2016 CAROLS APCS

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. (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. (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. (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. (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. (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. (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. (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. (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) 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)
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) 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) 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) 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.