Math quiz answers

[emmagrant01]

The quiz is here.



1. 1 is a prime number.
Answer: False. Prime numbers are defined to be those that have exactly two divisors: themselves and 1. So 1 only has one divisor and doesn't meet the criteria for a prime. But more importantly, the main reason that we're interested in prime numbers is that they are the building blocks of other numbers. Every integer can be written in a unique way as a product of prime numbers; so 24 = 2³ ⋅ 3. (This is called the Fundamental Theorem of Arithmetic.) But if we let 1 be a prime, we would lose that uniqueness -- so we could write 24 = 1² ⋅ 2³ ⋅ 3 = 1⁴⁵ ⋅ 2³ ⋅ 3, and so on. (More on this topic here.)

2. A square is a:
Answer: all of them. A square is a quadrilateral (a closed four-sided figure), a rectangle, a rhombus (an equilateral parallelogram), a parallelogram (opposite sides are parallel), and a regular polygon (a closed figure with all sides and angles equal).

3. Circumference is a measure of:
Answer: perimeter; specifically the perimeter of a circle.

4. If x squared is 9, then x is:
Answer: 3 or -3. In the equation x² = 9, what we are looking for are all the numbers that when substituted for x would make the equation true. 3² = 9 and (-3)² = 9, so both answers are correct.

5. If the square root of x is 9, x is:
Answer: 81. This is the only integer whose square root is 9. -81 doesn't have a real square root, and its complex square root is 9i.

6. 1/3 is
Answer: a rational number. Any number that can be written as a ratio (fraction) of two integers is rational. And contrary to what many of my students seem to think, 1/3 ≠ 0.3. Those two numbers are close, but not equal.

7. The number 1 is equal to the number 0.9999999999...
Answer: true! Just like we can write 1/3 = 0.3333..., we can write 1 = 0.99999... There are several interesting ways to prove this fact, but I'll direct anyone interested to a good explanation here.

8. If you draw a large triangle on a globe connecting three cities, what can say say about the sum of the angles inside the triangle?
Answer: The sum is greater than 180 degrees. To demonstrate this to yourself, draw three dots on an orange and then draw straight lines on the surface of the orange between them. You can probably see it by looking, but you can measure the angles to check. More info is here.

9. 0.555555555... is:
Answer: a rational number, also equal to 5/9. Decimal numbers that either terminate or repeat infinitely are rational numbers. I won't go into the technical details of why, but if you want to know more, go here (and scroll halfway down until you see "Rational Numbers").

10. A trapezoid is mathematically defined as:
Answer: both! This is a weird case where one mathematical definition wasn't agreed upon, and so both are considered valid. They have different consequences, so you have to specify which one you're using. For example, under the first definition, a parallelogram is not a trapezoid, but under the second, it is a trapezoid.

11. Which of the following situations represents 3 divided by 1/2?
Answer: I have 3 pizzas, and I want to give 1/2 pizza to each of my friends. How many friends can I feed? People often mistranslate the problem as "divide three into two halves", but the question really is "how many halves are in 3?" There are 6 halves in 3, 2 in each whole.

12. If a number is divisible by 24, is it divisible by 8?
Answer: Yes. If the number is divisible by 24, then it is divisible by the factors of 24, so it is also divisible by 2, 3, 4, 6, 8, and 12.

So, how'd you do?

Comments

[wordplay.livejournal.com]

I was really thrown by the trapezoid question, and I just don't like the "both" answer because, you know - it has been defined as both, but it can't actually be defined as both simultaneously. Totally missed the 1=0.9999999etc thing. Otherwise... it could have been worse? *laughs*

I would do one of these for lingustics, except that, OH YEAH, we don't do any real linguistics education in the US curriculum. So proud.

[tm-nicholas.livejournal.com]

Terribly.

I always hated math. Must be why I'm an accounting major. :-x

[phaballa.livejournal.com]

Wow, I got like, 2 of those right. I am dumb at math! But! I know so many funny stories about Calvin Coolidge!

[nimroddess.livejournal.com]

I had no idea about rational vs. irrational numbers, so I got those two parts wrong (at least I was consistent!) and I said 0.5555555... was 0.56 because it can be rounded to that and you used the phrase "is" rather than "is equal to" and so I basically created a trick question for myself by being too anal retentive. And I didn't know trapezoid had two definitions so I just picked one. But everything else I got spot on :)

[thalia]

That's really interesting about 0.99999... -- I didn't know that. I guess I would have said the limit as the number of digits approaches infinity would be 1, but it wouldn't actually get up to 1. Dr. Math's explanation was good, though.

(I'm ignoring the trapezoid question. [g])

[emmagrant01.livejournal.com]

It's actually interesting to see what other folks' expertise is, you know? I know a hell of a lot about something very small, and not much outside of that. But such is academia. :-P

The trapezoid thing is funny to me, because it seems perfectly reasonable to me that mathematicians couldn't decide which was better, and so accepted both. I was once asked which was right by someone from the state education agency (which designs the high-stakes tests kids take here), and they were unhappy when I told them both were accepted. Heh.

[emmagrant01.livejournal.com]

My mom's degree is in accounting, and I don't understand half of what she says when she's in accounting mode. :-P

[emmagrant01.livejournal.com]

Isn't it fun to see what narrow little area you know a lot in compared to others' little areas of expertise? Just goes to show how smart we all are when we work together. ;-)

[emmagrant01.livejournal.com]

I actually tried to keep the language more colloquial than I would at work, because I didn't want people to have to sift through the technical stuff. But it's actually really hard to talk about mathematical ideas without that very specific language. :-P

[letmypidgeonsgo.livejournal.com]

technically, i got 5 (& a half) right. i totally didn't think that pizza question through, & only realised the answer when i went to comment about it

:(

(psst, i re-stole this idea & did a history one!)

[emmagrant01.livejournal.com]

I teach a course for teachers and that's the problem that causes the most discussion every semester. People understand logically why it's true, but somehow they want 1 to be special and not subject to being represented in multiple ways like other numbers. Sometimes pointing out that 1 = 2/2 = 3/3 = 4/4 = ... helps, but there are always one or two who just say, "No, I don't believe it." ;-)

The trapezoid one is a rarity in school-level mathematics. But it doesn't really matter which definition you choose, which is why there is no consensus.

[emmagrant01.livejournal.com]

Oooh! Let me see how much I suck at history! ;-)

[jedirita.livejournal.com]

Woo-hoo! I got more than half right!

[jedirita.livejournal.com]

Have I mentioned how sexy you are when you talk math?

[emmagrant01.livejournal.com]

Go you! :-D

[emmagrant01.livejournal.com]

Hee! I do love it so! ;-)

[littleroo27.livejournal.com]

A) I got three right; I suck
B) What the hell middle school did you go to? I learned some of this stuff my sophomore and junior year in high school! Though obviously not well enough to remember, lol.

[acromantular.livejournal.com]

OK, you got me on the trapezoids- I didn't know it was under argument! I definitely remember that a parallelogram can be a trapezoid, so went with the "at least" answer. Tricksy!

Otherwise, I'm a rock-solid middle school math nerd. Hooray for nerd pride!

[emmagrant01.livejournal.com]

B) I had a shitty math education, so I didn't learn that stuff when I was a kid. But if you take a look at state and national standards for middle school math in the US, this is the sort of thing that's in there. The emphasis is now on moving abstract ideas, algebra, and geometry down into elementary school, so that kids see it throughout school and not just in high school, if ever.

[emmagrant01.livejournal.com]

That was the one "tricky" one, yeah. I figured the only people who would know that one would be teachers. :-P

Yay nerds! (I need a nerd icon.)

[littleroo27.livejournal.com]

certainly a good idea... at my high school we watched the movies instead of reading the books because it was just too insane to try and make rednecks read Shakespeare. I still have post traumatic stress over reading the part of Lady MacBeth the day she got horny in front of a class full of morons *shudders*

[emmagrant01.livejournal.com]

Ouch. I feel your pain!

[bibliokat.livejournal.com]

Half right and half wrong! Not as well as I thought I'd do but not horrible either. (Although really, I should have known about 1 not being prime *facepalm*)

I'm off to fail the American History one!

[zaph.livejournal.com]

10. A trapezoid is mathematically defined as:
Answer: both!

Aw, crap, really? That's the only one I missed, too.

Oh well. At least I can still prove that 1=2. :)

[emmagrant01.livejournal.com]

If you only missed one, you're way above average! ;-)