MATH 1007 UMASS Mathematics Practice Exam


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Weekly summary – week of 1/19-21
• What you should understand
– Math is about making up rules that fit our perception, then having fun with those
rules (but never breaking them)
– We want to focus on explaining our reasoning rather than getting to the “right
answer” (if there even is one)
– Probability is counterintuitive
• What you should be able to do
– Compute a probability as the ratio of the positive outcomes over all possible outcomes
– Reason your way through some simple puzzles
• Fun things to read/watch/play with
– Numberphile – Alcuin Numbers
– Numberphile – The Monty Hall problem
– Stand Up Maths – The Mathematics of Winning Monopoly
– Numberphile – The Shortest Math Papers
Quiz 01. You can take this however you like, but I recommend taking it alone and giving
yourself about 20-30 minutes, as though this were a test. Upload your answers to Gradescope
by 11:59 PM on Monday 1/24.
1. [4 points] You and a friend go to a restaurant to celebrate the start of the semester. As
you order, you are shocked to realize that the items your friend ordered cost exactly twice as
much as what you chose! The itemized bill is the following:
• Virgin Piña colada: 12$
• Garden Salad: 14$
• French Onion Soup: 16$
• Cup of tea: 8$
• Turkey Club: 13$
• Fish and Chips: 17$
• Steak and Fries: 25$
Assuming you did not split any of the items with your friend, what did you order and how much
did you spend? Fully justify your reasoning to get full credit; just saying what you ordered will
get you little partial credit.
2. [4 points] You need to replace the oil in your car, which requires you to pour in exactly 8
oz of oil; too much and you’ll make a mess, too little and the car will break. You find a large
container of oil, but only a 6 oz and a 10 oz measuring cups, but without the intermediate
markings, so you cannot estimate how much liquid is in the container unless it’s full. Describe
how you can obtain exactly 8 oz of oil using the two cups; assume you are able to transfer oil
from one cup to another or back to the container without any spillage or leftovers.
3. [1 point] Watch the short cartoon “Donald in MathMagic Land” found at https://youtu.
be/U_ZHsk0-eF0. In a couple of sentences, describe what part of it you found most interesting/fascinating.
4.[1 point] Go watch (or re-watch) the explanation on how worksheets and participation work
at the following link:
Do you have any questions about the syllabus or the class? Respond “None” if you don’t have

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Explanation & Answer:
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