Questions 1 & 2 are worth 4 points each.
 The relationship between the distance of an object (do) and its image (di) from a curved mirror, and the focal length of the mirror is given by the equation:
1/f = 1/do + 1/di
What is the focal length f of a mirror for which do = 25 cm and di = 5 cm?
- Simplify:
Questions 3- 7 are worth 6 points each.
- Solve for y in terms of a, b, x and z.
- Solve for x in terms of y. (x + y)
 - (x - y) = x + y
- A student has test scores of 87, 89, 84, and 95. What score does the student need on the next test to produce an average of 80?
- The price of a magazine subscription rose 4% this year. If the subscription now costs $26, how much did it cost last year?
- A jar contains 47 coins. Some are pennies and the rest are dimes. The total value of the coins is $2.18. How many pennies are there? How many dimes are there?
Questions 8-13 are worth 8 points each.
- Jeff leaves his house on his bicycle at 8:30 A.M. and averages 5 miles per hour. His wife, Joan, leaves at 9:00 A.M. following the same path and averaging 8 miles per hour. At what time will Joan catch up with Jeff?
- The relationship between the Fahrenheit temperature (F) and the Celsius temperature (C) is given by the formula F = (9/5)C + 32. At what temperature will a Fahrenheit thermometer and a Celsius thermometer read the same?
- The Lemonade Stand
At a lemonade stand, if 10 glasses of lemonade are sold, then $1.60 profit is earned. If 13 glasses are sold, then $2.80 profit is earned. Assume the relationship between the number of glasses sold and the profit earned is linear. How much profit would be earned if 20 glasses were sold?
- The Bicycle Shop
A bicycle shop owner has learned that the relationship between the price of one bicycle and the total profit earned from bicycles sold can be represented by the function f (x) = - x + 200x - 3000 where x is the price of one bicycle (in dollars). At what price should the bicycles be set in order to achieve maximum total profit? If this is done, how much profit will be earned?
- The Missing Dollar
Three men agreed to split the cost for a room at a hotel. The hotel manager was not available, so the bellboy attended the counter, charged the men $30, and showed them to their room. When the manager returned, he said, “You overcharged them. That room is only $25.” The manager handed the bellboy five one-dollar bills to return to the men. On his way to the room the bellboy reasoned, “How can three men split five one-dollar bills?” So he decided to give each man one dollar and keep two for himself.
We started with $30.
The three men each paid nine dollars or a total of $27.
$27 plus the two dollars that the bellboy has, equals $29.
Where is the missing dollar?
- Domino Checkers
A certain checkerboard is missing opposite corner squares. Is it possible to cover this checkerboard with dominoes? Each domino must cover two adjacent squares (not diagonal). If it can be done, show how. If not, explain why not.
- The Perfect Shuffle
Max the Magician has an interesting card trick. He takes an ordinary deck of 52 cards and shuffles it several times. Then he "predicts" the order from top to bottom of all 52 cards. After this he reveals the cards one at a time and his prediction is correct. How does he do it?
Let's assume that Max sets up the cards in the same order as his prediction before he begins the trick. Also assume that Max has the ability to give the cards a perfect shuffle. (Cards are separated into two equal piles and are combined into one pile in alternating fashion.)
- Call the top of a deck position 1 and the bottom of a deck position 52. Figure out where a card from each position will move to after one perfect shuffle. Create a formula that will determine where a card in position x will end up after one perfect shuffle.
- How many perfect shuffles does it take to unshuffle the cards and bring them back to their original order? Show work. (14 points)
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