Class: Date: Final Exam review Course II Short Answer 1. Mrs. Richland planted 12 tulip bulbs in her garden. All 12 bulbs bloomed the first year. The second year, 15 tulip blooms appeared, and the third year, 18 tulips grew. If the tulip blooms continue to increase at the same rate each year, after how many years will it take for Mrs. Richland to grow 39 tulips in her garden? 2. Caroline has 9 coins in her pocket that total $1.92. What are the coins? 3. Decide if the following statement is true, sometimes true, or false. Then give 2 examples. When a positive integer is divided by a negative integer, the quotient is a negative integer. Write each ratio as a fraction in simplest form. 4. Bob bought candy at the candy store. Of the candy he bought, 2 9 was gummy bears, and 4 was bubble gum. 9 What portion of the candy was gummy bears and bubble gum? 5. On a math test, 60% of the students used a pencil. Half of the remaining students used a red pen. If 6 students used a red pen, how many students are in the class? Write an equation, and then solve it. 6. Samantha is in a book club. She has read 7 books this month. Her book club requires her to read 4 books in one month. How many more books did she read than what she was required? 7. Ella recorded the time she practiced piano each day last week. If she practiced 4 of her weekly goal, what 5 was her goal? Write and solve an equation to answer the question. Day Time (hrs.) Monday 1 2 Tuesday 1 1 2 Thursday 3 4 Friday 2 Saturday 1 1 4 1
Find each unit rate. Round to the nearest tenth if necessary. 8. 159 miles in 6.5 gallons A real world measurement is given. Find the length of a model with the following scale. 9. a backyard fence 80 feet long; 1 inch = 10 feet 10. Use the two similar triangles to find the height of the tree. 11. On Monday, Chris has 60 e-mails in his inbox. He receives the same number of e-mails each day and deletes no e-mails. By Wednesday, he has 72 e-mails. By Friday, he has 84 e-mails. By Sunday, he has 96 e-mails. What is the rate of change in e-mails per day? Select the appropriate operation(s) to solve the problem. Justify your selection(s), and solve the problem. 12. Joanna purchased a car, paid for a full year of auto insurance, and filled the tank with gasoline. The total of her purchases was $28,745. The auto insurance cost $1,776, and the tank of gas cost $39.00. What was the cost of Joanna s car? 13. Make a scatter plot of the data. Determine the relationship between the week and the number of miles driven. Week 1 2 3 4 5 6 7 8 Miles Driven 47 56 23 95 76 11 114 78 14. Determine the constant variation from the below table which represents the amount of water and chlorine in a pool. Amount of water (gallons) 5,000 7,500 10,000 Chlorine (pounds) 10 15 20 2
15. Determine the constant of variation from the below table which represents the relationship between the number of quarts of milk and the number of cups they provide. Quarts of milk 1 2 3 4 Cups of milk 4 8 12 16 Find each number. Round to the nearest tenth if necessary. 16. What is 34% of 100? 17. What is the difference between 0.3% of 20 and 30% of 20? Hint: 30% = 0.3 18. In Mariemont, 45.8% of the residents attended the annual fall festival at least 1 of the 3 days, 18.9% of the residents attended at least 2 of the 3 days, and 11.4% attended all 3 days that it was held. Out of 4,290 residents, how many were unable to attend the annual fall festival? 19. During a walk-a-thon for a school fundraiser, 40% of the money raised will go toward a new gym. Each mile a student walked earned $0.75. The student body walked a total of 4,291 miles. How much money was raised for the gym? Find the total cost to the nearest cent. 20. $69.95 remote control car; 7% sales tax 21. Ralph earns $2,100 cutting lawns during the summer. Ralph invests his earnings for 18 months and earns $189. What was the rate of interest? 22. Ralph earns $2,100 cutting lawns during the summer. If he invests his money at 4% interest, in how many years will Ralph have $2,478? 23. Ralph earns $2,100 cutting lawns during the summer. Suppose Ralph spends $300 and invests the remaining $1,800 for 2 years at a rate of 4.4%. How much will he have after 2 years in the account? 24. When Bella was born, her grandparents put $5,000 into a college fund account that earned 6.75% simple interest. Find the total amount in the account after 5 years. For each situation, make a tree diagram or table to show the sample space. Then give the total number of outcomes. 25. choosing a silver, black, or red CD player and choosing a rock, country, or rap CD 26. Benjamin has to wear a uniform to school. His uniform is made up of tan or blue pants and a blue or white collared shirt. Benjamin has 2 pair of blue pants, 2 pair of tan pants, 3 white shirts, and 2 blue shirts. How many combinations can be made with the clothes Benjamin has to choose from? What is the probability that he will wear his favorite combination, tan pants and a white shirt? 3
Use the Fundamental Counting Principle to find the total number of outcomes in each situation. 27. picking a day of the week and a date in the month of April 28. choosing a password that consists of one letter and two numbers from 1 to 9 (Note: the digits can be repeated.) 29. Candace bought a $95 cell phone on sale for $72.50. What was the approximate percent of decrease from the original price to the sale price? Round to the nearest percent. For the following exercises, use the chart below. It shows the percent of students who prefer each season. Season Percent Winter 5% Spring 10% Summer 70% Autumn 15% 30. Walter Middle School has 973 students. Predict how many students prefer summer. 31. As a class assignment, you are to conduct a survey of students in the eighth grade to determine the number of students who spend more than one hour on homework each night. Describe an unbiased way to conduct the survey. Describe each sample. 32. A supermarket surveys every 30th customer about their choice of soft drink. 33. A company sells two different containers for shipping. One container is a box, and one container is a cylinder. Which container has the greater volume? Round your answer to the nearest tenth. 34. A rectangular prism has a base area of 22.3 square yards and a volume of 350.11 cubic yards. Write an equation that can be used to find the height (h) of the prism. What is the height of the prism? 4
35. The diagram shows the dimensions of the school gymnasium. It costs about $0.05 per year to heat one cubic yard of space. On average, how much does it cost to heat the gymnasium for one month? 36. Find the missing measure in each triangle. Then classify the triangle as acute, right, or obtuse. 37. Classify each triangle by its angles and by its sides. 5
38. Herb, Donna, and Jane placed first, second, and third at the school geography bee although not necessarily in that order. Herb and the third place winner ate lunch with Jane yesterday. Herb did not place first. Who placed first? Explain. 39. Classify this quadrilateral and find the value of x. 40. Yoshi has a garden in the shape of a quadrilateral with four congruent sides and four right angles. If the perimeter of the garden is 100 yards, what is the length of each side? Justify your answer. 41. The formula, d = 1.5h, can be used to approximate the distance d in miles to the horizon when h is the height of the eyes from the ground in feet. Use the formula to find the distance that can be seen from the Eiffel Tower, which is about 986 feet high. 42. Estimate the perimeter of the rectangular plot, the length of which is 3.2 m and the width of which is 6.9 m, to the nearest whole number. 43. Estimate 59 to the nearest whole number. Use the diagram of the slide and the Pythagorean Theorem to solve the problems. 44. Johan goes down the slide at a rate of 2 feet per second. How long will it take him to reach the bottom of the slide? Round to the nearest tenth. 45. How long is the slide in inches. Round to the nearest tenth. 46. The Taylor Mill Train can transport passengers from downtown to the station and vice versa. The train can accommodate 1,980 passengers per hour. If the train has 5 cars and each car carries 18 passengers, how many runs are made in one hour? Hint: A run is considered going from one location to another, not round trip. 6
47. A burger stand has 85 medium size burgers to sell each day. On average, 15 medium burgers are sold each hour. The total number of medium burgers that are left to sell for the day can be represented by y = 85 15x, where x is the number of hours since opening. Determine the slopes and y-intercepts of the line. Graph the equation. 48. Make a graph showing the length of one side of a square as a function of its perimeter. Explain whether the function is linear. 49. The table below shows the number of students who rode the school bus in the last five days. Determine whether the data is linear or non-linear. Weekday Number of students Monday 45 Tuesday 40 Wednesday 35 Thursday 30 Friday 25 Evaluate the expressions. Express answers in simplest form. 50. v 3 w 5, if v = 1 and w = 3. 2 7