# How Well Can You Do Grade 10 Math? Pop Quiz! **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [September 23, 2002, 3:12am UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222 "2002-09-23T03:12:08Z")\ **Posts on this page:** 15\ **Page:** 2
**Author:** ![Blackeyes](https://avatars.discourse-cdn.com/v4/letter/b/f6c823/32.png) [@Blackeyes](https://boards.straightdope.com/u/Blackeyes)\ **Post date:** [September 24, 2002, 1:36am UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/21 "2002-09-24T01:36:45Z")
> [@](#): > > . Right now he’s doing Algebra, making his own equations and solving them. It’s in the Grade 10 Academic Math Ciriculum from Ontario if anyone wants to indulge. :rolleyes: Algebra. He’s doing ALGEBRA? Sure, I took Algebra I. Like, in the EIGHTH grade! 😛 STUPID CANADIANS!😃 Hahahahahah! \<_smack_\> :smack: Ouch!! ---
**Author:** ![monica](https://avatars.discourse-cdn.com/v4/letter/m/a183cd/32.png) [@monica](https://boards.straightdope.com/u/monica)\ **Post date:** [September 24, 2002, 2:39am UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/22 "2002-09-24T02:39:25Z")
I’m also in tenth grade…you think that’s bad? Try my math analysis (pre-calc) homework. ---
**Author:** ![Soup\_du\_jour](https://avatars.discourse-cdn.com/v4/letter/s/848f3c/32.png) [@Soup\_du\_jour](https://boards.straightdope.com/u/Soup_du_jour)\ **Post date:** [September 24, 2002, 3:08am UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/23 "2002-09-24T03:08:02Z")
**phraser** , I can remember by differential calculus. 😉 Anyhoop, if anyone wants to know the error in the proof that A+B=B… [spoiler]If A=B, than A-B=0. Thus, in the next-to-last step, both sides are divided by zero. Any number divided by zero equals infinity, or does not exist, depending on your math persuasion. A nonzero devided by zero never equals a rational number. It’s an insidious version of the following proof… 1 x 0 = 0 2 x 0 = 0 Therefore, 1 x 0 = 2 x 0 Devide each side by zero… 1 = 2 This, obviously, doesn’t wash.[/spoiler] ---
**Author:** ![racinchikki](https://avatars.discourse-cdn.com/v4/letter/r/eada6e/32.png) [@racinchikki](https://boards.straightdope.com/u/racinchikki)\ **Post date:** [September 24, 2002, 3:19am UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/24 "2002-09-24T03:19:50Z")
I used to annoy my math teachers by giving my variables odd names. I’d be solving for the value of Ringo or 🙂 (yes, I had a sheet full of smiley-face stickers about the size of the eraser on a #2 pencil, and I placed a sticker onto my work paper every time I had to name the variable). My teacher eventually started to specify “USE X AS VARIABLE EXCEPT WHERE OTHERWISE NOTED” on the blackboard when he assigned the homework. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [September 24, 2002, 3:32am UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/25 "2002-09-24T03:32:17Z")
> [@](#): > > \*Originally posted by racinchikki \* > \*\*I used to annoy my math teachers by giving my variables odd names. I’d be solving for the value of Ringo or 🙂 (yes, I had a sheet full of smiley-face stickers about the size of the eraser on a #2 pencil, and I placed a sticker onto my work paper every time I had to name the variable). My teacher eventually started to specify “USE X AS VARIABLE EXCEPT WHERE OTHERWISE NOTED” on the blackboard when he assigned the homework. \*\* That’s no fun. ---
**Author:** ![MonkeyMensch](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@MonkeyMensch](https://boards.straightdope.com/u/MonkeyMensch)\ **Post date:** [September 24, 2002, 5:03am UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/26 "2002-09-24T05:03:34Z")
> [@](#): > > \*Originally posted by Soup\_du\_jour \* > > Thus, in the next-to-last step, both sides are divided by zero. Any number divided by zero equals infinity, or does not exist, depending on your math persuasion. I could be wrong here (and I have been from time to time) but division by zero is undefined. There is no such number as “infinity” and I’m not sure what it means for a number to be divided by zero and cease to exist. I’ll just divide my credit card balance by zero and… ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [September 24, 2002, 5:11am UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/27 "2002-09-24T05:11:32Z")
**MonkeyMensch** is correct about the division by zero bit. It ain’t infinity, that’s for damn sure. ---
**Author:** ![Jabba](https://avatars.discourse-cdn.com/v4/letter/j/b5e925/32.png) [@Jabba](https://boards.straightdope.com/u/Jabba)\ **Post date:** [September 24, 2002, 11:08am UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/28 "2002-09-24T11:08:25Z")
> [@](#): > > \*Originally posted by RTFirefly \* > OK, share. 🙂 THEOREM 1: All positive integers are equal. Proof: Given real numbers a,b define max{a,b} to be the larger of the two or either when they are equal. Thus max{3,7} = max{7,7} = 7. We shall prove For every positive integer n, if a and b are positive integers such that max{a,b} = n, then a = b. Clearly this will imply Thm 1. (i) If max{a,b} = 1 then a = b = 1. Thus the result holds when n = 1. (ii) In general, given a,b with max{a,b} = n let [symbol]a[/symbol] = a-1 and [symbol]b[/symbol] = b-1. Then max{[symbol]a[/symbol],[symbol]b[/symbol]} = n-1. By the inductive hypothesis it follows that [symbol]a[/symbol] = [symbol]b[/symbol] and so a = b. This completes the proof by induction. In the same spirit we can also prove THEOREM 2: In any exam all candidates achieve the same score. Proof: Again by induction on the number n of candidates. The theorem is trivial when n = 1. In general split the set of candidates into two subsets A and B which are both smaller than the whole set and which have one candidate in common. By the inductive hypothesis all the candidates in set A achieve the same score. Similarly for the candidates in B. Since A and B have one person in common this score is the same for A and B. Thus all the candidates get the same score and we are done. ---
**Author:** ![nightshadea](https://avatars.discourse-cdn.com/v4/letter/n/7ba0ec/32.png) [@nightshadea](https://boards.straightdope.com/u/nightshadea)\ **Post date:** [September 24, 2002, 12:21pm UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/29 "2002-09-24T12:21:10Z")
Does it count if your math teachers thought youd reached your math potential about the 6th grade and most of there time was spent making sure you didnt forget the basic stuff ? ---
**Author:** ![RTFirefly](https://avatars.discourse-cdn.com/v4/letter/r/c77e96/32.png) [@RTFirefly](https://boards.straightdope.com/u/RTFirefly)\ **Post date:** [September 24, 2002, 12:41pm UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/30 "2002-09-24T12:41:57Z")
Ah well, not all the ‘proofs’ can be interesting. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [September 24, 2002, 2:40pm UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/31 "2002-09-24T14:40:47Z")
Hmm…I’ve got a pretty good idea where the error is in **Jabba** ’s proof, but I don’t think I could explain it succinctly. More time… ---
**Author:** ![Ringo](https://avatars.discourse-cdn.com/v4/letter/r/779978/32.png) [@Ringo](https://boards.straightdope.com/u/Ringo)\ **Post date:** [September 24, 2002, 2:55pm UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/32 "2002-09-24T14:55:06Z")
It’s nice to know I can get work as a variable. 😉 ---
**Author:** ![Jabba](https://avatars.discourse-cdn.com/v4/letter/j/b5e925/32.png) [@Jabba](https://boards.straightdope.com/u/Jabba)\ **Post date:** [September 24, 2002, 2:56pm UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/33 "2002-09-24T14:56:35Z")
That’ll teach you to do vanity searches. ---
**Author:** ![Orbifold](https://avatars.discourse-cdn.com/v4/letter/o/779978/32.png) [@Orbifold](https://boards.straightdope.com/u/Orbifold)\ **Post date:** [September 24, 2002, 3:10pm UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/34 "2002-09-24T15:10:22Z")
The errors in **Jabba** ’s proof are pretty simple actually… [spoiler]In the first proof, neither a-1 nor b-1 are guaranteed to be positive integers, but the inductive step assumes that they are. In the second proof, it isn’t possible to construct “two subsets A and B which are both smaller than the whole set and which have one candidate in common” when n=2. [/spoiler] ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [September 24, 2002, 3:13pm UTC](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222/35 "2002-09-24T15:13:55Z")
I knew the second one. Thought I’d use it as an interview question (for a tech interview). The second one, I would’ve figured out soon. Thanks to **Math Geek**. [Previous page](https://boards.straightdope.com/t/how-well-can-you-do-grade-10-math-pop-quiz/129222.md?page=1)