chapter 2 Tell whether each number is a real number, a rational number, an irrational number, an integer, or a whole number. } 2. Ï 12 1. 20.75 Answers 1. 3. 10 Tell whether the statement is true or false. If it is false, give a counterexample. 2. 4. If a number is positive, then its opposite is negative. 5. If a number is an integer, then the number is an irrational number. 3. Order the numbers in the list from least to greatest. 1 1 6. 2}, 20.25, }, 1 5 3 14 1 7. 2}, 24.6, 24.07, 24 } 3 3 8. Let U be the set of integers from 25 to 5. Find A ø B and A ù B for the sets A 5 {22, 0, 1, 3, 5} and B 5 {22, 21, 0, 1, 3, 5}. 4. 5. Identify the property being illustrated. 9. (x p 0.5) p 8 5 x p (0.5 p 8) 6. 10. x 1 (2y) 5 2y 1 x 7. 11. 2(5z 2 9) 5 10z 2 18 12. 3a 1 (23a) 5 0 8. 13. 3 2 (212) 14. 222 1 16 15. 20.8 1 (28.9) 7 1 16. } 2 } 2 10 9. 10. In Exercises 17 and 18, use the table below. Name Double eagle Eagle Birdie Par Bogey Double bogey 11. Score 23 22 21 0 1 2 12. 17. In golf, the best total score is the lowest score. In 4 holes, you score a birdie, a par, a double eagle, and a double bogey. Your friend scores an eagle, a double eagle, a bogey, and a par. Who has the better total score? 13. 14. 15. 18. What is the difference between your friend’s total score and your total score? 16. 17. 18. 32 Algebra 1 Chapter 2 Assessment Book Copyright © Holt McDougal. All rights reserved. Find the sum or the difference. Name ——————————————————————— Chapter Test B CHAPTER 2 Date ———————————— continued For use after Chapter 2 Evaluate the expression when x 5 25.4 and y 5 2.8. Answers 20. x 1 ⏐y 2 10⏐ 19. y 2 x 2 1.4 19. 20. Find the product or the quotient. 21. 26(212) 22. 45 4 (23) 21. 5 3 23. } 2} 9 4 24. 27.2 4 8 22. 2 1 26. 2}(18) 2} 3 4 23. 1 2 2 25. 24 4 2} 9 1 2 1 2 24. 27. A person buys items and sells them on a website. The table shows the profit earned for each item. Suppose that in one week the person sells 8 mantel clocks, 5 framed mirrors, and 3 candles. Find the average daily profit. Item 25. 26. Mantel clock Framed mirror Candle 27. $4.13 2$1.65 $2.36 28. Profit 29. Simplify the expression. 28. 10x 2 (x 1 3) 30. 26x 1 15 30. } 210 29. 22x(x 2 6) 31. 31. Use the distributive property and mental math to find the total cost Copyright © Holt McDougal. All rights reserved. of 6 notebooks at $3.95 each. 32. 32. Find the perimeter and area of the rectangle with 6 the given dimensions. 4 + 2w Approximate the square root to the nearest integer. } } 33. Ï 35 33. 34. } 34. 2Ï 150 35. Ï 18 36. The area of a town’s square is 14,400 square feet. Find the side length of the square. 35. 36. 37. Evaluate the expression for the given value of x. } 37. 2 2 Ï x when x 5 25 } 38. 4 Ï x 1 9 when x 5 1 Complete the statement using , or .. 38. 39. 3 39. 5.7 ? 40. 3 } Î} 125 40. 3 } Î27 ? 2Î26 Algebra 1 Chapter 2 Assessment Book 33 Name ——————————————————————— CHAPTER 2 Date ———————————— Chapter Test C For use after Chapter 2 Tell whether the statement is true or false. If it is false, give a counterexample. Answers 1. 1. If a number is positive, then its absolute value is negative. 2. If a number is a whole number, then the number is an integer. 3. If a number is a real number, then the number is a rational number. 2. 4. A number is always greater than its opposite. Order the numbers in the list from least to greatest. } 5. 2Ï 12 , ⏐3.5⏐, 3. 23 }2, Ï16 , 23.48 } 5 6. Let U be the set of integers from 25 to 5. Find A9 3 B9 for the sets 4. A 5 {23, 21, 2, 4} and B 5 {25, 24, 23, 3}. 5. A market surplus or shortage is the difference of the quantity supplied and the quantity demanded. A positive difference is a surplus, and a negative difference is a shortage. The graph shows the quantities of a type of shoe supplied and demanded. 6. y 60 50 40 30 20 Demand Function Supply Function 7. 10 0 0 10 20 30 40 50 60 70 80 90 100 x Price (dollars) 8. 9. 10. 7. Find the market surplus or shortage when the price is $80. 8. Find the market surplus or shortage when the price is $30. 9. Market equilibrium occurs when the demanded quantity is equal to the supplied quantity. For what price is there market equilibrium? 10. Describe any trends in the surplus or shortage in relationship to the price. 11. Complete the statement using the given property. 12. 11. (2x 1 y) 1 z 5 13. 12. 24(6x 2 3) 5 13. 210y 1 34 ? ? ; Associative property of addition ? ; Distributive property 5 0; Inverse property of addition Algebra 1 Chapter 2 Assessment Book Copyright © Holt McDougal. All rights reserved. Quantity In Exercises 7-10, use the following information. Name ——————————————————————— Chapter Test C CHAPTER 2 Date ———————————— continued For use after Chapter 2 Evaluate the expression. Answers 14. 21.8 1 7.6 1 (23.7) 15. 26.3 2 (217.4) 2 11.2 14. 3 3 1 16. 23 } 1 26 } 19 } 5 2 10 17. 1.9(22.5)(3) 15. 1 6 18. 2} (232) 4 2} 2 5 19. 1 2 1 2 12}53 2 }83 2 4 12}34 p }89 2 16. 17. 20. Due to depreciation, the value of a new car is decreasing. Its value was $15,750 in 2005. For the first two years, the average rate of change in value of the car was about 2$4000 per year. For the next five years, the average rate of change in value of the car was about 2$1150 per year. Find the price of the car when it was bought new in 1998. 18. 19. 20. 21. Simplify the expression. 220x 212 21. } 212 22. 3x(x 2 6) 1 (x 2 3)(28) 2 23. 2} x(x 2 16) 3 24. 5xy 2 12xy 1 xy 2 6xy 1 10xy 22. 23. 24. Evaluate the expression. 25. x 2 2y 3 when x 5 22 and y 5 25 } 23Ïx 2 7 26. } when x 5 9 and y 5 21 xy Copyright © Holt McDougal. All rights reserved. } Ïx 27. } 2 y 3 when x 5 4 and y 5 22 x 25. 26. 27. 28. 2x 2y 28. } when x 5 1 and y 5 24 y2 2 4 29. 29. The area of a square park in a city is 22,500 square feet. Find the 30. perimeter of the park. 31. Complete the statement using , or .. 3 } 17 30. } ? Î 121 3 3 } 31. 2Î 29 ? 3 Î} 21 Algebra 1 Chapter 2 Assessment Book 35 Name ——————————————————————— CHAPTER 3 Date ———————————— Chapter Test A For use after Chapter 3 Solve the equation. 1. a 1 8 5 212 Answers 2. 6q 5 48 y 3. } 5 9 3 4. The rectangle has an area of 60 square feet. Write and solve an equation to find the value of x. 1. 2. 3. 4. x 5. 12 in. 6. Solve the equation. 5. 3t 2 5 5 16 7. b 6. } 11 5 3 4 7. 2m 1 7m 5 45 8. The output of a function is 6 more than 2 times the input. Write and 8. 9. solve an equation to find the input when the output is 210. 9. You have $25 to buy a gallon of milk for $3.75 and as many boxes of cereal as you can for $2.80 each. Write and solve an equation that represents this situation. Show that your answer is reasonable. 10. 10. 3p 2 7p 1 22 5 2 11. 11. z 1 3(z 2 7) 5 19 12. 3 12. }w 5 12 4 13. 14. In Exercises 13 and 14, use the following information. A young person should sleep 8 hours each night plus 1 4 } hour for every year the person is under 18 years old. Suppose a young person sleeps 9.5 hours. 13. Which equation could be used to find a, the age of the young person? 1 a. } a 5 9.5 4 1 b. } a 1 8 5 9.5 4 1 c. } (18 2 a) 1 8 5 9.5 4 14. Solve the equation to find the age of the young person. 50 Algebra 1 Chapter 3 Assessment Book Copyright © Holt McDougal. All rights reserved. Solve the equation. Name ——————————————————————— CHAPTER 3 Chapter Test A Date ———————————— continued For use after Chapter 3 Solve the equation, if possible. Answers 15. 4y 1 16 5 2y 2 14 15. 16. 8x 1 4 5 2(4x 2 3) 16. 17. 6(3b 1 5) 5 2(6b 2 21) 17. Solve the proportion. 18. 3 c 18. } 5 } 4 2 5 d 19. } 5 } 8 24 19. 15 3 20. } 5 } 5 n 17v 34 21. } 5 } 2 3 20. 2x 2 3 x22 22. } 5 } 3 2 5 22 23. } 5 } 3a 1 8 a21 21. 22. 24. A caterer knows that 18 heads of lettuce are needed to make dinner salads for 70 people. How many heads of lettuce are needed for a party of 175 people? 23. 24. Solve the percent problem. 25. Copyright © Holt McDougal. All rights reserved. 25. What percent of 80 is 36? 26. What number is 15% of 40? 26. 27. In a recent county election, 16,400 registered voters voted, which 27. was a 32% voter turnout. How many registered voters are there in the county? 28. In Exercises 28 and 29, identify the percent of change as an increase or decrease. Then find the percent of change. 29. 28. Original: 65 New: 78 29. Original: 46 New: 39.1 30. Write the equation so that y is a function of x. 30. 5x 1 y 5 12 31. 8x 1 4y 5 220 32. 9x 2 3y 5 12 1 33. The formula for the area of a triangle is given by A 5 } bh. 2 Solve for h. 31. 32. 33. Algebra 1 Chapter 3 Assessment Book 51 Name ——————————————————————— CHAPTER 3 Date ———————————— Chapter Test B For use after Chapter 3 Solve the equation, if posssible. Answers 1. 27 5 22 1 x 3 2 2. b 2 } 5 } 5 5 2 3. 2} d 5 8 3 4. 17 5 14 1 6y 5. 2t 2 5t 5 9 6. 13 2 9w 5 214 7. 7m 2 4 2 2m 5 6 3 8. } (c 1 4) 5 3 4 1. 2. 3. 9. 5(3 2 2y) 1 4y 5 3 11. 7a 2 3.9a 5 6.2 4. 5. 10. 4x 2 1 5 2(2x 1 3) 12. 9 2 5z 5 12 2 (6z 1 7) 6. 7. 13. A radio station has 722 different promotional CDs to possibly give away. Only 295 of the CDs are designed for individual distribution. The rest must be given away in sets of 3. How many complete sets can be given away? Write and solve an equation that represents this situation. Show that your answer is reasonable. 8. 9. 10. 14. A new plasma-screen television costs $5250. A family makes a down payment of $552 and pays off the balance in 24 equal monthly payments. Write and solve an equation to find the monthly payment. 11. 12. 15. On a class trip, there were 45 more girls than boys. The total number 13. Solve the proportion. 4 12 16. } 5 } 5 y 1.1 w 17. } 5 } 1.2 3.6 16 24t 18. } 5 } 9 27 8 4 19. } 5 } m13 m 6 12 20. } 5 } x14 5x 2 13 5 23 21. } 5 } 3z 2 4 1 2 2z 14. 15. 16. 17. 18. 19. 20. 52 Algebra 1 Chapter 3 Assessment Book 21. Copyright © Holt McDougal. All rights reserved. of students on the trip was 211. Write and solve an equation to find the number of girls and the number of boys on the class trip. Name ——————————————————————— CHAPTER 3 Chapter Test B Date ———————————— continued For use after Chapter 3 22. On Monday, biologists tagged 150 sunfish from a lake. On Friday, the biologists counted 12 tagged fish out of a sample of 400 sunfish from the same lake. Estimate the total number of sunfish in the lake. 2 23. A recipe for oatmeal raisin cookies calls for 1} cups of flour to 3 make 4 dozen cookies. How many cups of flour are needed to make 6 dozen cookies? Answers 22. 23. 24. 25. Solve the percent problem. 24. 3 is 1.5% of what number? 25. 9 is what percent of 6? 26. 26. What is 26.5% of 46? 27. 70 is 200% of what number? 27. 28. In a renovation project, a football stadium increased its 60,000-seat capacity by 15%. How many seats will be available when the project is completed? 28. 29. In Exercises 29 and 30, identify the percent of change as an increase or decrease. Then find the percent of change. 29. Original: 82.6 30. Original: 45 Copyright © Holt McDougal. All rights reserved. New: 70 30. New: 72 Write the equation in function form. 31. 31. 5x 2 y 5 7 32. 32. 10x 1 3y 1 2 5 9x 1 8 In Exercises 33–35, use the following information. Anthropologists can estimate the height of a woman by measuring the length (in centimeters) of her radius bone (from the wrist to the elbow). The length (in centimeters) of the radius bone b is given by b 5 0.26h 2 18.85 where h is the height (in centimeters) of the woman. 33. 34. 35. 33. Solve the equation for h. 34. If the length of a woman’s radius bone is 25 centimeters, estimate the height of the woman. Round your answer to the nearest centimeter. 35. If 1 in. 5 2.54 cm, convert the woman’s height to inches. Round your answer to the nearest inch. Algebra 1 Chapter 3 Assessment Book 53 Name ——————————————————————— CHAPTER 3 Date ———————————— Chapter Test C For use after Chapter 3 Solve the equation. Answers 3 1. 2} n 5 12 4 2. 218.4 5 b 2 14.7 1. 3 5 3. } 2 y 5} 4 8 7 4. } x 2 3 5 4 12 2. 1 5. 3 5 } 2 2b 3 2 2 6. } z 1 z 5 } 3 3 3. 7. A music venue has 410 possible tickets to give away in envelopes. 36 envelopes will contain 2 tickets each. The rest of the envelopes must contain 3 tickets each. How many envelopes will contain 3 tickets? Write and solve an equation that represents this situation. Show that your answer is reasonable. 4. 5. 6. 7. 8. A contractor wants to use 34 feet of molding, cut into three pieces, to trim the sides and top of a garage door. The long piece is 1.5 feet longer than three times the length of each shorter piece. Find the length of each piece. Solve the equation, if possible. 9. 3[2 2 3(m 2 2)] 5 12 8. 9. 10. 10. 21.6(b 2 2.35) 5 211.28 11. 2x 1 3(x 2 5) 5 15 12. 4 5 9 2 3(2w 1 1) 2 5w 1 13. 2(c 2 4) 1 8 5 } (6c 1 20) 2 14. 2q 2 4 1 8q 5 7q 2 8 1 3q 15. 27(t 2 3) 1 4t 5 3(7 1 t) 16. 2.1d 1 18 5 2.16(d 1 8) 11. 12. 14. 17. A jewelry maker produces necklaces that sell for $85 each. The jewelry maker’s costs include $35 in materials for each necklace plus fixed costs of $1650. How many necklaces must the jeweler sell to break even? 15. 16. 17. Solve the proportion. 15 72 18. } 5 } 45 a 9 b 19. } 5 } 12.8 3.2 18. 0.5 c 20. } 5 } 2.4 15 10 5 21. } 5 } d13 2d 2 3 19. f22 2f 22. } 5 } 14 7 23. 4.5 3 }5} g12 0.5g 2 1 20. 21. 22. 23. 54 Algebra 1 Chapter 3 Assessment Book Copyright © Holt McDougal. All rights reserved. 13. Name ——————————————————————— CHAPTER 3 Chapter Test C Date ———————————— continued For use after Chapter 3 24. The ratio of weight on the moon to weight on Earth is 1 : 6. How many pounds would a 144-pound person weigh on the moon? 25. A simple syrup used for ice cream toppings requires 2 cups of sugar 2 and }3 cup of boiling water. How many cups of sugar are required for Answers 24. 25. 26. 2 cups of boiling water? 27. Solve the percent problem. 26. 48 is 12% of what number? 27. What percent of 16 is 20? 28. What number is 175% of 76? 29. What percent of 200 is 96? 28. 29. 30. The cost of dinner for a party of eight people is $139.50. For large groups of people an 18% gratuity is added to the cost of the dinner, after a 6% sales tax. Find the total bill for the dinner. 30. 31. 31. The average lecture class size last year at a community college was Copyright © Holt McDougal. All rights reserved. 120 students. This year, the average lecture class at the same college has 216 students. Find the percent of change and tell whether it is an increase or a decrease. 32. Write the equation in function form. 33. 1 32. y 2 7 5 } (x 2 9) 3 34. 33. 4x 2 6y 2 8 5 0 In Exercises 34 and 35, use the following information. The surface area of a cylinder is given by S 5 2πrh 1 2πr 2 where r is the radius of the base and h is the height of the cylinder. 35. h r 34. Solve the formula for h. 35. What is the height of a cylinder when the surface area is 75.36 square inches and the radius is 2 inches? Use 3.14 for π. Algebra 1 Chapter 3 Assessment Book 55 Name ——————————————————————— CHAPTER 4 Date ———————————— Chapter Test A For use after Chapter 4 Write the coordinates of the point. Answers Y $ 1. A ! 1. 2. B 3. C # 4. D 2. X " 3. 4. 5. Graph the function y 5 22x 2 3 with 5. Y See left. domain 23, 22, 21, 0 in blue. Then 1 perform the transformation (x, y) → (x, }2y) and graph the image in red. Identify the domain and range of the function represented by the image. / 6. X 7. 8. See left. 9. See left. 10. See left. 11. See left. Tell whether the ordered pair is a solution of the equation. 6. y 5 2x 1 2; (23, 2) 7. 2x 1 y 5 21; (1, 23) 8. Is the amount of water in a bathtub as a function of the minutes since the water begins flowing discrete or continuous? Explain. Minutes since water begins flowing, x 1 2 3 4 5 15 25 35 13. 14. Draw the line that has the given intercepts. 9. x-intercept: 22 10. x-intercept: 1 y-intercept: 4 y ⫺6 11. x-intercept: 6 y-intercept: 3 y-intercept: 26 Y Y 6 2 ⫺2 ⫺2 2 x X Find the slope of the line that passes through the points. 12. (4, 2) and (3, 4) 70 Algebra 1 Chapter 4 Assessment Book 13. (5, 1) and (5, 22) 14. (21, 3) and (2, 4) X Copyright © Holt McDougal. All rights reserved. 12. Amount of water in the bathtub (in gallons), y Name ——————————————————————— CHAPTER 4 Chapter Test A Date ———————————— continued For use after Chapter 4 Identify the slope and y-intercept of the line with the given equation. 15. y 5 5x 1 2 16. y 5 x 2 4 Answers 15. 17. 2x 1 y 5 26 16. Solve the equation graphically. Then check your solution algebraically. 1 18. }(x 1 15) 5 5 19. 24x 2 9 5 22(x 1 5) 3 Y 18. Y / 17. X / 19. X 20. 21. 22. In Exercises 20 and 21, use the following information. The amount of precipitation varies directly with the duration of the storm. The table shows the amounts of precipitation for various durations of storms. 23. 24. Copyright © Holt McDougal. All rights reserved. 25. Duration of storm (in hours), d 2 4 6 Amount of rain (in inches), r 1 2 3 20. Write a direct variation equation that relates r and d. 21. How many inches of rain will fall after 5 hours? Evaluate the function for the given value of x. 22. f(x) 5 3x 1 12; 25 23. g(x) 5 2.25x; 100 Find the value of x so that the function has the given value. 24. h(x) 5 24x 1 3; 11 25. p(x) 5 9x 2 2; 1 Algebra 1 Chapter 4 Assessment Book 71 Name ——————————————————————— Date ———————————— Chapter Test B CHAPTER 4 For use after Chapter 4 Plot the point in the coordinate plane. Describe the location of the point. 1. A(21, 3) Answers 1. See left. 2. See left. 3. See left. 4. See left. 5. See left. 6. See left. 7. See left. 8. See left. y 3 2. B(4, 0) 1 3. C(2, 22) 23 21 1 3 x 4. D(21, 21) 23 1 5. Graph the function y 5 } x 2 1 with 2 Y domain 24, 22, 0, 2, 4 in blue. Then perform the transformation (x, y) → (x, y 1 3) and graph the image in red. Identify the domain and range of the function represented by the image. / X Graph the equation. 7. 3y 2 2x 5 26 y 8. y 5 23 y y 1 21 21 1 2 3 x ⫺2 2 6 x ⫺2 ⫺2 2 23 6 x 9. ⫺6 ⫺6 25 10. 9. Suppose the graph in Exercise 8 has the domain x ≥ 0. Classify the function as discrete or continuous. 11. Find the x-intercept and the y-intercept of the graph of the equation. 1 10. 6x 2 4y 5 12 11. 22x 1 5y 5 210 12. y 5 } x 2 2 2 72 Algebra 1 Chapter 4 Assessment Book 12. Copyright © Holt McDougal. All rights reserved. 6. 3x 2 y 5 5 Name ——————————————————————— CHAPTER 4 Chapter Test B Date ———————————— continued For use after Chapter 4 Answers The graph shows the distance of a car traveling along a straight road for 8 hours. A positive velocity is motion to the right, and a negative velocity is motion to the left. 13. 13. Determine the rates of Distance (miles) In Exercises 13–14, use the following information. y 120 100 80 60 40 14. 20 change in distance with respect to time. 0 15. 0 1 2 3 4 5 6 7 8 9 x Time (hours) 14. Between what two times is 17. the car not moving? Identify the slope and y-intercept of the line with the given equation. 15. y 5 8x 2 3 16. 16. 2x 1 9y 5 9 18. 19. 17. 23x 2 4y 5 216 20. 18. The number of tickets sold s (in millions) to a Florida theme park can be modeled by the function s 5 14.7t 1 411.6 where t is the number of years since 2000. Use a graphing calculator to approximate the year when the total number of tickets sold will be 600 million. 21. 22. See left. 23. Determine whether the equation represents direct variation. If so, identify the constant of variation. 20. 4x 2 3y 5 0 21. 2x 1 y 5 4 24. In Exercises 22–24, use the following information. An advertising company charges $150,000 each time a 30-second commercial is aired. The cost (in thousands of dollars) to produce the commercial and air it x times is given by the function C(x) 5 150x 1 300. 22. Graph the function. 23. Identify the domain and the range of the function. 24. How many times could a station air the commercial if the advertising company wants to spend $900,000? Cost (thousands of dollars) Copyright © Holt McDougal. All rights reserved. 19. y 5 2x C 1000 900 800 700 600 500 400 300 200 100 0 0 1 2 3 4 5 x Number of airings Algebra 1 Chapter 4 Assessment Book 73 Name ——————————————————————— CHAPTER 4 Date ———————————— Chapter Test C For use after Chapter 4 1. Plot the points P(22, 23), Q(1, 0), Answers y 3 R(3, 0), and S(5, 23) in the coordinate plane. Connect the points in order. Identify the resulting figure. Find its area. 1. See left. 2. See left. 3. See left. 1 1 21 21 3 x 5 23 Graph the given function in blue and identify the range. Then perform the indicated transformation and graph the image in red. 2. y 5 4x 1 3; domain 22 ≤ x ≤ 2 3. y 5 22x 2 1; domain x ≤ 0 Transformation: (x, y) → (x, 2y) 1 Transformation: (x, y) → 1 x, 2}2y 2 y ⫺9 9 3 3 1 ⫺3 ⫺3 4. y 3 9 x ⫺9 ⫺3 ⫺1 ⫺1 5. 6. 1 x 3 7. ⫺3 8. 4. Classify the function from Exercise 3 as discrete or continuous. 9. Copyright © Holt McDougal. All rights reserved. Find the x-intercept and the y-intercept of the graph of the equation. 3 5. 3x 2 2y 5 8 6. y 5 20.4x 1 1 7. y 5 2} x 1 3 4 The graph shows the distance of a car traveling along a straight road for 8 hours. 8. Give a verbal description of the trip. 9. What do the intercepts represent in this situation? Distance (miles) In Exercises 8 and 9, use the following information. y 120 100 80 60 40 20 0 0 1 2 3 4 5 6 7 8 9 x Time (hours) 74 Algebra 1 Chapter 4 Assessment Book Name ——————————————————————— Chapter Test C CHAPTER 4 Date ———————————— continued For use after Chapter 4 In Exercises 10 and 11, use the following information. Answers Your family and a friend’s family are going on vacation. The amount of fuel remaining in your family’s car after driving m miles is given by the equation a 5 20.03m 1 12 because it has a 12-gallon fuel tank and uses 0.03 gallon of fuel per mile driven. The amount of fuel remaining in your friend’s van is given by the equation a 5 20.08m 1 22. 10. 11. Use the graphs to find the difference of the amount of fuel remaining in the two fuel tanks after driving 100 miles. Fuel (gallons) 10. Graph both equations. a 24 20 16 12 8 12. See left. 14. 15. 0 100 200 300 400 m Distance (miles) 1 12. Solve 26x 5 23 x 1 } graphically. 3 1 11. 13. 4 0 See left. 2 16. See left. 17. See left. y 3 2 Check your solution algebraically. 1 3 2 1O 1 2 3 4 x 2 3 Copyright © Holt McDougal. All rights reserved. Given that y varies directly with x, write a direct variation equation that relates x and y. 1 14. x 5 }, y 5 2 3 13. x 5 28, y 5 5 15. x 5 23, y 5 24.5 Graph the function. Compare the graph to the graph of f(x) 5 x. 1 16. g(x) 5 x 2 5 17. h(x) 5 2} x 2 y ⫺6 y 6 3 2 1 ⫺2 ⫺2 ⫺6 2 6 x ⫺3 ⫺1 ⫺1 1 3 x ⫺3 Algebra 1 Chapter 4 Assessment Book 75 Name ——————————————————————— Date ———————————— Chapter Test A CHAPTER 5 For use after Chapter 5 Write an equation in slope-intercept form of the line that has the given slope and y-intercept. 3 2. slope: }; y-intercept: 21 4 1. slope: 22; y-intercept: 0 Write an equation in slope-intercept form of the line that passes through the given point and has the given slope m. 3. (2, 23); m 5 3 2 5. (3, 21); m 5 } 3 4. (21, 0); m 5 2 In Exercises 6–9, use the graph that shows gym membership costs. 6. How much was the initial Gym Membership Costs membership fee? 8. Write an equation in slope-intercept form that relates the total cost (in dollars) to the number of months of the gym membership. Cost (dollars) 7. What is the cost per month? C 400 350 300 250 200 150 100 50 0 Answers 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. See left. 11. See left. (5, 205) (2, 100) 0 1 2 3 4 5 6 7 8 9 10 11 m 9. Find the cost of a gym 12. Number of months Copyright © Holt McDougal. All rights reserved. membership for one year. 13. Graph the equation. 10. y 2 1 5 2(x 2 4) 11. y 1 2 5 2(x 2 1) y y 4 3 2 1 3 2 1 O 23 22 1 2 3 4 5 6 x O 1 2 3 x 22 23 Tell whether the sequence is arithmetic. If it is, find the next two terms. If it is not, explain why not. 12. 24, 4, 6, 10, ... 13. 0, 211, 222, 233, ... Algebra 1 Chapter 5 Assessment Book 89 Name ——————————————————————— Chapter Test A CHAPTER 5 Date ———————————— continued For use after Chapter 5 Write an equation for a linear function f that has the given values. 14. f(23) 5 2 and f(1) 5 0 Answers 14. 15. f (3) 5 23 and f(4) 5 1 15. In Exercises 16 and 17, use the following information. For a school band fundraiser, students are selling seat cushions for $4 each and license plate holders for $6 each. One student raises $304. 16. 17. 16. Write an equation in standard form of the line that models the possible combinations of seat cushions and license plate holders the student sold. 18. 17. List two of these possible combinations. 18. Write an equation of the line that passes through the point (4, 7) and 1 is (a) parallel to and (b) perpendicular to the line y 5 }2 x 2 1. 19. See left. 20. In Exercises 19–22, use the table that shows the number of calories in grams of fat. Fat (g) 31 39 19 34 43 39 35 Calories 580 680 410 590 660 640 570 24. 25. 0 10 20 30 40 50 x 20. Describe the correlation. 21. Draw a line of fit for the data. 22. Use the line of fit from Exercise 19 to predict the number of calories in a hamburger that contains 28 grams of fat. Find the zero of the function. 23. f(x) 5 x 2 8 Algebra 1 Chapter 5 Assessment Book 24. f (x) 5 3x 1 9 1 25. f (x) 5 } x 2 1 2 Copyright © Holt McDougal. All rights reserved. Calories 23. y 700 650 600 550 500 450 400 Fat (g) 90 See left. 22. 19. Make a scatter plot of the data. 0 21. Name ——————————————————————— Date ———————————— Chapter Test B CHAPTER 5 For use after Chapter 5 Write an equation in slope-intercept form of the line shown. 1. 2. y 1 3 O 3 4 4 3 2 1 5 x 22 4 25 2. 3. 1 x 25 24 23 22 24 1. y (25, 4) Answers (1, 22) 4. (0, 25) 5. In Exercises 3 and 4, use the following information. A delivery service charges a base price for an overnight delivery of a package plus an extra charge for each pound the package weighs. A customer is billed $22.85 for shipping a 3-pound package and $40 for shipping a 10-pound package. 3. Write an equation that gives the total cost of shipping a package as a function of the weight of the package. 6. 7. See left. 8. See left. 9. 4. Find the cost of shipping a 15-pound package. Find the missing coefficient in the equation of the line that passes through the given point. 5. Ax 1 y 5 3; (2, 25) 6. 3x 1 By 5 21; (2, 7) 10. Copyright © Holt McDougal. All rights reserved. Graph the equation. 2 7. y 2 2 5 }(x 2 4) 3 8. y 1 4 5 23(x 1 2) y y 3 3 2 1 2 1 22 1 2 O 3 4 x 24 22 23 22 O 1 2 x 22 23 In Exercises 9 and 10, use the table. x 2 4 6 9 11 y 23 5 13 25 33 9. Explain why the data can be modeled by a linear equation. 10. Write an equation in point-slope form that relates y to x. Algebra 1 Chapter 5 Assessment Book 91 Name ——————————————————————— CHAPTER 5 Chapter Test B Date ———————————— continued For use after Chapter 5 Tell whether the sequence is arithmetic. If it is, find the next two terms. If it is not, explain why not. 11. 3, 28, 219, 230, ... Answers 11. 12. 21, 22, 43, 65 ... 12. Write an equation in standard form of the line that passes through the given point and has the given slope m or that passes through the given points. 13. 14. 1 13. (24, 3), m 5 } 2 14. (2, 23), m 5 24 15. (22, 21), (2, 26) 16. (22, 5), (3, 5) 15. 16. In Exercises 17 and 18, use the following information. 17. A piggy bank contains only nickels and quarters. The total value in the bank is $3.80. 18. 17. Write an equation in standard form that models the possible combinations of nickels and quarters in the piggy bank. 18. List two of these possible combinations. 19. Write an equation of the line that passes through the point (24, 21) and is (a) parallel to and (b) perpendicular to the line 2x 1 7y 5 14. 19. Fat (g) 31 39 19 34 43 39 35 Calories 580 680 410 590 660 640 570 20. 20. Make a scatter plot of the data. 22. Use technology to find the equation of the best-fitting line for the data. 23. Graph the best-fitting line for the data on the scatter plot. Calories 21. Describe the correlation. y 700 650 600 550 500 450 400 0 24. Predict the number of calories in a hamburger that contains 28 grams of fat. See left. 21. 0 10 20 30 40 50 x Fat (g) 22. 23. 24. 92 Algebra 1 Chapter 5 Assessment Book See left. Copyright © Holt McDougal. All rights reserved. In Exercises 20–24, use the table. Name ——————————————————————— Date ———————————— Chapter Test C CHAPTER 5 For use after Chapter 5 Write an equation in the given form of the line shown. 1. Slope-intercept form 2. Point-slope form y 5 (21, 3) 22 2 1 O 1. y (0, 4) 2. 4 3 3. 23.5 1 2.5 x 1 Answers 2 3 4 23 22 5 3 x 3 4. 5. 22 3. The freezing point of water is 08C or 328F. The boiling point of water 6. See left. is 1008C or 2128F. Develop the formula that relates the number of degrees in Fahrenheit to the number of degrees in Celsius. 7. See left. Write an equation for a linear function f that has the given values. 4. f(23) 5 2 and f(22) 5 21 3 3 5. f (22) 5 2} and f (25) 5 } 4 4 8. 9. 10. Graph the equation. 4 6. y 1 2 5 2}(x 1 5) 3 1 7. y 2 4 5 }(x 2 1) 3 y y 5 4 3 Copyright © Holt McDougal. All rights reserved. 4 2 28 26 24 O 11. 2 4 x 2 1 24 26 28 23 22 O 1 2 3 x Find the value of k so that the three points lie on the same line. Write the equation of the line in point-slope form. 8. (1, 22), (22, 4), (4, k) 9. (2, 2), (21, 5), (3, k) Write a rule for the n th term of the sequence. Find a100. 10. 14, 22, 218, 234, ... 11. 12.7, 14.5, 16.3, 18.1 Algebra 1 Chapter 5 Assessment Book 93 Name ——————————————————————— Chapter Test C CHAPTER 5 Date ———————————— continued For use after Chapter 5 Write an equation in standard form of the line that passes through the given point and has the given slope m or that passes through the given points. Answers 2 12. (25, 24), m 5 } 5 13. (3, 22), m 5 0 13. 14. (4, 9), (4, 21) 15. (22, 4), (4, 1) 12. 14. 15. 16. Determine whether the figure is a right triangle. A right triangle contains one 90˚ angle. Justify your answer using slopes. 16. y 3 (4, 2) 2 (25, 1) 1 23 22 25 O 2 3 4 x 17. (22, 23) 23 See left. 18. In Exercises 17–21, use the table. It shows the gas mileages (in miles per gallon) for cars of different weights (in thousands of pounds). Weight 2 2.4 2.5 2.8 2.9 3.1 3.2 3.5 3.6 3.9 Mileage 34 34 28 23 25 23 23 22 24 18 19. 18. Describe the correlation. 19. Use technology to find the equation of the best-fitting line for the data. 20. Predict the gas mileage for a car the weights 3400 pounds. Miles per gallon 17. Make a scatter plot of the data. y 36 32 28 24 20 16 0 21. 0 2.0 2.5 3.0 3.5 21. Find the zero of the function from Exercise 19 and explain what it means in this situation. 94 Algebra 1 Chapter 5 Assessment Book 4.0 x Weight (thousands of pounds) Copyright © Holt McDougal. All rights reserved. 20. Name ——————————————————————— CHAPTER 6 Date ———————————— Chapter Test A For use after Chapter 6 Write an inequality represented by the graph. 1. Answers 2. 0 24 22 2 4 6 1. 26 25 24 23 22 21 2. Solve the inequality. Graph your solution. 3. 4. w 1 7 ≤ 5 3. x 2 6 . 23 See left. 0 29 26 23 3 6 9 0 26 24 22 2 4 6 4. n 6. } , 6 2 5. 24t ≥ 216 0 26 24 22 2 4 6 216 See left. 8 0 8 16 5. See left. 7. You want to buy a pair of sneakers at a shoe store, and you can spend at most $80. You have a coupon for $10 off any pair of shoes at the store. Write and solve an inequality to find the original prices p of sneakers that you can buy. 6. See left. Solve the inequality, if possible. 9. 3x 2 4 ≥ 8 11. 2(k 1 4) . 2k 2 3 12. 2a 2 1 , 6a 1 7 10. 4 2 5t ≥ 221 7. 13. 8p 1 7 2 6p . 2p 1 9 8. 14. Write and solve an inequality to find the possible values of x if the maximum area of the rectangle is to be 63 square meters. 10. 11. 3 meters (2x 1 1) meters 12. Solve the inequality graphically. / 14. Y Y / X 15. See left. 16. See left. X Write a compound inequality represented by the graph. 17. 17. 18. 18. 26 25 24 23 22 21 0 1 2 108 13. 16. 3x 2 5 ≤ 211 15. x 1 17 . 21 9. Algebra 1 Chapter 6 Assessment Book 23 22 21 0 1 2 3 4 5 Copyright © Holt McDougal. All rights reserved. 8. 5y 1 12 ≤ 7 Name ——————————————————————— Chapter Test A CHAPTER 6 Date ———————————— continued For use after Chapter 6 Solve the compound inequality. Graph your solution. Answers 19. x 1 2 . 5 or 3x ≤ 3 19. 20. 26 ≤ 5x 1 14 ≤ 24 See left. 23 22 21 0 1 2 3 4 5 25 24 23 22 21 0 1 2 3 20. Graph the function. Compare the graph with the graph of f (x) 5 ⏐x⏐ . 21. g(x) 5⏐x 1 1⏐ 22. g(x) 5⏐x⏐2 3 y y 3 3 3 1 1 1 O See left. 1 3 3 x 1 O 1 3 3 3 21. See left. 22. See left. x Determine whether the ordered pair is a solution of the inequality. Copyright © Holt McDougal. All rights reserved. 23. x 1 y , 7; (2, 4) 24. y ≥ 4x 2 3; (0, 0) 23. 25. x 1 2y . 4; (2, 1) 24. Graph the inequality. 25. 27. y ≥ 2x 1 3 26. y , 2x 2 1 y ⫺3 3 1 1 ⫺3 See left. y 3 ⫺1 ⫺1 26. 1 3 x ⫺3 ⫺1 ⫺1 27. 1 3 x ⫺3 Algebra 1 Chapter 6 Assessment Book 109 Name ——————————————————————— CHAPTER 6 Date ———————————— Chapter Test B For use after Chapter 6 Solve the inequality. Graph your solution. Answers y 2. } , 23 24 1. x 1 8 . 210 1. See left. 220 216 212 28 0 24 6 8 10 12 14 16 18 2. 3. 7 2 5d , 23 24 0 22 See left. 4. 4a 2 8 , 2a 2 4 24 23 22 21 0 1 2 3 4 3. See left. In Exercises 5 and 6, use the following information. 4. To be eligible for the playoffs, a baseball team cannot lose more than 40% of its remaining games. The team has 18 games remaining in the regular season. 5. Write and solve an inequality to find the number of games g that the team could lose and still be eligible for the playoffs. See left. 5. 6. If the baseball team loses 8 of its remaining games, will the team advance to the playoffs? Explain your answer. 6. Solve the inequality, if possible. 8. 3(2p 2 5) ≥ 8p 2 5 7. 9. 5(2s 1 7) 2 4 . 10s 2 7 8. Copyright © Holt McDougal. All rights reserved. 7. 2(3x 2 1) . 6(x 1 1) 9. In Exercises 10 and 11, use the following information. The photography club at your school decides to publish a calendar to raise money. The initial cost for equipment and software is $600. In addition to the initial cost, each calendar costs $2.50 to produce. The club plans to sell the calendars for $8 each. 10. Write and solve an inequality to find the number n of calendars that 10. 11. the photography club must sell in order to raise at least $1200. 11. Will the club reach their fundraising goal if they sell 110 calendars? Explain your answer. 12. See left. Solve the compound inequality. Graph your solution. 12. 5 2 x . 2 or 5 ≤ x 2 7 13. 210 ≤ 2(x 2 1) , 14 13. See left. 0 110 5 10 Algebra 1 Chapter 6 Assessment Book 15 ⫺5 0 5 10 Name ——————————————————————— Chapter Test B CHAPTER 6 Date ———————————— continued For use after Chapter 6 14. The water pressure p (in pounds per square inch) exerted on an 6 object in the ocean can be given by the function p 5 15 1 } d 11 Answers 14. where d is the depth (in feet) below the surface of the water. What are the possible water pressures of an object when the depth ranges from 102 feet to 468 feet? Graph the function. Compare the graph with the graph of f (x) 5 ⏐x⏐. 15. g(x) 5⏐x 1 1⏐2 2 16. See left. 17. See left. 18. See left. Y / See left. 16. g(x) 5 2 2⏐x⏐ Y 15. X / X Graph the inequality. 17. y . 23x 2 2 18. x 2 3y , 6 y y 3 3 1 1 ⫺3 ⫺1 1 3 x ⫺3 ⫺3 ⫺1 ⫺1 x 1 See left. 3 20. ⫺3 In Exercises 19 and 20, use the following information. A concert promoter needs to take in at least $380,000 from ticket sales. The promoter charges $30 for floor seats and $20 for bleacher seats. 19. Write and graph an inequality that describes the goal in terms of selling bleacher seat tickets and selling floor seat tickets. 20. Identify and interpret one of the solutions. Bleacher seats Copyright © Holt McDougal. All rights reserved. 19. 20,000 18,000 16,000 14,000 12,000 10,000 8,000 6,000 4,000 2,000 0 0 4,000 8,000 12,000 Floor seats Algebra 1 Chapter 6 Assessment Book 111 Name ——————————————————————— CHAPTER 6 Date ———————————— Chapter Test C For use after Chapter 6 Solve the inequality, if possible. Answers 1. x 1 5.8 ≤ 4.6 3 1 2. x 2 } , } 8 4 1. 3. 6(x 2 2) . 3(2x 2 5) 4. 4x . 0.2(50 1 20x) 2. (2x 1 3) feet 3. 5. Write and solve an inequality to find the possible values of x if the minimum area of the trapezoid is to be at least 45 square feet. 4. 9 feet 5. (4x 2 6) feet Translate the verbal sentence into an inequality. Then solve the inequality. 6. 6. The product of 23.9 and w is at most 19.5. 7. The quotient of the difference of 5 times a number n and 9 and 2 is 7. greater than 22 and less than or equal to 3. Solve the inequality graphically. 9 1 26 8. 2} x 2 } ≤ 2} 9. 0.8x 1 34.5 . 42.5 2 6 4 8. See left. 9. See left. Y Y / X / X 10. See left. Solve the inequality, if possible. Graph your solution. 3 2 11. 2} x , 4 and } x , 26 3 4 2 10. 1 ≤ 3 1 } x , 7 3 11. See left. 24 22 0 2 4 6 8 1 12. }(x 1 1) . 3 or 0 , 22 2 x 2 24 22 0 2 4 6 8 212 210 28 26 24 22 12. 13. 3x 2 9 ≤ 9 or 4 2 x ≤ 3 0 1 2 3 4 5 6 7 8 See left. 13. See left. 14. Your test scores are 93, 69, 89, and 97. After the next test, you want your average to be at least 84. What are the possible scores for your next test? 15. Solve the equation, if possible. ⏐ ⏐ 5 15. 23 2 2 } x 5 18 4 112 Algebra 1 Chapter 6 Assessment Book 14. 16. 2⏐3x 1 8⏐ 2 13 5 25 16. Copyright © Holt McDougal. All rights reserved. Name ——————————————————————— CHAPTER 6 Chapter Test C Date ———————————— continued For use after Chapter 6 Write an absolute value equation represented by the graph. Answers 17. 17. 18. 1 2 3 4 5 6 7 8 9 0 25 24 23 22 21 1 2 18. Graph the function. Compare the graph with the graph of f (x) 5 ⏐x⏐. 19. g(x) 5 0.25⏐x⏐ 2 2 See left. 20. See left. 20. g(x) 5 2 2⏐x 1 1⏐ 2 0.5 Y Y / / X X 21. See left. 22. Solve the inequality. Graph your solution. ⏐ 19. ⏐ See left. 5 22. }⏐7 2 4x⏐ 2 9 . 6 3 1 21. 23 4 2 } x . 212 2 23. 216 0 28 8 16 22 21 0 1 2 3 4 5 6 23. For your chemistry experiment, you are trying to keep the water Graph the inequality. See left. See left. y 3 3 1 1 1 3 x ⫺3 ⫺3 ⫺1 ⫺1 27. 1 3 x ⫺3 In Exercises 26 and 27, use the following information. To mail a package, the sum of the length x (in inches) and twice the sum of the width y (in inches) and the height of the box must not exceed 108 inches. 26. Write and graph an inequality that describes the possible lengths and widths of a 24-inch high box that can be sent by priority mail. 27. 25. 25. 2x 2 3(y 1 1) ≥ y 2 (4 2 x) y ⫺1 ⫺1 See left. 26. 24. 4(x 2 2) , y 2 5 ⫺3 24. Identify and interpret one of the solutions. Width (inches) Copyright © Holt McDougal. All rights reserved. temperature at 358C. For the experiment to work properly, the actual temperature can vary by as much as 1%. Write and solve an absolute value inequality to find the acceptable temperatures of the water. y 30 25 20 15 10 5 0 0 10 20 30 40 50 60 x Length (inches) Algebra 1 Chapter 6 Assessment Book 113 Name ——————————————————————— CHAPTER 7 Date ———————————— Chapter Test A For use after Chapter 7 Use the graph to solve the linear system. 1. x 1 2y 5 4 Answers 2. 2x 2 y 5 3 2x 1 y 5 21 1. 3x 1 y 5 2 2. y 23 y 3 1 1 21 21 21 21 1 3 x 3. 13 x 4. 23 See left. 5. In Exercises 3–5, use the following information. 6. You are painting the white lines around the perimeter of a tennis court. You measure and find that the perimeter is 228 feet and the length is 42 feet longer than the width. 7. 3. Write a linear system. Let w be the width of the tennis court and let l be the length of the tennis court. 9. 10. 11. 12. 0 20 60 100 Width of tennis court w 5. Find the length and width of the tennis court. Solve the linear system using substitution. 6. x 5 2 3x 1 2y 5 4 9. 3x 2 y 5 2 y 5 2x 2 9 7. 3x 2 2y 5 6 y53 10. 3x 1 y 5 4 4x 2 3y 5 1 8. x 5 y 1 1 x 1 2y 5 7 11. x 1 y 5 12 3x 2 2y 5 6 12. A cosmetologist has a bottle of 7% hydrogen peroxide solution and a bottle of 4% hydrogen peroxide solution. The cosmetologist needs 300 milliliters of a 5% hydrogen peroxide solution for a hair dye. Write and solve a linear system to find how many milliliters of each solution the cosmetologist needs to mix together. 132 Algebra 1 Chapter 7 Assessment Book Copyright © Holt McDougal. All rights reserved. Length of tennis court 4. Graph the linear system. 120 100 80 60 40 20 0 8. Name ——————————————————————— Chapter Test A CHAPTER 7 Date ———————————— continued For use after Chapter 7 Solve the linear system using elimination. Answers 13. x 1 y 5 4 14. 9x 1 2y 5 4 15. 4x 2 5y 5 22 x2y56 9x 2 y 5 25 x 1 2y 5 21 17. 4x 1 3y 5 7 18. 2x 2 3y 5 16 16. x 2 2y 5 4 3x 1 4y 5 2 7x 1 2y 5 9 3x 1 4y 5 7 Determine whether the linear system has one solution, no solution, or infinitely many solutions. 19. y 5 2x 2 1 20. 3x 1 y 5 12 21. 3x 2 y 5 5 y 5 2x 1 1 y 5 3x 1 12 y 5 3x 2 5 23. y > 1 15. 16. 17. 18. 20. y≤x13 x>2 14. 19. Graph the system of linear inequalities. 22. y < 21 13. 21. y y 3 22. See left. 23. See left. 3 1 21 21 1 13 1 5 x 23 21 21 1 35 x 24. 23 During the summer, you want to earn at least $150 per week. You earn $10 per hour working for a farmer, and you earn $5 per hour babysitting for your neighbor. You can work at most 25 hours per week. 24. Write and graph a system of linear inequalities that models the situation. Let x be the number of hours per week working on the farm and let y be the number of hours per week babysitting. Babysitting hours Copyright © Holt McDougal. All rights reserved. In Exercises 24 and 25, use the following information. y 30 25 See left. 25. 20 15 10 5 0 0 5 10 15 20 25 30 x Farm hours 25. If you work 10 hours per week on the farm and 12 hours per week babysitting, will you earn at least $150? Algebra 1 Chapter 7 Assessment Book 133 Name ——————————————————————— Date ———————————— Chapter Test B CHAPTER 7 For use after Chapter 7 Tell whether the ordered pair is a solution of the linear system. 1. (4, –1) 2. (8, 5) x 1 2y 5 2 x 2 2y 5 6 Answers 1. 3. (–3, 5) 5x 2 4y 5 20 3y 5 2x 1 1 9x 1 7y 5 8 8x 2 9y 5 269 In Exercises 4–6, use the following information. 2. 3. 4. Tickets for a school play cost $4 for adults and $2 for students. At the end of the play, the school sold a total of 105 tickets and collected $360. 4. Write a linear system. Let x be the number of adult tickets sold and 5. See left. let y be the number of student tickets sold. 6. y 180 160 140 120 7. 8. 100 80 60 9. 10. 40 20 0 11. 0 20 60 100 Adult tickets x 12. 6. Find the number of adult tickets sold and the number of student tickets sold. Solve the linear system using substitution. 7. 4x 1 3y 5 25 x5y23 10. 3x 1 y 5 24 2x 1 y 5 0 8. x 1 3y 5 228 y 5 25x 11. 3x 2 y 5 13 2x 1 5y 5 20 9. x 1 4y 5 21 2x 2 5y 5 11 12. x 2 4y 5 23 23x 1 5y 5 2 13. A hotel rents a double-occupancy room for $30 more than a single- occupancy room. One night, the hotel took in $3115 after renting 15 double-occupancy rooms and 26 single-occupancy rooms. Write and solve a linear system to find the cost of renting a doubleoccupancy room and the cost of renting a single-occupancy room. 134 Algebra 1 Chapter 7 Assessment Book 13. Copyright © Holt McDougal. All rights reserved. Student tickets 5. Graph the linear system. Name ——————————————————————— Chapter Test B CHAPTER 7 Date ———————————— continued For use after Chapter 7 Solve the linear system using elimination. 14. 3x 2 y 5 9 15. 5x 1 7y 5 10 2x 1 y 5 1 3x 2 14y 5 6 Answers 16. 4x 1 3y 5 15 14. 2x 2 5y 5 1 15. 17. 2x 1 3y 5 1 18. 2x 2 3y 5 22 19. 2x 1 9y 5 16 5x 5 1 2 3y 16. Without solving the linear system, tell whether the linear system has one solution, no solution, or infinitely many solutions. 17. 20. y 5 2 2 3x 19. 3x 2 5y 5 28 22y 1 3x 5 12 21. y 5 x 1 2 6x 1 2y 5 7 22. 2x 2 y 5 1 x1y56 18. 4x 2 2y 5 2 20. 23. On Monday, the office staff at your school paid $8.77 for 4 cups of coffee and 7 bagels. On Wednesday, they paid $15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel? Explain. 21. Graph the system of linear inequalities. 24. y ≥ x 2 3 25. x < 3 y ≤ 2x 1 2 22. y>1 y ≥ 2x y 3 y 1 23. ⫺1 ⫺1 1 3 x 23 ⫺3 21 21 1 x 23 26. In an academic competition, scoring is based on a written examination and an oral presentation. The written examination score cannot exceed 65 points and the oral presentation cannot exceed 35 points. Write and graph a system of inequalities for the scores a school team can receive. Oral presentation Copyright © Holt McDougal. All rights reserved. 1 y 35 30 25 24. See left. 25. See left. 26. See left. 20 15 10 5 0 0 10 20 30 40 50 60 70 x Written examination Algebra 1 Chapter 7 Assessment Book 135 Name ——————————————————————— CHAPTER 7 Date ———————————— Chapter Test C For use after Chapter 7 Solve the linear system by graphing. 1. 3x 1 5y 5 218 Answers 2. 2x 2 y 5 6 4x 1 2y 5 210 4x 2 2y 5 8 1 ⫺3 ⫺1 ⫺1 See left. y y ⫺5 1. ⫺1 ⫺1 1 x 1 3 x 2. See left. ⫺3 ⫺3 ⫺5 3. ⫺5 See left. 3. 3x 2 4y 5 24 3 2 y 6 4. 2 5. }x 1 y 5 3 2 6 x 6. 26 7. 8. Solve the linear system using substitution. 4. 3x 2 2y 5 6 4y 5 28 5. 4x 1 3y 5 11 3x 2 y 5 5 1 7. x 1 6y 5 217 8. x 2 } y 5 1 2 0.4x 1 0.5y 5 21.1 2 1 }x 2 }y 5 1 3 3 6. 4x 1 5y 5 18 3x 2 9y 5 212 8 1 9. 4x 1 } y 5 } 3 3 3 5 1 } x 1 } y 5 2} 2 4 2 10. A restaurant owner wants to add imitation maple syrup that costs $4.00 per liter to 50 liters of pure maple syrup that costs $9.50 per liter. How many liters of imitation maple syrup should be added to make a mixture that costs $5.00 per liter? 12. 4x 1 3y 5 4 9x 2 3y 5 8 8x 1 6y 5 8 13. 3x 2 4y 5 8 5x 1 3y 5 26 2 1 14. 5y 1 2x 5 5x 1 1 15. 5x 2 2y 5 8x 2 1 16. } x 2 } y 5 1 5 3 3x 2 2y 5 3 1 3y 2x 1 7y 5 4y 1 9 3 2 }x 1 }y 5 5 5 3 17. Flying with the wind, a pilot travels 600 miles between two cities in four hours. The return trip into the wind takes five hours. The speed of the wind remains constant during the trip. Find the average speed of the plane with no wind and the speed of the wind. 136 Algebra 1 Chapter 7 Assessment Book 10. 11. 12. 13. 14. 15. Solve the linear system using elimination. 11. 3x 2 6y 5 6 9. 16. 17. Copyright © Holt McDougal. All rights reserved. 22 22 Name ——————————————————————— Chapter Test C CHAPTER 7 Date ———————————— continued For use after Chapter 7 Without solving the linear system, tell whether the linear system has one solution, no solution, or infinitely many solutions. Answers 18. 12x 2 16y 5 8 19. 19. 0.4x 1 0.5y 5 0.2 20. 0.2x 2 0.6y 5 0.6 3x 2 4y 5 2 0.3x 2 0.1y 5 1.1 0.4x 2 1.2y 5 2.4 Write a system of linear inequalities for the shaded region. 21. 22. y 18. 20. 21. y 3 3 1 23 1 ⫺1 1 3 22. 3 x 21 21 5 x 23 23. In Exercises 23– 25, use the following information. A bakery sells cookies and cakes. The table shows the time that it takes to bake and decorate each batch of cookies and each batch of cakes, and the time the bakery can devote to baking and decorating cookies and cakes. Time to decorate (hours) Cakes Available Time 1.5 2 15 24. 2 3 3 13 25. } 23. Write and graph a system of linear inequalities for the number x of batches of cookies and the number y of batches of cakes that the bakery can make under the given constraints. Batches of cakes Copyright © Holt McDougal. All rights reserved. Time to bake (hours) Cookies See left. y 8 7 6 5 4 3 2 1 0 0 4 8 12 16 20 x Batches of cookies 24. Find the vertices (corner points) of the graph. 25. The bakery makes a profit of $20 for each batch of cookies and $30 for each batch of cakes. The profit P is given by the equation P 5 20x 1 30y. Find the profit for each ordered pair in Exercise 24. Which vertex results in the maximum profit? Algebra 1 Chapter 7 Assessment Book 137 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 Name ——————————————————————— CHAPTER 9 Date ———————————— Chapter Test A For use after Chapter 9 Find the sum or difference. Answers 1. (4a 2 4a ) 1 (6a 1 5a ) 3. (3x 2 1 2x 2 2) 2 (5x 2 2 5x 1 6) 4. (2h 2 7h 1 10) 1 (h 1 4h 1 7) 3 2 3 2 2 2. (2y 2 4y) 2 (2y 1 2) 2 3 1. 2. 2 3. In Exercises 5 and 6, use the following information. 4. For 1990 through 2000, the number of fiction books F (in 10,000s) and nonfiction books N (in 10,000s) borrowed from a library can be modeled by F 5 0.01t2 1 0.09t 1 6 5. 6. N 5 0.004t2 1 0.06t 1 4 7. where t is the number of years since 1990. 5. Write an equation that gives the total number of books borrowed B 8. from the library in a year from 1990 to 2000. 9. 6. What was the total number of books borrowed in 2000? 10. Find the product. 9. (d 2 1 3d 1 2)(d 1 1) 11. (t 2 4)2 11. 8. (2w 2 3)(4w 2 7) 10. ( p 1 3)( p 2 3) 12. 12. (2s 2 5)(2s 1 5) 13. 14. In humans, the gene B is for brown eyes, and the gene b is for blue eyes. Any gene combination with a B results in brown eyes. Suppose the parents have the same gene combination Bb. The Punnett square shows the possible gene combinations of the offspring and the resulting eye color. Father In Exercises 13 and 14, use the following information. Mother B b 15. B BB Bb 16. b Bb bb 13. What percent of the possible gene combinations of the offspring result in blue eyes? 14. Show how you could use a polynomial to model the possible gene combinations of the offspring. Solve the equation. 15. (q 1 7)(q 2 4) 5 0 172 Algebra 1 Chapter 9 Assessment Book 16. (4z 2 1)(z 1 5) 5 0 Copyright © Holt McDougal. All rights reserved. 7. n(2n3 2 3n 1 2) Name ——————————————————————— CHAPTER 9 Chapter Test A Date ———————————— continued For use after Chapter 9 Factor out the greatest common monomial factor. Answers 17. 4c8 2 8c 5 17. 18. 6f 2g 3 1 12g 19. 2k 3 1 6k 2 2 14k 18. Solve the equation. 20. 3m2 2 9m 5 0 21. 7u2 5 3u 19. In Exercises 22 and 23, use the following information. 20. A frog leaps from a lily pad in a pond into the air with an initial vertical velocity of 20 feet per second. The height h (in feet) of the frog can be modeled by h 5 216t 2 1 vt 1 s where t is the time (in seconds) the frog has been in the air, v is the initial vertical velocity (in feet per second), and s is the initial height. 21. 22. 23. 22. Write an equation that gives the height of the frog as a function of the time (in seconds) since leaving the lily pad. 24. 23. After how many seconds does the frog land in the water? 25. Factor the trinomial. 26. 24. x2 1 9x 1 14 25. y 2 2 y 2 12 26. 3m2 1 20m 1 12 27. Find the dimensions of the triangle that has an area of 27. 28. 30 square centimeters. 29. (x 1 17) cm Copyright © Holt McDougal. All rights reserved. 30. Not drawn to scale 31. x cm Factor the polynomial completely. 32. 28. 3x 3 1 15x 2 1 18x 33. 29. 2s2 2 18 30. r(r 1 3) 1 7(r 1 3) Solve the equation. 31. b4 2 3b3 2 10b2 5 0 32. j( j 1 3) 5 28 33. A small vegetable garden has an area of 80 square feet. Its length is 2 feet more than the width. Find the dimensions of the garden. x x12 Algebra 1 Chapter 9 Assessment Book 173 Name ——————————————————————— CHAPTER 9 Date ———————————— Chapter Test B For use after Chapter 9 Find the sum or difference. Answers 1. (4a3 2 2a 1 1) 2 (a3 2 2a 1 3) 1. 2. (3x3 1 4x 1 14) 1 (24x2 1 21) 2. 3. (3d 2 5d 3 1 2d 2) 2 (8d 3 1 6d 2 1) 3. 4. (23n 1 7n) 1 (4n3 2 2n2 1 12) In Exercises 5 and 6, use the following information. During the period 1985–2012, the projected enrollment B (in thousands of students) in public schools and the projected enrollment R (in thousands of students) in private schools can be modeled by B 5 218.53t 2 1 975.8t 1 48,140 and 4. 5. R 5 80.8t 1 8049 where t is the number of years since 1985. 6. 5. Write an equation that models the difference in the projected enrollments for public schools and private schools as a function of the number of years since 1985. 7. 8. 6. Find the difference in projected enrollments for public schools and 9. private schools in 2005. Find the product. 9. (s2 1 6s 2 5)(5s 1 2) 11. (w 2 5) 2 8. ( y 1 4)(5y 2 3) 10. (4p 1 1)(4p 2 1) 10. 11. 2 12. (2b 1 3) 12. In Exercises 13 and 14, use the following information. 13. You are making an open box from a rectangular sheet of cardboard by cutting squares 2 inches in length from each corner and folding up the sides. The length of the sheet of cardboard is 8 inches more than the width. 2 in. 2 in. 13. Write a polynomial that represents the total volume of the open box. 14. Find the volume of the open box when the width of the sheet of cardboard is 6 inches. 174 Algebra 1 Chapter 9 Assessment Book 14. Copyright © Holt McDougal. All rights reserved. 7. 24c(29c 2 1 5c 1 8) Name ——————————————————————— CHAPTER 9 Chapter Test B Date ———————————— continued For use after Chapter 9 Solve the equation. Answers 15. (h 2 7)(2h 1 1) 5 0 15. 16. 4g 2 2 32g 5 0 16. 2 17. 3m 5 26m 17. In Exercises 18 and 19, use the following information. 18. The room and the hallway shown in the floor plan below have different dimensions but the same area. w11 Bedroom Hall 19. w 20. 21. w22 3w 22. 18. Write an equation that relates the areas of the rooms. 23. 19. Find the value of w. Factor the trinomial. 20. n2 2 14n 2 72 21. 2x 2 1 14x 2 45 22. 6k 2 2 k 2 12 24. 25. Copyright © Holt McDougal. All rights reserved. In Exercises 23 and 24, use the following information. A juggler throws a ball from an initial height of 4 feet with an initial vertical velocity of 30 feet per second. The height h (in feet) of the ball can be modeled by h 5 216t 2 1 vt 1 s where t is the time (in seconds) the ball has been in the air, v is the initial vertical velocity (in feet per second), and s is the initial height. 23. Write an equation that gives the height (in feet) of the ball as a function of the time (in seconds) since it left the juggler’s hand. 26. 27. 28. 29. 30. 24. If the juggler misses the ball, after how many seconds does it hit the ground? 31. Factor the polynomial completely. 25. x5 2 x 3 26. 5a(a 2 3) 2 7(a 2 3) 27. 9t 4 1 30t 3 1 25t 2 28. b 3 1 5b2 2 3b 2 15 32. Solve the equation. 29. x 2 1 8x 1 15 5 0 30. 7y 2 2 5 5y 2 31. 72 5 32q2 32. u3 1 6u2 5 4u 1 24 Algebra 1 Chapter 9 Assessment Book 175 Name ——————————————————————— Date ———————————— Chapter Test C CHAPTER 9 For use after Chapter 9 Find the sum or difference. Answers 1. (10p2 2 5p3 1 4 2 12p) 1 (8p3 2 4p2 1 5) 1. 2. (24x 2y 2 5xy 2 y) 2 (25x 2y 1 6xy 1 3) 2. 3. (6cd 1 3c 1 9d) 1 (3cd 2 5d) 3. In Exercises 4 and 5, use the following information. During the period 1985–2012, the projected enrollment B (in thousands of students) in public schools and the projected enrollment R (in thousands of students) in private schools can be modeled by B 5 218.53t 2 1 975.8t 1 48,140 and 4. 5. R 5 80.8t 1 8049 where t is the number of years since 1985. 4. Write an equation that models the difference in the projected enrollments for public schools and private schools as a function of the number of years since 1985. 6. 7. 5. Describe the trend in the difference in projected enrollments for public schools and private schools over time. 9. 1 8. (a 2 b)(5a 1 7b) 10. (7t 1 3u)(7t 2 3u) 2 7. (3s 2 2 s 2 8)(4 2 s) 9. (5z 2 4)2 11. 1 3q 2 }12 21 3q 1 }12 2 10. 11. 12. 13. In Exercises 12–14, use the following information. You are making an open box from a rectangular sheet of cardboard by cutting squares of equal length from each corner and folding up the sides. The dimensions of the sheet of cardboard are 15 inches by 12 inches. x in. x in. 15 in. 12 in. 12. Write a polynomial that represents the total volume of the open box. 13. What is a reasonable domain for the function? 14. Find the volume of the open box when 2-inch squares are cut from each corner. 176 Algebra 1 Chapter 9 Assessment Book 14. Copyright © Holt McDougal. All rights reserved. Find the product. 1 6. 6xy 2x2 2 3xy 1 } y 2 3 8. Name ——————————————————————— CHAPTER 9 Chapter Test C Date ———————————— continued For use after Chapter 9 Find the zeros of the function. 15. f (x) 5 242x 2 2 14x Answers 16. g(x) 5 210x 2 1 3x 1 27 17. The stopping distance of a car is modeled by the function d 5 0.05r(r 1 2) where d is the stopping distance of the car measured in feet and r is the speed of the car in miles per hour. If skid marks left on the road are 48 feet long, how fast was the car traveling? Factor the trinomial. 16. 17. 18. 19. 18. x 2 2 14xy 2 51y 2 2 15. 20. 2 19. 4m 1 9mn 1 5n 21. 20. 2c3 2 7c 2d 1 3cd 2 22. Find the dimension of the rectangle or triangle that has the given area. 21. Area: 15 square meters 22. Area: 2.5 square centimeters (2x 2 3) cm 23. 24. 25. (2x 2 1) m (2x 1 1) cm (x 1 3) m 27. Copyright © Holt McDougal. All rights reserved. Factor the polynomial completely. 3 26. 28. 3 2 23. 36p 2 49p 24. 9y 1 30y 1 25y 25. uv 1 wx 2 wv 2 ux 26. 25a2 2 20ab3 1 4b6 27. 23c 2 1 75u2 28. x3 1 2x2 2 49x 2 98 29. A seagull flying over a lake drops a fish from a height of 81 feet. 29. 30. 31. After how many seconds does the fish land in the water? 32. Solve the equation. 30. 26w 3 5 2150w 31. x3 1 12 5 3x2 1 4x 33. Write a polynomial equation with integral coefficients that has the given roots. 32. 0, 22, and 1 2 33. 24 and } 3 Algebra 1 Chapter 9 Assessment Book 177 Name ——————————————————————— Date ———————————— Chapter Test A CHAPTER 10 For use after Chapter 10 Graph the function. Compare the graph with the graph of y 5 x 2. 1. y 5 3x 2 Answers 1. See left. 2. See left. 2 2. y 5 2x 1 2 y y 5 1 3 23 3 x 1 21 21 1 23 23 3 x 1 21 21 In Exercises 3–5, use the following information. A baseball player hits a baseball into the air with an initial vertical velocity of 48 feet per second from a height of 3 feet. 3. Write an equation that gives the baseball’s height as a function of the time (in seconds) after it is hit. 4. After how many seconds does the baseball reach its maximum height? 3. 5. What is the maximum height? 4. 2 7. See left. Y X / X 8. Solve the equation using the graph. 8. x 2 2 2x 2 8 5 0 9. x 2 2 3x 1 5 5 0 y 9. y 2 6 5 x 3 1 210 192 See left. 7. y 5 3x 1 21x 1 36 Y 2 6. 2 6. y 5 2x 1 9 / 5. Algebra 1 Chapter 10 Assessment Book 21 1 3 x Copyright © Holt McDougal. All rights reserved. Graph the quadratic function. Label the vertex, axis of symmetry, and x-intercepts. Identify the domain and range of the function. Name ——————————————————————— Chapter Test A CHAPTER 10 Date ———————————— continued For use after Chapter 10 Solve the equation. Round the solutions to the nearest hundredth, if necessary. 10. a 2 5 28 11. 2w 2 2 72 5 0 Answers 10. 12. (t 1 5)2 5 4 11. 13. Describe and correct the error in solving the equation x2 2 6x 2 3 5 0 by completing the square. 12. 2 x 2 6x 5 3 13. x2 2 6x 1 36 5 3 (x 2 6)2 5 3 } x 2 6 5 6Ï3 } x 5 6 6 Ï3 Write the function in vertex form, then graph the function. Label the vertex and axis of symmetry. 14. y 5 2x 2 1 6x 2 7 15. y 5 x 2 2 2x 1 2 Y Y 14. X / See left. X / Copyright © Holt McDougal. All rights reserved. 15. Use the quadratic formula to solve the equation. Round your solutions to the nearest hundredth, if necessary. 16. 4p2 2 8p 2 1 5 0 17. 4d 2 1 12d 1 9 5 0 See left. s2 2 2s 5 5 16. 19. For the period 1990–2001, the number of tickets sold (in millions) 17. 18. for Broadway road tours can be modeled by the function y 5 210.4x 2 1 132x 1 332 where x is the number of years since 1990. In what year was 750 million tickets sold for Broadway road tours? Tell whether the equation has two solutions, one solution, or no solution. 20. 3r 2 2 r 1 2 5 0 21. 5c 2 2 2c 2 8 5 0 22. 3z 2 1 6z 5 23 Tell whether the graph represents a linear function, an exponential function, or a quadratic function. 23. 24. y 5 3 3 1 1 19. 20. 21. 22. 23. y 5 18. 24. 21 1 3 x 21 1 3 x Algebra 1 Chapter 10 Assessment Book 193 Name ——————————————————————— CHAPTER 10 Date ———————————— Chapter Test B For use after Chapter 10 Graph the function. Compare the graph with the graph of y 5 x 2. 1 1. y 5 } x 2 2 1 4 Answers 1. See left. 2. See left. 2. y 5 2x 2 1 5 y y 3 1 23 3 3 x 1 21 21 1 23 23 3 x 1 21 21 Tell whether the function has a minimum value or a maximum value. Then find the minimum and maximum value. 1 3. y 5 22x2 1 8x 1 3 4. y 5 } x 2 2 2x 1 5 5. y 5 6x 2 1 7 2 6. An arch of balloons decorates the entrance to a high school prom. The balloons are tied to a frame. The shape of the frame can be 1 modeled by the graph of the equation y 5 2}4 x 2 1 3x where x and y are measured in feet. What is the maximum height of the arch of balloons? 3. 8. y 5 x 2 1 4x 7. y 5 21(x 1 2)(x 2 4) 4. Y y 10 / X 5. 6 2 1O x 1 6. Solve the equation by graphing. 9. x 2 1 5x 2 14 5 0 See left. 8. See left. 10. 2x 2 1 3x 1 4 5 0 y 22 24 7. y x 5 212 9. 1 1 194 Algebra 1 Chapter 10 Assessment Book 3 x 10. Copyright © Holt McDougal. All rights reserved. Graph the quadratic function. Label the vertex, axis of symmetry, and x-intercepts. Identify the domain and range of the function. Name ——————————————————————— CHAPTER 10 Chapter Test B Date ———————————— continued For use after Chapter 10 Solve the equation. Round the solutions to the nearest hundredth, if necessary. 11. 16t 2 2 9 5 0 12. 2(x 2 6)2 5 24 completing the square. x 2 8x 5 x2 2 8x 1 (x 2 x2 ? 11. 13. 4n 2 2 13 5 220 14. Complete the steps to solve the equation x 2 2 8x 2 3 5 0 by 2 Answers 12. 13. ? 14. 5 19 ? )2 5 19 ? 5 ? x5 ? 15. See left. Write the function in vertex form, then graph the function. Label the vertex and axis of symmetry. 15. y 5 23x 2 2 12x 2 8 16. 16. y 5 2x 2 2 12x 1 21 See left. Y y 17. 18. 1 O 19. 1 / Copyright © Holt McDougal. All rights reserved. x X Use the quadratic formula to solve the equation. Round the solutions to the nearest hundredth, if necessary. 17. p2 1 8p 2 15 5 0 18. 2y 2 2 7y 5 10 20. 21. 22. 19. 9z 2 1 12z 1 4 5 0 23. 20. During the period 1998–2002, the number y (in millions) of juvenile books shipped to bookstores can be modeled by the equation y 5 215x 2 1 64x 1 360 where x is the number of years since 1998. In what years were there 400 million juvenile books shipped to bookstores? 24. 25. 26. Find the number of x-intercepts that the graph of the function has. 21. f(x) 5 3x2 2 3x 1 4 22. f(x) 5 4x2 2 2x 2 1 23. f(x) 5 4x2 1 12x 1 9 Tell whether the ordered pairs represent a linear function, an exponential function, or a quadratic function. 24. (–2, 213), (21, 28), (0, 23), (1, 2), (2, 7) 25. (22, 0), (21, 23), (0, 24), (1, 23), (2, 0) 26. 1 22, }19 2, 1 21, }13 2, (0, 1), (1, 3), (2, 9) Algebra 1 Chapter 10 Assessment Book 195 Name ——————————————————————— Date ———————————— Chapter Test C CHAPTER 10 For use after Chapter 10 Tell how you can obtain the graph of g from the graph of f using transformations. Answers 1. 1 2. f (x) 5 } x 2 1 3 2 1. f(x) 5 2x 2 2 2 g(x) 5 x 2 1 5 g(x) 5 4x 2 1 1 In Exercises 3 and 4, use the following information. 2. The distance a lookout in a submarine can see is related to how high the periscope is above the surface of the water. The height (in feet) of the periscope can be modeled by the function h 5 0.51d 2 where d is the distance (in miles) the lookout can see. 3. Graph the function. Height (feet) 4. Use the graph to estimate how many feet above the surface of the water the periscope must be in order to see a ship 4 miles away. h 12 10 8 6 4 2 0 3. 4. 0 1 2 3 4 5 d Distance (miles) Graph the function. Label the vertex and the axis of symmetry. 3 6. y 5 2 x 2 } (x 2 3) 4 1 y y 1 21 21 2 3 5 x 23 1 21 21 1 3 5 x In Exercises 7–10, use the following information. In the past, a concert promoter sold 8000 tickets when the tickets were priced at $10 each. He wants to increase the price of a ticket, but he estimates he will lose 500 ticket sales for each $1 increase in the price of a ticket. 7. Write a function for the revenue R generated by selling tickets in terms of the number n of $1 increases. 8. Write the function in Exercise 7 in standard form. 9. Find the maximum revenue. 10. At what price should the tickets be sold to generate the most revenue? 196 Algebra 1 Chapter 10 Assessment Book See left. 6. See left. 7. 8. 9. 10. 3 1 5. Copyright © Holt McDougal. All rights reserved. 1 5. y 5 2} x 2 1 x 2 1 4 See left. Name ——————————————————————— CHAPTER 10 Chapter Test C Date ———————————— continued For use after Chapter 10 11. Approximate the zeros of the function Answers y 2 2 f(x) 5 2x 2 4x 2 9 to the nearest tenth. 22 11. x 1 12. 13. 210 14. Solve the equation by completing the square. Round the solutions to the nearest hundredth. 12. v 2 5 14 1 16v See left. 15. 13. 2w 2 2 4w 2 1 5 0 23 4 14. Write the function y 5 2x2 1 } x 1 } 3 9 16. Y in vertex form, then graph the function. Label the vertex and the axis of symmetry. 17. / 18. X 19. Use the quadratic formula to solve the equation. Round the solutions to the nearest hundredth. 15. 6q 2 1 4q 5 5q 2 2 16. 4d 1 2 5 (d 2 1)(d 1 3) 20. Copyright © Holt McDougal. All rights reserved. In Exercises 17 and 18, use the following information. The fuel efficiency E (in miles per gallon) for a mid-sized car can be modeled by the equation E 5 20.018v 2 1 1.476v 1 3.4 where v is the speed (in miles per hour) of the car. 21. 17. At what speed should the car travel on the highway to get 30 miles per gallon? 18. Does the mid-sized car ever get 35 miles per gallon? If so, at what speed(s)? 19. Give a value of c for which the equation 5x 2 1 10x 1 c 5 0 has (a) two solutions, (b) one solution, and (c) no solutions. Tell whether the table of values represents a linear function, an exponential function, or a quadratic function. Then write an equation for the function. 20. x 22 –1 0 1 2 y 2 2.5 3 3.5 4 21. x 22 –1 0 1 2 y 3 23 25 –3 3 Algebra 1 Chapter 10 Assessment Book 197 Name ——————————————————————— Date ———————————— Chapter Test A CHAPTER 11 For use after Chapter 11 Graph the function and identify its domain and range. Then } compare the graph with the graph of y 5 Ï x . } Answers } 1. y 5 3Ï x 1. See left. 2. See left. 2. y 5 Ï x 21 y y 7 7 5 5 3 3 1 1 1 7 x 5 3 1 7 x 5 3 Simplify the expression. } 9 } 3. Ï 32 } 6. 4 5. } } Ï7 Ï}16 4. } Ï81x 6y 3 } 7. 3Ï 5 2 7Ï 5 } 3. } 8. Ï 2 (10 2 Ï 2 ) 4. In Exercises 9 and 10, use the figure. 9. Find the exact perimeter of the rectangle. 5. 4 3 cm 3 cm 10. Find the exact area of the rectangle. Copyright © Holt McDougal. All rights reserved. Simplify the expression. Assume variables are nonnegative. 11. 3} 3} Ï16 • Ï4x 3 3} 3} Ï8 1 Ï2y 12. 13. 3 } 6. 7. 8. 7 Ï}64 9. Solve the equation. Check for extraneous solutions. } 10. 14. Ï 3x 1 2 5 5 } } 15. Ï 5x 1 2 5 Ï 3x 1 8 11. } 16. Ï x 1 12 5 x 12. 17. Near the Earth’s surface, the speed of sound s (in meters per second) 13. through air is given by s 5 20Ï T 1 273 where T is the air temperature (in degrees Celsius). At what air temperature is the speed of sound about 340 meters per second? 14. } 15. Find the unknown length. 18. 16. 19. x 8 14 17. 9 18. 15 x 19. Algebra 1 Chapter 11 Assessment Book 211 Name ——————————————————————— Chapter Test A CHAPTER 11 For use after Chapter 11 Date ———————————— continued Tell whether the triangle with the given side lengths is a right triangle. 20. 12, 16, 20 21. 8, 11, 14 Answers 20. 21. 22. A support wire is attached to a telephone pole at a point 30 meters above the ground. The wire is anchored to the ground at a point 10 meters from the base of the pole. Find the length of the wire to the nearest tenth of a meter. 22. 23. 24. 25. 26. 30 m 27. 10 m 28. Find the distance between the two points. 23. (9, 2), (4, 7) 29. 24. (25, 0), (2, 6) Find the midpoint of the line segment with the given endpoints. 25. (8, 3), (10, 5) 26. (210, 8), (2, 26) y 2 22 2 x r 26 27. Find the coordinates of the ordered pair that represents the center of the circle. 28. Find the length of the radius of the circle. 29. Find the area of the circle. Use 3.14 for π. Round your answer to the nearest tenth. 212 Algebra 1 Chapter 11 Assessment Book Copyright © Holt McDougal. All rights reserved. In Exercises 27–29, use the following graph of a circle. Name ——————————————————————— Date ———————————— Chapter Test B CHAPTER 11 For use after Chapter 11 Graph the function and identify the domain and range. Then } compare the graph with the graph of y 5 Ï x . 1 } 1. y 5 }Ï x 2 3 2 Answers 1. See left. 2. See left. } 2. y 5 2Ï x 1 2 y y 1 1 21 21 3 5 1 x 1 21 3 5 x 23 23 25 Simplify the expression. } 3. Ï72a } 5 } } } Ï } 4. 5Ï 2 2 3Ï 2 1 12Ï 2 5. 3Ï 12 2 5Ï 27 7. } 4p 2 } 6 6 6. } } Ï3b 8. q } (2Ï7 1 4)2 In Exercises 9 and 10, use the following information. The time t (in seconds) it takes an object dropped from a height h (in feet) } Ï h to reach the ground is given by the equation t 5 } . 16 3. Copyright © Holt McDougal. All rights reserved. 9. Write the equation in simplified form. 10. Find the exact time it takes a stone to reach the ground if it is 4. dropped from a bridge that is 200 feet high. 5. Simplify the expression. Assume variables are nonnegative. 11. 3} 3} Ï32 1 Ï264 3} Ï4a 12. } 3} Ï3 3} 6. 3} 13. 2Ï 135x 2 8Ï 5x 7. 8. 9. 10. 11. 12. 13. Algebra 1 Chapter 11 Assessment Book 213 Name ——————————————————————— CHAPTER 11 Chapter Test B For use after Chapter 11 Date ———————————— continued Solve the equation. Check for extraneous solutions. Answers } 14. Ï 4x 1 5 5 2 } 14. } 15. Ï 3x 1 4 5 Ï 12x 2 14 15. } 16. Ï 6x 1 7 1 3 5 x 1 5 16. 17. A person’s maximum running speed s (in meters per second) can 17. } Ï 9.8l be approximated by the function s 5 π } where l is the person’s 6 leg length (in meters). To the nearest tenth of a meter, what is the leg length of a person whose maximum running speed is about 3.4 meters per second? 18. 19. 20. Find the unknown lengths. 18. A right triangle has one leg that is twice as long as the other leg. The 21. } hypotenuse is 2Ï5 inches. 22. 19. A right triangle has a hypotenuse that is 3 feet longer than one leg. The other leg is 4 feet. 24. Find the midpoint of the line segment with the given endpoints. 25. 21. (21, 1), (24, 23) 22. (9, 22), (3, 22) In Exercises 23 and 24, use the following graph. 23. Find the length of each line segment. 27. (24, 3) 3 y 24. Use the converse of the Pythagorean theorem to determine whether the points are the vertices of a right triangle. (22, 1) 25 23 21 21 (28, 21) x The distance d between two points is given. Find the value of b. 25. (b, 22), (6, 1); d 5 5 } 26. (5, 1), (0, b); d 5 Ï 29 27. A fire is sighted in the forest from a helicopter. The forest ranger can send a crew from one of the two towers, as shown on the map. The distance between consecutive grid lines represents 0.5 mile. Which tower is closer to the fire? 3.5 2.5 y Fire 1.5 0.5 214 Algebra 1 Chapter 11 Assessment Book Tower B Tower A 0.5 26. 1.5 2.5 3.5 x Copyright © Holt McDougal. All rights reserved. 20. (5, 4), (1, 1) 23. Name ——————————————————————— Date ———————————— Chapter Test C CHAPTER 11 For use after Chapter 11 Graph the function and identify the domain and range. Then } compare the graph with the graph y 5 Ï x . Answers 1. See left. 2. See left. 4 } 2. y 5 2} Ï x 2 4 1 2 5 } 1. y 5 3Ï x 1 1 2 4 y y 6 1 21 21 1 3 5 2 x 22 22 2 6 10 x 23 26 In Exercises 3 and 4, use the following information. The speed at which water travels through a pipe can be measured by the height to which the water shoots out an elbow in the pipe. If the elbow has a height of 10 centimeters, then the velocity (in centimeters per second) of } the water can be modeled by the function v 5 44.3Ï h 1 10 where h is the height (in centimeters) of the water above the elbow. 3. 4. 3. Identify the domain and range of the function. 4. About how high should the water be above the elbow if the speed of 5. the water is 250 centimeters per second? 6. Simplify the expression. } } 6. 2aÏ 18a 3b10 Copyright © Holt McDougal. All rights reserved. 5. 3Ï 90 7. } } } 7. 4Ï 8 2 10Ï 2 } 9. 8. } Ï 15x 6y 7 } 7 9 3 10. } } 5 1 Ï5 (3Ïx 2 2y)(5Ïx 2 4y) 8. 3x y 9. 10. In Exercises 11 and 12, use the following information. The time t (in seconds) for a pendulum to complete one swing can be 11. } L found using the equation t 5 2π } where L is the length (in feet) of the 32 pendulum. Ï 12. 13. 11. Write the equation in simplified form. 12. Find the exact time it takes for a 4-foot pendulum of a grandfather clock to complete one swing. 14. 15. Simplify the expression. Assume variables are nonnegative. 3} 3} } 3 13. Ï 28t 2 3 1 Ï –27t 1 1 2 15. 3} 3} 3} 3} 1 Ï36 2 Ï5 2 1 Ï6 1 Ï25 2 3}1 3Ï a 2Ï a2 2 14. } 3} Ï5 Algebra 1 Chapter 11 Assessment Book 215 Name ——————————————————————— CHAPTER 11 Chapter Test C For use after Chapter 11 Date ———————————— continued Solve the equation. Check for extraneous solutions. } Answers } 16. Ï 10x 2 8 2 3Ï x 5 0 16. } 17. x 2 3 2 Ï 4x 5 0 17. } 18. Ï 5x 1 1 2 1 5 x 18. In Exercises 19–21, use the following information. } A museum curator can use the equation C 5 3x 1 Ï 50x 1 9000 to find the cost C (in dollars) for taking x people on a tour of the museum. 19. If the cost is $160, how many people went on a tour? 19. 20. 21. 20. If the curator charges each person $10 to go on the tour, write an 22. expression for the revenue generated. 21. How many people must go on the tour for the curator to break even? 23. Find the unknown lengths. 22. 5 3 23. x 21 x 14 3x 1 4 x 24. 3x 2 2 25. 24. A sail has the shape of an isosceles triangle. The two equal side lengths are 36 inches and the third side is 54 inches. Find the area of the sail. Round your answer to the nearest tenth. 25. endpoint: (2, 3); midpoint: (24, 26) 27. 26. endpoint: (21, 5); midpoint: (0, 4) 28. In Exercises 27–29, use the following graph. 29. 27. Find the slope of the line passing through the points. 28. Find the slope of line perpendicular to the line segment. 29. Write an equation of the perpendicular bisector of the line segment. 216 Algebra 1 Chapter 11 Assessment Book 5 y (4, 4) 3 1 21 21 1 3 5 (6, 0) x Copyright © Holt McDougal. All rights reserved. 26. The midpoint and an endpoint of a line segment are given. Find the other endpoint. Then find the length of the line segment. Name ——————————————————————— CHAPTER 12 Date ———————————— Chapter Test A For use after Chapter 12 Tell whether the equation represents direct variation, inverse variation, or neither. 1. y 5 2x 1 9 Answers 1. 3. xy 5 4 2. y 5 25x 2. In Exercises 4 and 5, use the following information. The time t (in days) to make campaign signs for student council officers varies inversely with the number n of volunteers helping. It takes 5 days for 12 volunteers to make all the campaign signs. 3. 4. 4. Write the inverse variation equation that relates t and n. 5. 5. If only 4 volunteers are available to help, find the number of days it 6. See left. 7. See left. will take them to complete the campaign signs. Graph the function and identify its domain and range. Then 1 compare the graph with the graph of y 5 } . x 1 6. y 5 } 1 2 x y 3 1 23 21 21 y 1 1 3 x 23 23 21 21 1 3 x 23 Identify the vertical asymptote and horizontal asymptote of the function. 210 8. y 5 } x 6 10. y 5 } 2 2 x 4 9. y 5 } 1 7 x12 Divide. 11. (12x 3 2 20x 2 1 32x) 4 4x 12. (x 2 1 11x 1 16) 4 (x 1 8) (in feet per second) of a skydiver as he falls towards Earth, which can 1000t be modeled by v 5 } where t is 5t 1 8 the time elapsed (in seconds). Describe how the velocity changes over time. 230 Algebra 1 Chapter 12 Assessment Book Velocity (feet/second) 13. The graph shows the velocity v Velocity of a Skydiver v 200 9. 10. 11. 12. 150 100 50 0 8. 13. 0 10 20 30 40 50 60 70 t Time (seconds) Copyright © Holt McDougal. All rights reserved. 3 1 7. y 5 } x21 Name ——————————————————————— CHAPTER 12 Chapter Test A For use after Chapter 12 Date ———————————— continued Divide using synthetic division. Answers 14. (x2 1 11x 1 28) 4 (x 1 4) 14. 15. (x2 1 7x 2 1) 4 (x 2 2) 15. 16. (x3 1 2x2 2 8x 1 5) 4 (x 2 1) 16. Simplify the expression, if possible. Find the excluded values. 16x 5 17. }2 24x x25 19. } x 2 2 2x 2 15 x 2 14 18. } x17 20. Write and simplify a rational expression 18. x 1 12 for the ratio of the perimeter to the area of the rectangle. 19. 2x Find the product or quotient. 20. 21. 8x 2 3 21. } p }3 9 4x 6x 4x 2 22. } 4 } 5 15 6x 2 1 7x 6x 3 1 7x 2 23. } 4 } 36x 2 9 12x 2 3 x 2 2 8x 1 7 x 2 1 3x 2 10 24. } p} x 2 1 3x 2 4 x 2 2 9x 1 14 3 5 26. } 1 } 4x 3x 22. 23. 24. Find the sum or difference. 6x 11x 25. } 2 } 4x 1 1 4x 1 1 17. 2 3x 27. } 1 } x16 x24 25. 26. Copyright © Holt McDougal. All rights reserved. In Exercises 28 and 29, use the following information. Dan drives 300 miles to attend college. On the drive back home, his average speed decreases by 10 miles per hour. 28. Write an equation that gives the total driving time t (in hours) as a function of average speed r (in miles per hour) when driving to college. 27. 28. 29. 29. Find the total driving time if he drives to college at an average speed of 60 miles per hour. Algebra 1 Chapter 12 Assessment Book 231 Name ——————————————————————— CHAPTER 12 Date ———————————— Chapter Test B For use after Chapter 12 Tell whether the table represents inverse variation. If so, write the inverse variation equation. 1. Answers 1. 2. x 210 5 10 15 x 28 21 12 32 64 y 240 220 20 40 60 y 26 248 4 1.5 0.5 25 2. 3. 4. In Exercises 3 and 4, use the following information. In chemistry, Boyle’s law states that at a constant temperature, the volume V of a gas varies inversely with the pressure P. For a certain gas, the pressure is 5 when the volume is 20. 5. See left. 6. See left. 3. Write the inverse variation equation that relates V and P. 4. Find the volume of the gas when the pressure is 10. Graph the function and identify its domain and range. 1 Then compare the graph with the graph of y 5 } . x 2 5. y 5 } x13 21 6. y 5 } 1 2 x 3 y y 3 1 x 1 23 23 21 21 1 3 x Write a function whose graph is a hyperbola that has the given asymptotes and passes through the point. 7. x 5 5, y 5 6; (4, 2) 8. x 5 21, y 5 23; (1, 22) 8. Divide. 9. (x 2 1 3x 2 6) 4 (x 1 1) 7. 10. (6x 2 2 3x 1 5) 4 (2x 2 3) 9. Divide using synthetic division. 10. 11. (x3 2 7x2 1 13x 2 15) 4 (x 2 5) 12. (x3 1 5x2 2 1) 4 (x 1 2) 11. 12. 232 Algebra 1 Chapter 12 Assessment Book Copyright © Holt McDougal. All rights reserved. 21 21 Name ——————————————————————— Chapter Test B CHAPTER 12 Date ———————————— continued For use after Chapter 12 Simplify the expression, if possible. Find the excluded values. 6 2 2x 2 18 14. } 92x 235x 13. } 25x 2 2x 2 x 2 15 15. } x 2 1 x 2 12 Answers 13. 14. 16. Write and simplify a rational expression x12 for the ratio of the surface area to the volume of the rectangular solid. 3x x 17. The percent p of salt in a saltwater solution can be modeled 100x 1 100 Percent of salt by p 5 } where x is the x 1 10 number of grams of salt that are added to the solution. Write the a model in the form y 5 } 1 k. x2h Then graph the equation. 15. 16. 17. y 90 80 70 60 50 40 30 20 10 See left. 18. 19. 20. 21. 0 0 10 20 30 40 50 60 70 80 90 x Salt (grams) 22. Copyright © Holt McDougal. All rights reserved. Find the product or quotient. 18x 4 50x 5 18. }2 p }6 25x 27x 30 20 19. }3 4 }5 x x 23. x2 2 9 1 20. } p } x 1 3 6 2 2x 2x 1 10 x 2 2 25 21. } 4} x2 2 1 x 2 2 4x 2 5 24. In Exercises 22 and 23, use the following information. 25. 26. For the period of 1990-2002, the number Y of rushing yards gained by 860 1 1800x Emmitt Smith can be modeled by Y 5 } where x is the number 1 1 0.024x of years since 1990. 22. Rewrite the model so that it has only whole number coefficients. Then simplify the model. 23. Approximate the number of rushing yards Smith gained in 1999. Find the sum or difference. x18 x22 24. } 1 } x13 x13 2 1 25. }2 2 } 9x 3x 2x 1 3 x 26. } 1 } x21 x2 2 1 Algebra 1 Chapter 12 Assessment Book 233 Name ——————————————————————— CHAPTER 12 Date ———————————— Chapter Test C For use after Chapter 12 Tell whether the situation represents direct variation, inverse variation, or neither. Answers 1. 1. Your grade on the next algebra exam and the number of hours you spent studying 2. 2. The outside temperature in degrees Celsius and the same outside temperature in degrees Fahrenheit 3. The time spent popping a bag of popcorn in the microwave and the number of unpopped kernels 3. 4. 5. In Exercises 4 and 5, use the following information. The length of time T (in seconds) for a cassette tape to play varies inversely with the operating speed s (in inches per second) of the cassette player. It takes 50 minutes for you to listen to a cassette tape on a system that plays 6. 7. 3 at 3}4 inches per second. 4. Write an inverse variation equation that relates T and s. 5. Your friend borrows the cassette tape and plays it on her system that 1 operates at 4 }2 inches per second. How many seconds faster does the 8. 9. tape play on your friend’s system? 10. A committee of 5 people is responsible for mailing 1200 flyers for a charity golf tournament. The committee hopes to recruit extra volunteers to help. 6. Write an equation that gives the average number f of flyers mailed per person as a function of the number n of extra volunteers recruited for the task. 7. Identify the domain and range of the equation. Then compare the 1 graph of the equation with the graph of y 5 }x . Write a function that has the given asymptotes and passes through the given point. 8. x 5 24, y 5 2; (23, 21) 1 9. x 5 }, y 5 24; (1, 1) 2 Divide. 10. (4x 3 2 6x 2 1 5) 4 (x 2 2 4) 11. (25x 1 6x 2 1 24) 4 (3x 2 1) Divide using synthetic division. 12. (3x3 1 4x2 1 3x 1 14) 4 (x 1 2) 234 Algebra 1 Chapter 12 Assessment Book 13. (x3 1 64) 4 (x 1 4) 11. 12. 13. Copyright © Holt McDougal. All rights reserved. In Exercises 6 and 7, use the following information. Name ——————————————————————— CHAPTER 12 Chapter Test C Date ———————————— continued For use after Chapter 12 5x 1 6 14. Graph the function y 5 } . x12 Answers y 10 14. 6 15. See left. 2 26 22 2 x 16. Simplify the expression, if possible. Find the excluded values. 2x 1 33 15. } x 1 11 9 2 x2 16. } 2 x 1 x 2 12 2x3 1 2x 2 2 4x 17. }} x 3 1 2x 2 2 3x 17. 18. Write and simplify a rational expression for the ratio of the perimeter to the area of the triangle. 2x 1 3 3x 1 2 3x 18. 4x 1 4 19. Find the product or quotient. 18x 2 36 6x 2 12 19. } 4 } 10x 1 40 8x 1 32 20. x 2 2 3x 2 4 x 2 1 5x 1 6 20. } p} x 2 1 6x 1 5 8 1 2x 2 x 2 22. Simplify the complex fraction. x2 2 9x 1 14 x23 } x2 26x 1 8 } 2x 2 6 Copyright © Holt McDougal. All rights reserved. 2x2 1 5x 2 3 3x 2 5x 2 28 } x3 2 9x } 9x 1 21 }} 2 } 21. 22. 23. 24. 25. Find the sum or difference. x14 3x 2 23. } 2} 2 x2 2 1 x 21 21. 32x x12 24. } 1} x 2 1 2x 2 3 x2 1 x 2 2 26. 27. Solve the equation. 1 5x 25. } 5 } x 14x 1 13 1 2 1 26. } 1 } 5 } 2 x21 x2 2 1 28. In Exercises 27 and 28, use the following information. A cyclist rode the first 20 miles of a trip at a constant average speed. Due to fatigue, the cyclist’s speed decreased by 2 miles per hour for the next 16 miles. 27. Write an equation that gives the total time t (in hours) as a function of the cyclist’s average speed r (in miles per hour). 28. If the total trip takes 4 hours, find the cyclist’s average speed for the last 16 miles of the trip. Algebra 1 Chapter 12 Assessment Book 235 Answers Pre-Test 52a. 10.5; Number of States Visited Multiple Choice Stem Short Response 1 38a. u 5 }a 8 37. 16.5h 1 40 0 2 2 3 3 4 4 6 7 8 9 1 2 5 8 2 0 0 1 6 3 0 2 5 ANSWERS 1. B 2. G 3. B 4. H 5. C 6. J 7. D 8. F 9. B 10. H 11. C 12. J 13. C 14. F 15. D 16. F 17. B 18. G 19. A 20. F 21. C 22. F 23. C 24. G 25. C 26. G 27. A 28. H 29. B 30. J 31. C 32. F 33. A 34. H 35. C 36. G Leaves Key: 1 | 5 = 15 states visited 52b. 50%; Number of States Visited 38b. u 9 8 7 6 5 4 3 2 1 0 8 2 4 12 16 10.5 20 24 28 32 20.5 36 35 Chapter 1 1 2 3 4 5 6 7 8 9 a 300 100 1 38c. 7} 39a. } 5t m 1} 4 m 1 2.5 39b. 6 minutes 36 seconds or 396 sec 40. 6186 ft 41. 240 min 42. 54% 43. 445 min 44a. l 5 0.25t 1 5 220 min 44b. u Copyright © Holt McDougal. All rights reserved. 4 9 8 7 6 5 4 3 2 1 Quiz 1 1 1 1. 13 2. 6 3. 4 4. 16 5. 6 } 6. 4 } 2 2 1 7. sometimes 8. always 9. 10 1 } r 2 10. 2d 11. 19 2 t 12. p 1 b2 Quiz 2 1. 2d 1 3 5 12 2. 4j 2 6 5 18 3. 8q ≥ 32 4. 10 2 w ≤ 8 5. never 6. sometimes 7. no 8. yes 9. yes 10. no 11. $114 12. 60 mi/h Quiz 3 1 2 3 4 5 6 7 8 9 a 1 1 45a. c ≥ } m; c ≤ 9 2 } m 2 2 c 9 8 7 6 5 4 3 2 1 1. no 2. yes y 3. 4. 5 4 3 2 1 ⫺2 O 1 2 3 4 5 6 x ⫺2 ⫺3 y 7 6 5 4 3 2 1 O 1 2 3 4 5 6 7 8 x 5. y 5 x 1 2 6. domain: 1, 2, 3, 4, 5 1 2 3 4 5 6 7 8 9 m 45b. Yes 46. x 5 24, y 5 3 47a. $113.17 47b. $101.92 48. No; (22)2 1 3(22) 5 4 1 (26) 5 22, not 210 49. 0.94 mile 50. b 5 3 51a. mean 5 2.6, median 5 2, mode 5 0 and 6 51b. The median; 6 of Benita’s 10 shots are within 2 inches of the bull’s-eye. 7. range: 3, 4, 5, 6, 7 8. no 9. yes Chapter Test A 1. 4 2. 27 3. 8 4. 6 5. 10 p 10 p 10 p 10 6. 2.6 p 2.6 p 2.6 7. n p n p n p n p n p n 8. 56 in. 9. 1 10. 4 11. 25 12. x 1 9 Algebra 1 Assessment Book A1 Chapter 1, continued 13. 4d 14. 2b 1 3 5 13 15. 5k < 60 16. yes 24. function 25. not a function 17. no 18. no 19. yes 20. 22.5 mi 21. always Chapter Test C 8 1. } 2. 12 3. 5 mi 4. 5 5. 23 6. 26 27 n 1 7. } 8. 50 cm2 9. 5(n 1 7) < } 3 2 Input, x 0 1 2 3 Output, y 1 3 5 7 10. 3(4 1 y 2) 5 14 2 y 11. sometimes Range: 1, 3, 5, 7 26. 12. sometimes 13. no 14. yes 15. no 16. 2% Input, x 0 2 4 6 Output, y 20 14 8 2 17. y 5 10 2 0.75x; Range: 20, 14, 8, 2 Height (in feet) 27. H 28 24 20 16 12 8 4 0 H 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 t Number of books 0 1 2 3 4 5 6 t Time (in seconds) 18. 28. function 29. not a function Chapter Test B 3 1 1. 138 2. } 3. 625 4. 1 5. } 6. 958F 10 32 7. 5 8. 33 9. 11 10. 25 11. 108 in.3 t2 k 12. } 13. 6(2 1 x) ≥ 45 14. 4 1 } 5 12 14 9 1 15. yes 16. yes 17. 18 } ft 18. always 2 x 19. always 20. y 5 2x 21. y 5 } 3 22. Range: 3, 3.5, 4, 4.5, 5 Input, x 12 15 21 30 Output, y 3 4 6 9 Range: 3, 4, 6, 9 y 9 8 7 6 5 4 3 2 1 O 3 6 9 12 15 18 21 24 27 30 x 19. not a function 20. function y 6 5 4 3 2 1 ⫺4 ⫺3 ⫺2 O Standardized Test A 1. B 2. D 3. A 4. A 5. C 6. B 7. C 8. D 9. C 10. B 11. A 12. D 13. B 14. C 1 2 3 4 x ⫺2 23. Range: 4, 6, 8, 10, 12 y 16 14 12 10 8 6 4 2 O A2 2 4 6 8 10 12 14 16 18 x Algebra 1 Assessment Book 15. A 16. A 17. D 18. 11 19 a. 2a 1 3g ≤ 25 b. 5 pounds of grapes c. no; 6 pounds of grapes and 3 pounds of apples cost $24, leaving me with only $1. x 20 a. y 5 }; domain: 2, 4, 6, 8, 10; range: 1, 2, 3, 2 4, 5 Copyright © Holt McDougal. All rights reserved. 25. Amount left (in dollars) ANSWERS 22. sometimes 23. function 24. not a function Chapter 2, continued Quiz 2 1. Associative property of multiplication 2. Multiplicative property of 21 3. Commutative property of multiplication 4. Multiplicative property of zero 5. 224 6. 20 7. 26 8. 30x 9. 221x 10. 28.28x 1 addition 13. 15 14. 26 15. 29.7 16. 2}5 17. your friend 18. 22 19. 6.8 20. 1.8 5 21. 72 22. 215 23. 2} 24. 20.9 25. 18 12 11. 23x 2 1 12. 29y 1 63 13. 12x 1 9 26. 3 27. $4.55 28. 9x 2 3 29. 22x 2 1 12x Quiz 3 3 3 30. }x 2 } 31. 6(4 2 0.05) 5 $23.70 5 2 3 1 1. 23 2. } 3. 210 4. 6 5. 2 } 6. 5 2 2x 8 8 32. P 5 20 1 4w; A 5 24 1 12w 33. 6 7. 4x 2 2 8. 7 9. 2 and 22 10. 24 11. . 12. , 13. 4 14. 28 34. 212 35. 4 36. 120 ft 37. 23 38. 13 Chapter Test A Chapter Test C 1. real number, rational number 2. real number, rational number, integer 3. real number, rational number 4. real number, rational number, integer, whole number 5. 24 23 22 21 0 1 2 3 ; 1 23, 22, }2 , 0 6. A < B 5 {0, 1, 2, 3, 5, 8}; A ù B 5 {8} 7. Associative property of addition 8. Inverse property of addition 9. Distributive property 10. Commutative property of multiplication 11. 25 12. 6 13. 27 14. 20,320 ft 15. 20 16. 212 17. 27 18. false; 23 is not a whole number. 19. true 20. 2478F 21. 320 m 22. 4 23. 10 24. 24 25. 227 26. 0 27. 29 28. 6 29. 24 30. 230 31. 23 32. 210 33. 28 34. 3 35. 23a 1 7 36. 9x 2 30 37. 7x 2 1 38. P 5 4x 1 38; A 5 10x 1 70 39. 65 40. 11 41. 211 Chapter Test B 1. real number, rational number 2. real number, irrational number 3. real number, rational number, integer, whole number 4. true 5. false; 5 is an integer, but 5 is not an irrational number. 1 1 14 1 6. 20.25, 2}, }, 1 7. 2}, 24.6, 24 }, 24.07 5 3 3 3 A4 8. A < B 5 {22, 21, 0, 1, 3, 5}; A ù B 5 {22, 0, 1, 3, 5}; 9. Associative property of multiplication 10. Commutative property of addition 11. Distributive property 12. Inverse property of Algebra 1 Assessment Book 39. . 40. , 1. false; Sample answer: ⏐2⏐5 2 2. true } 3. false; Sample answer: Ï 2 is a real number, but it is not a rational number. 4. false; Sample answer: 22 is not greater than its opposite, 2. } } 2 5. 23.48, 2Ï 12 , 23 }, ⏐3.5⏐, Ï 16 5 } } 6. A 3 B 5 {(25, 23), (25, 22), (25, 0), (24, 23), (24, 22), (24, 0), (21, 23), (21, 22), (21, 0)} 7. surplus of 27 8. shortage of 18 9. $50 10. As the price increases, the market surplus increases. 11. 2x 1 ( y 1 z) 12. 224x + 12 13. 10y 4 14. 2.1 15. 20.1 16. 2} 17. 214.25 5 5 1 1 18. 213 } 19. 6 } 20. $29,500 21. } x 1 1 3 2 3 2 22. 3x 2 2 26x 1 24 23. 2} x 3 2 4x 24. 22xy 3 7 1 1 25. 129 26. 1} 27. 8 } 28. } 29. 600 ft 9 2 2 30. . 31. . Standardized Test A 1. C 2. D 3. D 4. B 5. C 6. A 7. B 8. B 9. D 10. A 11. C 12. A 13. D 14. B 15. D 16. A 17. A 18. C 19. D 20. C 21. B 22. 21 Copyright © Holt McDougal. All rights reserved. ANSWERS 6. Commutative property of addition 7. Inverse property of addition 8. Associative property of addition 9. 22.5 10. 22 11. 2 12. 29 13 27 14. 21 Chapter 2, continued 23. a. 210e + (23)r, or 210e 2 3r b. descended 174 feet; Standardized Test B 1. C 2. A 3. C 4. B 5. B 6. D 7. D 8. C 9. D 10. B 11. A 12. A 13. D 14. A 15. D 16. B 17. C 18. C 19. A 20. D 21. C 22. 25 23. a. C 5 0.15t 1 0.10m b. $3.70; The total cost for 104 minutes and 7 text messages is $16.30 and you have pre-paid $20, so the remaining balance is $3.70. 24. a. 296 ft b. 6 rolls; Five rolls would only be 250 feet of fencing which is not enough. Six rolls would be 300 feet which is a little more than what is needed. c. 4 ft; 296 feet of fencing is needed and 300 feet is purchased, so 4 feet of fence is leftover. d. $290.33; Six rolls of fencing costs $273.90. 6% tax is $16.43 rounded to the nearest cent. The total cost including tax is $290.33. Standardized Test C 1. D 2. B 3. B 4. A 5. C 6. D 7. C 8. B 9. A 10. D 11. B 12. D 13. A 14. B Copyright © Holt McDougal. All rights reserved. 15. C 16. D 17. D 18. C 19. A 20. A 21. 3 22. a. Sample answer: C 5 2.49p 1 3.29w where C represents total cost, p represents pounds of peanuts purchased and w represents pounds of walnuts purchased b. 5 packs; The cost of the nuts is 6(2.49) 1 3(3.29) 5 24.81, leaving $5.19 for gum. When $5.19 is divided by $0.95, the quotient is about 5.5, so 5 packs of gum can be purchased. 23. a. 18 feet b. 121 ft; The landscaper needs 12(18), or 216, feet of fencing, so 216 2 95, or 121, feet of fencing is still needed. c. $257.10; Because 121 4 15 ø 8.07, 9 rolls are needed. The rolls, with tax, cost 9($26.95)(1.06) 5 $257.10. d. 4 ft; The landscaper will have 9(15) 2 121, or } } 14, feet leftover. Because Ï14 is between Ï 9 and } Ï16 , the side length will be between 3 and 4 feet, but closer to 4 feet because 14 is closer to 16. SAT/ACT Chapter Test 1. C 2. E 3. B 4. A 5. A 6. C 7. B 8. D 15. C 16. A 17. $331 18. 8.5 19. 0.2 ft Performance Assessment 1. Complete answers should include: an explanation that a rational number is a ratio of two integers; an explanation that irrational numbers cannot be expressed as a ratio of two integers, or a discussion of the differences between the decimal representations of rational numbers and irrational numbers; an example of a rational number and an example of an irrational number. 2. a. 119 points b. 175 points c. 99 points; 17 correct answers, 6 incorrect answers, 2 left blank ANSWERS 210e 2 3r 5 210(15) 2 3(8) 5 2150 2 24 5 2174 24. a. 240 feet b. 10 rolls; 240 4 25 5 9.6; Because 9 rolls would not be enough, the gardener must purchase 10 rolls. c. 10 feet; 10 rolls 5 250 feet and 250 2 240 5 10 d. $169.50 9. A 10. E 11. E 12. C 13. D 14. B 5 d. 121 points; distributive property e. } 7 f. Neither; both scored 117 points. g. Explanations may vary; 10x 2 75 h. 85 points Chapter 3 Quiz 1 1. n 5 216 2. t 5 27 3. f 5 90 4. w 5 24 5. d 5 30 6. y 5 12 7. z 5 2 8. h 5 24 9. x 5 1 10. 132 tiles 11. 80.75 5 32.50 1 8.25x; x ø 5.8; You can buy 5 t-shirts. The number of t-shirts must be a whole number. The total cost with 6 t-shirts would be $82. Quiz 2 1. x 5 1 2. y 5 2 3. no solution 4. t 5 25 5. b 5 7.6 6. j 5 5 7. m 5 12 8. d 5 5 9. f 5 6 10. 60 dogs Quiz 3 1. 25 2. 52% 3. 18 4. 8% 5. 130 6. 94.4 7. 22 8. 27.2 9. 77.625 10. 25.092 8 4 11. y 5 2} x 1 } 12. y 5 5x 1 8 5 5 7 I 13. y 5 2} x 1 3 14. r 5 } 3 Pt Chapter Test A 1. a 5 220 2. q 5 8 3. y 5 27 4. 12x 5 60; x 5 5 in. 5. t 5 7 6. b 5 8 7. m 5 5 8. y 5 2x 1 6; x 5 28 9. 25 5 3.75 1 2.80x; x ø 7.6; 7 boxes. The number of cereal boxes must be a whole number. The total cost with 8 boxes would be $26.15. Algebra 1 Assessment Book A5 10. p 5 5 11. z 5 10 12. w 5 16 13. c 16. d 5 12 17. 33 necklaces 18. a 5 216 14. 12 years old 15. y 5 215 16. no solution 19. b 5 36 20. c 5 3.125 21. d 5 3 17. b 5 212 18. c 5 6 19. d 5 15 1 20. n 5 25 21. v 5 1 } 22. x 5 0 3 23. a 5 21 24. 45 heads 25. 45% 26. 6 2 22. f 5 2} 23. g 5 214 24. 24 pounds 3 27. 51,250 voters 28. increase; 20% 29. 48% 30. $174.49 31. 80% increase 29. decrease; 15% 30. y 5 25x 1 12 2 1 4 32. y 5 } x 1 4 33. y 5 } x 2 } 3 3 3 S 2 2π r 2 } 34. h 5 35. 4 in. 2π r 2A 31. y 5 22x 2 5 32. y 5 3x 2 4 33. h 5 } b Chapter Test B 1 1. x 5 25 2. b 5 1 3. d 5 212 4. y 5 } 2 5. t 5 23 6. w 5 3 7. m 5 2 8. c 5 0 9. y 5 2 10. no solution 11. a 5 2 12. z 5 24 13. 722 5 295 1 3x; x ø 142.3; 142 sets. The number of sets must be a whole number. The radio station needs 2 more CDs to make 143 complete sets. 14. 24x 1 552 5 5250; $195.75 15. x 1 x 1 45 5 211; 128 girls; 83 boys 16. y 5 15 17. w 5 3.3 18. t 5 212 19. m 5 3 20. x 5 7 21. z 5 27 1 22. 5000 sunfish 23. 2 } cups of flour 24. 200 2 25. 150% 26. 12.19 27. 35 28. 69,000 seats 29. decrease; about 15.3% 30. increase; 60% 1 31. y 5 5x 2 7 32. y 5 2}x 1 2 3 b 1 18.85 33. h 5 } 34. about 169 cm 0.26 25. 6 cups 26. 400 27. 125% 28. 133 Standardized Test A 1. D 2. B 3. D 4. C 5. C 6. A 7. B 8. A 9. D 10. B 11. C 12. B 13. D 14. B 7 15. C 16. C 17. D 18. D 19. 23.5 or 2} 2 20. a. S 5 0.85p b. $15.30 21. a. $120 b. $702; Add the amount of interest I earned, $52, to the principal, $650. c. P 5 } rt d. $1500 Standardized Test B 1. B 2. A 3. D 4. A 5. C 6. A 7. B 8. B 9. D 10. D 11. C 12. A 13. B 14. C 15. B 16. C 17. D 18. A 19. 21 20. a. C 5 0.65P or C 5 P 2 0.35P b. $85; solve the equation 55.25 5 0.65P 21. a. $5437.50 b. $31,562.50; The simple interest calculates to be $6562.50. This amount must be added to the original $25,000 borrowed I for a total of $31,562.50. c. P 5 } rt d. $12,500 Standardized Test C 1. A 2. D 3. C 4. D 5. D 6. A 7. A 8. B 35. about 67 in. 9. C 10. C 11. D 12. B 13. A 14. B Chapter Test C 1 1. n 5 216 2. b 5 23.7 3. y 5 2} 8 15. B 16. A 17. B 18. D 19. 4.25 4 2 4. x 5 12 5. b 5 2} 6. z 5 } 3 5 equation 440 5 0.88p. 21. a. $319.31 b. $15,493.75; Add the amount of interest, $14,800(0.0625)(0.75), or $693.75, to the I principal. c. r 5 } d. 2.5% Pt 7. 410 5 36(2) 1 3x; x ø 112.7; 112 envelopes. The number of envelopes must be a whole number. The venue needs 2 more free tickets to make 113 envelopes. 4 8. 6.5 ft, 6.5 ft, and 21 ft 9. m 5 } 3 2 11 10. b 5 9.4 11. x 5 6 12. w 5 } 13. c 5 210 14. no solution 15. t 5 0 A6 Algebra 1 Assessment Book 20. a. v 5 0.88p b. 500 volunteers; Solve the SAT/ACT Chapter Test 1. D 2. A 3. C 4. D 5. B 6. A 7. C 8. D 9. C 10. B 11. A 12. E 13. C 14. D 15. A 16. 5 ft 17. 210 18. 89.1 19. $143 Copyright © Holt McDougal. All rights reserved. ANSWERS Chapter 3, continued Chapter 4, continued 8. y 4 3 2 1 ANSWERS ⫺4 ⫺3 ⫺2 ⫺1 1 2 4 x 3 ⫺4 9. y 4 3 2 1 ⫺4 ⫺3 ⫺2 1 ⫺1 ⫺2 ⫺3 ⫺4 2 4 x 3 Because the slope of the graph of g is greater than the slope of the graph of f, the graph of g rises faster from left to right. The y-intercept for both graphs is 0, so both lines pass through the origin. Because the slope of the graph of h is less than the slope of the graph of f, the graph of h rises more slowly from left to right. The y-intercept for both graphs is 0, so both lines pass through the origin. 18. 555 Y zX 19. 1 X Y zX 1 20. r 5 } d 21. 2.5 in. 22. 23 23. 225 2 1 24. x 5 22 25. x 5 } 3 Chapter Test B 1.–4. y 10. A 5 ks 4 3 2 Chapter Test A 1 D ; domain: 23, 22, 21, 0; range: 1.5, 0.5, 20.5, 21.5 y 3 1 B ⫺4 ⫺3 ⫺2 ⫺1 1. (3, 2) 2. (0, 22) 3. (22, 21) 4. (22, 2) 1 2 3 4 x C ⫺2 ⫺3 ⫺4 1. Quadrant II 2. x-axis 3. Quadrant IV 3 x 1 22 2 9 5 22(5.5); 211 5 211 1 ; 241 }2 2 2 9 5 221 }2 1 5 2; Y A 3 X 2 5. 15 1 ; }3 (0 1 15) 5 5; } 5 5; 3 Y 4. Quadrant III 5. 6. no 7. yes 8. continuous; The amount of water in a bathtub can be calculated for any amount of time since it began flowing. y 9. 6 4 10. (0, 4) 26 ⫺4 2 ⫺2 4 x / y 22 21 21 22 23 2 3 x 6. ⫺2 ⫺2 ⫺4 ⫺6 X 7. y 1 ⫺2 ⫺1 ⫺1 1 y 4 2 2 3 x ⫺4 ⫺2 ⫺4 ⫺6 ⫺3 ⫺4 ⫺5 12. 22 13. undefined y 2 (1, 0) 1 ⫺2 11. 3 (0, 3) 2 1 (22, 0) domain: 24, 22, 0, 2, 4 range: 0, 1, 2, 3, 4 Y (6, 0) 2 4 6 8 x 8. (0, 26) y 4 2 ⫺4 ⫺2 ⫺2 1 14. } 15. m 5 5; b 5 2 16. m 5 1; b 5 24 3 17. m 5 22; b 5 26 2 4 6 x ⫺4 ⫺6 9. continuous 10. x-intercept 5 2, y-intercept 5 23 A8 Algebra 1 Assessment Book 4 6 x Copyright © Holt McDougal. All rights reserved. 3 Chapter 4, continued 12. x-intercept 5 4, y-intercept 5 22 9. The intercepts represent the hours when the car is at the starting position. 13. 30 mi/h, 60 mi/h, 0 mi/h, 230 mi/h 10. 14. hours 3 and 4 2 15. m 5 8, b 5 23 16. m 5 2}, b 5 1 9 3 } 17. m 5 2 , b 5 4 18. 2013 19. yes; a 5 21 4 4 20. yes; a 5 } 21. no 3 Cost (thousands of dollars) 22. 4 0 100 300 200 400 m Distance (miles) 12. 1 ; }3 ; 1 1 1 261 }3 2 5 231 }3 1 }3 2 Y 600 500 400 300 200 Y zX 2 22 5 231 }3 2 X 22 5 22 100 13. y 5 20.625x 14. y 5 6x 15. y 5 1.5x 0 1 2 3 4 5 x 16. Number of airings 23. domain: x ≥ 0; range: C ≥ 300 24. 4 times 1. 2. y 1 ⫺8 ⫺6 ⫺4 ⫺2 ⫺2 ⫺4 Y 4 3 2 6 8 x 2 The graphs of f and g have the same slope, so the lines are parallel. Also, the y-intercept of g is 5 less than the y-intercept of f. ⫺8 Q(1, 0) ⫺3 ⫺2 ⫺1 ⫺1 1 2 R(3, 0) 3 4 X 5 x P(22, 23) original range: 25 ≤ y ≤ 11 ; original range: y ≥ 21 y 3 17. y 4 3 2 1 S(5, 23) 27 trapezoid; A 5 } 2 3. y 8 6 4 2 Chapter Test C Copyright © Holt McDougal. All rights reserved. 0 11. 5 gallons C 1000 900 800 700 0 a 24 20 16 12 8 ANSWERS Fuel (gallons) 11. x-intercept 5 5, y-intercept 5 22 ⫺4 ⫺3 ⫺2 ⫺1 ⫺1 ⫺2 ⫺3 ⫺4 2 3 4 x The slope of the graph of h is negative, so the line falls from left to right. The y-intercept is the same for both graphs, so both lines pass through the origin. Standardized Test A 1 3 1 1 2 x 1. B 2. D 3. B 4. D 5. A 6. C 7. A 8. B 9. A 10. D 11. B 12. A 13. D 14. C 3 15. B 16. 23 4. continuous 8 5. x-intercept 5 }, y-intercept 5 24 3 5 6. x-intercept 5 }, y-intercept 5 1 2 7. x-intercept 5 4, y-intercept 5 3 8. The car is traveling to the right at 30 miles per hour for the first 2 hours. Then the car speeds up to 60 miles per hour for the next hour. The car stops for an hour. It then turns around and travels 30 miles per hour for the last 4 hours of the trip. Algebra 1 Assessment Book A9 Chapter 4, continued SAT/ACT Chapter Test 10. an 5 36.1 1 (n 2 1)22.2; 2233.9 1. E 2. D 3. B 4. D 5. C 6. A 7. B 8. C 9 9. A 10. E 11. D 12. B 13. C 14. } or 1.8 5 15. $12 16. 5 years 11. C 5 12(m 2 1) 1 10 12. $94 1. Complete answers should include: a list of the three methods that can be used to graph a linear equation: make a table, use intercepts, and use the slope and y-intercept; an explanation of how to graph 2x + y = 3 using each method. 2. a. x-intercept: 80; y-intercept: 25 Large plants b. 6. Lines a and c are parallel. 7. relatively no correlation 8. negative correlation 9. 4 10. 18 Chapter Test A y 30 25 20 15 10 5 0 3 1 1. y 5 5x 2 7 2. y 5 }x 1 } 2 2 2 3. y 5 2} x 2 6 4. y 5 3x 2 9 5 5. Lines a and b are perpendicular. 3 1. y 5 22x 2. y 5 } x 2 1 3. y 5 3x 2 9 4 2 4. y 5 2x 1 2 5. y 5 } x 2 3 6. $30 7. $35 3 0 16 32 48 64 80 96 x Small plants 8. C 5 35m 1 30 9. $450 10. plants that can be placed in the garden if no large plants are used. The y-intercept represents the number of large plants that can be placed in the garden if no small plants are used. d. Sample answer: 16 small and 20 large; 32 small and 15 large; 48 small and 10 large 5 5 e. 2} f. y 5 2} x 1 25 16 16 Large plants 3 2 1 1 2 3 x 23 22 1 2 3 4 5 6 x 22 23 12. not arithmetic; There is no common difference. 13. arithmetic; 244, 255 1 1 14. f (x) 5 2} x 1 } 15. f (x) 5 4x 2 15 2 2 16. 4s 1 6l 5 304 17. Sample answer: 1 seat 25 cushion and 50 license plate holders; 10 seat cushions and 44 license plate holders 20 15 10 1 18. Parallel: y 5 } x 1 5; 2 5 0 0 16 32 48 64 80 96 x Small plants Perpendicular: y 5 22x 1 15 19. h. The slope remained the same, but the y-intercept increased by 5 units. Chapter 5 Quiz 1 1. y 5 2x 2 1 2. y 5 2x 1 1 1 7 4 3. y 5 2} x 1 5 4. y 5 } x 1 } 2 5 5 5. y 1 2 5 3(x 2 2) or y 2 7 5 3(x 2 5) Calories Copyright © Holt McDougal. All rights reserved. y 30 O y 11. y 4 3 2 1 c. The x-intercept represents the number of small g. ANSWERS Performance Assessment Quiz 2 y 700 650 600 550 500 450 400 0 0 10 20 30 40 50 x Fat (g) 20. The scatter plot shows a positive correlation. As the grams of fat increased, the number of calories tends to increase. 3 3 6. y 2 4 5 }(x 2 6) or y 2 1 5 }(x 2 2) 4 4 7. 3x 1 y 5 3 8. x 2 y 5 2 9. an 5 218 1 (n 2 1)13; 1269 Algebra 1 Assessment Book A11 Chapter 5, continued 22. 520 calories 23. 8 24. 23 25. 2 y 700 650 600 550 500 450 400 0 0 10 20 30 40 50 x Fat (g) Chapter Test C 7 4 1. y 5 2} x 1 4 2. y 2 3 5 2}(x 1 1) 5 6 9 3. F(C) 5 } C 1 32 4. f (x) 5 23x 2 7 5 7 1 5. f (x) 5 2} x 2 } 2 4 6. Chapter Test B 28 4 1. y 5 } x 2 5 2. y 5 2x 2 1 3 7. y 4 2 O 24 2 4 x 2 1 24 23 22 3. y 5 2.45x 1 15.50 4. $52.25 5. A 5 4 6. B 5 21 8. 3 2 1 22 O 1 2 3 4 x 24 22 23 22 O 22 23 y 1 3 5 4(x 2 2) 11. arithmetic; 241, 252 12. not arithmetic; There is no common difference. 13. 2x 1 2y 5 10 14. 4x 1 y 5 5 15. 5x 1 4y 5 214 16. y 5 5 17. 0.05n 1 0.25q 5 3.80 18. Sample answers: 26 nickels and 10 quarters; 1 nickel and 15 2 15 quarters 19. Parallel: y 5 2}7 x 2 } ; 7 7 Perpendicular: y 5 }2 x 1 13 Calories y 700 650 600 550 500 450 400 As the grams of fat increase, the number of calories tends to increase. 22. y 5 11x 1 211 23. 24. 519 calories y Calories 12. 2x 2 5y 5 10 13. y 5 22 14. x 5 4 15. x 1 2y 5 6 16. The figure is not a right 1 5 4 triangle because the slopes are 2}3, 2}9, and }6 , none of which are negative reciprocals. 17. y 36 32 28 24 20 16 0 0 2.0 2.5 3.0 3.5 4.0 x Weight (thousands of pounds) 18. The scatter plot shows a negative correlation. As the weight of the car increases, the gas mileage tends to decrease. 19. y 5 28x 1 49 20. 22 mi/gal 21. x ø 6; There will be no gas mileage for a car that weighs 6000 pounds. 1. D 2. B 3. C 4. D 5. A 6. B 7. D 8. C 0 10 20 30 40 50 x 21. The scatter plot shows a positive correlation. 700 650 600 550 500 450 400 0 10 20 30 40 50 x Fat (g) A12 11. an 5 12.7 1 (n 2 1)1.8; 190.9 Standardized Test A Fat (g) 0 3 x 10. an 5 14 1 (n 2 1)(216); 21570 1 2 x 4 for each increase of 1 in the x-value. 10. Sample answer: 0 1 2 9. k 5 1; Sample answer: y 2 2 5 2(x 2 2) 9. The y-values increase at a constant rate of 20. O 8. k 5 28; Sample answer: y 2 1 5 22(x 1 2) y 3 2 1 Miles per gallon y 7. y 5 4 3 Algebra 1 Assessment Book 9. A 10. A 11. D 12. B 13. D 14. 24 15. a. The situation can be modeled by a linear equation because the cost increases by a constant amount. b. $210 c. $40 16. a. y 5 2.5x 1 10 b. y 5 2.5x 1 5 c. The graphs are linear and have the same slope of 2.5. This means that the graphs are parallel. d. Regardless of the number of movies rented, the difference will always be $5. Each person pays the same amount per rental. The only difference is in the registration fee. Copyright © Holt McDougal. All rights reserved. ANSWERS Calories 21. Chapter 6, continued 5. The graph of g(x) 5 2⏐x 1 1⏐ opens down and is 1 unit to the left of f (x) 5⏐x⏐. 21. The graph of g(x) 5⏐x 1 1⏐ is 1 unit to the left of f (x) 5⏐x⏐. Y Y F X \X \ / G X \X \ X G X \X \ 6. x ≤ 25 or x ≥ 5; 22. The graph of g(x) 5⏐x⏐2 3 is 3 units below the graph of f (x) 5⏐x⏐. 0 26 24 22 4 7. 0 < x < }; 3 2 4 6 Y 4 3 0 23 22 21 8. 25 ≤ x ≤ 21; 1 2 0 26 24 22 2 4 10. y 3 F X \X \ 3 X 6 y G X \X \ 3 23. yes 24. yes 25. no 1 5 x 1 21 21 23 3 x 1 21 21 23 26. 3. x > 3; 0 3 6 9 26 24 22 0 2 4 3 ⫺3 1. x > 218; 220 216 212 28 6 24 0 2. y > 12; 0 26 24 22 2 4 6 6 8 10 12 14 16 18 3. d > 2; 8 216 0 8 24 16 7. p 2 10 ≤ 80; p ≤ 90 8. y ≤ 21 9. x ≥ 4 10. t ≤ 5 11. all real numbers 12. a > 22 13. no solution 14. 3(2x 1 1) ≤ 63; x ≤ 10 16. x ≤ 22 15. x . 4 y 8 6 4 (4, 0) 2 4 (2, 0) 8 x 6 4 6 8 2 4 4 6 8 17. 25 < x ≤ 1 18. x < 0 or x ≥ 3 19. x > 3 or x ≤ 1; 23 22 21 0 1 2 3 4 5 20. 24 ≤ x ≤ 2; 25 24 23 22 21 0 1 2 3 Algebra 1 Assessment Book 2 4 4. a < 4; 24 23 2221 0 1 2 3 4 g 5. } ≤ 0.40; g ≤ 7.2 6. No, the team can lose 18 at most 7 games. 7. no solution 8. p ≤ 25 3600 10. 8n 2 2.50n 2 600 $ 1200; n $ } 11 11. No, they must sell at least 328 calendars. 2 8 6 4 2 O 0 22 9. all real numbers y 8 6 4 2 1 Chapter Test B 6. n < 12; 8 6 4 2 O x ⫺1 ⫺1 ⫺3 3 x 1 ⫺3 1. x < 2 2. x ≥ 25 5. t ≤ 4; 1 ⫺1 Chapter Test A 4. w ≤ 22; y 3 1 23 29 26 23 27. y 3 ⫺3 A14 X 9. F X \X \ 6 8 x 12. x < 3 or x $ 12; 0 13. 24 # x < 8; ⫺5 5 0 10 5 15 10 7 14. The pressure is between from 70 } lb/in.2 and 11 3 lb/in.2. to 270 } 11 Copyright © Holt McDougal. All rights reserved. ANSWERS Chapter 6, continued 15. The graph of g(x) 5⏐x 1 1⏐2 2 is one unit to the left and two units below the graph of f (x) 5⏐x⏐. 8. x ≤ 210 ANSWERS 5 10 15 20 25 x (10, 0) 5 10 15 5 10 15 x 1510 5 (10, 0) 10 15 F X \X \ / 5 5 y y 15 10 Y 9. x . 10 20 25 X G X \X \ 10. 23 # x < 6; 24 22 0 2 4 6 8 11. not possible; 212 210 28 16. The graph of g(x) 5 22⏐x⏐ opens down and is narrower than the graph of f (x) 5⏐x⏐. 26 24 22 12. x < 22 or x > 5; 24 22 0 2 4 6 8 13. all real numbers; 0 1 2 3 4 5 6 7 8 Y 14. You must score at least 72 on the next algebra test. 15. no solution F X \X \ / 4 16. x 5 2}; x 5 24 17. ⏐x 2 5⏐ 5 3 3 18. ⏐x 1 1⏐ 5 2 X 19. The graph of g(x) 5 0.25⏐x⏐2 2 is wider than and 2 units below the graph of f (x) 5⏐x⏐. G X \X \ 17. 18. y 3 y 3 1 ⫺3 ⫺1 Y 1 1 ⫺3 3 x ⫺1 ⫺1 ⫺3 x 1 3 ⫺3 F X \X \ / X G X \X \ Bleacher seats Copyright © Holt McDougal. All rights reserved. 19. 30x 1 20y $ 380,000 20,000 18,000 16,000 14,000 12,000 10,000 8,000 6,000 4,000 2,000 0 20. The graph of g(x) 5 22⏐x 1 1⏐2 0.5 is 1 unit to the left, 0.5 of a unit below, and narrower than the graph of f (x) 5⏐x⏐. y 3 2 1 6 4 2 O 0 4,000 8,000 12,000 Floor seats 20. Sample answer: (10,000, 12,000); The promoter could sell 10,000 tickets for floor seats and 12,000 tickets for bleacher seats. Chapter Test C 5 1. x # 21.2 2. x < } 3. all real numbers 8 13 1 } 4. no solution 5. (6x 2 3)9 $ 45; x $ } 2 6 2 3 6 x 4 g(x )2 \x 1 \0 .5 21. 0 < x < 16; 216 28 22. x < 20.5 or x > 4; 0 8 16 20.5 22 21 0 1 2 3 4 5 6 23. ⏐x 2 35⏐ # 3.5, 31.5 # x # 38.5; The actual temperature can be between 31.58C and 38.58C. y 24. y 25. 3 3 1 6. 23.9w # 19.5; w $ 25 5n 2 9 7. 22 < } # 3; 1 < n # 3 2 f (x )\x \ 2 ⫺3 ⫺1 ⫺1 ⫺3 1 1 3 x ⫺3 ⫺1 ⫺1 1 3 x ⫺3 Algebra 1 Assessment Book A15 Chapter 6, continued 34.3 1 x 18. a. } ≥ 9; x ≥ 10.7 b. no; To win, the 5 y 30 25 20 15 10 score must be 10.7 or greater, but these scores are impossible to receive. 5 0 0 10 20 30 40 50 60 x Length (inches) 27. Sample answer: (15, 10); The box could have a length of 15 inches and a width of 10 inches. Standardized Test A 5 19. a. 20 ≤ } (F 2 32) ≤ 25; 68 ≤ F ≤ 77 9 c b. 68 ≤ } 1 37 ≤ 77; 124 ≤ c ≤ 160 4 c. SAT/ACT Chapter Test 1. A 2. A 3. C 4. D 5. A 6. C 7. B 8. B 1. D 2. A 3. C 4. E 5. A 6. B 7. D 8. C 9. D 10. B 11. A 12. B 13. C 14. D 9. D 10. C 11. B 12. B 13. A 14. D 17. a. 3.50 1 0.45t ≤ 7.50, where t is the number of lines of text b. 3 ≤ 8.9; 8 lines of text at most; I rounded down because I cannot afford 9 lines of text. 18. a. 105 ≤ a ≤ 145 b. 180 ≤ t ≤ 200 c. 500 ≤ p ≤ 700; The student must sell at least $800 worth of covers, but she cannot sell more than $1000 worth of covers because she has only 200 calculators to sell. Subtract $300 from each amount to find the profit. Standardized Test B 1. D 2. B 3. A 4. B 5. D 6. C 7. B 8. D 9. A 10. C 11. A 12. B 13. A 14. C 15. C 16. 8.5 min 98 1 85 1 72 1 78 1 x 17. a. }} $ 85; x $ 92 5 b. No, it is not possible to earn an average of 92. A score of 100 on the last test would still only give you an average of 86.6. 18. a. a $ 285 b. t $ 800 c. c # $500 or $0 # c # $500; Selling 750 tickets would raise $1500 for the club. Anything over that amount is used to purchase calculators. After selling 750 tickets, there are 250 tickets remaining, which would total $500. So, the maximum amount that can be used towards calculators is $500 and the minimum amount is $0. Standardized Test C 1. D 2. B 3. A 4. A 5. D 6. C 7. B 8. A 9. B 10. D 11. C 12. B 13. A 14. D 15. B 16. C 17. 10.5 15. $850 16. 218 17. 83 cm Performance Assessment 1. Complete answers should include: a discussion of the equivalent compound inequality ax 1 b > 9 or ax 1 b < 29; a discussion of how to solve each part of this compound inequality; a rough sketch of a solution consisting of two rays having open circles that point in opposite directions. 12 2. a. 125 1 8.5p ≤ 250; p ≤ 14} 17 b. 0 2 6 4 8 10 12 14 16 ; 14 door prizes c. $1256 d. 11x 1 9y 1 56 ≤ 1256 e. y Number of chicken entrées 15. B 16. 280 140 120 90 60 30 0 0 30 60 90 120 x Number of beef entrées f. Sample answer: 100 beef and 10 chicken; 50 beef and 70 chicken; 25 beef and 100 chicken g. For sample answer in part (f ): $10, $20, and $25, respectively. Chapters 1–6 Cumulative Test 1. 19 2. 82 3. 22 4. 77 5. sometimes 75 6. 5x 1 17 7. 21 2 5y < 7 8. } 5 25 z12 } } 9. 21a 1 15c; $129 10. 2Ï 5 , 21.6, 0, Ï 4 , 3.1 3 11. {4, 6} 12.218 13. 25 14. 23 15. 2} 4 1 16. 290 17. 42 18. 3 19. 249 20. 2} 50 21. 219 22. 17 23. 49 24. 22 25. 3x 2 18 A16 Algebra 1 Assessment Book Copyright © Holt McDougal. All rights reserved. Width (inches) ANSWERS 26. x 1 2( y 1 24) # 108; Chapter 7, continued 4. 5. y Chapter Test B y 3 1 23 23 6. 3 x 1 21 21 5. 23 7. y 3 Studnet tickets y 3 1 21 23 3 x 1 23 3 x 1 y 180 160 140 120 100 80 60 40 20 0 60 100 Adult tickets x 6. 75 adult tickets and 30 student tickets Chapter Test A 7. (22, 1) 8. (2, 210) 9. (3, 21) 1. (22, 3) 2. (1, 21) 3. 2w 1 2l 5 228 and l 5 w 1 42 10. (24, 8) 11. (5, 2) 12. (1, 1) 4. 13. y 5 x 1 30, 26x 1 15y 5 3115; $65 for 5. 78 feet by 36 feet 6. (2, 21) 7. (4, 3) a single-occupancy room and $95 for a double-occupancy room 14. (2, 23) 15. (2, 0) 16. (3, 1) 17. (21, 1) 18. (8, 6) 19. (21, 2) 20. no solution 21. one solution 22. infinitely many solutions 23. There is no solution, so you cannot determine the cost of a bagel. 8. (3, 2) 9. (27, 223) 10. (1, 1) 11. (6, 6) 24. 100 80 60 40 20 0 0 20 60 100 Width of tennis court w 12. x 1 y 5 300, 0.04x 1 0.07y 5 15; 100 mL of 7% solution and 200 mL of 4% solution 13. (5, 21) 14. (2, 27) 15. (3, 22) 16. (2, 21) 17. (1, 1) 18. (5, 22) 19. no solution 20. one solution 21. infinitely many solutions 22. 23. y 3 1 13 5 x 21 21 1 35 x 23 Babysitting hours 24. x ≥ 0, y ≥ 0, 10x 1 5y ≥ 150, x 1 y ≤ 25; y 30 25 1 x 3 23 21 21 ⫺3 x 1 23 26. x ≥ 0, y ≥ 0, x ≤ 65, y ≤ 35; y 35 30 25 20 15 10 5 0 0 10 20 30 40 50 60 70 x Written examination Chapter Test C 1. (21, 23); 20 15 10 5 0 y 1 1 ⫺1 ⫺1 y 1 21 25. y 3 Oral presentation Length of tennis court 120 2. no solution; y y 1 0 5 10 15 20 25 30 x Farm hours 25. Yes, you will earn $160 per week. A18 0 20 Copyright © Holt McDougal. All rights reserved. ANSWERS 3 x 1 21 21 23 1. yes 2. no 3. yes 4. x 1 y 5 105, 4x 1 2y 5 360 Algebra 1 Assessment Book ⫺3 ⫺1 ⫺1 1 x ⫺1 ⫺1 ⫺3 ⫺5 1 x Chapter 7, continued Standardized Test B y 3. (4, 23); 6 1. D 2. B 3. A 4. B 5. D 6. B 7. C 2 22 22 1 2 x 5. (2, 1) 6. (2, 2) 7. (1, 23) 8. no solution 9. (1, 24) 10. 225 liters 2 2 11. }, 2} 3 3 1 2 12. infinitely many solutions 13. (0, 22) 14. no solution 15. (23, 5) 16. (5, 3) 17. 135 miles per hour; 15 miles per hour 18. infinitely many solutions 19. one solution 20. no solution 21. y ≤ 5, y > x 22. y ≤ 2, 3x 2 y ≤ 3 Batches of cakes 2 23. x ≥ 0, y ≥ 0, 1.5x 1 2y ≤ 15, } x 1 3y ≤ 13 3 same slope, they are parallel. Therefore, there will never be exactly one solution. 14. a. x 1 y 5 500 and 0.02x 1 0.07y 5 25 b. The car wash owner would use 200 gallons of the 2% liquid soap and 98% water solution and 300 gallons of the 7% liquid soap and 93% water solution. c. The car wash owner would use more of the 7% liquid soap and 93% water mix than in the original mix because in the original mix the other solution contained soap. In the new mix, there is no soap being added to the 7% liquid soap and 93% water mix. Standardized Test C D 9. A 10. B 11. D 12. 21.5 1 13. a. m 5 2} and n 5 2 b. The value of m 2 1 would be anything other than 2}2 because when 4 3 2 1 0 4 8 12 16 20 x Batches of cookies 1 24. 0, 4 } , (10, 0), (0, 0), (6, 3) 3 1 Copyright © Holt McDougal. All rights reserved. 13. a. m 5 4 b. No; because the lines have the 1. B 2. A 3. A 4. C 5. C 6. D 7. A 8. y 8 7 6 5 0 8. A 9. C 10. D 11. C 12. 1 ANSWERS 2 4. }, 22 3 2 2 1 25. 0, 4 } : $130, (10, 0): $200, (0, 0): $0, 3 1 2 (6, 3): $210; (6, 3) Standardized Test A 1. D 2. C 3. C 4. A 5. B 6. B 7. D 8. C 9. B 10. D 11. C 12. 23 13. a. m 5 6; For the system to have infinitely many solutions, the lines must have the same slope and the same y-intercept. b. Sample answer: m 5 2; For the system to have no solution, the lines must be parallel, so they must have the same slope and different y-intercepts. 14. a. Sample answer: x 1 y 5 41 and 0.10x 1 0.05y 5 3.30; Let x represent the number of dimes and y represent the number of nickels. The first equation gives the number of coins and the second gives the value of the coins. b. 25 dimes and 16 nickels c. Sample answer: The second equation could have been written using cents instead of dollars: 10x 1 5y 5 330. the slopes are the same, there is either no solution or infinitely many solutions. The variable n could then take any value. 14. a. x 1 y 5 3 and 0.35x 1 0.2y 5 0.75 b. 1 L of 35% solution and 2 L of 20% acid solution c. about 2.14 L of 35% solution and about 0.86 L of water SAT/ACT Chapter Test 1. E 2. B 3. A 4. D 5. C 6. C 7. B 8. E 9. E 10. D 11. E 12. 1 13. 3.5 lb 14. $6.50 15. 3 touchdowns Performance Assessment 1. Complete answers should include: mention of all three categories for the number of solutions to a system of two linear equations (one solution, no solution, infinitely many solutions); a description of the graph of the system as intersecting, parallel, or coincidental lines. 2. a. x 1 y 5 108 x 5 2y Algebra 1 Assessment Book A19 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 x 23 1 21 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 1 1 21 3 x 23 1 21 1 21 y 3 x 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 1 21 21 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 Chapter 9, continued 5. 4z2 1 z 2 18 6. p2 2 6p 2 7 4. 4n3 2 2n2 1 4n 1 12 7. 64m2 1 48m 1 9 8. 25y2 2 60y 1 36 5. D 5 218.53t 2 1 895t 1 40,091 9. w 2 1 4w 6. 50,579,000 students 7. 36c 3 2 20c 2 2 32c 1. 3x(4x 1 y) 2. 7ab(3b 1 5) 3. 9z2(1 2 2z) 4. 4p(1 2 2p) 5. (w 1 1)(w 1 14) 6. (m 2 10)(m 2 2) 7. (2k 2 1)(k 1 3) 8. (3b 1 1)(b 2 7) 9. (2y 1 5)(4y 1 3) 12. 4b2 1 12b 1 9 13. V 5 2(x 2 4)(x 1 4) 5 2x 2 2 32 1 14. 40 in.3 15. 2}, 7 16. 0, 8 17. 22, 0 2 1 10. 2(2d 1 5)(d 1 1) 11. 26, 4 12. 0, } 3 7 18. 3w(w 2 2) 5 w(w 1 1) 19. } 2 13. 3, 4 14. 22, 0 15. 2, 5 16. 23, 22 20. (n 2 18)(n 1 4) 21. 2(x 2 9)(x 2 5) 22. (3k 1 4)(2k 2 3) 23. h 5 216t 2 1 30t 1 4 Quiz 3 1. (x 1 9)(x 2 9) 2. (3z 1 11)(3z 2 11) 3. (10m 1 7n)(10m 2 7n) 4. (h 1 7)2 24. 2 sec 25. x 3(x 1 1)(x 2 1) 26. (a 2 3)(5a 2 7) 27. t 2(3t 1 5)2 10. 3(z 1 5)2 11. 2k(k 2 9)2 2 28. (b 1 5)(b2 2 3) 29. 25, 23 30. 1, } 5 3 31. 6} 32. 26, 62 2 12. (x 1 y)(x 1 2) 13. 25 14. 22, 2 Chapter Test C 5. (8t 2 1)2 6. 4(a2 1 b2) 7. 6(x 1 y)(x 2 y) 8. 5(m 1 2n)(m 2 2n) 9. x(x 2 5)(x 1 2) 15. 27, 0, 7 16. 0, 1, 5 17. 6 in. long by 2 in. 1. 3p3 1 6p2 2 12p 1 9 2. x2y 2 11xy 2 y 2 3 wide by 8 in. high 3. 9cd 1 3c 1 4d 4. D 5 218.53t 2 1 895t 1 40,091 Chapter Test A 3 1. 10a 1 a 2 3 2 2. y 1 2y 2 4y 2 2 2 3. 22x 1 7x 2 8 4. 3h2 2 3h 1 17 5. θ 5 0.014t 2 1 0.15t 1 10 Copyright © Holt McDougal. All rights reserved. 10. 16p2 2 1 11. w 2 2 10w 1 25 6. 129,000 7. 2n4 2 3n2 1 2n 8. 8w 2 2 26w 1 21 9. d 3 1 4d 2 1 5d 1 2 10. p2 2 9 11. t 2 2 8t 1 16 12. 4s2 2 25 2 2 13. 25% 14. 0.25B 1 0.5Bb 1 0.25b 1 4 15. 27, 4 16. 25, } 17. 4c 5(c 3 2 2) 18. 6g (f 2g 2 1 2) 19. 2k(k 2 1 3k 2 7) 20. 0, 3 3 21. 0, } 22. h 5 216t 2 1 20t 23. 1.25 seconds 7 5. The difference was increasing until it peaked in 2009 and then it began decreasing. 6. 12x 3y 2 18x 2y 2 1 2xy 3 7. 23s 3 1 13s 2 1 4s 2 32 8. 5a2 1 2ab 2 7b2 9. 25z 2 2 40z 1 16 1 10. 49t 2 2 9u2 11. 9q2 2 } 4 12. V 5 x(15 2 2x)(12 2 2x) 13. 0 < x < 6 3 9 1 14. 176 cubic inches 15. 0, 2} 16. 2}, } 3 2 5 17. 30 mi/h 18. (x 1 3y)(x 2 17y) 19. (4m 1 5n)(m 1 n) 20. c(2c 2 d)(c 2 3d) 24. (x 1 7)(x 1 2) 25. (y 2 4)( y 1 3) 21. 3 m by 5 m 22. 1 cm by 5 cm 26. (3m 1 2)(m 1 6) 27. 3 cm by 20 cm 23. p(6 2 7p)(6 1 7p) 24. y(3y 1 5)2 28. 3x(x 1 2)(x 1 3) 29. 2(s 1 3)(s 2 3) 25. (v 2 x)(u 2 w) 26. (5a 2 2b3)2 30. (r 1 7)(r 1 3) 31. 0, 22, 5 32. 27, 4 27. 23(c 2 5u)(c 1 5u) 33. 8 ft by 10 ft 1 28. (x 2 7)(x 1 7)(x 1 2) 29. 2 } sec 4 30. 0, 65 31. 62, 3 Chapter Test B 3 ANSWERS 8. 5y 2 1 17y 2 12 9. 5s3 1 32s2 2 13s 2 10 Quiz 2 3 2 1. 3a 2 2 2. 3x 2 4x 1 4x 1 35 32. Sample answer: x3 1 x2 2 2x 5 0 3. 213d 3 1 2d 2 2 3d 1 1 33. Sample answer: 3x2 1 10x 2 8 5 0 Algebra 1 Assessment Book A23 Chapter 10, continued Quiz 2 6. domain: all real } } 1. 23, 3 2. 2Ï 7 , Ï 7 3. 25, 1 4. 4, 6 } } Y numbers; range: y ≤ 9 } X X 9. y 5 22(x 2 1)2 1 4 7. domain: all real y (1, 4) 1 O x 1 y 7 x 5 22 numbers; 3 range: y ≥ 2}4 2 (24, 0) (23, 0) (2 x 1 ANSWERS 5. 2, 6 6. 1 2 Ï11 , 1 1 Ï11 7. 23 2 Ï7 , } } } 23 1 Ï 7 8. 24 2 2Ï3 , 24 1 2Ï 3 7 2 3 ,2 4 1 ) x 8. 22, 4 9. no solution 10. 65.29 11. 66 10. y 5 (x 1 2)2 2 1 12. 27, 23 13. You must add 9 to both sides of the equation; Y X x 2 2 6x 5 3 x 2 2 6x 1 9 5 3 1 9 / X (x 2 3) 2 5 12 } x 2 3 5 6 2Ï 3 } 1 1 11. 2}, 2 12. 23, 5 13. 23 14. }, 3 2 3 x 5 3 6 2Ï 3 14. y 5 2(x 2 3)2 1 2 y Quiz 3 (3, 2) 1. no solution 2. two solutions 1 3. one x-intercept 4. two x-intercepts x 1 x Copyright © Holt McDougal. All rights reserved. 5. linear function; y 5 2x 2 1 6. quadratic function; y 5 2x 2 1 1 15. y 5 (x 2 1)2 1 1 3 Y Chapter Test A 1. y 5 X 3 X 1 23 1 21 21 3 x The graph is a vertical stretch (by a factor of 3) of the graph of y 5 x 2. 21 19. 1996 20. no solution 21. two solutions 22. one solution 23. exponential function Chapter Test B 1 23 18. 21.45, 3.45 24. quadratic function y 2. 16. 20.12, 2.12 17. 21.5 1 3 x 1. y 3 23 1 3 x 23 The graph is a reflection in the x-axis and a vertical translation (of 2 units up) of the graph of y 5 x 2. 3. y = 216x 2 + 48x + 3 4. 1.5 sec 5. 39 ft 23 The graph is a vertical 1 shrink (by a factor of }4 ) and a vertical translation (of 1 unit down) of the graph of y 5 x 2. Algebra 1 Assessment Book A25 Chapter 10, continued 2. 20. 1998 and 2001 21. none 22. two 23. one y 24. linear function 25. quadratic function 3 26. exponential function 21 21 Chapter Test C 3 x 1 The graph is a reflection in the x-axis and a vertical translation (of 5 units up) of the graph of y 5 x 2. 3. maximum value; f (2) 5 11 4. minimum value; f (2) 5 3 5. minimum value; f (0) 5 7 6. 9 ft 7. domain: all real y numbers; 10 (1, 9) range: y ≤ 9 6 x 1 h 12 10 8 6 4 2 0 0 1 2 3 4 5 d Distance (miles) y 5. (4, 0) x 1 3. 4. about 8 feet 2 ( 2, 0) 1O 1. The graph of g would be a reflection in the x-axis and a shift 7 units up from the graph of f. 2. The graph of g would be a vertical stretch by a factor of 8 and a shift 2 units down from the graph of f. 6. 1 8. domain: all real Y / 1 X 1 1 x52 23 X 1 3 y 9. 22 24 7. R 5 (10 1 n)(8,0002500n) 10. 8. R 5 2500n2 1 3000n 1 80,000 9. $84,500 10. $13 11. 21.3, 3.3 12. 20.83, 16.83 y x 13. 20.22, 2.22 2 2 14. y 5 2 x 2 } 1 3 3 5 1 212 2 Y 1 1 3 27, 2 21, 4 11. 60.75 12. 2.54, 9.46 13. no solution } } 14. 3; 16; 4; 4; 6Ï 19 ; 4 6 Ï 19 15. y 5 23(x 1 2)2 1 4 y ( 2, 4) 1 O 5 x (1.875, 2.53125) 1.875 5 x 21 x 3 (2, 0) numbers; range: y ≥ 24 y 1 x X X 15. no solution 16. 21.45, 3.45 17. 27 mi/h or 55 mi/h 18. no 19. (a) Sample answer: c 5 4; (b) c 5 5; (c) Sample answer: c 5 6 1 20. linear function; f(x) 5 } x 1 3 2 21. quadratic function; f(x) 5 2x 2 2 5 x 2 x Standardized Test A 16. y 5 2(x 2 3)2 1 3 Y 1. B 2. D 3. B 4. C 5. A 6. B 7. D 8. C 9. A 10. D 11. A 12. D 13. B 14. 22 15. a. linear function; y 5 6x 1 15 b. no; X / X 2 17. 29.57, 1.57 18. 21.09, 4.59 19. 2} 3 A26 Algebra 1 Assessment Book Sample answer: Six hours is twice three hours, but $51 is not twice $33. Copyright © Holt McDougal. All rights reserved. 23 Height (feet) ANSWERS 1 Chapter 10, continued 16. a. y 5 22x2 1 40x 1 600 b. $800 c. 10 more students; when x 5 10, y 5 800 c. 13.8 ft d. 0.78125 sec e. 0.30 sec and 1.27 sec after release f. 1.52 sec Standardized Test B Chapter 11 sample answer: 225 fliers is three times 75 fliers, but $35 is not three times $17. 16. a. R 5 25n 2 1 200n 1 2500 b. $4500 c. $30; According to the function, the maximum amount of revenue is $4500. The maximum amount of revenue is made when n is 20. This means they can increase their price by $20 to make their maximum amount of revenue. So, the new selling price would be $30. Quiz 1 1. y 3 1 21 21 23 1 23 The domain is x} ≥ 2. The range is y ≥ 0. The graph of y 5 Ï x 2 2 is a horizontal translation } (of 2 units to the right) of the graph of y 5 Ï x . 9. C 10. B 11. A 12. C 13. D 14. 15 15. a. quadratic function; y 5 3x2 b. no; Sample answer: After 10 weeks, the frog count is 300, which is not twice the count after five weeks. 16. a. R 5 220n2 1 150n 1 2480 b. $2761.25 c. $11.75; The maximum occurs when n 5 3.75 and $8 1 $3.75 5 $11.75. SAT/ACT Chapter Test 1. C 2. A 3. D 4. B 5. D 6. A 7. B 8. A 9. C 10. E 11. A 12. E 13. B 14. D 15. 21 16. 12 17. 1 } 3 } 3} 3} 3} Ï3 1 Ï211 10. }} 11. 23Ï 2 12. 81 13. 1 3 14. 1, 3 15. 31 Quiz 2 } } 4. c 5 6Ï 2 5. x 5 3, 3x 5 9 6. x 5 8, x 2 2 5 6, x 1 2 5 10 7. 4 8. 6 9. (7, 3) 10. (5, 25) Chapter Test A ; domain: x ≥ 0; range: y ≥ 0; The graph is a vertical stretch }of the graph of y 5 Ï x . y 7 5 3 1 1 2. 3 Height (feet) 5 7 x ; domain: x ≥ 1; range: y ≥ 0; The graph is a shift 1 unit to the right of the } graph of y 5 Ï x . y 7 5 3 1 1 0 } 1. c 5 17 2. a 5 2Ï 10 3. b 5 5Ï3 1. Complete answers should include: an (0.78125, 13.765625) } 3 3 2Ï3 k 7. } 8. 9 9. 12Ï x2 2 3Ï 2x2 g 1. explanation that the differences in successive y-values will be equal for linear functions; an explanation that the ratios in successive y-values will be equal for exponential functions; an explanation that the differences in successive first differences in y-values will be equal for quadratic functions; an example of an equation for each type of function. 2. a. h 5 216t 2 1 25t 1 4 } x } Performance Assessment h 14 12 10 8 6 4 2 } 5Ï 5 2. 3Ï 10 3. 6y 4. 3Ï 3 2 1 5. 2Ï 5 6. } 2 1. D 2. D 3. B 4. B 5. A 6. B 7. D 8. A b. x 3 } Standardized Test C Copyright © Holt McDougal. All rights reserved. ANSWERS 1. B 2. B 3. D 4. C 5. D 6. B 7. A 8. B 9. D 10. C 11. A 12. C 13. B 14. 4 3 15. a. Linear function; y 5 }x 1 8 b. no, 25 3 5 7 x } } } 3 4Ï 7 4. } 5. } 6. 9x3y Ï y 7. 24Ï 5 7 4 } 3. 4Ï 2 } } 8. 10Ï 2 2 2 9. 10Ï 3 cm 10. 12 cm2 11. 4x 3} Ï7 12. 2 1 Ï 2y 13. } 14. 3 15. 3 16. 16 4 3 0 0.4 0.8 1.2 Time (seconds) 1.6 t } } 17. 16ºC 18. 17 19. Ï 115 20. yes 21. no Algebra 1 Assessment Book A27 Chapter 11, continued } } } 23. 5Ï 2 24. Ï 85 25. (9, 4) 22. 31.6 m } 26. (24, 1) 27. (0, 22) 28. 4Ï 2 units ANSWERS 29. 100.5 square units Chapter Test B 1. ; domain: x ≥ 0; range: y ≥ 23; The graph is a x vertical shrink and a shift 3 units down from the } graph of y 5 Ï x . y 1 1 21 21 3 5 23 25 y 2. 1 1 3 5 23 ; domain: x ≥ 22; range: y ≤ 0; The graph is a x reflection in the x-axis and a shift 2 units to the} left of the graph of y 5 Ï x . } 3} πÏ2L Ï2 π 11. t 5 } 12. } sec 13. 7Ï t 2 3 4 2 3} 6aÏ25 3} 3} 14. } 15. Ï 900 2 Ï 30 1 1 16. 8 17. 9 5 18. 0, 3 19. 20 people 20. 10x 21. about 14 people 22. 3.1, 8.1 23. 36.3, 106.9, 112.9 } 24. 642.9 in.2 25. (210, 215); 6Ï 13 } 1 26. (1, 3); 2Ï 2 27. 22 28. } 2 1 1 29. y 5 } x 2 } 2 2 Standardized Test A 1. A 2. D 3. B 4. C 5. A 6. A 7. C 8. B 9. C 10. D 11. D 12. B 13. A 14. C 15. A 16. B 17. C 18. D 19. 19 20. Train station; It is closest to the midpoint of } } 3. 6a 2Ï 2a 4. 14Ï 2 5. 29Ï 3 } 2p } 2Ï3b 6. } 7. }3 8. 44 1 16Ï 7 b q } } 3} Ïh 5Ï 2 9. t 5 } 10. } sec 11. 2Ï 4 2 4 4 2 3} 3} Ï36a 12. } 13. 22Ï 5x 14. no solution 3 15. 2 16. 21, 3 17. 0.7 m 18. 4 in., 2 in. 7 25 5 19. } ft, } ft 20. 3, } 6 6 2 1 2 } 5 21. 2}, 21 2 1 } 2 } 22. (6, 22) 23. 2Ï 2 , 2Ï 10 , 4Ï 2 24. yes 25. 2 or 10 26. 3 or 21 27. Tower A Chapter Test C ; domain: x ≥ 21; range: y ≥ 24; The graph is a 21 1 3 5 x vertical stretch, shift 1 21 unit to the left and 4 units down } from the graph of y 5 Ïx . y 2. ; domain: x ≥ 4; range: 6 y ≤ 2; The graph is a 2 reflection in the x-axis, a 22 2 6 10 x 22 vertical shrink, and a shift 4 units to the right and 2 26 units up from the graph of } y 5 Ïx . } 3. h ≥ 210; v ≥ 0 4. about 22 cm 5. 9Ï 10 y 1. 1 2 5Ï 6. 6a b } Ï 5x 2a 7. 22Ï2 8. } xy } } } } 15 2 3Ï5 9. 15x 2 22yÏ x 1 8y 2 10. } 20 A28 Algebra 1 Assessment Book (7, 4). It is 1 unit away and the distances to the other locations are greater than 1. 21. a. 32 ft; 24(16) 5 384 and 384 4 12 5 32 } b. 40 ft; Ï 242 1 322 5 40 c. 11 ft more Standardized Test B 1. C 2. D 3. A 4. B 5. B 6. A 7. C 8. D 9. D 10. B 11. A 12. C 13. B 14. C 15. A 16. D 17. A 18. C 19. 11 20. You would meet at the fountain. The midpoint between the two locations is the point (4, 3). The two locations closest to this point are the school and the fountain. You can use either the distance formula or your knowledge of right triangles to determine that the fountain is closest. 21. a. Twenty-four steps are needed. The height from floor to ceiling is 12 feet or 144 inches. If the riser of each step is 6 inches, you would need 24 steps to reach the second floor. b. 24 ft; Each step has a tread of 12 inches and there are 24 steps, so the linear distance would be 288 inches or 24 feet. c. A 322 inch rail is needed. Standardized Test C 1. B 2. A 3. A 4. D 5. C 6. B 7. C 8. B 9. A 10. D 11. D 12. B 13. C 14. A 15. D 16. D 17. B 18. C 19. 21 20. Stadium; It is closest to the midpoint of } (20.5, 0.5). It is Ï6.5 , units away and the distances to the other locations are greater than that. Copyright © Holt McDougal. All rights reserved. } Chapter 11, continued 21. a. 39 steps; 26 ft 5 312 in. and 312 4 8 5 39 b. 39 ft; Each step is one-foot long and there are 39 steps. c. 46.9 ft; 9.5 ft more 8. ; The domain and range are all nonzero real numbers. y 1 23 x 1 21 21 1. D 2. B 3. C 4. E 5. D 6. B 7. B 8. D ANSWERS SAT/ACT Chapter Test 23 9. A 10. C 11. E 12. A 13. D 14. 9 15. 117 yd 16. 6 Performance Assessment 1. Complete answers should include: an 3 Time (seconds) explanation of each property of radicals; an example illustrating why there is no sum property of radicals; an example illustrating why there is no difference property of radicals. 2. a. ; Domain: 0 ≤ h ≤ 36 t 1 23 21 1 1.5 Quiz 2 1.0 1. x 2 3 2. x 1 9 0.5 0 y 3. 4. 10 y 10 0 6 12 18 24 30 36 h Height (feet) 6 b. (0, 1.5), (36, 0); 1.5 seconds after the object is Copyright © Holt McDougal. All rights reserved. ; The domain is all real numbers except x 5 21. The range is x all real numbers except y 5 0. y 9. 6 2 2 dropped it has a height of 0 feet; the object is at a height of 36 feet right before it is released. c. 36.03 units d. 32 ft e. 20 ft f. 1.06 sec g. Less time; The object is in the air for a total of 1.5 seconds, and it takes just over 1 second to fall the first 18 feet, which means it takes less than 0.5 second to fall the second 18 feet. 27 5. x2 1 7x 2 4 6. x2 2 5x 1 4 1 } x+5 1 7. }; The excluded values are 21 and 1. x11 Chapter 12 x23 8. }; The excluded value is 0. 2 Quiz 1 12x3 9. }; The excluded value is 0. 5 1. direct variation 2. inverse variation 35 35 224 3. neither 4. y 5 }; } 5. y 5 }; 212 x 2 x 7 7 6. y 5 }; } x 2 7. ; The domain and range are all nonzero real numbers. y 6 2 22 22 22 2 10 x 210 2 26 26 6 x 26 x25 10. }; The excluded values are 23 and 3. x23 Quiz 3 2(x 2 7) 7 4 1. } 2. } 3. } 4. 2x(x 2 5) 15x x x24 8x 1 7 2x 1 9 5. } 6. }} (x 1 8)(x 1 1) x26 7. 0 and 5 8. 0 and 2 9. 12 h 2 6 x Chapter Test A 1. neither 2. direct variation 60 3. inverse variation 4. t 5 } n 5. 15 days Algebra 1 Assessment Book A29 Chapter 12, continued 1 ANSWERS 23 1 21 3 ; domain: all real numbers except 0; range: all real numbers except 2; The x graph is a vertical shift (of 2 units up) of the graph 1 of y 5 }x . ; domain: all real numbers except 1; range: all real 1 numbers except 0; The 3 x graph is a horizontal translation (of 1 unit to the 23 1 right) of the graph of y 5 }x . 8. x 5 0; y 5 0 9. x 5 22; y 5 7 10. x 5 0; y 5 22 11. 3x 2 2 5x 1 8 28 12. x 1 3 1 } x18 7. y 3 13. The velocity increases, but never reaches 200 feet per second. 14. x 1 7 27x 4 2x 1 5 13. }; 0 14. 22; 9 15. }; 24, 3 5 x14 2(7x 1 8) 16. } 3x(x 1 2) 2900 17. y 5 } 1 100; x 1 10 y 90 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 x Salt (grams) 17 2x 3 15. x 1 9 1 } 16. x2 1 3x – 5 17. }; 0 x22 3 1 18. not possible; 27 19. }; 23, 5 x13 3(x 1 4) 2x 2 20. } 21. } 22. } 23. 3x 3x 9 x(x 1 12) 1 4x 2x 2 x21 18. } 19. } 20. 2} 21. } 2 3 3 2 860,000 1 1,800,000x 22. Y 5 }}; 1000 1 24x 107,500 1 225,000x 23. 14,030 yd 24. 2 Y 5 }} 125 1 3x x15 5x 29 24. } 25. } 26. } x14 4x 1 1 12x 3 2 2x x 2 1 3x 1 3 }} 25. } 26. (x 2 1)(x 1 1) 9x 2 600r 2 3000 3x 2 1 20x 2 8 27. }} 28. t 5 } 29. 11 h r(r 2 10) (x 2 4)(x 1 6) Chapter Test C Chapter Test B 48 100 1. no 2. yes; y 5 } 3. V 5 } 4. 10 P x 5. ; domain: all real numbers except 23; range: all real numbers except 0; The x graph is a vertical stretch and horizontal shift (of 3 units to the left) of the graph 1 of y 5 }x . y 3 1 21 21 23 6. y 3 1 23 21 21 1 3 4 7. y 5 } 1 6 x25 A30 28 14 9. x 1 2 1 } 10. 3x 1 3 1 } x11 2x 2 3 11 11. x2 2 2x 1 3 12. x2 1 3x 2 6 1 } x12 Algebra 1 Assessment Book ; domain: all real numbers except 0; range: all real numbers except 2; The graph is a reflection in the x x-axis and a vertical shift (of 2 units up) of the graph 1 of y 5 }x . 2 8. y 5 } 2 3 x11 1. direct variation 2. neither 3. inverse variation 11,250 1200 4. T 5 } 5. 500 sec 6. f 5 } n15 s 7. domain: all real numbers except 25; range: all real numbers except 0; The graph is a vertical stretch and vertical shift (of 5 units to the left) 1 of the graph of y 5 }x . 23 5 8. y 5 } 1 2 9. y 5 } 2 4 x14 2x 2 1 16x 2 19 33 10. 4x 2 6 1 } 11. 2x 1 9 1 } 2 3x 21 x 24 2 2 12. 3x 2 2x 1 7 13. x 2 4x 1 16 14. y 10 6 26 2 x Copyright © Holt McDougal. All rights reserved. y 3 Percent of salt 6. Chapter 12, continued } 3x 2 4 6 7 6 Ï 114 23. } 24. }} 25. } 5 x21 (x 1 3)(x 2 1) 4(9r 2 10) 26. 23 27. t 5 } 28. 8 mi/h r(r 2 2) substitute $2.25 for C in the equation, you would get a negative answer for p. It is not possible to sell a negative number of packages. Standardized Test C 1. C 2. A 3. A 4. B 5. B 6. C 7. D 8. A 9. D 10. C 11. D 12. D 13. C 14. 27 345 1 15. a. t 5 } ; r 1} 2 ANSWERS 31x 15. not possible; 211 16. 2}; 24, 3 x14 2(x 1 2) 3 5 17. }; 23, 0, 1 18. } 19. } x13 2x 12 2(x 2 7) 3(2x 2 1) x13 20. 2} 21. } 22. }} x15 x24 x(x 2 4)(x 2 3) t Standardized Test A 1. D 2. D 3. B 4. A 5. C 6. A 7. C 8. B 9. A 10. D 11. D 12. 22 15 t 13. a. t 5 } r 1 0.5 40 r 5 b. The graph stretches vertically and shifts 1 10 units to the right and }6 unit up. The vertical 2 2 r b. The graph shifts 5 units to the left and 0.5 unit down. The shift of 5 units is due to the fact that the average speed increases by 5 miles per hour. The shift of 0.5 unit down is due to the fact that you did not take a break, so the time decreases by one-half hour. 80 1 2t 14. a. C 5 } b. $2.80 c. 40 tins t 1 of }6 unit up is due to the fact that the total break time increases by one-sixth of an hour. 150 1 2.5t 150 1 2.5t 16. a. C 5 } b. 3.75 5 } ; t t 120 tins c. 600 tins d. no; Substituting 2 for C makes t negative which does not make sense for the situation. SAT/ACT Chapter Test 1. D 2. D 3. B 4. B 5. C 6. D 7. A 8. B 9. C 10. A 11. D 12. 25 t 300 13. a. t 5 } 1 0.75; r 1. D 2. E 3. A 4. C 5. A 6. C 7. E 8. D 9. A 10. D 11. B 12. C 13. E 14. 4 15. 2.6 h 16. 2 Performance Assessment 1. Complete answers should include: work 10 10 r b. The graph shifts 5 units to the right and 0.25 unit down. The shift of 5 units to the right is due to the fact that the average speed is decreased by 5 miles per hour. The shift of 0.25 unit down is the difference between the 0.75 hour and 0.5 hour lunch breaks. 350 1 3p 350 1 3p 14. a. C 5 } b. } 5 4; You would p p need to sell 350 packages to reduce the cost of each package to $4. c. No; If you were to showing each operation being carried out; explanations of the steps being used to carry out each operation. 400 1 4.75x 2. a. C 5 } x b. C Average Cost per person Copyright © Holt McDougal. All rights reserved. Standardized Test B stretch is due to the increase in the distance. The shift of 10 units is due to the fact that the average speed decreases by 10 miles per hour. The shift 1200 1000 800 600 400 200 0 0 2 4 6 8 10 12 x Number of people c. $12.75 d. over 320 people Algebra 1 Assessment Book A31