Honors Midterm Study Guide

Transcription

1 Name Date Unit 1: Rational Numbers (No Calculator) Honors Midterm Study Guide Classify each number below. Use a check to indicate if a number is part of a given category. Leave the space blank if it does not belong that category 1. Natural Number Whole Number Integer Rational Number Irrational Number Real Number Imaginary Number Simplify each expression ( ) ( 4 9 ) (-3.5)

2 Simplify each expression below (6 + 3x) (9x - 15) x 4 x x x 13. x(4x + 5) + 7x x + 2x 2 Unit 2: Equations and Inequalities (No Calculator) 14. 8m m 34 = x+2 8 = (25 15x) + 16 = (r 5) = n 2 = 3n x = 1 x 20. 5(x + 12) = 2x x 21. 2(2x + 2) = 4(x + 1) 22. x(x + 4) = 4x + 9

3 For each word problem, define x and write an equation to express the situation. Then solve the equation. 23. Mrs. Smith is making cupcakes for the class for Ruby s birthday. She already has 8 cupcakes, but needs to make a total of 32 cupcakes. If each batch makes 6 cupcakes, write and solve an equation to determine how many more batches of muffins Mrs. Smith needs to make. 24. To become a member at Planet Fitness, you have to pay a one-time membership fee of $39 and an additional $12 per month. To become a member at Commitment Fitness, there is no initial membership fee but a monthly payment of $25 per month. After how many months would the cost of both gyms be the same? 25. Find the value of x if both shapes have the same perimeter. *You do not need to write a let statement. 4x + 1 4x + 1 4x 3x - 4 4x 4x 6x - 4

4 Solve and graph each inequality 26. 6(n+10) x (6n + 7) x + 18 < 4x (2x 1) > x 31. 3(1 2x) > 3 6x (5 + 6n) < 6( 8 2n) 33. 7v 5 65 or -3v < 3p 6 < -15 For each word problem, define x and write an inequality to express the situation. Then solve the inequality. 35. Jessica wants to get at overall test average of at least an 85 in her social studies class. If her tests scores are currently 81, 87, and 78, what must she get on her last marking period test to achieve her goal?

5 36. Your sister and her friends rent a limo for prom. The limo cost $700 for the night and $0.15 per mile. Your sister and her friends have at most $750 to spend. Write and solve an inequality to determine how many miles the limo can travel. 37. The perimeter of the rectangle is at least 20 inches. The area is no more than 40 inches. Write and solve an inequality for each condition. Give two possible values for x. 5 in x + 1 in Unit 3: Ratios and Proportions (Calculator Allowed) Write each ratio in simplest form th grade girls to 8 th grade girls 39. Total 6 th graders to total 7 th graders MJS Students 6 th Grade 7 th Grade 8 th Grade Girls Boys Bethany is making Shirley temples by mixing grenadine and sprite. She likes the flavor that comes from mixing 1 cup of grenadine and 1 4 cup of sprite. If Bethany wants to 8 5 make 7 cups of Shirley temples for a dinner party, how much of each ingredient should she use?

6 Find the unit rate. 41. Peter grew 4 1 inches in 3 31 months. How 2 much did peter grow in 1 month? 42. $3.92 for 8 juice boxes 43. What is the unit rate, (1, r) for the Florida Turnpike graph? Solve each proportion to find the value of x = x x = Write and solve a proportion for each problem below. Be sure to label your units. 46. Nina made 12 copies at Staples for $0.66. At this rate, how much will it cost Nina to make 56 copies? 47. An amusement park line is moving about 4 feet every 15 minutes. At this rate, approximately how long will it take for a person at the back of the 50-foot line to reach the front of the line? (Round your answer to the nearest minute.) 48. People magazine is offering two different subscriptions, an 18-issue subscription for $40.50 or a 12-issue subscription for $ Which is the better deal?

7 49. For every person who actually has the flu, there are 6 people who have only have the symptoms, but really only have a cold. If a doctor sees 42 people, how many of them can you except to have just a cold? For each of the following word problems or figures, determine the length of the missing side. 50. A photogram measuring four inches wide and five inches long is enlarged to make a wall mural. If the mural is 120 inches wide, how long is the mural? 51. A six-foot-tall person is standing next to a flagpole. The person is casting a shadow feet in length, while the flagpole is casting a shadow 5 feet in length. How tall is the flagpole? L Z 52. Triangle LMN is similar to triangle XYZ. What is the length of YX? Y 8 feet X 24 feet 18 feet N 12 ft M Solve for x and y in the similar figures below. 53.

8 Unit 4: Linear Equations (Calculators Allowed) Determine if each of the following show direct variation. Explain how you know. If so, determine the constant of proportionality. 54. x + y = y = x 56. x y Determine the slope of a line given the coordinates, a graph, or a table. 58. (-5, -4) and (1, -3) 59.

9 The graph shows the cost of traveling by car on the Florida Turnpike. a. Fine the slope of the line. b. Explain the meaning of the slope as a rate of change. 62. The graph shows the amount of money you and a friend are saving for a camping trip. a. Compare the steepness of the lines. What does this mean in the context of the problem? b. Find the slope of each line. c. How much more money does your friend save each week than you? d. The camping trip costs $165. How long will it take you to save enough money?

10 Graph the linear equations: 63. y = 2x x + 6y = 12 Write the equation of the line for the following; 65. A line that passes through (4, 5) and has a slope of A line that passes through (2, -4) and (5, 2). 67. Write the equation of a line that passes through point (3, -3) and is parallel to the line which passes through (1, -2) and (4, 6). 68. Write the equation of a line that passes through (-4, 5) and is perpendicular to the line whose equation is y = 2x + 5.

11 Unit 5: Percents (Calculators Allowed) Whenever necessary, round your answer to the nearest hundredth. 69. What percent of 56 is 12? is 65% of what number? 71. The temperature at noon was 22. The temperature decreased by 40% over the next two hours. What was the temperature at 2:00? 72. Amanda has $242 in her bank account. After going shopping for her brother s birthday present, Amanda only has $205 in her bank account. Find the percent change for this situation. 73. Channel 2 News predicted that we could expect 8 of snow on Monday. When the storm came, it only brought 5 of snow. Find the percent error in this situation? 74. Macy s buys a jacket from a manufacturer for $ They then markup the price by 125% before selling it to the customer. If a customer has a 10% off coupon, how much will they pay for the jacket?

12 75. Chet goes out to lunch with a friend and their bill comes to $ They have to pay 7% sales tax in addition to leaving an 18% on the pre-tax bill. Find the total cost of the bill. 76. Rich is shopping for a new snowboard at Ski Barn. After using a 15% off coupon, the board comes to $ Find the original price of the snowboard. 77. You deposit $650 in a savings account that earns 0.4% simple interest per year. If you leave the money in the account for 6 years, how much interest will you have earned? What will be the balance on the account? 78. You deposit money into a savings account which earns 0.6% simple interest per year. After 9 months, the account has earned $5.63. Find the amount of the initial deposit. 79. Cooper is buying a new pair of jeans. The jeans cost $ Luckily, Cooper has a 15% off coupon. In addition, Cooper has to pay 7% sales tax. Find the total cost of the jeans.