Optional Homework
(No calculator)
In Plants vs. Zombies Heroes there are 2 plants called Dark Matter Dragon Fruit (DMDF) and Forget Me Nuts. For each DMDF on the field, the cost of zombie tricks is increased by 6. For every FMN on the field, the cost is increased by 1. If there are 3 DMDF and 2 FMN on the field, how much would a trick that normally costs 11 now cost after including the DMDF and FMN?
31
(No calculator)
Starting at 1:00 p.m., Charles watched three Hallmark movies. The first movie was 2 hours and 20 minutes long. He took a 20 minute break and then watched the second movie, which was 1 hour and 45 minutes long. He again took a 20 minute break and then watched the last movie, which was 2 hours and 10 minutes long. At what time did the final movie end?
What should Charles do after he finishes the final movie?
The final movie ends at 7:55 p.m.
Charles should now take a walk outside to stretch his legs!
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
A Pea Shooter shoots a pea. The pea makes it \(x\) meters to the end of the lawn after \(a\) seconds. What is the average speed of the pea?
\(\frac{x}{a}\) m/s
(No calculator)
Mr. Yeti participates in a prize draw at the annual Yeti convention held at the Las Vegas Sphere. He receives one prize that is equally likely to be worth $5, $10 or $20. Mrs. Yeti participates in a different prize draw at the convention. She receives one prize that is equally likely to be worth $30 or $40. What is the probability that the total value of their prizes is exactly $50?
\(\frac{1}{3}\)
(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)
(Calculator allowed)
A Pea Shooter does damage to a zombie. The zombie dies after five hits. What is the range of possible values for damage if the zombie has 12.3 health and the damage taken is the same for each hit?
Let \(x\) be equal to damage.
\(2.46\le x\lt 3.075\)
(Calculator allowed)
A few kids go to a gift shop to buy cool-looking snow globes (no pun intended). They bring the globes to the cashier, but the cashier says they can get 50% off their purchase if they answer a math question correctly. Here is the question they must answer:
A positive integer \(n\) is a multiple of 7. The square root of \(n\) is between 17 and 18. How many possible values of \(n\) are there?
What should the kids answer in order to get 50% off?
There are 5 possible values for \(n\).
(The kids could also pull out an airsoft gun and answer with "Give me the discount or else!")
(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)
(Calculator allowed)
It takes 7 hits for a Pea Shooter to kill a zombie with 91.7 health. It takes 3 hits for a Melon-pult to kill a zombie with the same initial health. What is the range of the possible values for the damage per hit of this Pea Shooter if the damage for each hit of a Pea Shooter is the same? What is the range of the possible values for the damage per hit of this Melon-pult if the damage for each hit of a Melon-pult is the same?
Let \(x\) be equal to the damage per hit of the Pea Shooter.
\(13.1\le x\lt 15.28\overline{3}\)
Let \(a\) be equal to the damage per hit of the Melon-pult.
\(30.5\overline{6}\le a\lt 45.85\)
(Calculator allowed)
Wendy is working at a Wendy's fast food restaurant. As she imagines snow falling outside, the Frosty (ice cream) machine starts making strange sounds. After a few seconds, a large \(5\times 5\times 5\) cube of ice suddenly explodes out from the machine (ignore units). This large cube of ice is formed using 125 small \(1\times 1\times 1\) cubes of ice. There are three central columns, each passing through the small cube at the very centre of the large cube: one from top to bottom, one from front to back, and one from left to right. All of the small cubes that make up these three columns are removed. What is the surface area of the resulting solid? (Do not worry about units.)
192
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)
This question is actually worth 1000 points. You can submit your answer at our next meeting, and it will be graded out of 10 (eventually).
In Plants vs. Zombies Heroes there is a mechanic called the block meter. When you hit your opponent, their block meter will gain 1, 2, or 3 charges. When their block meter reaches 8 or above, your opponent will block the damage of the attack that caused it to reach 8 or above. After this, your opponent's block meter will be reset to 0. What is the chance that your opponent will block exactly 3 times after exactly 10 hits.
To be determined...
Assume there is a special Pea Shooter in Plants vs. Zombies that has a 50% chance of missing a zombie completely (not dealing any damage) and a 50% chance of actually doing damage. This Pea Shooter shoots two different zombies, and at least one of them takes damage. What is the probability that both zombies take damage?
This question is somewhat ambiguous. Explain why.
The answer could be \(\frac{1}{3}\) or \(\frac{1}{2}\)
Frosty The Snowman has four bricks, each in the shape of a rectangular prism and each with dimensions \(2\times 3\times 6\). He carefully stacks these four bricks on a flat (glass) table to form a tower that is four bricks high. The number of possible heights for this tower is...
14 possible heights.
(but Frosty ended up breaking the table, so he will have to build these towers on the floor now)
(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)