Applications of Mathematics
Name at least five academic disciplines that involve the application of mathematics.
There are many. Here are some common examples:
Physics, Chemistry, Computer Science, Engineering, Biology, Economics, etc.
Write the number 40 using roman numerals.
XL
(No calculator allowed)
When taking a 30 multiple choice test on trigonometry, you notice that you’re running low on time. You're about to start question 12 on the test and you have 30 minutes remaining. You start panicking and decide to calculate how many minutes you can spend on each question. In your calculations, you take account of time wasting tasks:
Making unnecessary calculations - 2 minutes
Putting your answers on the bubble sheet - 3 minutes
Writing down your name/drawing on the back - 5 minutes
Taking these facts into account, how much time should you spend per question in order to finish the test on time?
\(\frac{20}{19}\) minutes/question or 1.05 minutes/question
When writing down numbers 1 through 1000 (ex. 32 \(\rightarrow\) Thirty Two) how many numbers contain the letter ‘a’ in their spelling?
1 number (1000 \(\rightarrow\) One Thousand)
(No calculator allowed)
The tire of a kids toy tricycle has 16 spokes that are distributed evenly throughout the tire. In addition, the circumference of the tire is 0.314 m. Using the information given, calculate the area in between two spokes that are next to each other. (Round \(\pi\) to 3.14). Round your answer to 4 decimal placements.
0.0005 m2
There is a bookstore in Logicland that has some very interesting books. Some of these books are reference books that list lots of books related to a topic. For example, a reference book about brainrot memes lists many books about brainrot memes. Some reference books list themselves. For example, a reference book listing all books would list itself. Suppose there is a reference book that lists all reference books that do not list themselves. Does this reference book list itself? Explain your answer.
This is a paradox.
The reference book lists itself if and only if it does not list itself. (contradiction)
On Monday, Ronald McDonald travelled \(x\) km at a constant speed of 90 km/h. On Tuesday, he travelled on the same route at a constant speed of 120 km/h. His trip on Tuesday took 16 minutes less than his trip on Monday. The value of \(x\) is...
96
Trig!
(No calculator allowed)
Legend says that a full moon causes the magical and mysterious mathematician to turn into a matherewolf (mathematician werewolf). Some townspeople call these wolves \(\Sigma\) wolves because of their amazing mathematical ability. Assume a full moon is a perfect circle with a radius of \(\pi\). What equation using the variables \(x\) and \(y\) on a Cartesian coordinate system can be used to represent this circle? Give four exact value solutions to this equation.
\(x^2+y^2=\pi^2\)
\((\pi, 0),(-\pi, 0),(0, \pi),(0, -\pi)\)
(and more)
(No calculator allowed)
In a particular egg, when measuring the farthest possible points between the shell, you get a length of 7.6 cm. In addition you find that the total volume of the egg is 68 cm3. The yolk of the egg (a perfect sphere) happens to have a diameter that is a quarter of the longest length between the shell. Find how many times smaller the volume of the yolk is compared to the volume of the egg white (the rest of the egg that is not the yolk) (Round \(\pi\) to 3.14). Answer as a whole value or as a percentage.
18 times smaller
(No Calculator)
Simplify the expression below so that it reaches the form of \(3^{\frac{a}{b}}x^{\frac{c}{d}}\)
\(\frac{3((\frac{1}{x})^{-32})^{\frac{1}{4}}}{\sqrt[\frac{23}{4}]{x^{\frac{-5}{6}}\cdot \frac{1}{3}x^{\frac{-6}{7}}}}\)
\(3^{\frac{27}{23}}x^{\frac{4006}{483}}\)
(Potentially with a domain restriction)