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# 2016 CAROLS APCS

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2016 CAROLS APCS

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### 2016 CAROLS APCS

1. 1. (01) New Math (342-173 BASE10) by Tom Lehrer You can't take three from two, Two is less than three, So you look at the four in the tens place. Now that's really four tens So you make it three tens, Regroup, and you change a ten to ten ones, And you add 'em to the two and get twelve, And you take away three, that's nine. Is that clear? Now instead of four in the tens place You've got three, 'Cause you added one, That is to say, ten, to the two, But you can't take seven from three, So you look in the hundreds place. From the three you then use one To make ten ones... (And you know why four plus minus one Plus ten is fourteen minus one? 'Cause addition is commutative, right!) And so you've got thirteen tens And you take away seven, And that leaves five... Well, six actually... But the idea is the important thing! Now go back to the hundreds place, You're left with two, And you take away one from two, And that leaves...? Everybody get one? Not bad for the first day! Hooray for New Math, New-hoo-hoo Math, It won't do you a bit of good to review math. It's so simple, So very simple, That only a child can do it!
2. 2. (02) New Math (342-173 BASE08) by Tom Lehrer Now, that actually is not the answer that I had in mind, because the book that I got this problem out of wants you to do it in base eight. But don't panic! Base eight is just like base ten really - if you're missing two fingers! Shall we have a go at it? Hang on… You can't take three from two, Two is less than three, So you look at the four in the eights place. Now that's really four eights, So you make it three eights, Regroup, and you change an eight to eight ones And you add 'em to the two, And you get one-two base eight, Which is ten base ten, And you take away three, that's seven. Ok? Now instead of four in the eights place You've got three, 'Cause you added one, That is to say, eight, to the two, But you can't take seven from three, So you look at the sixty-fours... "Sixty-four? How did sixty-four get into it?" I hear you cry! Well, sixty-four is eight squared, don't you see? "Well, ya ask a silly question, ya get a silly answer!" From the three, you then use one To make eight ones, You add those ones to the three, And you get one-three base eight, Or, in other words, In base ten you have eleven, And you take away seven, And seven from eleven is four! Now go back to the sixty-fours, You're left with two, And you take away one from two, And that leaves? Now, let's not always see the same hands! One, that's right. Whoever got one can stay after the show and clean the erasers. Hooray for New Math, New-hoo-hoo Math! It won't do you a bit of good to review math. It's so simple, So very simple, That only a child can do it! Come back tomorrow night we're gonna do fractions!
3. 3. (03) Geometry Guide by Angeline (to the tune of Jingle bells) Geometry , geometry Is real fun to learn Oh how easy it becomes when you know these termssss If you want to find the length of a triangle's side SOH, CAH and TOA Will be your guide Geometry , geometry Is real fun to learn Oh how easy it becomes when you know these termssss Angles are real simple complementary is 90 and Linear supplementary equals 180 Geometry , geometry Is real fun to learn Oh how easy it becomes when you know these termssss Proving Triangles are congruent is called a proof You need to find relationships that make congruent the truth like ASA, SAA, HL but never ASS Because ASS is trash Geometry , geometry Is real fun to learn Oh how easy it becomes when you know these termssss
4. 4. (04) Conic Section Carol ("God Rest ye Merry Gentlemen") God rest ye merry ellipses And hyperbolae too! Parabolas and Circles, All curves of degree two! Degenerate and involute, The mathematician’s toy, Oh sections of conics and joy, Conics and joy, etc. Of symmetry and foci And fun directrices! Both smooth and sharply pointed curves Can have some vertices. To prove this Polar Mode Is such a clever ploy! Oh sections of conics and joy, Conics and joy, etc.
5. 5. (05) Write in C Lyrics (in memory of Dennis Ritchie) When I find my code in tons of trouble, Friends and colleagues come to me, Speaking words of wisdom: "Write in C." As the deadline fast approaches, And bugs are all that I can see, Somewhere, someone whispers: "Write in C." Write in C, write in C, Write in C, oh, write in C. LISP is dead and buried. “Write in C.” I used to write a lot of FORTRAN, For science it worked flawlessly. Good Luck using it for graphics! Write in C. If you've just spent nearly 30 hours Debugging some assembly, Soon you will be glad to: :Write in C.” Write in C, write in C, Write in C, yeah, write in C. BASIC is for wimps. “Write in C.” Write in C, write in C, Write in C, oh, write in C. Pascal won't quite cut it. Write in C. Write in C, write in C, Write in C, yeah, write in C. Don't even mention COBOL. “Write in C.” And when the screen is fuzzy, And the editor is bugging me. I'm sick of ones and zeros, “Write in C.” A thousand people swear that T.P. Seven is the one for me. I hate the word PROCEDURE, “Write in C.” Write in C, write in C, Write in C, yeah, write in C. PL1 is '80s, Write in C. Write in C, write in C, Write in C, yeah, write in C. The government loves ADA, “Write in C.” Write in C, write in C, Write in C, yeah, write in C. Java's not quite there yet, “Write in C.”
6. 6. (06) Program! (tune = "Dreidel!") I have a computer program. I made it out of codes. And when it is started, Oh program, think of all the modes! Oh code, code, code, I made you out of a method. And when you’re being written, Code, you’re understood! Oh method, method, method, I made you out of commands. And when you have an error, I shall give you demands! Oh command, command, command, I mage you out of variables. And when you are inputted, I will make up symbols! Oh program, program, program, You are in the terminal. And when you are tested, I shall make it final!
7. 7. (07) Pi to the World ("Joy to the World") Pi to the world, twenty two over (eight minus one), Irrational though it be. Let every round thing now fit the expounding with each and every degree, with each and every degree, with each, with each, and every degree.
8. 8. (08) Arcs the Mighty Compasses Bring ("Hark the Herald Angels Sing") Arcs the mighty compasses bring, constructed with a steady swing. Geese are worth not twenty Yen, Shucks! I've torn my diagram of Venn. A triangle within a semicircle lies. Incongruent triangles are not the same size. But, congruent ones are the same. Geometry drives one insane. But, congruent ones are the same. Geometry drives one insane.
9. 9. (09) Go work Ye Merry Protractors ("God Rest Ye Merry Gentlemen") Go work ye merry protractors make straight lines here today. Remember every angles not made of just one ray. Euler was a greaser, but that's not what textbooks say. Oh, tangents of circles and spheres, circles and spheres. Oh, tangents of circles and spheres.
10. 10. (10) Oh Number PI! ("Oh Christmas Tree") Oh, number PI, Oh, number PI, Your digits are non-ending! Oh, number PI, Oh, number PI, No pattern are you sending? You’re three point one four one five nine, And even more if we had time! Oh, number PI, Oh, number PI, For circle lengths unbending. Oh, number PI, Oh, number PI, You are a number very sweet! Oh, number PI, Oh, number PI, Your uses are so very neat? There’s 2 PI r and PI r squared, A semi-circle and you’re there! Oh, number PI, Oh, number PI, We know that PI’s a tasty treat!
11. 11. (11) On The 12th Day of Math Class (" On The 12th Day of XMas") On the 12th day of Math Class, my teacher gave to me: 12 mean averages, 11 equations regressing, 10 graphs plotting, 9 surveys polling, 8 experiments failing, 7 random numbers, 6 crazy teachers, 5 preCalculus problems! 4 charts and data, 3 wrong assumptions, 2 assignments whinning And a brand new TI-83!
12. 12. (12) Rudolph the Statistician 02 (tune = "Rudolph") Rudolph the statistician Sampled data everywhere! Mean heights and heart conditions Calculated with great care! All the population Living from coast to coast Sought out his data samples He would always give the most! Then one foggy Xmas Eve Santa came to say, “Rudolph, with your pencil write, What gifts I should bring tonight.” Quickly, he polled the children, And Rudolph shouted with glee, “Stats did provide the answer: Give Nintendos and Barbies!
13. 13. (13) Hanukkah in Santa Monica by Tom Lehrer [Verse] I'm spending Hanukkah in Santa Monica Wearing sandals Lighting candles by the sea I spent Shavuos in East St. Louis A charming spot But clearly not the spot for me Those eastern winters, I can't endure 'em So every year I pack my gear And come out here to Purim Rosh Hashana, I spend in Arizona And Yom Kippur, way down in Mississippa But in December There's just one place for me [Tag 1] Amid the California flora I'll be lighting my menorah Like a baby in his cradle I'll be playing with a dreidl Spending Hanukkah In Santa Monica by the sea! [Verse] [Tag 2] Amid the California flora I'll be lighting my menorah Like a baby in his cradle I'll be playing with a dreidl Here’s to Judus Maccabeus Boy, if he could only see us Spending Hanukkah In Santa Monica by the sea!
14. 14. (14) A Christmas Carol by Tom Lehrer Christmas time is here, by golly, Disapproval would be folly, Deck the halls with hunks of holly, Fill the cup and don't say "when." Kill the turkeys, ducks and chickens, Mix the punch, drag out the dickens, Even though the prospect sickens, Brother, here we go again. On christmas day you can't get sore, Your fellow man you must adore, There's time to rob him all the more The other three hundred and sixty-four. Relations, sparing no expense'll Send some useless old utensil, Or a matching pen and pencil. "just the thing I need! how nice!" It doesn't matter how sincere it Is, nor how heartfelt the spirit, Sentiment will not endear it, What's important is the price. Hark the herald tribune sings, Advertising wondrous things. God rest ye merry, merchants, May you make the yuletide pay. Angels we have heard on high Tell us to go out and buy! So let the raucous sleigh bells jingle, Hail our dear old friend kris kringle, Driving his reindeer across the sky. Don't stand underneath when they fly by.