Honors Algebra Midterm Study Guide

Transcription

1 Honors Algebra Midterm Study Guide Short Answer What is an algebraic expression for the word phrase? 1. the sum of n and the quotient of d and times the sum of g and f 4. the quotient of 9 and the difference of d and c What word phrase can you use to represent the algebraic expression? 5. 9x + 5 What is the simplified form of each expression? Evaluate, for u = 12, x = 5, y = 3, and z = 6. What property is illustrated by each statement? x = x 10. What is each difference? What is each product? 13. What is the simplified form of each expression?

2 What is the simplified form of each expression? 16. (4 c)( 1) 17. What sum or difference is equivalent to the expression? What is the simplified form of each expression? 20. What is the solution of each equation? Use mental math. 21. x + 9 = 28? = d x = Steven wants to buy a $520 bicycle. Steven has no money saved, but will be able to deposit $40 into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $80 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike? x + 4 6x = 6

3 Angela and Neil are going to the movies. They each bought a medium popcorn, and Neil got a small soft drink. Angela had a $10 gift certificate to put toward the cost, and Neil paid the rest, which came to $ A movie ticket costs $8.00 and a medium popcorn costs $5.30. How much does a soft drink cost at the theater? 30. 2(y 2) = x 3.2 = x 9 = 4x x + 2 = 7 5x 35. A camera manufacturer spends $1500 each day for overhead expenses plus $8 per camera for labor and materials. The cameras sell for $14 each. How many cameras must the company sell in one day to equal its daily costs? If the manufacturer can increase production by 50 cameras per day, what would their daily profit be? 36. A copy center offers its customers two different pricing plans for black and white photocopies of 8.5 in. by 11 in. pages. Customers can either pay $0.08 per page or pay $7.50 for a discount card that lowers the cost to $0.05 per page. Write and solve an equation to find the number of photocopies for which the cost of each plan is the same What equation do you get when you solve for x? 40. At an automobile factory, 1136 parts are made in 4 hours. What is the average rate at which parts are made per hour? 41. A flock of Canadian geese migrated 819 miles in 30 days. What was the average rate at which these geese traveled in miles per day? 42. The total cost to rent a row boat is $18 times the number of hours the boat is used. How long can you rent the boat for $558?

4 43. You are shopping for jeans. City Express sells 3 pairs of jeans for $55. Denim Planet sells 2 pairs of jeans for $73. New Threads sells 4 pairs of jeans for $112. Which store has the best deal? 44. Lenny runs a 250-meter course in 45.5 seconds. Gary runs a 350-meter course in 63.6 seconds. Bruford runs a 950-meter course in seconds. Which athlete is the fastest? Round each speed to one decimal place. What is the given amount converted to the given units? cm; meters ft; inches 47. An office building is 131 ft high. About how tall is this in meters? 48. On a certain day 1 US dollar is equivalent in value to 90 Japanese yen. Lucy is going on a trip to Japan. She has $1000 to spend. How many yen is this? 49. A pool is filled at a rate of 75 gal/min. What is the rate in ml per second? 50. In the diagram, the figures are similar. What is x? 10 ft x 8 ft Drawing not to scale 1 ft 51. A tree casts a shadow 10 ft long. A boy standing next to the tree casts a shadow 2.5 ft. long. The triangle shown for the tree and its shadow is similar to the triangle shown for the boy and his shadow. If the boy is 5 ft. tall, how tall is the tree?

5 Drawing not to scale Use the scale and map measurements to find the actual distance from New Wilmington to Sharon through the specified town in. Sharon New Wilmington 1.5 in. Mercer 2.25 in. 1.5 in. Volant Scale 1 in. : 12 mi 52. What is the actual distance from New Wilmington to Sharon through Mercer? 53. A map has a scale of 1 cm : 19 km. Two cities are 5.9 cm apart on the map. To the nearest tenth of a kilometer, what is the actual distance corresponding to the map distance? 54. What percent of 71 is 42.6? 55. A dress that normally costs $ is on sale for 65% off. What is the sale price of the dress? 56. Glen is looking into buying a piece of land. He estimates that the land measures 650 yd by 1150 yd. The land is actually 670 yd by 1090 yd. What is the percent error in the estimated area of the land? What inequality represents the verbal expression? 57. all real numbers less than 1 What inequality represents the graph? What inequality describes the situation? 60. Let t = the amount Thomas earned. Thomas earned $54 or more. What are the solutions of the inequality? Graph the solutions.

6 What are the solutions of the inequality? Graph the solutions Your class hopes to collect at least 375 cans of food for the annual food drive. There were 134 cans donated the first week and 100 more the second week. Write an inequality that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass your goal. How many cans are needed to meet or surpass your goal? What are the solutions of the inequality? 65. 7(w 11) > 7 What are the solutions of the inequality? What are the solutions of the inequality? Graph the solution. 68. The ideal width of a safety belt strap for a certain automobile is 7 cm. The actual width can vary by at most 0.45 cm. Write an absolute value inequality for the range of acceptable widths and solve the inequality. 69. The bulk food section of a grocery store has two bins with different types of mixed nuts. The first bin contains walnuts, peanuts, and pistachios. The second bin contains pecans, almonds, Brazil nuts, and walnuts. What is a set that represents all the types of nuts in both bins? 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}. 70. What is? 71. What is? 72. What are the solutions of? Write the solutions as either the union or the intersection of two sets. Write a function for the situation. Is the graph continuous or discrete? 73. A movie store sells DVDs for $17 each. What is the cost, C, of n DVDs?

7 What is the graph of each function rule? Describe a pattern in each sequence. What are the next two terms of each sequence? 76. 8, 12, 16, 20, , 4, 8, 16,... Tell whether the sequence is arithmetic. If it is, what is the common difference? 78. 3, 11, 19, 27, , 7.7, 11.4, 15.1, , 1 1 2, 1, 1 2, Is the equation true, false, or open? Explain. 82. You received a $24.00 credit for a website that sells movie and music files. A movie costs $4.80 to download and a song costs $1.20. The equation, where m is the number of movies and s is the number of songs, models the situation. How many songs can you download if you download four movies? How do you write the set in roster form? In set builder notation? 83. G is the set of odd natural numbers that are less than or equal to 15. What compound inequality represents the phrase? Graph the solutions. 84. all real numbers at least 8 and at most Alexandria wants to go hiking on Saturday. She will consider these conditions when she chooses which of several parks to visit: She wants to hike for 2 hours. She wants to spend no more than 7 hours away from home. She can drive an average speed of 60 miles per hour to and from any park. Write and solve an inequality to find possible distances from Alexandria s home to a park that satisfies the conditions.

8 number of handbags distance What are the variables in each graph? Describe how the variables are related at various points on the graph. 86. 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. Lena's Deliveries time 87. The graph shows the number of handbags that Mandy made in one day. What are the variables? Describe how the variables are related at various points on the graph. Mandy's Handbags time 88. Elaine has a business repairing home computers. She charges a base fee of $45 for each visit and $35 per hour for her labor. The total cost C for a home visit and x hours of labor is modeled by the function rule. Use the function rule to make a table of values and a graph. x 0 C 1 2

9 3 C x Use the vertical line test to determine whether the relation is a function y x The function represents the number of guitar lessons, g(t), you can complete in t months. How many guitar lessons can you complete in 6 months? 91. The table shows the relationship between the number of red triangles and the total number of square tiles in each figure. Complete the table and extend the pattern. What is the total number of red triangles in a figure with 14 square tiles?

10 Number of square tiles (s) Number of red triangles (t) Justify each step. 92.