Algebra 1 Semester 1 Review

Transcription

1 Class: Date: Algebra 1 Semester 1 Review What is the simplified form of each expression? ,384 16,807 2,401 Ê ËÁ 4 7 ˆ What is the simplified form of each expression? 3. 5 ( 14 2) È Ê ˆ ËÁ ÎÍ Evaluate u z + xy 2, for u = 20, x = 4, y = 7, and z = Evaluate (ab) 2 for a = 4 and b = To which subsets of the real numbers does the number 22 belong? whole numbers, natural numbers, integers rational numbers whole numbers, integers, rational numbers integers, rational numbers 9. To which subsets of the real numbers does the number 42 belong? whole numbers, natural numbers, integers irrational numbers rational numbers whole numbers, integers, rational numbers 1

2 What is each sum? Ê 3 ˆ ËÁ What is the value of x y when x = 9 4 and y = 3 5? What is each difference? What is each product? What is the simplified form of each expression? 1 (21m + 27) 3 63m + 9 7m + 9 7m m (2 9c)( 8) c c 16 72c 16 72c m n 3.2n + 5.3m 2 5.9n 7.8m 2 1.3n 2.8m 2 1.3n 7.8m n 2.8m n What is the simplified form of each expression? ( 8d 3w) 8d 3w 8d + 3w 8d + 3w 8d 3w 2

3 What is the solution of the equation? = 5 17 n u + 2 = = s t = 9 What is the solution of the equation? = d x = x 8 = What is the solution of the equation? = 5 + z b 3 5 = What is the solution of the equation? = 6p 8 5p x 9 5x = d d 2d + 8 3d = y y =

4 What is the solution of the equation? 31. 4(y + 2) = (y 5) + 2 = p = x = What is the solution of the equation? 35. 6x 3 = 5x t = 2t What is the solution of the equation? ( 10x 10) = 5 ( 4x + 4) p + 7 = 3(2p 3) 4( p) p = 6 p = 5 p = 7 p = 12 What is the solution of each equation? 39. 2(h 8) h = h infinitely many solutions no solution z = z infinitely many solutions no solution 41. You are shopping for jeans. City Express sells 3 pairs of jeans for $61. Denim Planet sells 2 pairs of jeans for $73. New Threads sells 4 pairs of jeans for $110. Which store has the best deal? City Express Denim Planet New Threads All jeans are the same price What is the given amount converted to the given units? s; minutes 4.5 min 3 min 3.25 min 2.5 min 4

5 cm; meters 0.86 m 860 m 8600 m 8.6 m ft; inches 1728 in in. 12 in in. 45. A car is driving at a speed of 45 mi/h. What is the speed of the car in feet per minute? 3,960 ft/min 1,935 ft/min 237,600 ft/min 2,700 ft/min 46. A pool is filled at a rate of 105 gal/min. What is the rate in ml per second? ml/s 1.66 ml/s 6300 ml/s 0.6 ml/s What is the solution of the proportion? = 25 x y = What is the solution of the proportion? x 8 5 = w w + 6 = What inequality represents the verbal expression? 51. all real numbers greater than or equal to 67 x 67 x < 67 x 67 x > 67 5

6 Which number is a solution of the inequality? < b k What is the graph of the inequality? 54. d < x 3 What inequality represents the graph? x 8 x < 8 x > 8 x < 8 m 1 2 m > 1 2 m 1 2 m 1 2 What inequality describes the situation? 58. Let n = the number. A number exceeds 45. n 45 n 45 n < 45 n > 45 6

7 What are the solutions of the inequality? Graph the solutions. 59. x 3 12 x b b 32 x 12 3 b 12 x 15 b 4 x 9 b 4 What are the solutions of the inequality? Graph the solutions. What are the solutions of the inequality? Graph the solutions. 60. q > 1 2 q > x 5 2 x 7 q > 1 x 7 q > 5 6 x 10 q < 0 x 10 7

8 What are the solutions of the inequality? Graph and check the solutions. 63. x 4 2 x 8 x 6 x 8 x 8 What are the solutions of the inequality? Graph the solutions x 12 x 3 x 3 x 8 x > 8 What are the solutions of the inequality? Check the solutions x 9 < 9 10 x > x < x < x < x + 6 < 6 x < 3 x > 3 x > 6 x < + 6 What are the solutions of the inequality? 67. 2(b 8) > 12 b > 20 b > 6 b > 14 b < q (q 22) > 0 q < 32 q > 32 q > 56 q < 56 What are the solutions of the inequality? w 8(w + 12) w 42 w 48 w 42 w 54 8

9 70. 12x 3x + 11 > 4x (17 9x) x > 7 x < 7 x < x > n 14 13n + 6 n n n 4 n 8 21 What are the solutions of the inequality? ( 2x + 2) 10x 17 x 7 x 19 all real numbers no solution x 10 7x 3x 2 x 8 x 8 all real numbers no solution How do you write the set in roster form? In set builder notation? 74. D is the set of whole numbers less than 3. D = {0,1,2,3,4,5}; D = {x is a whole number, x < 3} D = {0,1}; D = {x x < 3} D = {0,1,2}; D = {x x is a whole number, x < 3} D = {0,1,2,3,4,5,6,7}; D = {x < 3} 75. G is the set of odd natural numbers that are less than or equal to H is the set of even integers less than 6 but greater than or equal to 0. In set builder notation, how do you write the solutions of the inequality? 77. 3x Ï Ì Ô x x 2 ÓÔ Ô Ô Ï Ì Ô x x 2 ÓÔ Ô Ô Ï Ì Ô x x 2 ÓÔ Ô Ô Ï Ì Ô x x 2 ÓÔ Ô Ô What are all the subsets of the set? 78. { 1, 9},{ 1},{9} { 1},{9},{ 1,9},{ 1},{9},{ 1,9} { 1},{9} 79. Suppose U = { 10, 6, 2, 0, 3, 5} is the universal set and T is the set { 10, 6, 0}. What is the complement of set T? { 2, 3, 5} { 10, 6, 0} { 6, 2, 0, 3, 5} {0, 3, 5} 9

10 What compound inequality represents the phrase? Graph the solutions. 80. all real numbers that are greater than 8 and less than 8 8 < x < 8 8 < x < 8 8 < x 8 8 x 8 What are the solutions of the compound inequality? Graph the solutions x 4 < 8 1 x < 2 3 x < 8 1 x < 6 0 x < < 4x 10 < 6 4 < x < 12 3 < x < 1 16 < x < 8 2 < x < 4 10

11 What are the solutions of the compound inequality? Graph the solutions x 2 < 12 or 2x + 3 > What is the graph of ( 8, 2]? x < 5 or x > 2 x < 5 or x > 5 x < 7 or x > 5 x < 12 or x > x or 3 x 10 or x 2 8x How do you write x 6 and x < 3 in interval notation? [ 6, 3] ( 6, 3) [ 6, 3) ( 6, 3] x 2 or x 2 x 4 or x 9 8 x 10 or x 2 11

12 87. What is the graph of (, 8) or (6, )? 88. How do you write (,8) or (10, ) as an inequality? x < 8 or x > 10 x < 10 or x > 8 x < 8 and x > 10 x < 10 and x > You have two boxes of colored pens. The first box contains a red pen, a blue pen, and green pen. The second box contains a yellow pen, a red pen, and a black pen. What is the set that represents all the pens? {red pen, blue pen, green pen} {red pen} {red pen, red pen, green pen, yellow pen, black pen} {red pen, blue pen, green pen, yellow pen, black pen} Let X = {x x is a whole number less than 15}, Y = { x x is a multiple of 3}, Z = {x x is a real number greater than or equal to 5.5}. 90. What is X Y? {0,3,6,9,12} {3,6,9,12,15} {..., 6, 3,0,3,6,9,...} {..., 6, 3,0,3,6,9,12} 91. What is X Z? {6,7,8,9,10,11,12,13,14} {6,9,12,15} {5,6,7,8,9,10,11,12,13,14,15} 12

13 92. Bob is comparing the ingredients for three different muffin recipes. Which ingredients do all three recipes have in common? {honey, salt, wheat} {wheat, baking soda, salt} {bran, water} {milk, sugar, raisins} 93. Of 410 consumers polled, some purchase music on CDs, some only download music, and some do both. If 290 people polled purchase CDs and 220 purchase CDs and download music, how many people download music? What are the variables in each graph? Describe how the variables are related at various points on the graph. 95. The graph shows the height of a hiker above sea level. The hiker walks at a constant speed for the entire trip. What are the variables? Describe how the variables are related at various points on the graph. 94. Of 480 consumers polled, some purchase ice cream, some purchase frozen yogurt, and some purchase both. If 260 people polled purchase ice cream and 200 purchase both ice cream and frozen yogurt, how many people purchase frozen yogurt?

14 The variables are height and time. For the first part of the graph, the height is increasing slowly, which means the hiker is climbing a steep incline. Flat parts of the graph show where the elevation does not change, which means the hiker stopped to rest. The steep part at the end of the graph shows that the hiker is descending a gentle slope. The variables are height and time. For the first part of the graph, the height is increasing slowly, which means the hiker is walking up a gentle slope. Flat parts of the graph show where the elevation does not change, which means the trail is flat here. The steep part at the end of the graph shows that the hiker is descending a steep incline. The variables are height and time. For the first part of the graph, the height is increasing slowly, which means the hiker is climbing a steep incline. Flat parts of the graph show where the elevation does not change, which means the trail is flat here. The steep part at the end of the graph shows that the hiker is descending a steep incline. What is the graph of the function rule? 97. y = 3x 2 All of the above. 96. Lena makes home deliveries of groceries for a supermarket. Her only stops after she leaves the supermarket are at traffic lights and the homes where she makes the deliveries. The graph shows her distance from the store on her first trip for the day. What are the variables? Describe how the variables are related at various points on the graph. 14

15 98. A taxi company charges passengers $1.00 for a ride, and an additional $0.30 for each mile travele The function rule C = 0.30m describes the relationship between the number of miles m and the total cost of the ride If the taxi company will only go a maximum of 40 miles, what is a reasonable graph of the function rule? 15

16 Write a function for the situation. Is the graph continuous or discrete? 99. A movie store sells DVDs for $11 each. What is the cost, C, of n DVDs? C = 11n; continuous C = 11 + n; discrete C = 11 + n; continuous C = 11n; discrete 100. A produce stand sells roasted peanuts for $1.90 per poun What is the cost, C, of p pounds of peanuts? C = 1.90p; continuous C = 1.90p; discrete C = p; continuous C = p; discrete What is the graph of each function rule? 101. y = x 1 16

17 102. y = x The length of a field in yards is a function f(n) of the length n in feet. Write a function rule for this situation. f(n) = 3n f(n) = 1 3 n f(n) = 12n f(n) = n 12 17

18 104. Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $.59. c(p) = 59p c(p) = p 0.59 c(p) = p c(p) = 0.59p 105. A snail travels at a rate of 2.35 feet per minute. Write a rule to describe the function. How far will the snail travel in 5 minutes? d(t) = 5t; ft d(t) = t ; 7.35 ft d(t) = t ; 2.13 ft 2.35 d(t) = 2.35t; ft 106. A zucchini plant in Darnell s garden was 12 centimeters tall when it was first plante Since then, it has grown approximately 0.5 centimeter per day. Write a rule to describe the function. After how many days will the zucchini plant be meter tall? h(d) = d + 12; 3 days 0.5 h(d) = 0.5d + 12; 13 days h(d) = 0.5d; 37 days h(d) = 12d + 0.5; 1.4 days The relation is a function. The relation is a function Identify the mapping diagram that represents the relation and determine whether the relation is a function. Ï Ì Ô ( 3, 6), ( 1, 6), (5, 6), (8, 6) ÓÔ Ô Ô The relation is not a function. The relation is not a function The function j(x) = 39x represents the number of jumping jacks j(x) you can do in x minutes. How many jumping jacks can you do in 5 minutes? 195 jumping jacks 7 jumping jacks 144 jumping jacks 234 jumping jacks 109. You have 8 cups of flour. It takes 1 cup of flour to make 24 cookies. The function c(f) = 24f represents the number of cookies, c, that can be made with f cups of flour. What domain and range are reasonable for the function? What is the graph of the function? 18

19 The domain is 0 c(f) 192. The range is 0 f 8. The domain is 24 c(f) 192. The range is 1 f 8. The domain is 0 f 8. The range is 0 c(f) 192. The domain is 1 f 8. The range is 24 c(f)

20 The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation The table shows the cost of a ski rental package for a given number of people. People Cost ($) dollars per person; the cost is $1 for 280 people dollars per person; the cost is $160 for each person. 1 1 dollars per room; the cost is $40 for each person dollars per person; the cost is $40 for each person. 1 Find the slope of the line What is the slope of the line that passes through the pair of points? 112. (1, 7), (10, 1)

21 What is the slope of the line? undefined 0 0 undefined What are the slope and y-intercept of the graph of the given equation? 115. y = 9x + 2 The slope is 9 and the y-intercept is 2. The slope is 9 and the y-intercept is 2. The slope is 2 and the y-intercept is 9. The slope is 2 and the y-intercept is 9. Write an equation of a line with the given slope and y-intercept m = 1, b = 4 y = 4x + 1 y = 1x + 4 y = x 4 y = x

22 Write the slope-intercept form of the equation for the line What equation in slope intercept form represents the line that passes through the two points? 118. (2, 5), (9, 2) y = 3 7 x 41 7 y = 7 3 x 41 7 y = 7 3 x y = 3 7 x y = 5 8 x y = 8 5 x 1 2 y = 5 8 x (6.9, 5.9), (10.9, 2.1) y = 0.5x 19.7 y = 2x y = 0.5x 19.7 y = 2x y = 8 5 x Graph the equation y = 4x 3 22

23 121. y = 3x Giselle pays $210 in advance on her account at the athletic clu Each time she uses the club, $15 is deducted from the account. Model the situation with a linear function and a graph. 23

24 b = x b = x b = x b = x Write an equation in point-slope form for the line through the given point with the given slope (8, 3); m = 6 y + 3 = 6 (x 8) y 3 = 6(x 8) y 3 = 6 (x + 8) y + 3 = 6 x + 8 Graph the equation y + 5 = 2(x 4) 124. (3, 10); m = 0.83 y 10 = 0.83(x + 3) y 10 = 0.83(x 3) y 3 = 0.83(x + 10) y + 10 = 0.83(x 3) 24

25 126. y 3 = 3 (x + 4) 2 25

26 What is an equation of the line? 127. y + 3 = 2(x + 2) y + 5 = 1 (x + 2) 2 y 3 = 1 (x 2) 2 y + 3 = 2(x 2) Find the x- and y-intercept of the line x 6y = 12 x-intercept is 12; y-intercept is 2 x-intercept is 6; y-intercept is 1 x-intercept is 2; y-intercept is 12 x-intercept is 1; y-intercept is x 7.8y = x-intercept is 7.8; y-intercept is 6.9 x-intercept is 9.2; y-intercept is 10.4 x-intercept is 10.4; y-intercept is 9.2 x-intercept is 6.9; y-intercept is x 7 5 y = 4 x-intercept is 4; y-intercept is 20 7 x-intercept is 4; y-intercept is 20 7 x-intercept is 4; y-intercept is 20 7 x-intercept is 20 ; y-intercept is 4 7 Match the equation with its graph x 5y = 40 26

27 What is the graph of the equation? 132. y = 3 27

28 133. x = 4 28

29 134. Write y = 2 x + 7 in standard form using integers. 3 2x + 3y = 21 3x 2y = 21 2x 3y = 21 2x + 3y = A paint store sells exterior paint for $28.25 a gallon and paint rollers for $6.25 each. Write an equation in standard form for the number of gallons p of paint and rollers r that a customer could buy with $ = p 28.25p = 6.25r r p = p r = The video store rents DVDs for $4.75 each and video games for $2.00 each. Write an equation in standard form for the number of DVDs d and video games g that a customer could rent with $ d = 2g g + 2d = d + 2g = = d Write an equation for the line that is parallel to the given line and passes through the given point y = 5x + 10; (2, 14) y = 1 5 x + 4 y = 1 5 x 4 y = 5x 68 y = 5x y = 1 x 10; (15, 16) 5 y = 5x + 19 y = 1 5 x y = 1 5 x 19 y = 5x y = 5.7x + 1.5; (2.7, 7.1) y = 5.7x y = 5.7x y = 5.7x y = 5.7x Tell whether the lines for each pair of equations are parallel, perpendicular, or neither y = 7 8 x 1 32x 28y = 36 parallel perpendicular neither 141. y = 1 4 x x + 8y = 6 parallel perpendicular neither 29

30 142. y = 7 2 x 9 14x 4y = 20 parallel perpendicular neither Write the equation of a line that is perpendicular to the given line and that passes through the given point x 12y = 2; (10, 1) y = 3x + 29 y = 1 3 x + 29 y = 3x + 29 y = 1 3 x What type of relationship does the scatter plot show? 144. y = 10 9 x 22 ; (4, 2) 9 y = 9 10 x 8 5 y = 9 10 x 22 9 y = 9 10 x 8 5 y = 9 10 x y 3 = 8 (x + 2); ( 2, 3) 3 y + 3 = 3 (x 2) 8 y 3 = 3 (x + 2) 8 y 2 = 3 (x + 3) 8 y + 3 = 3 (x 2) 8 positive correlation negative correlation no correlation 30

31 The scatter plot below shows the height of a tree over time. What is the approximate height of the tree after 10 years? positive correlation negative correlation no correlation 13 ft 20 ft 17 ft 21 ft Use a graphing calculator to find the equation of the line of best fit for the dat Find the value of the correlation coefficient r. Predict the missing value in the table John s Best Discus Throws Year Distance (meters) ? y = 0.465x , r = 0.994; y = 2.086x , r = 0.994; y = 0.465x , r = 0.994; y = 0.465x , r = 0.994; Hours Studying Exam Mark (%) ? y = x , r = 0.991; about 95% y = 3x + 65, r = 0.951; about 92% y = 2.964x , r = 0.991; about 89% y = 2.964x , r = 0.991; about 99% 31

32 In the following situations, is there likely to be a correlation? If so does the correlation reflect a causal relationship? Explain the number of hours spent studying for a test and your test mark There is a positive correlation and also a causal relationship. The more you study for a test the better your mark is likely to be. There is a negative correlation. The more you study for a test, the worse your mark is likely to be. There is no correlation the average daily winter temperature and your heating bill There is a positive correlation. The higher the average daily winter temperature the higher your heating bill. There is a negative correlation and a causal correlation. The higher the average daily winter temperature the lower your heating bill. There is no correlation Identify the domain and range of the relation. Ï Ì Ô ( 9, 2), ( 4, 2), (3, 2), (9, 2) ÓÔ Ô Ô 154. Identify the domain and range of the relation. Ï Ì Ô ( 4, 2), ( 9, 5), ( 4, 12), (8, 8) ÓÔ Ô Ô Use the vertical line test to determine whether the relation is a function Ï 156. Ì Ô (0, 1), ( 5, 1), ( 3, 3), ( 5, 5) ÓÔ Ô Ô Ï 158. Ì Ô (3, 0), (2, 1), ( 1, 4), (1, 2) ÓÔ Ô Ô 159. Find the range of f( x) = 2x + 6 for the domain { 1, 3, 7, 9} Find the range of f x ( ) = 4.7x + 1 for the domain { 1, 3, 5, 8}. 32

33 What is the solution of the equation? Justify each step = 13 8x 162. Sketch a graph of the speed of a city bus on a daily route. Label each section. A - bus pulls away from a stop and increases speed B - bus is at a constant speed between stops C - bus is stopped D - bus increases speed after stopping 33

34 Algebra 1 Semester 1 Review Answer Section 1. D 2. B 3. D 4. D 5. B 6. B 7. D 8. D 9. B 10. A 11. B 12. D 13. A 14. B 15. A 16. A 17. B 18. A 19. u = s = t = B 23. C 24. A 25. C 26. C 27. D 28. C 29. D 30. C 31. B 32. D 33. D 34. A 35. B 36. D 37. A 38. A 39. C 40. D 41. A 1

35 42. C 43. A 44. A 45. A 46. A 47. B 48. C 49. C 50. C 51. A 52. D 53. D 54. B 55. B 56. C 57. C 58. D 59. D 60. A 61. D 62. D 63. D 64. B 65. A 66. A 67. C 68. D 69. C 70. B 71. C 72. C 73. D 74. C 75. G = {1}; G = {x x is an odd natural number, x 1} Ï 76. H = Ì Ô 0,2,4 ÓÔ Ô Ô ; H = {x x is an even integer, x < 6, x 0} 77. A 78. C 79. A 80. A 81. C 82. D 83. A 84. A 85. C 86. C 2

36 87. C 88. A 89. D 90. A 91. A 92. C 93. A 94. D 95. B 96. The variables are distance and time. The distance from the store increases as she drives, and it stays constant each time she stops for a traffic light or to stop at a customer s house. After her third stop, she starts heading back to the store. The distance from the store decreases as she drives, and it stays constant for one more stop. Finally, she makes it back to the store and the distance is zero again. 97. B 98. A 99. D 100. A 101. D 102. C 103. A 104. D 105. D 106. B 107. B 108. A 109. B 110. D 111. B 112. B 113. B 114. B 115. B 116. D 117. C 118. D 119. D 120. D 121. B 122. A 123. B 124. D 125. A 126. B 127. A 128. A 129. C 3

37 130. A 131. C 132. A 133. B 134. A 135. D 136. C 137. D 138. C 139. A 140. B 141. C 142. A 143. C 144. A 145. B 146. A 147. B 148. C 149. A 150. C 151. A 152. B 153. The domain is { 9, 4, 3, 9}. The range is {2} The domain is { 9, 4, 8}. The range is { 8, 5, 2, 12} The relation is a function The relation is not a function The relation is not a function The relation is a function {8, 0, 8, 12} 160. {5.7, 13.1, 22.5, 36.6} 4

38 161. Steps Reasons 17 = 13 8x = 13 + ( 8x) = ( 8x) 30 = 8x 30 8 = 8x = x Original equation Addition Property of Equality Commutative Property of Addition Use addition to simplify. Division Property of Equality Use division to simplify [4] OR similarly shaped graph with appropriately placed labels [3] one error in graph shape or labeling [2] two errors in graph shape or labeling [1] three errors in graph shape or labeling 5