Coordinate Algebra A Final Exam Review

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1 Class: Date: Coordinate Algebra A Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. Do NOT write on the test. You may use your calculator. 1. Salvador s class has collected 88 cans in a food drive. They plan to sort the cans into x bags, with an equal number of cans in each bag. Write an expression to show how many cans there will be in each bag. a. 88 x c x b. 88x d. 88 x 2. Isabel reads 15 books from the library each month for y months in a row. Write an expression to show how many books Isabel read in all. Then, find the number of books Isabel read if she read for 12 months. a y; 27 books c. 15y; 180 books 15 b. 15 y; 27 books d. ; 180 books y 3. Evaluate the expression 2m + n for m = 7 and n = 9. a. 25 c. 23 b. 18 d Solve 2 10 b = 99. a. b = 20 c. b = 10 b. b = 495 d. b = If 4x = 32, find the value of 35 5x. a. 5 c. 3 b. 3 d Solve the proportion 5 6 = x 30. a. x = 0.03 c. x = 26 b. x = 36 d. x = Solve 44 = 14 2a. a. a = 15 c. a = 29 b. a = 29 d. a = Solve 43a a = 27. a. a = 1 c. a = 17 b. a = 17 d. a = 1 9. Solve 50q 43 = 52q 81. a. q = 38 c. q = 38 b. q = 19 d. q = 19 1

2 10. Solve n 8 + n = 1 4n. a. n = c. n = b. n = d. n = Describe the solutions of 6 + y < 10 in words. a. The value of y is a number less than or equal to 3. b. The value of y is a number less than 4. c. The value of y is a number equal to 3. d. The value of y is a number greater than To join the school swim team, swimmers must be able to swim at least 500 yards without stopping. Let n represent the number of yards a swimmer can swim without stopping. Write an inequality describing which values of n will result in a swimmer making the team. Graph the solution. a. n 500 b. n 500 c. n > 500 d. n < Solve the inequality n + 6 < 1.5 and graph the solutions. a. n < 4.5 b. n < 7.5 c. n < 7.5 d. n < 4.5 2

3 14. Solve the inequality x 8 > 3 and graph the solutions. a. x > 3 8 b. x > 24 c. x > 24 d. x > Solve the inequality z z 4 and graph the solutions. a. z 1 b. z 1 c. z 3 d. z 3 3

4 16. Solve the inequality and graph the solution. 3x + 2.5x 1.5(x + 4) a. x 3 b. x 3 c. x 3 d. x Which of the following is a solution of x 6 < 6 AND x + 4 1? a. 2 c. 14 b. 6 d Find the x- and y-intercepts. a. x-intercept: 10, y-intercept: 5 c. x-intercept: 10, y-intercept: 5 b. x-intercept: 5, y-intercept: 10 d. x-intercept: 10, y-intercept: Find the x- and y-intercepts of x + 2y = 8. a. x-intercept: 8, y-intercept: 4 c. x-intercept: 11, y-intercept: 4 b. x-intercept: 8, y-intercept: 3 d. x-intercept: 11, y-intercept: 3 4

5 20. Find the slope of the line. a. 2 3 c. 3 5 b. 2 3 d. 21. Find the slope of the line. 3 2 a. 0 c. undefined b. 10 d

6 22. Tell whether the slope of the line is positive, negative, zero, or undefined. a. negative c. positive b. zero d. undefined 6

7 23. Graph the line with the slope 1 and y-intercept 2. 3 a. c. b. d. 24. Write the equation that describes the line in slope-intercept form. slope = 4, point (3, 2) is on the line a. y = 4x + 14 c. y = 4x + 10 b. y = 4x 14 d. y = 4x 2 7

8 25. Write the equation 4x + 8y = 24 in slope-intercept form. Then graph the line described by the equation. a. y = 1 2 x 3 c. y = 1 2 x 3 b. y = 1 2 x 3 d. y = 1 2 x 3 8

9 26. Graph the line described by the equation y 2 = 5 (x 3). 3 a. c. b. d. 27. Which expression represents the perimeter of the triangle below? a m c m b m d m 28. If x = 1, in which quadrant does the point (2x, x) lie? a. Quadrant I c. Quadrant III b. Quadrant II d. Quadrant IV 9

10 29. The scoring for a football game by quarters was recorded as the ordered pairs {(1, 7), (2, 10), (3, 21), (4, 21}. Which of the following statements is true? a. The relation is a function with domain c. The relation is not a function. {1, 2, 3, 4}. b. The relation is a function with domain {7, 10, 21}. d. The relation is a function with domain { 1 x 4} 30. A local video store has two new renting plans. Plan A charges a $10 monthly fee and $2 for every movie rented. Plan B charges $40 per month but then each movie rented is only 25. How many movies must be rented in a month to make plan B the cheaper option? a. 17 c. 28 b. 18 d. 29 Ï 3x + 4y = Solve the system Ô Ì by graphing. ÓÔ 2x + 4y = 16 a. (4, 6) c. (4, 6) b. ( 4, 6) d. ( 4, 6) 10

11 32. The Fun Guys game rental store charges an annual fee of $5 plus $5.50 per game rented. The Game Bank charges an annual fee of $17 plus $2.50 per game. For how many game rentals will the cost be the same at both stores? What is that cost? a. 4 games; $27 c. 3 games; $22 b. 6 games; $38 d. 2 games; $ If the pattern in the table continues, in what month will the number of sales of CDs and movie tickets be the same? What number will that be? Total Number Sold Month CDs Movie tickets a. Month 10; 550 c. Month 8; 580 b. Month 9; 580 d. Month 11; 550 Ï 3x + y = Solve Ô Ì by substitution. Express your answer as an ordered pair. ÓÔ y = x + 5 a. ( 3, 2) c. ( 4, 1) 3 b. ( 2, 3) d. ( 8 3, 3) Ï 2x 3y = Solve Ô Ì by elimination. Express your answer as an ordered pair. ÓÔ 3x + 3y = 9 a. ( 1, 4) c. ( 2, 5) b. (4, 1) d. (9, 2.33) 36. At the local pet store, zebra fish cost $2.10 each and neon tetras cost $1.85 each. If Marsha bought 13 fish for a total cost of $25.80, not including tax, how many of each type of fish did she buy? a. 5 zebra fish, 8 neon tetras c. 8 zebra fish, 5 neon tetras b. 7 zebra fish, 6 neon tetras d. 6 zebra fish, 7 neon tetras 37. The sum of the digits of a two-digit number is 8. If the number is multiplied by 4, the result is 104. Write and solve a system of equations. Find the number. Ï Ï x + y = 8 a. Ô Ì c. Ôx + y = 8 Ì ÓÔ 4(x + y) = 104 ÓÔ 4(2x + y) = 104 The number is 35. The number is 18. Ï Ï x + y = 8 b. Ô Ì d. Ôx + y = 8 Ì ÓÔ 4(10x + y) = 104 ÓÔ 4(10x + y) = 104 The number is 17. The number is

12 Ï y = x Solve Ô Ì. ÓÔ x + y = 7 a. This system has infinitely many solutions. b. This system has no solutions. c. ( 1, d. ( 1 2, 17 2 ) 39. Temperature changes throughout the hours of a day. Early in the morning, temperature increases slowly. At noon, the temperature rises sharply. During the afternoon, the temperature stays the same for several hours. As night falls, the temperature decreases slightly. Choose the graph that best represents this situation. a. c. b. d. 12

13 40. Jamie throws a ball up into the air. Sketch a graph for the situation that describes the distance of the ball from the ground at every second since it was thrown up. Tell whether the graph is continuous or discrete. a. c. b. The graph is continuous. d. The graph is continuous. The graph is continuous. The graph is continuous. 13

14 41. Write a possible situation for the graph. a. A pool is filled with water, and people are having fun swimming and jumping in and out of the pool. b. A pool is filled with water using one valve. A little time after the pool is filled to its capacity, the pool needs to be emptied because of some problems. Then, the pool is refilled immediately, using two valves this time. c. A pool is filled with water using one valve. Then, immediately after the pool is filled to its capacity, the pool needs to be emptied because of some problems. The pool is refilled right after it is completely empty, using two valves this time. d. A pool is filled with water. A little time after the pool is filled to its capacity, the pool needs to be emptied because of some problems. Then, the pool is refilled immediately at the same rate as before. 42. Which situation is best represented by the graph? a. An airplane starts slowly on the runway, and then quickly takes off before finding a nice cruising speed. b. A swimmer starts at a steady pace, slows down to a stop, and then starts up swimming again, but at a slower pace than when she first started. c. After a ball is thrown into the air, it falls back to the ground and bounces. d. A car starts on flat ground and drives quickly up a hill, and then it keeps driving. 14

15 43. Express the relation for the math test scoring system {(1, 2), (2, 3), (3, 5), (4, 10), (5, 5)} as a table, a graph and a mapping diagram. 15

16 a. Problem Point value b. Problem Point value c. Problem Point value

17 d. Cannot determine. The set of ordered pairs is not a relation, because the elements 3 and 5 in the domain are both paired with the element 5 in the range. 44. Give the domain and range of the relation. x y a. D: { 5, 0, 4, 6}; R: { 9, 0, 9, 13} c. D: {4, 6, 5, 9, 13, 9}; R: {0} b. D: { 5, 4, 6}; R: { 9, 9, 13} d. D: { 9, 0, 9, 13}; R: { 5, 0, 4, 6} 45. Give the domain and range of the relation. a. D: 0 x 7; R: 1 y 7 c. D: 1 x 7; R: 1 y 6 b. D: 1 x 6; R: 1 y 7 d. D: 2 x 6; R: 4 y Give the domain and range of the relation. a. D: { 2, 4, 5, 9}; R: {0, 3, 8} c. D: 2 < x < 9; R: 0 < x < 8 b. D: {0, 3, 8}; R: { 2, 4, 5, 9} d. D: 2 < x < 9; R: 0 < x < 8 17

18 47. Give the domain and range of the relation. Tell whether the relation is a function. a. D: 3 x 3; R: 2 y 2 The relation is not a function. b. D: 2 x 2; R: 3 y 3 The relation is not a function. c. D: 3 x 3; R: 2 y 2 The relation is a function. d. D: 2 x 2; R: 3 y 3 The relation is a function. 18

19 48. Which graph represents a function? a. c. b. d. 49. For f(x) = 4x + 2, find f(x) when x = 1. a. 4 c. 2 b. 2 d Brian has 64 flowers for a big party decoration. In addition, he is planning to buy some flower arrangements that have 18 flowers each. All of the arrangements cost the same. Brian is not sure yet about the number of flower arrangements he wants to buy, but he has enough money to buy up to 5 of them. Write a function to describe how many flowers Brian can buy. Let x represents the number of flower arrangements Brian buys. Find a reasonable domain and range for the function. a. f(x) = 18x + 64; D: {0, 1, 2, 3, 4}; R: {64, 82, 100, 118, 136} b. f(x) = 18x + 64; D: {0, 1, 2, 3, 4, 5}; R: {64, 82, 100, 118, 136, 154} c. f(x) = 64x + 18; D: {1, 2, 3, 4}; R: {82, 100, 118, 136, 154} d. f(x) = 64x + 18; D: {5}; R: {154} 19

20 51. Graph 2x + 4y = 4 for the domain D: { 8, 4, 0, 4, 8}. a. c. b. d. 52. Use the graph of the function f(x) = 2x + 2 to find the value of y when x = 2. a. 2 c. 6 b. 7 d. 0 20

21 53. Translate the point (1, 1) right 2 units and down 2 units. Give the coordinates of the translated point. a. c. b. d. 54. Fabric that regularly sells for $4.90 per square foot is on sale for 10% off. Write an equation that represents the cost of s square feet of fabric during the sale. Write a transformation that shows the change in the cost of fabric. a. 4.90s 10; (x, y) (x, 0.1y) c. 4.90s 10; (x, y) (x, 0.9y) b. ( )s; (x, y) (x, 0.1y) d. ( )s; (x, y) (x, 0.9y) 55. Determine whether the sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence. 5, 11, 17, 23, 29,... a. Not an arithmetic sequence b. Yes; common difference 7; next three terms are 36, 43, 50 c. Yes; common difference 6; next 3 terms are 35, 41, 47 d. Yes; common difference 6; next three terms are 23, 17, Find the 20th term in the arithmetic sequence 4, 1, 6, 11, 16,... a. 96 c. 95 b. 72 d

22 57. Let g(x) be the transformation, vertical translation 3 units down, of f(x) = 4x + 8. Write the rule for g(x). a. g(x) = 4x + 8 c. g(x) = 4x + 5 b. g(x) = 4x 3 d. g(x) = 3x Let g(x) be a horizontal compression of f(x) = 3x + 5 by a factor of 1. Write the rule for g(x) and graph the 2 function. a. g(x) = 2x + 5 c. g(x) = 3 2 x + 5 b. g(x) = 3 2 x d. g(x) = 6x

23 59. Give two different combinations of transformations that would transform f( x) = 5x + 3 into g( x) = 15x 12. a. 1. A horizontal stretch by a factor of 3, followed by a vertical shift 15 units down. 2. A vertical compression by a factor of 1, followed by a vertical shift 21 units down. 3 b. 1. A vertical shift 15 units down, followed by a horizontal compression by a factor of A vertical stretch by a factor of 3, followed by a vertical shift 21 units down. c. 1. A horizontal compression by a factor of 1, followed by a vertical shift 15 units down A vertical shift 21 units down, followed by a vertical stretch by a factor of 3. d. 1. A horizontal shift 15 units left, followed by a horizontal compression by a factor of A vertical stretch by a factor of 3, followed by a vertical shift 21 units down. 23