For questions 1-3 you may draw a diagram, create a table, explain how you would guess and check, but DO NOT USE ANY ALGEBRA.
1. Michelle had some pennies, nickels, dimes and quarters in his pocket. When he reached in and pulled out some change, he had less than 10 coins whose value was 42 cents. What are ALL the possibilities for the coins he had in his pocket?
2. Andrea, Tyler and Heinz played 3 rounds of a game. On each round there are 2 winners and 1 loser. The person who loses on a round has to double the number of chips that each of the other players has by giving up some of his chips. Each person loses one round. At the end of 3 rounds, each person has 64 chips. How many did each person have at the beginning of the game?
3. Jin recently surveyed 75 people about which reality TV programs they watch. The results are as follows: 45 people watch Survivor, 40 watch Big Brother, and 38 watch The Bachelor. 18 watch Survivor and Big Brother, 21 watch Big Brother and the Bachelor and 22 watch Survivor and the Bachelor. She also found that 10 watch all three. How many people surveyed did not watch any of the three shows?
4. Consider the pattern of tile pieces having the following first three figures:
(Be sure to explain your reasoning or show your work in parts b and c.)
a) Sketch the 4th figure in this pattern (next to the 3rd figure).
b) How many tile pieces will be in the 50th figure?
c) Which figure (if any) will have exactly 303 tile pieces?
5. List the next three terms that complete a possible pattern in each of the following:
a. 5, 12, 19, 26, ______, ______, ______ b. 2, 18, 162, 1458, _______, _______, _______
What is the nth term in the sequences above?
6, Jorge discovered that the second number in a geometric sequence is 28, and the sixth number is 7,168. What is the first number in the sequence? Explain how you arrived at your answer.
7. The 20th and 22ndt Fibonacci numbers are 6,765 and 17,711. What is the 21st Fibonacci number?
For the remainder of the application problems, use whatever method you like---diagrams, guess and check, algebra, etc.
8. Abby has recently become interested in developing her own pictures. In the first class that she took, she found that the film developer solution is to be kept between 18 and 25 degree Celcius. What is this range in degrees Fahrenheit if the conversion formula is C = 5/9(F-32)?
9. Julie was working in her yard this weekend. She was trying to rake some pine needles up that the wind blew down a few weeks ago. It would take her 5 hours if she was working by herself, but her nephew came over to help. If they were able to finish raking up the pine needles in two, how long would it have taken her nephew to finish the job by himself?
10. When Derrick rented a boat to cruise on the Sandy River, he was told that the boat takes 1.5 times as long to go 360 miles up a river than to return. If the boat cruises at 15 miles per hour in still water, what is the rate of the current?
11. Rosa found that the total cost C for a product is expressed by C = 250x^2- 24,000, and the total revenue R at a price of $200 per unit to be R = 200x - 1,000, where x is the number of units sold. What is the break-even point (where total cost = total revenue) to the nearest unit?
GRAPH the following and comment what the results of the graph show about the algebraic relationship. Please attach your GRAPH PAPER to the exam.
12. Michelle learned in Science 110 that the top number of a person's normal blood pressure increases with age, and is approximated by the equation, y = ½ (x) + 110, where x is a person's age. Construct the graph for this equation for 20 ≤ x ≤ 45. What should that number be for someone who is 35 years old?
13. If Tyler invested $375 at an annual rate of 4.5% compounded continuously, what amount to the nearest cent will be in his account after 2 years? The formula for interest compounded continuously is: A = Pe^rt, where P is principle invested at an annual rate r and grows to the amount A in t years. Graph the amount in his account over the first 8 years. (4.5% = .045).