Algebra 1 Enriched- Midterm Review Know all vocabulary, pay attention to the highlighted words in the text, and understand the various types of directions in each of the sections of the textbook. Practice with old homework problems, worksheets, and quiz and test problems. DO NOT ONLY study this review packet. DO NOT WAIT until the last night to review. Be prepared to work with integers, fractions and decimals. Prepare: Get pencils, erasers, calculator! Chapter 1 Variables Exponents and Order of Operations Types of Real Numbers Operations on real numbers: addition, subtraction, multiplication, division, matrices Properties of real numbers: Distributive, Commutative, Associative, Identity, Inverse, Multiplication of Zero, and Multiplication of 1 Graphing points on a coordinate plane (and the vocabulary associated with it) Review exercises start on page 67 Chapter 2 Solving one-step, two-step, and multi-step equations, equations with variables on both sides and associated word problems (area, consecutive integer, rate-time-distance) Formulas and literal equations- be able to solve an equation for one of the letters in it Measures of central tendency- mean, median, mode, range Stem-and-leaf plots Review exercises start on page 125 Chapter 3 Solve and graph inequalities in one variable [remember to flip the arrow when multiplying/dividing by a negative number] Solve word problems involving inequalities Solve and graph compound inequalities Solve and graph absolute value inequalities Review exercises start on page 175 Chapter 4 Find ratios and rates, including unit rate Convert rates (dimensional analysis) Work with proportions Find parts of similar figures Use proportions with percent problems is % Use of 100 Change from percent to fraction to decimal and back again Find percent of change (increase or decrease) Review exercises start on page 227
Chapter 5 Relate graphs to events Identify relations and know what makes it a function Find domain and range from a set of ordered pairs, a graph, a mapping, or a table Use function notation [ f x ] Employ the vertical line test for a function Model functions using rules, tables and graphs Graph linear (lines), quadratic (parabolas u-shaped) and absolute value (v-shaped) functions Direct variation Describe patterns Know when a pattern is arithmetic vs. geometric A n a n 1 d and A(n) = ar n 1 Use the formulas Review exercises start on page 275 Chapter 6 Find rate of change Find slope from a graph or two ordered pairs Know about positive, negative, zero and undefined slopes Find and use the slope-intercept form of a linear equation Use the x- and y-intercepts to graph a line Write equations in standard form and point-slope form Find the equation of a line given: two points, one point and a slope, or a graph Know that parallel lines have the same slope and perpendicular lines have slopes that are opposite reciprocals of each other Review exercises start on page 331
Chapter 1 1. Simplify the expression: (30 2 3 12 3 + 12) 6 2. Simplify the expression: 13[6 3 (5 2 4 2 ) + 9] 3. Name the set(s) of numbers to which -3 belongs. 4. Are whole numbers, integers, or rational numbers the most reasonable for the situation? The number of desks in a classroom 5. Order the numbers from least to greatest: 8.36, 7 4, 24, 1 6. Simplify the expression: 19 ( 8) 7. Evaluate the expression x( y + z) for x = 2, y = 1, z = 5. 8. Simplify the expression: ( 2) 4 9. Evaluate the expression a b for a = 5 6 and b = 7 12 10. Write an expression for the phrase: -3 times the quantity 9 times a minus 4 11. Simplify the expression: 1 (81m + 18) 9 12. Give a reason to justify each step. 13. Complete the statement. If the x-coordinate of an ordered pair is negative, and the y-coordinate is negative, the ordered pair is in Quadrant. 14. Describe the trend in the scatter plot.
Chapter 2 15. Solve and check: x 3 = 24 16. Define a variable and write an equation for the situation. Then solve. A customer went to a garden shop and bought some potting soil for $12.50 and 6 shrubs. If the total bill was $71.00, what did the shrubs cost? 17. In the triangle, the measure of angle A = measure of angle B. Find the value of x. 18. Find the value of x. (Hint: The sum of the measures of the angles in a triangle is 180 ) 19. Solve the equation and check: 4m 6 + 3 4 = 7 8 20. Solve the equation and check: 6(4.5y 12) = 9 21. Solve the equation and check: 3p 1 = 5(p 1) 22. Solve the equation & check your answer: 3m 4 = -9 + m 23. Write and solve an equation for the situation: A buyer for a clothing store is interested in ordering a certain sweater. Company A charges $15.00 per sweater plus a $30.00 shipping and handling fee per order. Company B charges $12.75 per sweater plus a $75.00 shipping and handling fee per order. How many sweaters must the buyer purchase to justify using Company B? 24. Determine whether the equation is an identity or whether it has no solution: 8x + 4x 15 = 11 + 3(4x 1) 25. Solve the equation. If the equation is an identity, write identity. If it has no solution, write no solution: 4(x 4) = 16 + 4x 26. The sum of four consecutive odd integers is -56. a. If n is the first odd integer, write an expression for the second odd integer. b. Write the expressions for the third and fourth odd integers. c. Use these expressions to write and solve an equation to find the four integers.
27. Solve the equation for x: dx + fy = g 28. The formula for converting degrees Fahrenheit (F) to degrees Celsius (C) is C = 5 (F 32). 9 a. Transform the formula to find Fahrenheit temperature in terms of Celsius. b. Find the Fahrenheit temperature when the Celsius temperature is 25. 29. Find the mean, median, mode, and range of: 3, 30, 30, 27, 13, 30, 21, 30. 30. The data below show the average daily high temperature for Fargo, North Dakota for each month of the year. Use a stem-and-leaf plot to organize the set of data: 65, 61, 56, 67, 77, 74, 53, 84, 70, 59, 63, 81 31. Determine whether each number is a solution of the given inequality: x(7 x) > 8 a. 8 b. -1 c. 2 32. Write an inequality for the graph: 33. Tina can type at least 60 words per minute. Write and graph an inequality to describe this statement. 34. Rewrite the inequality so that the variable is on the left. Then, graph the solution. 3 x 35. Graph the inequality from the given description: x is at most -1 36. Tell what you must do to the first inequality in order to get the second. r 6 < 3 r > 18 37. Solve the inequality: x 2 2(x 8) > 0 38. Write an inequality that represents the situation & graph the solution: all real numbers between -5 and 5 39. Solve the inequality & graph the solution: 7 < 5 2x 1 40. Write a compound inequality that the graph could represent: 5 41. Solve the equation. If there is no solution, write no solution. 2 r 7 = 28 42. Write an absolute value equation that has the given values as solutions: 7 and 11 43. Solve & graph the solution: 2x + 1 > 3
Chapter 4 44. Complete the statement: 47 ft/hr = mi/wk 45. A worker on an assembly line takes 6 hours to produce 21 parts. At this rate, how many parts can she produce in 12 hours? 46. Solve the proportion 6 4 13 b 2 0.5b 47. Find the missing side, x, of the similar figures. 48. Use a percent equation to solve: What percent of 24 is 6? 49. Use a percent proportion to solve: What is 42% of 800? 50. Write and solve a percent proportion to find the whole, if 12 is 20% of it. 51. A ski club planned a trip to Squaw Valley, and 6 of the members are going. If this is 10% of the club, how many members are in the ski club? 52. Rose earns 6.7% commission on her camera sales. In January, she earned $217.08 in commissions. What were her sales for the month? 53. Use the formula for simple interest, I = prt. Find the missing value. t =, I = $318.33, p = $535, r = 8.5% 54. Find the percent of change and describe it as an increase or decrease. Round to the nearest percent. 5.35 lb to 6.6 lb 55. The circulation of a newsletter decreased from 7,900 to 6,162. Find the percent of decrease in circulation to the nearest percent. Chapter 5 56. Label each section of the graph.
57. Find the domain and range of the relation 4 4 1 2 1 7,1,,,,5,, 5 5 3 7 8 8 58. Plot the points 4, 3, 2, 1, 4,7, 5,9 the relation is a function. Use the vertical-line test to determine whether 59. Use the vertical line test to determine whether the graph represents a function. 60. Use a mapping diagram to determine whether the relation is a function. {( 8, 3), ( 5, 3), (0, 3), (2, 3)} 61. Determine whether the relation is a function. If the relation is a function, state the domain and range. x y 2 1 8 4 1 5 2 2
62. Evaluate the function for x = 30. f(x) = 6 5 x + 2 63. Find the range of the function rule y = 2x + 8 for the domain. { 5, 4, 2, 1, 5} 64. Graph the function. y = 3 x 65. Graph the function. f(x) = 2 x 2 66. An employee receives a weekly salary of $250 and an 8% commission on all sales. a. Write a rule to describe the function. b. Find her earning for a week with $1556 total sales. 67. Is the equation a direct variation? If it is, find the constant of variation. 3 6 x y 5 5 68. Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern. 9, 13, 17, 21,... 69. Is the given sequence arithmetic or geometric? Justify your answer. 3, 9, 27, 81,... 70. Find the third, sixth, and eighth terms of the sequence. A(n) = 12.2 + (n 1)( 3.4) 71.Write a rule for the given sequence: 3, -12, 48,
72. The rate of change is constant in the graph. Find the rate of change. Explain what the rate of change means for the situation. Chapter 6 73. Find the slope of the line that passes through the pair of points. 1 3 6, 6, 7,8 5 5 For questions 74 and 75: State whether the slope is zero or undefined. 74. 75. ( 8, 7), ( 2, 7) 76. Tell whether each statement is true or false. If false, give a counterexample. Justify your answer. a. All vertical lines have the same slope. b. The slope of a line that passes through Quadrant IV must be positive. c. A line with slope zero must pass through the origin. 77. Find the slope and y-intercept of the equation. 3 y = x 9 4
78. Write the slope-intercept form of the equation for the line. 79. Use the slope and y-intercept to graph the equation. 1 y = x 4 2 80. Is the ordered pair on the graph of the given equation? (2, 4); y = 3x 2 81. Find the x- and y- intercepts of the equation. 3x 6y = 24 82. Graph the equation using x- and y- intercepts. 3x 8y = 24
83. For each equation, tell whether its graph is a horizontal or a vertical line. a. y 4.75 b. x 2.5 84. Write the equation in standard form. 4 8 y x 3 3 85. Graph the equation. y 8 5( x 1) 86. A line passes through (2, -4), (5, -6). Write an equation for the line in point-slope form, in slopeintercept form, and in standard form. 87. Find the slope of a line parallel to the graph of the equation. 3x y 6 88. Are the graphs of the pair of lines parallel, perpendicular, or neither? Explain 1 y x 17 2 x 2y 14 89. Write an equation for the line that is parallel to the given line and passes through the given point. 3 y x 11;(0,0) 2 90. Find the slope of a line perpendicular to the graph of the equation. 3x 4y 6
91. Tell whether the lines for the pair of equations are parallel, perpendicular, or neither. y 2x 5 y x 4 92. Tell whether each statement is true or false. Explain your choice. a. Two lines with negative slopes can be perpendicular. b. Two lines are perpendicular if the product of their slopes is 1.
Algebra I Enriched Midterm Review Answer Key 1. 5400 2. 429 3. Integers, rational numbers 4. Whole Numbers 5. 6. 27 7. -8 8. 16 9. 7 24,1,,8.36 4 10 7 10. 3 9a 4 11. 9m 2 12. a. Commutative Prop. Of Mult. 13. III b. Associative Prop. Of Mult. c. Multiply w/ parentheses first d. Simplify 14. Negative correlation 15. 72 16. p = price of shrubs 17. 46.5 6 p $12.50 $71.00 p $9.75 18. x 80 19. 20. 3 3 16 21. p 2 22. 5 2 23. 21 24. No Solution 25. Identity
26. a. n 2 b. n + 4 and n + 6 c. n n 2 n 4 n 6 56 the integers are 11, 13, 15, & 17 27. g 28. a. d fy 9 F c 32 5 b. F 77 29. range = 27, mean = 23 30. Median = 28.5, and mode = 30 31. a. no b. no c. yes 32. m < 3 33. x 60 34. x 3 35. 36. Both sides of the first inequality must be multiplied by 6 to get the second. 37. x < 14
38. 5 < x < 5 39. 0 x < 20 40. x 7 or x > 5 41. r = 7 or r = 21 42. Sample answer: x 9 2 43. x 2 or x > 1 44. 1.5 45. 42 46. 40 47. 1 x 7 cm 5 48. 25% 49. 336 50. 60 51. 60 members 52. $3240 53. 7 years 54. 23%, increase 55. 22% 56. Answer may vary A speed is about to slow for some time, as if skating uphill B gaining speed quickly, as if beginning a downhill descent
C high speed briefly, as if just skating down a hill D constant speed for some time, as if skating on an even surface 57. 4 1 2 domain :,, 5 8 7 1 7 range :,,1,5 3 8 58. the relation is not a function 59. Function 60. It is a function 61. The relation is not a function 62. 23 63. { 2, 0, 4, 10, 18} 64.
65. 66. a. f(p) = 0.08s + 250 67. b. $374.48 1 yes,: k 2 68. Add 4 to the previous term; 25, 29 69. Geometric; common ratio = 3 70. 5.4, 4.8, 11.6 71. A(n) = 3( 4) n 1 72. 73. 10 100, the balloon ascends 100 ft/sec 3 74. Undefined 75. 0 76. a. True, the slope of any vertical line is undefined 77. b. False, the slope of y = x passes through Quadrant IV and it has a negative slope c. False, unless the line is y = 0, it will pass above or below the origin 3 m and b 9 4 78. y = 2x + 5
79. 80. no 81. x-intercept:8 y-intercept: 4 82. 83. a. horizontal b. vertical 84. 4x 3y = 8
2 86. Point-Slope Form: y 4 ( x 2) or 3 87. 3 Slope-Intercept Form: Standard Form: 2x + 3y = 8 88. parallel; the slopes are equal 89. 90. 3 y x 2 4 3 91. Neither 2 8 y x 3 3 2 y 6 ( x 5) 3 92. a. False, for two lines to be perpendicular one slope must be the opposite reciprocal of the other. Therefore, one line must have a positive slope. b. False, two lines are perpendicular if the product of their slopes is 1.