1-1 Practice Patterns and Expressions Form G Describe each pattern using words. Draw the next figure in each pattern. 1. 2. 3. Copy and complete each table. Include a process column. 4. 5. 6. Input Output Input Output 1 4 1 2 2 9 2 4 3 14 3 6 4 19 4 8 5 5 6 6 Input Output 1 0.5 2 1.0 3 1.5 4 2.0 5 6 n n n 7. Describe the pattern using words. 3
1-1 Practice (continued) Patterns and Expressions Form G A gardener plants a flower garden between his house and a brick pathway parallel to the house.the table at the right shows the area of the garden, in square feet, depending on the width of the garden, in feet. 8. What is the area of the garden if the width is 8 feet? Width Area 1 3.5 2 7 3 10.5 4 14 9. What is the area of the garden if the width is 15 feet? Identify a pattern and find the next three numbers in the pattern. 10. 5, 10, 20, 40,... 11. 5, 8, 11, 14,... 12. 3, 1, 1, 3,... 13. 1, 3, 6, 10, 15,... 14. 2 3 4 5,,,,... 3 4 5 6 15. 10, 9, 6, 1, 6,... The graph shows the cost depending on the number of DVDs that you purchase. 16. What is the cost of purchasing 5 DVDs? 17. What is the cost of purchasing 10 DVDs? 18. What is the cost of purchasing n DVDs? Keesha earns $320 a week working in a clothing store. As a bonus, her employer pays her $15 more than she earned the previous week, so that at the end of the second week she earns $335, and after 3 weeks, she earns $350. 19. How much will Keesha earn at the end of the fifth week? 20. How much will Keesha earn at the end of the tenth week? 4
1-2 Practice Properties of Real Numbers Form G Classify each variable according to the set of numbers that best describes its values. 1. the area of the circle A found by using the formula πr 2 2. the number n of equal slices in a pizza; the portion p of the pizza in one slice 3. the air temperature t in Saint Paul, MN, measured to the nearest degree Fahrenheit 4. the last four digits s of a Social Security number Graph each number on a number line. 5. 1 6. 3 7. 2.8 8. Compare the two numbers. Use > or <. 9. 2, 2 10. 4, 17 11. 29,5 12. 50,6.8 1 2 2 13. 11, 130 14. 6, 30 15. 1 7, 67 2 16. 10, 12 Name the property of real numbers illustrated by each equation. 17. 23 ( + 5) = 23 + 2 5 18. 16 + ( 13) = 13 + 16 19. 1 7, = 1 7 20. 5( 0.2 7 ) = (5 0.2) 7 13
1-2 Practice (continued) Properties of Real Numbers Estimate the numbers graphed at the labeled points. 21. point A 22. point B 23. point C 24. point D Geometry To find the length of side b of a rectangular prism with a V square base, use the formula b= where V is the volume of the h' prism and h is the height. Which set of numbers best describes the value of b for the given values of V and h? 25. V = 100, h = 5 26. V = 100, h = 25 27. V = 100, h = 20 28. V = 5, h = 20 Write the numbers in increasing order. 29. 4 5 2 2,,,0.9, 1 30. 5, 6, 2, π, 0.5 5 4 8 3 Justify the equation by stating one of the properties of real numbers. 31. (x + 37) + ( 37) = x + (37 + ( 37)) 32. x 1 = x 33. x + (37 + ( 37)) = x + 0 34. x + 0 = x 14
1-3 Practice Form G Algebraic Expressions Write an algebraic expression that models each word phrase. 1. seven less than the number t 2. the sum of 11 and the product of 2 and a number r Write an algebraic expression that models each situation. 3. Arin has $520 and is earning $75 each week babysitting. 4. You have 50 boxes of raisins and are eating 12 boxes each month. Evaluate each expression for the given values of the variables. 5. 4v + 3(w + 2v) 5w; v = 2 and w = 4 6. c(3 a) c 2 ; a = 4 and c = 1 7. 2(3e 5f) + 3(e 2 + 4f); e = 3 and f = 5 Surface Area The expression 6s 2 represents the surface area of a cube with edges of length s. What is the surface area of a cube with each edge length? 8. 3 inches 9. 1.5 meters The expression 4.95 + 0.07x models a household s monthly long-distance charges, where x represents the number of minutes of long-distance calls during the month. What are the monthly charges for each number of long-distance minutes? 10. 73 minutes 11. 29 minutes Simplify by combining like terms. 12. 5x 3x 2 + 16x 2 13. ( a b) 3 4 + b 9 9 2 t 2 14. t+ + t + t 15. 4a 5(a + 1) 2 16. 2(j 2 k) 6(j 2 + 3k ) 17. x(x y) + y(y x) 23
1-3 Practice (continued) Form G Algebraic Expressions 18. In a soccer tournament, teams receive 6 points for winning a game, 3 points for tying a game, and 1 point for each goal they score. What algebraic expression models the total number of points that a soccer team receives in a tournament? Suppose one team wins two games and ties one game, scoring a total of five goals. How many points does the team receive? Evaluate each expression for the given value of the variable. 19. t 2 (3t + 2); t = 5 20. i 2 5(i 3 i 2 ); i = 4 21. Perimeter Write an expression for the perimeter of the figure at the right as the sum of the lengths of its sides. What is the simplified form of this expression? 22. Simplify (2x 5y) + 3(4x + 2y) and justify each step in your simplification. 23. Error Analysis Alana simplified the expression as shown. Do you agree with her work? Explain. 24. Open-Ended Write an example of an algebraic expression that always has the same value regardless of the value of the variable. Match the property name with the appropriate equation. 25. Opposite of a Difference A. [( r) + 2p] = ( r) 2p 26. Opposite of a Sum B. 16d (3d + 2)(0) = 16d 0 27. Opposite of an Opposite C. 5(2 x) = 10 5x 28. Multiplication by 0 D. (4r + 3s) + t = ( 1)(4r + 3s) + t 29. Multiplication by 1 E. (8 3m) = 3m 8 30. Distributive Property F. [ (9 2w)] = 9 2w 24
1-4 Practice Form G Solving Equations Solve each equation. 1. 7.2 + c = 19 2. 8.5 = 5p d 3. = 31 4. s 31 = 20.6 4 Solve each equation. Check your answer. 5. 9(z 3) = 12z 6. 7y + 5 = 6y + 11 7. 5w + 8 12w = 16 15w 8. 3(x + 1) = 2(x + 11) Write an equation to solve each problem. 9. Two brothers are saving money to buy tickets to a concert. Their combined savings is $55. One brother has $15 more than the other. How much has each saved? 10. Geometry The sides of a triangle are in the ratio 5 : 12 : 13. What is the length of each side of the triangle if the perimeter of the triangle is 15 inches? 11. What three consecutive numbers have a sum of 126? Determine whether the equation is always, sometimes, or never true. 12. 6(x + 1) = 2(5 + 3x) 13. 3(y + 3) + 5y = 4(2y + 1) + 5 Solve each formula for the indicated variable. 14. S = L(1 r), for r 15. A = lw + wh + lh, for w Solve each equation for y. 16. 4 ( 3) 9 y + = g 17. a(y + c) = b(y c) 18. y t + 3 = 2 19. 3y yz = 2z t 33
1-4 Practice (continued) Form G Solving Equations Solve each equation. 20. 0.5(x 3) + (1.5 x) = 5x 21. 1.2(x + 5) = 1.6(2x + 5) u u u 22. 0.5(c + 2.8) c = 0.6c + 0.3 23. + = 1 5 10 6 Solve each formula for the indicated variable. π 24. V= rh 2, for h 25. 3 T T = L 2 1 D ka for T1 Write an equation to solve each problem. 26. Two trains left a station at the same time. One traveled north at a certain speed and the other traveled south at twice that speed. After 4 hours, the trains were 600 miles apart. How fast was each train traveling? 27. Geometry The sides of one cube are twice as long as the sides of a second cube. What is the side length of each cube if the total volume of the cubes is 72 cm 3? 28. Error Analysis Brenna solved an equation for m. Do you agree with her? Explain your answer. Solve each problem. 29. You and your friend left a bus terminal at the same time and traveled in opposite directions. Your bus was in heavy traffic and had to travel 20 miles per hour slower than your friend s bus. After 3 hours, the buses were 270 miles apart. How fast was each bus going? 30. Geometry The length of a rectangle is 5 centimeters greater than its width. The perimeter is 58 centimeters. What are the dimensions of the rectangle? 31. What four consecutive odd integers have a sum of 336? 34
1-5 Practice Form G Solving Inequalities Write the inequality that represents the sentence. 1. Four less than a number is greater than 28. 2. Twice a number is at least 15. 3. A number increased by 7 is less than 5. 4. The quotient of a number and 8 is at most 6. Solve each inequality. Graph the solution. 5. 3(x + 1) + 2 < 11 6. 5t 2(t + 2) 8 7. 2[(2y 1) + y] 5(y + 3) 8. 1 (7a 1) 2a+ 7 3 9. 5 2(n + 2) 4 + n 10. 2(w 7) + 3 > w 1 Solve each problem by writing an inequality. 11. Geometry The length of a rectangular yard is 30 meters. The perimeter is at most 90 meters. Describe the width of the yard. 12. Geometry A piece of rope 20 feet long is cut from a longer piece that is at least 32 feet long. The remainder is cut into four pieces of equal length. Describe the length of each of the four pieces. 13. A school principal estimates that no more than 6% of this year s senior class will graduate with honors. If 350 students graduate this year, how many will graduate with honors? 14. Two sisters drove 144 miles on a camping trip. They averaged at least 32 miles per gallon on the trip. Describe the number of gallons of gas they used. 43
1-5 Practice (continued) Form G Solving Inequalities Is the inequality always, sometimes, or never true? 15. 3(2x + 1) > 5x (2 x) 16. 2(x 1) x + 7 17. 7x + 2 2(2x 4) + 3x 18. 5(x 3) < 2(x 9) Solve each compound inequality. Graph the solution. 19. 3x > 6 and 2x < 6 20. 4x 12 and 7x 7 21. 5x > 20 and 8x 32 22. 6x < 12 or 5x > 5 23. 6x 18 or 2x > 18 24. 2x > 3 x or 2x < x 3 Solve each problem by writing and solving a compound inequality. 25. A student believes she can earn between $5200 and $6250 from her summer job. She knows that she will have to buy four new tires for her car at $90 each. She estimates her other expenses while she is working at $660. How much can the student save from her summer wages? 26. Before a chemist can combine a solution with other liquids in a laboratory, the temperature of the solution must be between 39 C and 52 C. The chemist places the solution in a warmer that raises the temperature 6.5 C per hour. If the temperature is originally 0 C, how long will it take to raise the temperature to the necessary range of values? 27. The Science Club advisor expects that between 42 and 49 students will attend the next Science Club field trip. The school allows $5.50 per student for sandwiches and drinks. What is the advisor s budget for food for the trip? 44
1-6 Practice Form G Absolute Value Equations and Inequalities Solve each equation. Check your answers. 1. 3x = 18 2. 5y = 35 3. t + 5 = 8 4. 3 z + 7 = 12 5. 2x 1 = 5 6. 4 2y + 5= 9 Solve each equation. Check for extraneous solutions. 7. x+ 5 = 3x 7 8. 2t 3 = 3t 2 9. 4w + 3 2= 5 10. 2 z+ 1 3= z 2 Solve each inequality. Graph the solution. 11. 5 y + 3 < 15 12. 2t 3 5 13. 4b 3> 9 14. 1 2 1 3 1 2 w 15. 24x + 1 5 1 16. 3z 2 + 5> 9 Write each compound inequality as an absolute value inequality. 17. 7.3 a 7.3 18. 11 m 19 19. 28.6 F 29.2 20. 0.0015 t 0.0018 Write an absolute value equation or inequality to describe each graph. 21. 22. 53
1-6 Practice (continued) Form G Absolute Value Equations and Inequalities Solve each equation. 23. 32x+ 5= 9x 6 24. 4 3m = m+ 10 25. 2 4w 5 = 12w 18 26. 3 8 12 6( 1) 4 t = t 27. 5p+ 3 4= 2p 28. 7y 3 + 1= 0 Solve each inequality. Graph the solution. 29. 32t + 1< 9 30. 2x + 4 4 31. y + 2 3 1< 2 32. 1 4 5 2 5 7 z + + > Write an absolute value inequality to represent each situation. 33. To become a potential volunteer donor listed on the National Marrow Donor Program registry, a person must be between the ages of 18 and 60. Let a represent the age of a person on the registry. 34. Two friends are hiking in Death Valley National Park. Their elevation ranges from 228 ft below sea level at Badwater to 690 ft above sea level at Zabriskie Point. Let x represent their elevation above sea level. 35. The outdoor temperature ranged between 37 F and 62 F in a 24-hour period. Let t represent the temperature during this time period. The diameter of a ball bearing in a wheel assembly must be between 1.758 cm and 1.764 cm. 36. What is the tolerance? 37. What absolute value inequality represents the diameter of the ball bearing? Let d represent the diameter in cm. 54