Algebra 1 Third Quarter Study Guide 1. Evaluate:. 2. Evaluate: 8 5 5 t. 2 s t when s = 5 and 7 Simplify. 3. 2 0 5 3 2x y x y 4. 4 3 54xy 5. 4 24 6. 3x 2 y 3 7. Is 3 a solution of? 8. A store that sells gift baskets is having a promotional sale. Customers can make their own fruit baskets to use as gifts. Customers pay $1.50 for a basket and add $0.90 per pound for all types of fruit. The cost for a basket containing p pounds of fruit is $7.90. Write and solve an equation to solve for p. 9. Make an input-output table to represent the function. 10. Write a function rule for the input-output table. Use 0, 1, 2, and 3 as the domain. Input x 2 3 4 5 Output y 10 15 20 25 State the domain and range. Then identify if each relation is a function. 11. 12. 13. 14. 15. Distribute: 4(x 4) 16. Simplify the expression. 17. Dividing by 7 is the same as multiplying by what fraction? 18. Solve: 19. Solve:
20. Tommy has 600 pennies in his collection. He plans to give 120 to his little brother and split the rest between himself and his two sisters. He wants to know how many pennies to keep for himself. Write an equation to model this situation and then solve. Solve the equation: 21. 22. 23. 24. 26. Solve for. 26. Graph the line of 27. Sketch the line given by 2y 4x 8. Identify the x and y-intercepts Identify the slope and y-intercept. 28. Find the slope of the line through the points 29. Explain the difference between a horizontal line (4, 7) and ( 6, 2). and a vertical line in terms of slope. 30. Find the slope and y-intercept of the line 31. In the equation y =, does y vary directly with the equation. with x? 32. The weight, W, of a beam varies directly with 33. Graph the function. its length, l. A 10 foot beam weighs 530 pounds. Compare the graph with the graph of. Write an equation relating W to l.
34. Find the value of x so that 35. Write an equation of the line with 36. Write an equation of the line 1 f( x ) 13 when f ( x) x slope and y-intercept 4. shown. 4 37. An amusement park charges $10.00 for admission and $4.00 per ride. Write an equation that gives the cost (in dollars) as a function of number of rides. 38. Write an equation of a line with slope 2 passing through the point (3, 2). 39. Write the equation in slope-intercept form of the line that passes through the points ( 3, 5) and (2, 5). 40. Write an equation for the linear function in the form that has the given values., 41. A grocer knows that if he sells his canned hams for $6 each, he can sell 550 per month, and if he sells the same hams for $9, he will sell 400 per month. Assuming the relationship between price and sales is linear; write an equation you could use to predict sales for other prices. 42. Write an equation in point-slope form of the line that passes through the point ( 7,1) and has a slope m = 43. Write an equation in point-slope form of the line that passes through the given points. (4, 4), (7, 6) 44. Write an equation of the line that passes through (2, 1) and is parallel to the line. 45. Write an equation of the line that passes through (5, 7) and is perpendicular to the line.
46. This year the Wolverine basketball team scored the following number of points in its 10 games. Game 1 2 3 4 5 6 7 8 9 10 Points 72 73 83 84 78 85 84 93 85 93 a. Find a line of fit. b. Predict the score for game 12. 47. Solve Graph your solution. 48. Solve and graph the solution. 3x 12 48. Solve. 49. Solve the inequality Graph your solution 50. The grade you earn in math varies inversely with the number of minutes per night you watch television. If you watch 90 minutes per night, you get a 60 in math. How much tv can you watch if you want to make an 80 in math class. 51. Joel sells ice cream cones at the county fair. He has to rent the equipment for $36 and spend $0.52 on ingredients for each cone. What is the minimum number of ice cream cones Joel must sell at $1.40 each in order to make a profit? 52. Graph. 53. Graph: 54. Solve the system by graphing:
Solve the system. 55. x 4y 1 2x y 7 56. 57. 58. Does the system of equations have 59. Solve the system of inequalities graphically: no solution, one solution, or many solutions? Explain how you can tell without graphing the system. Simplify. 60. (3c 2 )(-3c -3 d 2 ) 61. 62. (8x 3 ) -2 (2x 2 ) 4 63. 64. 65. 3xy 0 (- 2x 6 ) 66. 3 2 2 6 12 67. 3 5 10 125c d 68. The mean amount of time that a manager spends in annual performance review with an employee is 27.2 minutes, with a standard deviation of 4.9 minutes. What percentage of the annual performance reviews in the department take between 22.3 and 32.1 minutes? Between 17.4 and 37 minutes? Between 12.5 and 41.9 minutes? 69. Heights of adult males have a mean of 69 and a standard deviation of 2.8 inches. Basketball player Michael Jordan has a height of 78 inches. Is he exceptionally tall when compared to the general population of adult males? Find the z-score for his height and place it on the bell curve.
70. The junior high basketball team played ten games. Find the standard deviation and the mean for the number of baskets scored by the team for the ten games: 8, 4, 6, 6, 7, 7, 9, 4, 8, 5. 69. The scores on a math test are normally distributed. The mean score is 84 with a standard deviation of 3.5. If a student got a 92 on the test, within how many standard deviations from the mean is his score? 70. A z-score of 1.3 was found from an observation coming from a normal distribution with mean 15 and standard deviation 5. Find the raw score. 71. Evaluate f ( x) x 7 for x = 4. 72. Given g( x) 2x for what value of x does gx ( ) 98 73. Use the graph at the right to answer the following: a. State the slope of the line. b. State the y-intercept of the line. c. What is f (7)? d. What is x when f( x ) 2? e. State the domain and range in interval notation.