Class: Date: Unit 3 Practice Test Describe a pattern in each sequence. What are the next two terms of each sequence? 1. 24, 22, 20, 18,... Tell whether the sequence is arithmetic. If it is, what is the common difference? 2. 15, 19, 23, 27,... 3. 2, 7, 13, 20,... a. yes; 5 b. yes; 6 c. yes; 2 d. no 4. Suppose your business has a special checking account used just for paying the phone bill. The balance is $740.00 this month. Next month the balance will be $707.60, after that it will be $675.20, and on the third month the balance will be $642.80. Write an explicit formula to represent the balance in the account as an arithmetic sequence. How many months can you pay your phone bill without depositing any more money in the account? a. A(n) = 740.00 32.40n; 22 months b. A(n) = 740.00 + (n 1)( 32.40); 23 months c. A(n) = 740.00 32.40n; 23 months d. A(n) = 740.00 + (n 1)( 32.40); 24 months 5. Write a recursive formula for the arithmetic sequence below. What is the value of the 8th term? 1, 5, 9, 13,... 6. An arithmetic sequence is represented by the recursive formula A(n) = A(n 1) + 8. If the first term in the sequence is 4, write the explicit formula. a. A(n) = 4 8n c. A(n) = 4 + 8(n 1) b. A(n) = 4 8(n 1) d. A(n) = 4 + 8n 7. An arithmetic sequence is represented by the explicit formula A(n) = 2 + 9(n 1). What is the recursive formula? a. A(n) = A(n 1) + 2 c. A(n) = A(n 1) 9 b. A(n) = A(n 1) + 9 d. A(n) = A(n 1) 2 8. Marta s starting annual salary is $24,900. At the beginning of each new year, she receives a $2700 raise. Write a recursive formula to find Marta s salary f(n) after n years. What will Marta s salary be after 4 yr? a. f(n) = 2700f(n 1); $33,000 c. f(n) = f(n 1) 2700; $35,700 b. f(n) = f(n 1) + 2700; $33,000 d. f(n) = 2700f(n 1); $35,700 1
9. Elaine has a business repairing home computers. She charges a base fee of $30 for each visit and $35 per hour for her labor. The total cost C for a home visit and x hours of labor is modeled by the function rule C = 35x + 30. Use the function rule to make a table of values and a graph. x 0 1 2 3 C 2
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. 10. The table shows the number of miles driven over time. 11. Time (hours) Distance (miles) 4 204 6 306 8 408 10 510 a. 51 ; Your car travels 51 miles every 1 hour. 1 b. 204; Your car travels 204 miles. c. 1 ; Your car travels 51 miles every 1 hour. 51 d. 10; Your car travels for 10 hours. Find the slope of the line. What is the slope of the line that passes through the pair of points? 12. (1, 7), (10, 1) 3 a. b. 2 2 3 13. ( 5.5, 6.1), ( 2.5, 3.1) c. 3 2 d. 2 3 14. ( 5 3, 1), ( 2, 9 2 ) 3
What is the slope of the line? 15. 16. a. undefined b. 0 a. 0 b. undefined 4
17. The number of sofas a factory produces varies directly with the number of hours the machinery is operational. Suppose the factory can produce 455 sofas in 48 hours. What is an equation that relates the number of sofas produced, n, with the amount of time, t, in hours? What is the graph of your equation? a. n = 9.48t c. t = 4.74n b. n = 0.11t d. t = 9.48n What are the slope and y-intercept of the graph of the given equation? 18. y = 4x + 2 Write an equation of a line with the given slope and y-intercept. 19. m = 5, b = 3 5
Write the slope-intercept form of the equation for the line. 20. What equation in slope intercept form represents the line that passes through the two points? 21. (6.6, 2.5), (8.6, 10.5) a. y = 4x + 23.9 c. y = 4x + 23.9 b. y = 0.25x 23.9 d. y = 0.25x 23.9 6
Graph the equation. 22. y = 4x 3 7
23. Giselle pays $240 in advance on her account at the athletic club. Each time she uses the club, $15 is deducted from the account. Model the situation with a linear function and a graph. a. c. b. b = 240 15x d. b = 225 15x b = 225 + 15x b = 240 + 15x Write an equation in point-slope form for the line through the given point with the given slope. 24. (8, 3); m = 6 a. y + 3 = 6(x 8) c. y 3 = 6(x + 8) b. y 3 = 6(x 8) d. y + 3 = 6x + 8 25. (3, 10); m = 0.83 8
Graph the equation. 26. y 4 = 5(x + 1) 9
27. y 4 = 2(x 2) 28. What is an equation of the line? a. y + 3 = (x + 4) c. y + 3 = (x 4) b. y 3 = 2(x 4) d. y + 5 = 2(x + 4) 10
29. The table shows the height of a plant as it grows. What equation in point-slope form gives the plant s height at any time? Let y stand for the height of the plant in cm and let x stand for the time in months. Time (months) Plant Height (cm) 3 15 5 25 7 35 9 45 a. y 15 = 5 2 (x 3) c. y 3 = 5 (x 15) 2 b. y 15 = 5(x 3) d. The relationship cannot be modeled. 30. The table shows the height of an elevator above ground level after a certain amount of time. Model the data with an equation in slope-intercept form. Let y stand for the height of the elevator in feet and let x stand for the time in seconds. Time (s) Height (ft) 10 202 20 184 40 148 60 112. Find the x- and y-intercept of the line. (Remember --to find the x-intercept you plug 0 in for y and solve & for the y-intercept you plug 0 in for x and solve.) 31. 4x + 2y = 24 11
Match the equation with its graph. 32. 4x 2y = 8 a. c. b. d. 12
What is the graph of the equation? 33. y = 2 a. c. b. d. 13
34. x = 1 a. c. b. d. 35. Write y = 1 x + 5 in standard form using integers. 6 a. x 6y = 30 c. x + 6y = 30 b. 6x y = 30 d. x + 6y = 5 36. Write y = 0.2x 0.3 in standard form using integers. 37. A paint store sells exterior paint for $35.75 a gallon and paint rollers for $6.00 each. Write an equation in standard form for the number of gallons p of paint and rollers r that a customer could buy with $190. a. 35.75 + 6 = p c. 35.75r + 6p = 190 b. 35.75p + 6r = 190 d. 35.75p = 6r + 190 Write an equation for the line that is parallel to the given line and passes through the given point. 38. y = 5x + 8; (2, 16) 14
Tell whether the lines for each pair of equations are parallel, perpendicular, or neither. 41. 39. y = 1 6 x 5 24x 4y = 12 Write the equation of a line that is perpendicular to the given line and that passes through the given point. 40. x + 3y = 16; ( 3, 4) What type of relationship does the scatter plot show? a. positive correlation b. negative correlation c. no correlation 15
42. The scatter plot shows the number of mistakes a piano student makes during a recital versus the amount of time the student practiced for the recital. How many mistakes do you expect the student to make at the recital after 6 hours of practicing? a. 55 mistakes c. 63 mistakes b. 37 mistakes d. 45 mistakes Use a graphing calculator to find the equation of the line of best fit for the data. Find the value of the correlation coefficient r. Predict the missing value in the table. 43. John s Best Discus Throws Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 Distance (meters) 69.08 69.18 69.80 70.24 70.86 71.16 71.86 72.08? 44. Hours Studying 1 2 3 4 5 6 7 8 9 Exam Mark (%) 65 67 73 74 77 80 84 85? In the following situations, is there likely to be a correlation? If so does the correlation reflect a causal relationship? Explain. 45. the average daily winter temperature and your heating bill a. There is a positive correlation. The higher the average daily winter temperature the higher your heating bill. b. There is a negative correlation and a causal correlation. The higher the average daily winter temperature the lower your heating bill. c. There is no correlation. 16
46. The graph below represents one function, and the table represents a different function. How are the functions similar? How are they different? x 2 1 0 1 2 y 0 1 2 3 4 a. The functions have the same slope, but different y-intercepts. b. The functions have the same y-intercept but different slopes. c. The function have the same slope and the same y-intercept. d. The functions are both linear, but have different slopes and different y-intercepts. Which ordered pair is a solution of the inequality? 47. y 4x 5 a. (3, 4) b. (2, 1) c. (3, 0) d. (1, 1) 48. 2y + 6 < 8x a. (4, 13) b. ( 5, 2) c. (0, 6) d. (4, 8) 17
Graph the inequality. 49. y < 3x 5 18
50. 4x + 6y 10 19
51. x 4 What is the graph of the inequality in the coordinate plane? a. c. b. d. 20
52. An electronics store makes a profit of $72 for every television sold and $90 for every computer sold. The manager s target is to make at least $360 a day on sales from televisions and computers. Write a linear inequality and graph the solutions. What are three possible solutions to the problem? a. 72s + 90p 360 c. 90s + 72p 360 (5, 2), (3, 3), and (1, 4) are three possible solutions. b. 72s + 90p 360 (3, 1), (2, 2), and (1, 0) are three possible solutions. d. 90s + 72p 360 (4, 0), (2, 2), and (1, 1) are three possible solutions. (4, 0), (3, 3), and (1, 4) are three possible solutions. 21
Which inequality represents the graph? 53. 22
Unit 3 Practice Test Answer Section 1. subtract 2 from the previous term; 16, 14 2. yes; 4 3. D 4. B 5. A(n) = A(n 1) + 4; 29 6. C 7. B 8. B 9. x C 0 30 1 65 2 100 3 135 10. A 11. 1 2 12. B 13. 1 14. 33 2 15. B 16. B 17. A 18. The slope is 4 and the y-intercept is 2. 1
19. y = 5x 3 20. y = 5 8 x + 1 2 21. C 22. 23. A 24. B 25. y + 10 = 0.83(x 3) 26. 2
27. 28. A 29. B 30. y = 1.8x + 220 31. x-intercept is 6; y-intercept is 12 32. B 33. D 34. D 35. C 36. 2x + 10y = 3 37. B 38. y = 5x + 6 39. perpendicular 40. y = 3x + 5 41. A 42. A 43. y = 0.465x 862.515, r = 0.994; 71.67 44. y = 2.964x + 62.286, r = 0.991; about 89% 45. B 46. B 47. D 48. D 3
49. 50. 51. C 52. A 53. y 3x + 4 4