High School Math

MISSION STATEMENT: To encourage and promote a greater use of the internet and computer technology in the math classroom. For educators, students, parents and homeschoolers.

Monday, February 28, 2005

Terms?

There is an Arithmetic Series
whose fifth term is 11, and
whose twelfth term is 25.
What is the first term?
What is the common difference between terms?

If you need help click     www.TheMathWebSite.com
and on the index of topics page click
Arithmetic Series/Given Two Terms. Find the A.S./Quiz. Then
click on any question or its steps, to see the full solution.

Squares

If the same circle is used, then what is the ratio of -
(the area of its circumscribed square) to
(the area of its inscribed square).

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!
The correct solution (to this and all the other puzzles) will be posted after 2 carefully explained solutions are submitted as comments.

Sunday, February 27, 2005

Make This!

At what angle are the two vertical pieces cut?
Should it be made from Maple, Pine or Oak?
Why would this be difficult to make out of Steel?

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!
The correct solution (to this and all the other puzzles) will be posted after 2 carefully explained solutions are submitted as comments.

Cards

How many cards must you pick
from a deck of 52 cards to ensure that
at least two are of the same suit?
.... of the same type?

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!
The correct solution (to this and all the other puzzles) will be posted after 2 carefully explained solutions are submitted as comments.

There was a young lady of Lee,
Whose age had its last digit three.
If you total the two,
Which is easy to do,
One less than a square you will see.

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!

Konigsberg

A river divides the town of Konigsberg into four separate land areas. Seven bridges connect the various parts of town (see diagram).
Some of the town's curious citizens wondered if it were possible to take a journey across all seven bridges without having to cross any bridge more than once. All who tried ended up in failure.
Try it yourself. You may start anywhere.
Why is this not possible?

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!

Saturday, February 26, 2005

Fair Maid

There was a fair maid in Rabat,
Who was plump, not excessively fat.
The square of her weight,
When divided by eight,
All in pounds was a cube. How was that?

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!

Mobius Strip

Take a strip of paper and some sticky tape. Turn the paper into a loop, but before you stick it down, flip one end of the paper over. This should give you a piece of paper with a half-twist in it. This is a Möbius strip (see diagram).

The Möbius strip has only got one side. If you draw a line down the middle of the strip until you get back to your starting point, you will find that you draw on both sides of the paper.

Cut down the middle of the strip. Instead of getting two separate strips, the Möbius strip becomes one long strip. (To start the cut off, fold the strip and make a small cut, then unfold the strip and use the hole as a starting point.) This long strip has four half-twists in it. If you cut it down the middle, you get two strips wound around each other.

Using a new strip, cut about a third of the way in from the edge (you will need to go around the loop twice). You will get two strips. One is a thinner Möbius strip, the other is a long strip with four twists in it.

This time flip the strip twice before sticking it down. This will give you a strip with two half-twists in it. This strip has two sides and two edges. When you cut down the middle of the strip it will split into two linked rings.

Now, make a strip with three half-twists. This strip will have only one side and one edge. When you cut down the middle, the strip will become a knotted loop.

Coins

A purse contains 8 more dimes than nickels.
Their total value is \$1.85
How many of each coin are there?

Click on     www.TheMathWebSite.com if you need help. Then on the index of topics page
click Word Problems/Coins/Quiz and then click
on any question to get its solution & answer.

Stone

A stone is thrown into a cylindrical water tank 2 feet in diameter, causing the water to rise 1.5 inches. What is the volume of the stone?

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!

Horse

A horse travels half his route, with no load, at 12 miles per hour. The rest of the way a load slows him to 4 miles per hour.
what is his average speed?
(The answer is not 8 mph.)

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!

Thursday, February 24, 2005

Empty Boxes

Of 10 boxes, five contain pencils, four contain pens, and two contain both pencils and pens.
How many boxes are empty?

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!

To Infinity

Find the sum of the infinite geometric series.

2 + 0.6 + 0.18 + ....

Click on     www.TheMathWebSite.com     if you need help, and on the index of topics page click Geometric Series/Summing an Infinite Series/Quiz. Then click on any question and on its steps for a full solution.

Wednesday, February 23, 2005

Can

The most economical tin can to manufacture is one that is a right circular cylinder with height equal to the diameter. One such can has a volume of 54π cubic cms. What is the total surface area of this can?

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!

Birthday

How many people must be in a
room to be sure that at least four
of them have the same birthday?

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!

There was an old lady in Sheen,
Whose grandchildren numbered sixteen.
Four-fifth of the boys
Were too old to want toys,
So how many girls must that mean?

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!

Keyboard Puzzles

Can you figure out these keyboard puzzles?

`1)   PERSON/          /ALITY`
`2)       ZERO    ---------------    B.A. M.A. Ph.D. `
`3)         |       DARK | LIGHTS ON           | `
`Answers: 1) Split personality         2) Three degrees below zero         3) Lights on after dark `

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!

Monday, February 14, 2005

Keyboard Puzzles 2

Can you figure out these keyboard puzzles?
`a)      eggs        easy`
`b)     -attitude`
`c)      orseman`
`d)     everything           pizza`
`e)     swear       bible       bible       bible`
`f)     bet your        dollar`

Click     www.TheMathWebSite.com     and put a weekly
puzzle, amusement, enrichment or challenge question
like this one on your school's website!

Bumblebee

The Ignorant Bumblebee

The bumblebee is such a fool
Because he never went to school.
If he had gone, then he would wot
That what he does he shouldn't ought.

He'd have learned his bulky form
With aeronautics can't conform,
For scientists have not a doubt
He doesn't know what he's about.

His wings are short, his body round.
He should not ever leave the ground,
But because he passed up school
He's flying still - the silly fool.

-- Harriet Cooper