2011-2012 Algebra I Final Study Guide Short Answer Source: www.cityoforlando.net/public_works/stormwater/rain/rainfall.htm 1. For which one month period was the rate of change in rainfall amounts in Orlando the greatest? 2. What was the rate of change in rainfall amounts in Orlando from August to September in 2003?
Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation. 3. 100 90 80 Strawberries Picked Quarts Picked 70 60 50 40 30 20 10 1 2 3 4 5 6 7 8 9 10 Time (hours) Domestic Traveler Spending in the U.S., 1987-1999 450 425 400 375 350 325 300 275 250 225 1986 1988 1990 1992 1994 1996 1998 2000 Source: The World Almanac, 2003 Year 4. Use the scatter plot that shows the domestic traveler spending. Use the points (1987, 235) and (1999, 446) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.
Write a linear equation in slope-intercept form to model the situation. 5. A television repair shop charges $35 plus $20 per hour. Find the slope of the line that passes through the pair of points. 6. ( 1, 4), ( 5, 5) Write a direct variation equation that relates x and y. Assume that y varies directly as x. Then solve. 7. If y = 49 when x = 7, find x when y = 140. Write an equation of the line with the given slope and y-intercept 8. slope: 1, y-intercept: 8 9. Write an equation of the line that passes through each point with the given slope. 10. Write an equation of the line that passes through the pair of points. Write the point-slope form of an equation for a line that passes through the point with the given slope. 11. (4, 2), m = 1 2
Write each equation in standard form. 12. y + 3 = (x + 2) 13. Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. 14. Use substitution to solve the system of equations. 15. 16. Use elimination to solve the system of equations. 17.
Use the graph below to determine the number of solutions the system has. 8 y 7 y = 2x 6 5 4 3 12x 3y = 3 x = 4 2 1 7 6 5 4 3 2 1 1 2 3 4 5 6 7 x 1 y = 3 2 3 4 y = 4x 1 5 6 7 y = 2x + 5 8 18. 19. At a local electronics store, CDs were on sale. Some were priced at $14.00 and some at $12.00. Sabrina bought 9 CDs and spent a total of $114.00. How many $12.00 CDs did she purchase? 20. Dakota s math test grade was 7 points less than his science test grade. The sum of the grades was 183%. What did Dakota get on his math test? 21. Reid and Maria both play soccer. This season, Reid scored 4 less than twice the number of goals that Maria scored. The difference in the number of goals they scored was 6. How many goals did each of them score?
22. Dylan has 15 marbles. Some are red and some are white. The number of red marbles is three more than six times the number of the white marbles. Write a system of equations that can be used to find the number of white marbles, x, and the number of red marbles, y. 23. Solve the system of inequalities by graphing. 7 y 6 5 4 3 2 1 7 6 5 4 3 2 1 1 1 2 3 4 5 6 7 x 2 3 4 5 6 7 Suppose a car dealer receives a profit of $500 for each mid-sized car m sold and $750 for each sport-utility vehicle s sold. The dealer must sell at least two mid-sized cars for each sport-utility vehicle and must earn at least $3500 per week. 24. Write a system of inequalities for the situation. 25. Simplify. Assume that no denominator is equal to zero.
26. 27. 28. 29. Find the degree of the polynomial. 30. Find the sum or difference. 31. 32.
Find the product. 33. Find the product. 34. 35. 36. 37. 38. Find the product of each sum and difference. 39. Solve the equation. 40.
41. 42. 43. Factor the polynomial. 44. 45. Factor the trinomial. 46. Solve the trinomial equation. 47. Factor the trinomial, if possible. If the trinomial cannot be factored using integers, write prime. 48.
Factor the polynomial, if possible. If the polynomial cannot be factored, write prime. 49. Solve the equation by factoring. 50. Solve the equation. 51. 52. State the excluded values for each rational expression. 53. Simplify the expression. Find the quotient. 54. Simplify the expression. 55. 3 2 17
56. 57. 58. 59. 60.
Svetlana is planning to plant a garden in her backyard. Surrounding the garden will be a walkway represented by the shaded area. 61. a. Find the algebraic expression that represents the area of the whole backyard. b. Find the algebraic expression that represents the area of the garden (white region). c. Use your expressions from (a) and (b) to find the algebraic expression that represents the walkway (shaded region). d. If Svetlana s backyard is 81 ft., find the area of the garden. e. If she needs to put soil into the garden and one bag of soil covers 6 square feet, how many bags of soil will she need to buy?
Essay Megan wants to change her Internet Service Provider. She is considering three different plans. 62. Plan 1 charges a $12 monthly fee plus $0.11 per minute of use. Plan 2 charges a $14 monthly fee plus $0.09 per minute of use. Plan 3 charges a flat monthly fee of $51.95. a. For each plan, write an equation that represents the monthly cost C for m minutes per month. Plan 1 Plan 2 Plan 3 b. Graph each of the three equations on the same coordinate axes. Label each line. y 60 55 50 45 40 35 30 25 20 15 10 5 50 100 150 200 250 300 350 400 450 500 x c. Megan expects to use 400 minutes per month. Which plan is best for Megan? Explain.