My Math Day Quiz | Mixed Math

Quiz Answer Key and Fun Facts

1. My alarm clock beeps at the same time as my analog watch hands overlap. If my alarm clock wakes me up between 6:00am and 7:00am and it is exactly 18 minutes behind my analog watch, then what angle would the hands of an analog clock make if the analog clock said the same time as my alarm clock when it woke me up?

Answer: 99 degrees

Thank you to Diamondlance for helping me fix this question. This is their answer:
H=M (since the hands overlap) and
H=30 + M/12 (since the hour hand is at the 30 position at 6:00, and advances 1/12 of a minute space for every minute that passes).

Solving this system gives H=M=32.7272.

Thus the time on the alarm clock is 14.72727272... minutes after 6am, hence the hour hand is at the 31.22727272... position, hence the hands are 16.5 spaces apart, yielding a 99 degree angle between the hands.

Good luck on the rest of the quiz and another thank you to Diamondlance.

2. When I wake up, I immediately go eat breakfast. As a somewhat obsessive compulsive person, I will only eat my cereal bits in triangular numbers that aren't 1. Triangular numbers are the series: T(x) = x+x-1+x-2...+2+1, when xeW. What is the least number of cereal bits I must have in my bowl to be certain I can eat it and any number of bits greater than it? And what is the minimum number of bites I can take if I want to eat 34 pieces?

Answer: 18, 2

This is true: I really am that compulsive. The same goes for macaroni and cheese and for noodles in spaghetti/soup.
I could have written it sigma notation, but I think even less people would have understood that.
Examples of triangular numbers in case you didn't get it: 1, 3, 6, 10, 15, 21, 28, 36...

Proof that all numbers above and equal to 18 work:
Since I can't use '1', I have to find my own way of creating a '+1'.
If I change a 3 and a 6 to a 10, then there's a plus one.
If I change two 3's and two 6's to two 10's, then there's a plus two.
If I want a plus three, I can just add another three.
Therefore, to be certain I can eat my food, it must have at least two 3's and two 6's. In other words, it has to be at least 18.

Proof for that not all numbers below 18 work:
17 can't be done. Since seventeen isn't divisible by three, I will have at least one ten. Since seven still isn't divisible by three, and there is no way to add another ten, seventeen is finished and cannot be done.

34 pieces are eaten like so: 28-6.

3. Art class rolls along and I'm sitting there doodling. I start drawing random spirals, when the teacher comes along and looks at me. He says, "Wow. You just drew a perfect Fibonacci spiral there. The Fibonacci Spiral is made out of joined quarter-circles with radii corresponding to the Fibonacci sequence." When he brought up the math, I perked up. He noticed and gave me a question. "If you were to extend the Fibonacci Spiral until you reached and drew a quarter-circle with a radius of 55, how long would the line be?"

Answer: 71.5 pi

1-1-2-3-5-8-13-21-34-55
That's the first part of the Fibonacci sequence. With radius r, a quarter circle has length 1/4 of 2r*pi or (pi/2)*r. Therefore, you can add the radii and get the same result as doing the quarters separately.
The total of the ten numbers above is 143. So, the length is 143pi/2 or 71.5pi.

4. In biology class, one of the first mathematical lessons is the growth of a cell's surface area as opposed to its volume growth. This is the SA:V ratio. Most cells will not be perfect polyhedra, but let's assume some are. Given a perfectly cubic cell, what would the SA:V ratio be? (let s = side length)

Answer: 1 : s/6

Surface Area of Cube with side length s: Volume of Cube with side length s
6 * (s^2) : (s^3)
However, the s^2 can be divided from both sides and you are left with just 6:s.
Which can be turned into the unit ratio, 1:(s/6).

5. My friend showed me something mathematical at break. He went online and found proof that 2=1 using the following steps. During which transition, does the error occur? 1: Let A and B be equal real rationals. 2: A=B 3: A*A=A*B 4: (A*A)-(B*B)=(A*B)-(B*B) 5: (A+B)(A-B)=B(A-B) 6: (A+B)=B 7: 2B=B 8: 2=1

Answer: Steps 5 to 6

The reason there is an error there is the division. Steps 5 to 6 is when both sides have a common factor of (A-B) and both sides are factored by it. Because we declared in steps 1 and 2 that A and B are equal, (A-B) equals 0. And you can't divide by zero, because it is one of the mathematical sins.

If you have any more examples of this kind of problem, please send them to me. Thank you.

6. Calculus and Vectors Class. There really isn't a way to come up with an interesting story for this one. a=[1,2,3] b=[2,-1,0] c=[-1,-1,-1] d=[-2,2,-2] What is the dot product of the cross product of vectors A and B and the vector C+D?

Answer: 12

Cross product of [a,b,c] and [d,e,f] is [bf-ce,cd-af,ae-bd]. This makes a vector perpendicular to the original two.
Dot product of [a,b,c] and [d,e,f] is ad+be+cf. This makes a scalar.
Addition of [a,b,c] and [d,e,f] is [a+d,b+e,c+f]. If you put the original vectors end-to-end, this would be the result vector.

cross product of A and B = [3,6,-5]
addition vector of C and D=[-3,1,-3]
dot product of the two is -9+6+15 or 12.

7. After school, the jocks get warmed up for the basketball game. Red Team has an average of scoring 4/7 of their shots, but they get to shoot 90% of the times they get in shot range. Blue Team takes more time with their shots and gets points 23/25 of the time, but they also only shoot XX% of the times they get within shot range. If the ball is in shot range 210 times during the game, and it ends in a tie, which value is XX closest to? (Assume that the Blue Team gets the ball in shot range twice as often as Red Team.)

Answer: 34

210 shots=70 shots for Red team and 140 shots for Blue Team
Red Team gets (4/7)*(.9)*(70)=36 shots in.
Therefore, Blue Team gets (23/25)*(.XX)*(140)=36 shots in.
(.92)*(.XX)*(140)=36
(.XX)=(36/140)/(.92)
(.XX)=(.2795031056)
XX=27.95
The closest number is 34. If you said '56', you may have misread the final assumption of the question.

8. From 7:00pm to 9:00pm is designated homework time. Each assignment has a time required and a value based on how necessary the work is to my mark. English homework --> 20 min. --> 5 Math homework --> 10 min. --> 3 French assignment --> 45 min. --> 11 Geography essay --> 75 min. --> 16 Study for Science test--> XX min. --> +1 for every 5 minutes I study What is the maximum value of homework I can finish, if undone homework (not including studying) receives a negative value? What is the minimum value I can finish?

Answer: 19, -11

Geography Essay from 7:00 to 8:15 --Value = 16
French Assignment from 8:15 to 9:00 --Value = 27
Undone values: 5 and 3 --Value = 19 for maximum

Study for Science from 7:00 to 9:00 --Value = 24
Undone values: 16, 11, 5 and 3 --Value = -11 for minimum

9. Portion control at dinner time. Cook made exactly 1 full plate of each of three dishes: vegetables, mashed potatoes and fried rice. Cook: Wants no leftovers Jim: Wants less than XX% of his plate to be vegetables. Dave: Wants more than 60% of his plate to be mashed potatoes. You: Wants in between 30% and 40% of each dish. What is the lowest integer value of XX that fulfills all the requirements? (All percentages must be integers.)

Answer: 24

Jim: 23% of V, 8% of MP, 69% of FR
Dave: 39% of V, 61% of MP, 0% of FR
You: 38% of V, 31% of MP, 31% of FR

This is the best case scenario, where all dishes are full and finished and all requirements are met. Jim has 23% of his plate as vegetables, so XX must be greater than 23. It cannot be equal to 23, because the phrase says strictly 'less than'.

10. Maybe we'll end off this math day with a puzzle to rest one's mind for sleep. Or maybe not? What is the minimum number of pages my bed-time story must contain for all of the following fractions to be integers? 1) 7/9 of 5/7 of 3/5 of 1/3 of the book 2) 3% of 6/23 of the book and 3) 1/2 of 1/3 of 1/4 of 1/5 of the book

Answer: 41400

1) The fractions all simplify down to 1/9, amazingly. Therefore, the final prime factors must have at least 3*3.
2) A slightly longer one, but simplifies to 9/1150. Therefore, the final prime factors must have at least 2*5*5*23.
3) Multiplying it all together gets a final fraction of 1/120. Therefore, the final prime factors must have at least 2*2*2*3*5.
Final PF: 2*2*2*3*3*5*5*23 = 8*9*25*23 = 72*575 = 41400.

Congratulations and thank you for trying my very first quiz. Any feedback at all would be greatly appreciated. Thank you.

Source: Author Mercenary_Elk

This quiz was reviewed by FunTrivia editor crisw before going online.
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My Math Day Trivia Quiz

My ordinary day: explained by numbers.

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