IM1 Summative Practice #1 Name: Show all your Work Period: Simplify each expression below. 1. 5x (7 3x) 2. 5(x 12) + 15(x + y) 3. 8 2(x 2 3x) (9 3x 2 ) Solve each equation. Justify each step with a property of equality. 4. 12x + 6(8 3x) = 18) 5. 4x + 10 6x = 2x (8x 2) 8 6. Circle each equation with 1 solution, box each equation with no solution, and underline each equation with infinite solutions. A. 7x 2 = 7x + 2 B. 3x 8 = -8 + 3x C. 2x 5 = 4 2x 9 D. 2(x 6) = 2x 12 E. 2(5x 8 + x) = 4(3x 4) F. 3x + 22 = -2x 8 + 5x 7. The height of a scale model building is 18 inches. The scale is 3 inches to 5 yards. Find the height of the building in yards and in feet. 8. The sum of Phil and John s ages is 51 years. If Phil is three years less than twice John s age, then how old is Phil? 9. Keith is going to join a local fitness center. One fitness center charges a $75 membership fee and $12 per month. The other fitness center charges $15 per month and a $60 membership fee. How many months will pass before the total cost of the fitness centers will be the same and what is the total cost at that time? 10. What is the largest of three consecutive odd numbers whose sum in 417?
11. The perimeter of a rectangle is 300 meters. If the length is 10 meters less than 3 times the width, what is the measurement of the length and width of the rectangle? 12. The perimeter of a triangle is 81 feet. The longest side is three times the shortest side. The middle side is 3 feet more than twice the shortest side. What is the length of the middle side? Solve each equation/formula for the identified variable. m 13. I = prt for p 14. D for V. V 15. F = 9 C + 35 for C 16. P = 2L + 2W for W 5 Solve and graph each inequality. 17. -3(2x + 4) -24 18. -5(k + 5) < k 16 3k 0 0 19. A rope that is at least 76 inches long is cut into three pieces. The 1 st piece of rope is three times the length of the 3 rd piece of rope. The 3 rd piece of rope is 6 inches more than the 2 nd piece of rope. What is the minimum length of the 1 st piece of rope that is a whole number? 20. The Arden Leadership class wants to sell ice-cream to raise money for a spirit rally. They buy from an ice-cream factory that charges $200 plus $8 per quart. The leadership team wants to sell the ice-cream for $12 per quart. How many quarts of ice-cream will they have to sell to make a profit?
Total Cost Solve and graph each compound inequality below. 1 3x 1 21. 5 22. 3 2x > 7 or 5x 3 12 2 4 0 0 23. A bottle can hold 2.75 liters of water. About how many ounces of water can the bottle hold? 24. The average teenager spends $1742 per year on fashion related items. How much is this per week? 25. A train travels 125.5 miles in 150 minutes. What is the train s rate in kilometer per hour? 26. The cost to rent a canoe is $15 per hour plus a $20 nonrefundable deposit. Represent this relation as a table, graph, and a mapping diagram given a domain of {1, 2, 3, 4, 5}. x y 50 40 30 20 10 27. Given the function y = -2x 2 + 6x Part A: Write the function using function notation. 0 1 2 3 4 5 Hours Part B: Find f(-8), f(12) and f(40) 28. Is each of the functions a linear function? A. y = 4x 7 Yes No B. y = 6x 2 1 Yes No C. y = 1 + 10 Yes No D. y = 7 Yes No 2x
29. Identify the domain and range of each relation below, then tell whether the relation is a function. If the relation is not a function, explain why. A. {(2,5),(3,-5),(4,5),(5,-5)} B. {(-3,8),(-1,1),(0,0),(-1,-1),(-3,-8)} D: D: R: R: C. D. D: D: R: R: 30. Identify a value for x that will make the relation {(-5,3),(-3,2),(x,2),(5,3)} not a function. 31. Find the x- and y-intercepts for each function below. A. 3x + 4y = -24 B. 5x 6y = -10 C. 12y = 60 15x 32. Find the slope of each function below A. x y B. C. (-5,4) and (3,-8) -4 8-2 7 0 6 3 4.5 33. A line has an x-intercept of 2 and a y-intercept of 6. Find the slope of the line.
Graph each function below. 34. y = -3x + 2 35. y = -x 2 2 36. f(x) = 1 x 4 37. -4y = 8 6x 2 38. f(x) = 2x 2 5 39. 2x y = 3x + 6 40. 3x 4y = 12 41. 4x + 6y = -18
Total Calories Write the first 4 terms of each sequence defined by the given rule. 42. f(n) = 42 6(n 1) 43. f(n) = -4n + 14 44. f(1) = 24, f(n) = f(n 1) + 12 45. f(1) = 10, f(n) = -3 f(n 1) + 5 46. Given the explicit rule f(n) = 85 + 15(n 1) Part A: Find the 43 rd term in the sequence. Part B: Which term in the sequence is 970? Write a recursive rule and an explicit rule for each arithmetic sequence below. 47. 75, 125, 175, 225 48. 36, 22, 8, -6 49. -22, -25, -28, -31 50. -12, -4, 4, 12 51. The table below shows the relationship between the number of hours Tiana works and the amount she is paid in dollars. This relationship can be represented by an arithmetic sequence. Part A: Write an explicit rule for the sequence. Hours 1 2 3 4 Pay ($) 35 45 55 65 Part B: Find f(8) and interpret its meaning. 52. Given: f(5) = 48 and f(9) = 64. Write an explicit and recursive rule for the sequence. 100 80 53. The graph to the right shows the relationship between ounces of tortilla chips and total number of calories of the chips. Find and interpret the slope. 60 40 20 0 2 4 6 8 10 Pounds of Chips