Faster with Math

[QBPlayer]

Any tips on how to increase the pace of solving math problems so I can buzz faster?

Any resources? Books or worksheets to help with this problem.

Thanks

User reminded to add signature -mgmt

[a_noob_bot]

Most comp math tossups are only asking for concepts up to the algebra 2 level, so don't study past that. Prebuzzing helps a lot if you have all the clues and can solve it in five seconds. For bonuses make sure that more than 1 person does the math and that they are communicating with each other.

[quizzical1]

Most comp math are simple logic, but they ask frequently about two roots and y=mx+b
Also know Sohcahtoa, sine=opposite/hypotenuse cosine=adjacent/h tangent=o/a
Also c = pi x d, a = pi x r^2 for circle
And permutations are always factorials, which is represented as x!
Factorial multiplies number x and all numbers between it and 1
1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120, 6! = 720

[L.H.O.O.Q.]

Computation questions are usually going to come down to "who can do mental arithmetic the quickest?" I'm sure you can drill math problems and improve that skill, but that sounds awful. So, instead, let's talk about some number sense and word problem skills that can help you gain an advantage. I'll be using sample comp math tossups from NAQT's website as fodder to introduce some concepts.

Pencil and paper ready. Anirudh [ah-nee-“rude”] is randomly drawing a single card from a standard deck of 52 playing cards, and needs to know the probability that the card will be a red queen. Since the deck has 4 equal suits, 2 of which are (*) red, he finds—for 10 points—what probability of a red queen?
answer: 1/26 or 1 in 26 [There are 2 red queens (the queen of hearts and the queen of diamonds); 2/52 = 1/26.]

Here are some word problem instincts that trigger for me when hearing the first line of this question:
drawing a single card from a deck of 52: With a lead-in like this, or like "picking socks from a drawer" or "picking balls from a jar," we are almost certainly dealing with a probability question, so I need to set up a fraction.
probability that the card will be a red queen: This question is predicated on two pieces of knowledge: card suits and card faces. You should know that there are 4 card suits (and 2 of them are red), and 13 card faces (and 1 of them is a queen).

From that knowledge, we can create the probabilities: Anirudh has a 1/13 probability of drawing a queen, and provided he draws a queen, there's a 2/4 (or 1/2) probability that the queen is a red suit. Therefore, the probability of drawing a queen is (1/13)*(1/2) = 1/26.

Ways to gain an advantage: Recognize before it's stated what kind of problem you're dealing with. This gives you a head start on the calculation.

Pencil and paper ready. Amy needs to know how many nickels she has, given she has 3 times as many pennies as nickels, and the total value of her coins is 48 cents. By expressing the number of nickels as x and the number of pennies as 3x, she computes (*) —for 10 points—what number of nickels?
answer: 6 nickels (and 18 pennies) [One nickel and its accompanying 3 pennies are worth 5 + 3 = 8 cents; there must be 48/8 = 6 such groups, and thus 6 nickels.]

Here are the things you should be writing down as you hear them:
how many nickels she has: You are probably going to hear at least two kinds of coins, so I would write a note specifying "nickels."
she has 3 times as many pennies as nickels: I would express this as "p = 3n", where p is the number of pennies and n is the number of nickels. You can use whatever system makes sense to you.
the total value of her coins is 48 cents: Using the variable names from above, I write "p + 5n = 48," since a nickel is worth 5 cents.

Now, the quickest way to do this is to use "p = 3n" to replace "p" in the second equation with "3n," quickly getting "3n + 5n = 48." This is something where memorizing sums and products honestly helps the most: I would immediately infer "8n = 48," buzz here, and mentally divide 48 by 8 to get n = 6. If this doesn't come naturally to you, I don't know how to teach it other than rote memorization.

Ways to gain an advantage: The quicker you can parse the type of question you're being asked, the better you'll do, regardless of your math skills. You can also press the buzzer before the problem is fully solved, if you trust your math skills enough to complete the calculation in the 2 seconds you have to deliver an answer. This is especially useful for problems like this one, which simplifies very nicely.

Pencil and paper ready. Alan needs to know the value of x, given that the mean average of the three numbers [read slowly] 55, 62, and x equals 60. Since the mean is the sum of the values divided by the number of values, he knows 55 plus 62 plus x equals 3 times 60. (*) For 10 points—find the value of x.
answer: x = 63 [M = (55 + 62 + x)/3 = 60, so 117 + x = 180, and x = 63]

Taking an average by hand can be somewhat slow, so let's talk number sense and see if we can arrive at an answer implicitly using reasoning. The average is basically the exact middle of the set of numbers you're using. The numbers in the set "pull" the average based on how far they are from the average. We know the average is 60, and so 55 is pulling it "down" by 5 and 62 is pulling it "up" by 2. Therefore, to offset the impact of the 55, x should pull the average "up" by 3. You then instantly and intuitively get x = 63.

If that's too weird for you, another approach is to note that 55 is further from 60 than 62 is, so the third number in the set should be a little bit over 60. You can quickly note that 3 x 60 is 180, and 55+62+x should equal 180. The important thing is that the sum ends in zero. Adding the 5 and 2 from 55 and 62 gets you 7, so the third number should end in 3 to create a number that ends in zero. As a result, you infer that the third number is 63.

Ways to gain an advantage: Leverage your understanding of mathematical concepts to work around a slow calculation. Both of the methods above are intuitions based on a deep understanding of how averages work. In cases like this, it's only necessary to know roughly how the concept acts, and simply doing the problem in a straightforward way could even lose you time.

Pencil and paper ready. Miranda needs to know the tenth term of the arithmetic [“air”-ith-MET-ik] sequence whose fourth term is 8 and whose sixth term is 16. She can either write out the entire sequence up to the tenth term, or realize that the sequence must increase by 8 every (*) two terms. For 10 points—find the tenth term of the arithmetic sequence whose fourth term is 8 and whose sixth term is 16.
answer: 32 [Since the sequence went up by 16 - 8 = 8 between the fourth and sixth terms, it must have a similar increase between the sixth and eighth terms, and the eight and tenth terms, respectively—yielding a tenth term of 16 + 8 + 8 = 16 + 16 = 32.]

The funny thing about this is that they explain the optimal way to solve this problem in the question itself! The quickest way to solve this one is to figure out the trick that the sequence increases by 8 every two terms before it's explicitly stated. An arithmetic sequence increases linearly, so if you notice that the difference between terms two numbers apart is 8, then you can find that the eighth term is 16 + 8 = 24, and the tenth term is 24 + 8 = 32.

Ways to gain an advantage: Keep your eyes peeled for methods that are quicker than the simple, canonical method! Much like the averages example above, this requires a lot of number sense and conceptual understanding, so I suppose the best way to get good at comp math without drilling equation sheets is to just... learn more math!

Sorry that this really long post culminated to essentially "get good," but... what can I say? If calculation skills don't come naturally to you, don't worry about pointlessly drilling yourself to try and get faster; just try to study math actively. Think about the concepts, explore what you're doing with the numbers, and you'll hopefully find that your sense with numbers gets better naturally.

(This "talent gap" with comp math skills is why the larger community is so anti-comp math. I think good comp math questions are possible, but extraordinarily difficult to execute; of the four examples I just posted, I don't really think any of them serve as good probes of knowledge.)

[dni]

https://arithmetic.zetamac.com/

[Jacksondahammerbidney]

Any tips on how to increase the pace of solving math problems so I can buzz faster?

Any resources? Books or worksheets to help with this problem.

Thanks

User reminded to add signature -mgmt

Calculate as the question goes on. I powered one of these because I was able to calculate about 75% of the question before I buzzed, and it was still overall in power.