ALGEBRA 1 B ANSWERS Semester Exam Review

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1 1. a. A B C HAM HD b. 5 more hot dogs c. A B C HAM HD OR Stephan must bowl 165 in the fourth game. Sample responses: In order to have an average of 180, Stephan must total 70 pins. In the first three games, his total is 555. He needs to bowl = 165 pins. Solve the equation x D 4. a. False: the range is 30 = 8 b. False: the interquartile range is 5 14 = 11 c. True: each interval represents 5% of the data d. False: 4 is the median. It gives no information about how many weeks was worked at 4 hours. 5. Sample response. This is not a valid conclusion. Although Maryland s maximum points scored is greater than Duke s maximum points scored, the median of Duke s scores is higher than the 3 rd quartile of Maryland s. Also, Maryland s median is equal to Duke s first quartile (4 times 3 times ) 7. a. 1 ( times 3 times ) 1 b. or or 8.3% flavors of ice cream MCPS

2 a. or or 0.1 or 10% b or 0.8 or 8% a. or or 0.6 or 60% 0 5 b. 60% of 180 = 108 days a % b c. 7 $0 18 $111 $5 3 $10 1 $0 $13 1. Sample responses: The first method is not a simple random sample. The same 50 people could arrive in the math building each morning so each student does not have an equal chance of being selected. The second method is not a simple random sample since the students every possible set of 50 students is not equally likely to be chosen. The third method is a simple random sample. Each student has the same probability of being selected and every possible set of 50 students is equally likely to be chosen. 13. Sample response: Jack s sample is not likely to be representative. The sample excludes students are not in the orchestra. Jill s sample is more likely to be representative; every student has an equal opportunity to be in the sample or or 0. or 0% students 0% of 800 = Sample response The vertical scale on the first graph starts at 0 and increases by 1. The vertical scale on the second graph starts at 1 and increases by 0.. The smaller scale on the second graph exaggerates the differences in the scores. 16. The median of $80 would be the measure of central tendency that best represents Nancy s weekly income. The mode is $50, which is her lowest income, and the $300 income for one week makes the mean of $114, which is much higher than four of her weekly incomes. MCPS

3 17. C 18. Sample responses: Use a spinner with four equal sectors numbered 1,, 3, and 4. Assign the number 1 to the event of going to the movies and the numbers, 3, and 4 to not going to the movies. Roll a die. Assign the number 1 to the event of going to the movies,, 3, 4 to not going to the movies, and ignore 5 and C x x x x 5x 3x x y 8 6 5x y 6y 4 x x y 3 9x y 5x 7. 5 y x x 3 1 6m 8m 3 3 4x 5x 3x 3 t t 6 8x 6x 35 3x 3x 14 4x 0x 5 5x 30x x 81 MCPS

4 x 5y x 4x 3 8x y 4x y A 41. A or 1x x 11x 6 xx B 44. 6x x x y ( x 3 y) 46. x15x 47. x1x x9x x85x ( a 7) 51. x x 1, x 7, r 9, t 7, x 0.98 and 6.70 MCPS

5 x a..09 and (,9) y (0,5) ( 5,0) (1,0) O x b. y x 9 c. 5 and 1 d. x 59. a. The vertex is at 3, 4 b. The equation of the axis of symmetry is x 3. c. The y-intercept is 5. d. The x-intercepts are 1 and 5. e. The zeros are 1 and 5. f. f x x 3 4 MCPS

6 60. a. The graph has shifted units right and 9 units down. b. g x c. x 9 g x x 4x 5 d. The zeros of g xare 1 and 5. e. g xis increasing on the interval x or x f. The equation of the axis of symmetry is x. 61. x 7 6. C 63. Sample responses: The ball does not reach its maximum height at t = seconds. The graph is a parabola that opens downwards since the quadratic coefficient is negative. The first coordinate of the vertex is when the maximum height occurs. The second coordinate of the vertex of the parabola is the maximum height. The vertex has coordinates 1.565, Therefore the maximum height occurs at t = seconds. The ball hits the ground at t = 3.15 seconds. I solved the equation 16t 50t 0. There are two solutions: t = 0 and t = The football is being kicked at t = 0, which would not be when the football hits the ground after being kicked. The solution t = 3.15 seconds is the solution to the problem. 64. a. The maximum height that the animal reaches is meters. The vertex of the parabola is at the point 1.5, b. Setting the function rule equal to zero results in two solutions: t 0, t Since the zero solution gives the time that the animal started its leap, the.5 solution gives how long the animal was in the air. 1 III y x I y 4x 3 IV 1 y 5x II y x MCPS

7 66. x f x a. 1,, 4, 8, 16 b. f x 4() x or f x x c. increasing d. Yes, the function is continuous. e. All real numbers f. All positive real numbers ( y 0 ) g. The x-axis (y = 0) 68. D 69. The values of the function decrease and the values of the function get closer to zero. 70. The values of the function increase. 71. d 1 Nd marbles The tenth day. I continued the table by multiplying the number of marbles remaining by one-half to get the next day s number of marbles. After day 10, there were two marbles remaining. As the value of d increases, the number of marbles decreases and gets closer to A linear function. The x-values increase by 1, and the y-values increase by a constant of A quadratic function. The x-values increase by 1, and the second differences of y increase by a constant of. 74. An exponential function. The x-values increase by 1 and the ratio of consecutive y-values is a constant (). MCPS

8 75. a. V 00000(1.04) t b. 3 V 00000(1.04) $ 4, a. V 400(0.88) t b. 5 V 400(0.88) $1, a. absolute value b. quadratic c. exponential d. linear 78. a. f x, g x, h x, j x b. j x c. f x, g x d. f x, g x, h x, j x e. hx, j x f. f x, g x g. g x h. f x, g x, h x, j x i. f x, g x 79. a. day 8 b. 58 or 59 petals hours seconds 8. a. 0t 8 b. 40 W 160 c a. 0 t 350 b. 4C c. 50, 150, 00, 300 d. 4 MCPS