MATH-125

Math 125 - The Math Workshop American University

February 2023

Name:

Exam 1

• Please show all of your work, and justify your answers completely.

• You may use a calculator. You may also use a laptop, but only for a spreadsheet like Excel or an approved calculator like Desmos.

• You will be given 75 minutes to complete the exam.

• There are 7 pages to this exam including the cover.

• Correct answers with no justification may not receive credit.

• All work that you submit, must be your own and you are not allowed to communicate with other people or use the internet, except as noted above.

• This is considered a 100 point test, even though you can earn up to 108 points and have any points over 100 applied to your test average.

Good luck!

Problem Max Points Points Earned

1a 8

1b 8

1c 8

2a 8

2b 8

3 8

4 8

5 8

6 8

7 8

8 8

free points 20 20

1. You and two friends are obsessed with Japan and decide to take a trip to Tokyo. The exchange rate when you take your trip is 1 US Dollar = 138 Japanese Yen.

(a) (8 points) There is a service fee of 500U on all credit card transactions. What is the service fee when converted to dollars? Round to the nearest penny!

(b) (8 points) Your favorite Tombow pen is on sale at Takashimaya in Tokyo for 1000U. You notice that, if you include the service fee, it costs exactly the same (to the nearest penny) to buy 3 Tombow pens at Takashimaya as it does to buy them at JetPens in the the US (ignoring tax and shipping). What does JetPens charge for the pen (in US dollars to the nearest penny)?

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(c) (8 points) You buy 100 Tombow pens and sell them on eBay in the US for $20 apiece. If eBay charges a 15% commission fee on the total amount of the sale, how much of a profit do you make? (Ignore tax and shipping. Your answer should be to the nearest penny.)

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2. On the plane from DC to Tokyo, you listen to a playlist of your favorite J-Pop and K-Pop songs. You have 23 J-Pop songs and 21 K-Pop songs on the playlist and they are played in a random order with no repeats.

(a) (8 points) How many songs must be played before you are guaranteed to hear at least 2 from the same genre?

(b) (8 points) How many songs must be played before you are guaranteed to hear 2 in a row from the same genre?

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3. (8 points) On the plane, you decide to purchase your food and drink using a 5% off coupon from Japan Airlines. A 6% sales tax is applied to this reduced price. But then you charge everything on your Quicksilver VISA card which gives 2% off all charges. (The 2% reduction is after the coupon and the sales tax.) You end up paying $23.68. To the nearest penny, what was the original price of all your purchases?

4. (8 Points) After eating your food, you read an article about the prime minister of Japan, Fu- mio Kishida. The article is titled “Japan PM’s approval rating sinks to record-low 35%” and it mentions the following three data points:

Month May 2022 November 2022 December 2022

Approval rating 66% 37% 35%

Is the decline in percentage approval decreasing linearly, exponentially or neither? (Explain precisely! You won’t get partial credit for a vague explanation.)

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5. (8 Points) When you arrive at the Rihga Royal Hotel in Tokyo, a wedding with 100 guests is underway. Each guest clinks their champagne glass with every other guest exactly once, and each guest shakes hands with 12 other guests. How many clinks are there, and how many handshakes? (Explain your answer thoroughly.)

6. (8 Points) The population of Japan in 2021 was 125.7 million, but it decreased by 0.5% in 2022. If it continues to decrease at this rate, what will the population be in 2050?

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7. (8 points) While in Japan, you contract a new variant of COVID called the Zombie variant. Each person with the Zombie variant infects exactly one person a day for 30 days. (Assume that the same person is never infected twice.) When a person gets the Zombie variant, they always test positive for COVID exactly two days after being exposed to the virus, and they continue to test positive for 30 days. When a person tests positive for the Zombie variant on a given day then always they infect exactly one person on that day. How many people who were infected by you (or by people you infected) test positive on Day 5?

8. (8 Points) What is the most important thing you have learned about problem-solving so far in this course? (I’ll give you full credit, as long as you write something reasonable!)

End of Exam.

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