Topic 1: Writing and Solving Equations and Inequalities

Size: px

Start display at page:

Download "Topic 1: Writing and Solving Equations and Inequalities"

Teresa McCormick
5 years ago
Views:

1 Topic 1: Writing and Solving Equations and Inequalities In #1 3, solve each equation. Use inverse operations = = 2(4 5) 3. 2( + 2) = The rectangle and square have equivalent perimeters. Which equation would ou use to find the perimeter of each figure? A 5 1 = B 8 = 7 C 2(2 1) + 2(3) = D 2(2 1) + 2(3) = 4(3 + 8) In #5 7, solve and graph each inequalit. If ou multipl or divide b a negative number, flip the smbol!!! < (2 ) 6( 1) 7. 2( 2) 2(1 )

2 8. Canoe Rentals Inc. rents canoes for $8 plus $3 per hour or an part of an hour. Write and solve an inequalit to find how man hours ou can rent a canoe if ou want to spend at most $25? F > 25 5 hours H hours G hours J hours In #9 and 10, solve and graph each compound inequalit. There are two tpes!!! OR has a graph that goes in opposite directions, and AND has a graph that meets in the middle < or 12 > 36 In #11 and 12, write the compound inequalit represented b each graph Topic 2: Functions 13. Circle all the relations that are functions. There could be more than one answer!!! A { (1,1), (1,2), (1,3) } C { (2,0), (3, 5), (4, 10) } B { (-3,-3), (-1, -3), (1,-3) } D { (5,1), (-4, 5), (5,2) } 14. For which value of is the relation not a function? {(0, 1), (, 0), (3, 5), (2, 6)} F 0 H 5 G 1 J 6

3 In #15 17, determine whether or not the relation is a function. Each can be paired with onl one In #18 and 19, find the value of each function. 18. For f() = 3 + 2, find f(4). 19. For g() = 4, find the value of g() when = 5. Use the graph of function h for # Find h( 1). 21. Find h(3). 22. Find h(0). 23. What is the domain? 24. What is the range? A { 8, 6.5, 2, 3} F { 7 3} B { 8 3} G { 8 3} C { 5 3} H { 7, 5, 4, 5} D ( 7 5) J ( 7 5) 25. What is the range of the function f() = when the domain is { 8, 0, 2}? 2 A {10, 6, 5.5} C {2, 6, 7} B {10, 6, 5} D {4, 0, 1}

4 Use the following scenario for # Sketch a picture!!! A swimming pool has a volume of 8,500 gallons. It is being drained at a rate of 500 gallons per hour. 26. Which function represents the situation? F f() = 8, H f() = 8, G 8,500 = 500 J f() = 8, What is the greatest value in the range for this situation? A 8,500 C 500 B 17 D cannot be determined 28. What is the greatest value in the domain for this situation? F 8,500 H 500 G 17 J cannot be determined 29. The total cost of renting a pontoon boat is a function of the number of hours the boat is rented. A boat rental store charges a $125 cleaning/restock fee plus $65 per half hour up to a maimum of 6 hours. Which of the following statements is not correct? A There are a maimum of 12-half-hour intervals within the 6-hour time period. B The maimum value in the range is 905. C The total cost for renting the boat for 5 hours is $650. D The total cost for renting the boat for 4 hours is $645. Topic 3: Linear Functions m = In #30 and 31, use the slope formula to find the slope of the line that passes through the given points. 30. (-2,9) and (10,1) 31. (1,5) and (1,-3)

5 32. Which table shows the same rate of change of with respect to as = ? In #33 35, identif the slope, and write the equation of the graphed line in slopeintercept form slope: slope: slope: equation: equation: equation: 36. Which of the following is a correct description of the graphed line? I The line has a positive slope. II The line represents the linear parent function. III The line represents a direct variation. IV The equation of the line is = + 1. Answer Choices A I onl B I and II C III and IV D I, II, and III

37. Use the graph to identif each. 38. Find the - and -intercepts of the line 6 + 4 = 12. Then graph using onl the intercepts.

6 37. Use the graph to identif each. 38. Find the - and -intercepts of the line = 12. Then graph using onl the intercepts. a) -intercept: b) -intercept: a) slope: b) -intercept: c) -intercept: d) equation: 39. Find the -intercept of the line 40. Find the -intercept of the line whose equation is 3 5 = 15. whose equation is 4 + = 4. Write the answer as an ordered pair. Write the answer as an ordered pair. 41. Suppose is directl proportional to, and = 8 when = 20. What is the direct variation equation that relates and? F = 20 H 8 = 20 G = 2 5 J = The number of miles driven m varies directl with the number of gallons of gas used g. If Eric drove 297 miles on 9 gallons of gas, how far will he be able to drive on 14 gallons of gas? 43. Which statement is not correct? T-Shirt Shipment

7 44. Which statement correctl describes the rate of change of the following graph? F G H J The distance traveled is increasing at a constant rate of 50 miles per hour. The distance traveled is not a constant rate of change. The distance traveled is decreasing at a constant rate of 40 miles per hour. The distance traveled is increasing at a constant rate of 40 miles per hour. 45. The table represents some points on the graph of linear function g. Which situation can be modeled b this function? A B C D The cost in dollars of buing used cars for $11,950 each. The total cost of paing $325 in rent each month. The amount owed on a $24,550 loan after paing $325 per month for months. The distance traveled each da on a 24,550-mile trip. 46. Your on-campus apartment costs $750 per month after ou pa the earl deposit of $1500. The total amount spent on rent for the school ear can be found b using the function = Based on this information, which statement about the graph of this situation is true? F G H J The -intercept of the graph represents the cost per month The -intercept represents the amount of the deposit The variable represents the total amount spent on rent for the school ear The slope of the graph represents the number of months the apartment was rented

8 47. A bab pool that held 120 gallons of water is draining at a rate of 6 gal/min. The function f() = gives the amount of water in the pool after minutes. What does the -intercept represent? A The pool is draining at a rate of 6 gallons per hour. B C D The number of minutes required to drain one gallon of water The number of minutes required to drain the entire pool The maimum number of gallons the pool can hold In #48 53, use the following progression to help ou write equations. You must write the equation in the form that is specificall stated! Point-Slope Form Slope-Intercept Form Standard Form 1 = m( 1 ) = m + b A + B = C 48. Write the equation of the line that 49. Write the equation of the line that passes through (3, -4) with a slope contains the point (-6, 2) and has a of 2 in point-slope form. slope of 5 in slope-intercept form Write the equation of the line that 51. Convert = 18 to passes through (-6, -1) with a slope slope-intercept form. of -4 in standard form.

9 52. Write the slope-intercept form 53. Write the slope-intercept form equation of the line that is parallel equation of the line that is to = 2 4 and passes through 3 perpendicular to = 2 4 and the point (-3, 0). passes through the point (-2, 6). Use the graph to answer #54 and What would be the slope of a line that is parallel to the graphed line? 55. What would be the slope of a line that is perpendicular to the graphed line? 56. What is the equation of a line 57. What is the slope of a line parallel to the -ais that passes perpendicular to the -ais? through (-4, 5)? 58. Which of the following statements about + 2 = 3( 1) is not true? F The slope of the line is -3. G The line represented b the equation passes through point (1, -2). H When converted to slope-intercept form, the equation is = J The graph of the equation is as follows.

10 59. Some ice cream sales and the number of lifeguard rescues at a beach for various das are shown in the table. Determine which statement is not true. A The data has a strong positive correlation. B The correlation coefficient is approimatel C The graph of the data would trend upward. D This relationship represents a causation. 60. Look at the graphed line. What would be its new equation if the slope is multiplied b -1, and the -intercept decreases b 4. F = G = H = 4 J = A caterer charges an initial fee of $250 in addition to $12 per plate. If he decides to increase the cost per plate b $3 but keep the initial fee the same, what would he charge to cater an event for 500 people? Topic 4: Sstems 62. You have 27 coins that are all dimes and quarters. The value of the coins is $4.35. Write and solve a sstem of equations to find the number of quarters ou have. 63. Solve the following sstem b graphing. { = = 0

Math 154A Elementary Algebra Fall 2014 Final Exam Study Guide

Math 154A Elementary Algebra Fall 2014 Final Exam Study Guide Math A Elementar Algebra Fall 0 Final Eam Stud Guide The eam is on Tuesda, December 6 th from 6:00pm 8:0pm. You are allowed a scientific calculator and a " b 6" inde card for notes. On our inde card be