Algebra 1 End of Course Select the best answer to the Multiple Choice questions. Write one character per box for the Fill in Response questions. 1. Fill in Response What is the solution of the equation below? 3(x + 2) = 4 + 2(x 3) 2. Fill in Response The set W equals {1, 3, 5, 7, 9}. The set X equals {2, 4, 6, 8}. The set Y equals {4, 5, 6, 7}. How many distinct elements are in the set (X! Y)! W? 4. Javier earns a salary of $64,000 per year plus an 8% commission on all his sales. If his annual income is to be no less than $85,600, which inequality shows the minimum amount his sales, s, can be? F. s $270 G. s $2700 H. s $27,000 I. s $270,000 5. Fill in Response A function rule is given below. What is f( 2)? f(x) = 3 4x 3. What is an equation of a line in slope intercept form that contains points (0, 7) and ( 1, 0)? A. y = 7x 7 B. y = 7x 7 C. y = 7x + 1 D. y = 7x 1 6. Fill in Response A round trip in a helicopter lasted 4.5 hours. The helicopter flew away from the airport at 100 miles per hour and returned at 50 miles per hour. In miles, what was the helicopter s greatest distance from the airport? page 1
7. What is the x coordinate of the ordered pair solution of the system below? A. 3 B. 2 C. 2 D. 3 x 3y = 9 5x + 2y = 11 8. Fill in Response What is the solution of the equation below? "!! " = "! # $ 10. Fill in Response At the Lake Okeechobee Convention Center, meeting rooms are available in 3 sizes. The largest room seats 50 more than the smallest room and the mid sized room seats 32 more than the smallest room. The Women s Club has reserved 1 large room, 1 mid sized room, and 2 small meeting rooms to accommodate their 222 members. The equation below represents the situation, where x is the number seated in a small room. 2x + (x + 50) + (x + 32) = 222 How many people will the smaller room accommodate? 11. Solve the equation below for y. 3x + 5 = 5y 9. If t 10, which of the following shows the expression below in simplest form? F. 40 t G. 40 3t "##! "" $!! %#!" A. y = 3x + 1 B. y = 3 5 x + 5 C. y = 3 5 x + 1 D. y = 3 5 x + 1 H. 4(10 + t) I. 4(10 t) page 2
12. Fill in Response When the expression (xy) 3 (x 2 y 3 ) 2 (x 3 y 2 ) 0 is simplified, it is of the form x a y b. What is the value of (a + b), the sum of the exponents? 14. Which of the following shows the graph of 4x y = 2? A. 13. The graph shows the 4 month growth to maturity of an experimental corn plant fed by a special fertilizer. 1$"234&56&758'&9:;'4 B.. -, C. + 0 +, -. /0 /+ /,/-!"#$%&"'&($$)* Which of the following best describes the range of the function? F. 0 x 16 D. G. 8 x 16 H. 0 y 16 I. 0 y 8 page 3
15. Fill in Response Sonya inherited $35,000. She invested some of the money at 2.5% simple interest and the rest at 3.5% simple interest. In the first year, she earned $1,075 interest. How many dollars did she earn from her investment at 3.5% interest? 18. Which of the following functions is shown in the graph below? 16. A line has intercepts (0, 4) and (6, 0). Which of the following is the slope of the line? F. 6 G. 4 H. 3 2 I. 2 3 F. f(x) = x 2 2x 3 G. f(x) = x 2 + 2x + 3 H. f(x) = x 2 2x + 3 I. f(x) = x 2 + 2x 3 19. Fill in Response Tom worked 16 hours last week. He earned $8 per hour at a restaurant and $8.50 per hour at a grocery store. If he earned $132.50 last week, how many hours did he work at the grocery store? 17. Factor 10x 2 + 11x 6 completely. A. (5x 2)(2x 3) B. (5x + 2)(2x + 3) C. (5x 2)(2x + 3) D. (5x + 2)(2x 3) page 4
20. Simplify the expression below. (Assume all variables are positive Real numbers.) A. 40 3y B. 16 3y C. 14 3y D. 6 3y 4 27 y + 2 12y 22. Leah used the Quadratic Formula to solve the equation below. 2x 2 = 3x + 2 Which of the following shows a step in solving the equation? A. x = 3 ±5 2 B. x = 3 ±5 4 C. x = 1 ±5 2 D. x = 3 ±2 6 21. If x 0, y 0, z 0, which of the following is a simplified form of the expression below? x 3 y 2 z + x 2 yz 2 xyz xyz F. x 2 y + xz 1 23. Fill in Response The two rectangles below are similar. '(")"%*"#$ '(*"#$ G. x 4 y 3 + x 3 z 3 1 H. x 7 y 3 z 3 1 I. x 3 yz 1 %&"#$!"#$ In centimeters, what is the length of the shorter side of the unknown rectangle? page 5
24. The expression (3ab 2 ) 2 (2a 3 b) 0 (3a) 2 is equivalent to which of the following? F. 2a 3 b 5 G. b 4 H. 3b 4 I. 2b 2 3a 25. Fill in Response Multiply and simplify the expression below. 4(x 1)(x 2) 3x(5x 1) What is the coefficient of the x term? 27. Fill in Response The school band is selling sweatshirts and tee shirts as a fundraiser. Sweatshirts sell for a profit of $3 and tee shirts for $2 each. The goal is to raise $900. The profit function graphs as shown below. %"" &"" $"" #""!"" " 7.328-9,./63 :!"";-$""< :#"";-!%"<!"" #"" $"" &"" %"" '()*+,-./-01+23456,34 What is the slope of the segment? 28. The universal set U is represented below. 26. To earn a B in his Geometry class, Kevin must have an average of 80% or better. His test scores are 76%, 81%, and 79%. What minimum score on his fourth test would guarantee a B? A. 79% B. 80% C. 83% D. 84% U = {a, b, c, d, e, f, g, h} Subsets A, B, and C are defined below. A = {a, c, e, g} B = {a, d, g, h} C = {b, d, f, h} Which set is described by (A B ) C? F. {h} G. (a} H. I. {c, e} page 6
29. Which of the following best represents an equation of the line graphed below? 32. Which of the relations graphed below is NOT a function? A. A. 3x + 2y = 4 B. 2x + 3y = 4 C. 2x 3y = 12 D. 3x 2y = 4 B. 30. Simplify the expression (4 2) 2. F. 18 C. G. 18 8 2 H. 14 I. 14 2 2 31. Fill in Response The volume of a cube with side length s is given by the function V(s) = s 3. Find V(6). D. page 7
33. Julian has $5.50 in dimes and quarters. He has 8 more quarters than dimes. How many quarters does he have? F. 9 G. 10 H. 18 I. 20 35. There are a total of 30 students in a math class. The number of boys is 2 more than three times the number of girls. The equation below represents the situation, where x represents the number of girls. x + (3x + 2) = 30 How many boys are in this math class? F. 23 G. 21 H. 14 I. 7 34. Which expression represents the area of the shaded region of the rectangle below? A. 12x 2 14x + 4 B. 12x 2 4x + 16 C. 12x 2 28x + 16 D. 14x 8 36. Ella solved the quadratic equation below by factoring. 10x 2 = 13x + 3 Which of the following shows a step in solving the equation? A. (5x + 1)(2x 3) = 0 B. (5x + 1)(2x + 3) = 0 C. (5x 1)(2x 3) = 0 D. (5x 1)(2x + 3) = 0 page 8
37. Which function rule describes the function in the table below? x 0 1 2 3 y 1 1 7 17 F. f(x) = 2x 1 G. f(x) = 1 2x H. f(x) = 2x 2 1 I. f(x) = 2 x 2 38. Fill in Response Line m and point P are given as graphed. 39. Fill in Response At Band Camp, students can participate in outdoor activities. The Venn diagram below shows the number of students who chose to participate in each outdoor activity.!"#$$#%& Activities at Band Camp!" #$ #% ' % ( Based on the diagram, what is the total number of students who did NOT participate in sailing? & '()(*#%&!(#+#%& What is the slope of a line through point P and parallel to line m? 40. Solve the equation below for h. SA = 2πrh +2B A. h = SA 2B 2πr B. h = SA 2πr 2B C. h = SA 2B 2πr D. h = SA 2B 2πr page 9
For 41 43: In 2005, a company bought 3 pick up trucks for $19,000 each. In each of the next 5 years the company president had the trucks appraised. The president recorded the value of each truck each year on the scatter plot below. He drew a line of best fit for the scatter plot. 20345+>)?0)4,/@,A-. 8#!*!!! :!*+";!!!< 20345+6/73) 8"&*!!! 8"!*!!! 8&*!!! :%*+="!!<! " # $ % & = 9 '()*+,-+.)/01 41. Fill in Response What is the slope of the line of best fit, using the identified points in the scatter plot? 42. Which statement best expresses the meaning of the slope as a rate of change for this line of best fit? F. It represents the value of a truck after 1 year. G. It represents the cost to run a truck for 1 year. H. It represents how much the value of a truck goes up in 1 year. I. It represents how much the value of a truck depreciates in 1 year. 43. Fill in Response The company president found the equation of the line of best fit. Based on this data, in dollars, what will be the value of a truck when it is 5 years old? page 10
44. Fill in Response The standard form of a linear equation is 2x 5y = 10. What is the slope of the line? 47. Fill in Response What is the solution of the equation shown below? 0.25 0.5(x 3) = 0.25(5 x) 45. Simplify the expression below. 3(4 6 3) A. 12 2 3 B. 9 2 C. 12 2 9 D. 36 2 3 46. If m 0, n 0, which of the following is a simplified form of the expression below? 48. Fill in Response A deliveryman earns $350 per week. He also earns 15% commission on any sales he makes. The function E(s) = 350 + 0.15s relates his sales, s, to his total weekly earnings, E(s). What were his sales, in dollars, the week he earned $432.50? 18m 3 n 7 + 9m 5 n 6 3m 3 n 6 F. 6n +3m 2 G. 6m 6 n 13 +3m 8 n 12 H. 15n +6m 2 I. 6n 13 +6m 2 n 12 page 11
49. Fill in Response A chemist must mix 6 liters of a 30% acid solution with some of an 80% acid solution to get a 50% acid solution. How many liters of the 80% solution should be used? 50. Which graph shows the solution to the inequality below? 5 2(4x + 7) 15 51. Fill in Response A boat can travel 18 miles downstream in the Kissimmee River in 2 hours. It requires 6 hours to travel back to its starting point upstream. The set of equations below represents the situation, where r is the speed of the boat in still water and c is the speed of the current. 2(r + c) = 18 6(r c) = 18 What is the speed of the current in miles per hour? A. B. C.!!" 52. Fill in Response Evaluate 2 1 + 2 0 + 2 1. D.!!" 53. Fill in Response In feet, what is the length of the shorter side of a rectangle whose perimeter is 42 feet and whose area is 104 square feet? page 12
54. Fill in Response Solve the equation below for x. 1 3 (x 10) + 2 3 = x 5 57. George positioned the ramp he is constructing on a coordinate grid, as shown. )*+,$-.*/01.+.23/#$42$5..3 7!"#$%&!'(#$"& 6 55. Which expression is equivalent to the perimeter of the shaded portion of the rectangle below? Which of the following best represents the line that contains the slant face of the ramp? F. y = 2 5 x + 6 G. y = 2 5 x + 6 F. 16x 6 G. 16x + 2 H. 8x 3 I. 8x + 1 56. Factor 9x 2 3x 6 completely. A. (9x 6)(x + 1) B. (3x + 3)(3x 2) C. 3(3x + 2)(x 1) D. 3(3x 2)(x + 1) H. y = 6x + 15 I. y = 6x 15 58. Betty earns 55 travel credits for every 250 miles she flies on Jet Red Airline. To the nearest whole number of credits, how many travel credits will she earn on her next trip flying 1305 miles on Jet Red Airline? A. 5932 travel credits B. 2966 travel credits C. 669 travel credits D. 287 travel credits page 13
59. Dawn has $20 to spend on scrapbooking supplies. Stickers cost $1.50 per package and fringe edging costs $2.50 per strip. The equation below can be used to find how many packages of stickers and strips of fringe she can buy, where x is the number of packages of stickers and y is the number of strips of fringe. 1.5x + 2.5y = 20 Which of the following is the graph of this equation? F. H. G. I. page 14
60. The universal set only contains sets R, S, and T. These sets are related as shown in the Venn diagram below.! " #! & $ % ' * + # ( ) " Which set represents (R T ) S? A. B. {e, f} C. {c, g, h, i, j, k} D. {c, e, f, g, h, i, j, k} page 15