Circumference

Formula for Circumference?

Well - if you eat a pie a day, you will get a big circumference. (Distance around your middle.)

 

C = ∏   x  D    (diameter)

Find the diameter (or double the radius if the radius is given), multiply by pi and you will get the circumference.












Work Smart, Not Hard!

Do you know "Y" you were intercepted Part Three

"Do you know "Y" you were intercepted?" Part Three

 Which line has the equation          y = x + 6

Ok, smarty pants. What if 2 lines cross at the same spot and both have positive slopes? What then? (In this case, lines 5 and 8)

 

 

 

Then, we have to work out the slope of lines 5 and 8.

 

 

Think of jogging. If you want to go for a run up a slope in the morning, you must rise first before you run.

So...    to calculate the slope of a line...
use the formula...             slope = rise
                                                        run

Rise divided by run.

 

Rise is the vertical distance between two points on a slope. Run is the horizontal distance between two points on a slope.

 

Pick any 2 spots on line #5. Try to pick spots at the corners of the underlying grid.

 

slope = rise   2   = 1    run    2

 

Pick any 2 spots on line #8. Try to pick spots at the corners of the underlying grid.

 

 

slope = rise   4   = 2    run    2

 

Which line has the equation          y = x + 6

 

(Remember that this question can be written as y = 1x + 6. By convention, in algebra, the "1" in front of a letter or variable can be dropped for convenience.)

 

The slope of the line is associated with the value in front of the "x" in the given equation. The free floating number (in this case the "6"), is the place on the Y axis where the line crosses or intercepts.

 

Has to be line 5 for your answer, as it has a slope of 1. You are done.

 

Work SMART not HARD.

 

 

 

Do you know "Y" you were intercepted Part Deux

OK - so maybe the last post was a bit easy.

Perhaps there might be a harder question on the GED test?

A quick review... Which line has the equation

 

 y = x + 6

 

 

First of all, image you have been driving along and are suddenly "intercepted" by the police.

"Do you know "y" you were intercepted?" is probably the question you will be asked.

 

The key to this question is the "y" intercept, or the location at which the line crosses (intercepts) the "y" or vertical axis. (For some reason, nobody really cares about the poor old "x" axis. As with all "ex's", they are best left forgotten.)

 

y = x + 6 

 

The free floating number here is the 6. The only line that crosses/intercepts the "y"axis at 6 is line 5. Job done. You are finished.

 

                                 

 

OK, but what about...

 

 

 

 

 

 

Looks like 2 lines intercepting the "y" axis at 6. (Lines 5 and 7) So how now, brown cow?

 

Well, the next clue is the slope of the line. The free floating number corresponds with the intercept while the value associated with the "X" determines the slope. In this case, the slope is positive 1.

 

How can that be? (In algebra, values of positive 1 are dropped, being "understood" to be positive 1.) The formula for this line could have been written as y = 1x + 6

 

So we now need to find which line has a slope of positive 1.

 

By convention, lines that "rise" from the lower left to the upper right are considered to have a positive slope, Lines that "fall" from the upper left to the lower right have negative slopes. That rules out line 7.

 

 

Work SMART, not HARD!

Do you know "Y" you were "intercepted"?

Look familiar? - Which line has the equation

 

 y = x + 6

These questions look harder than they are.

 

First of all, image you have been driving along and are suddenly "intercepted" by the police.

"Do you know "y" you were intercepted?" is probably the question you will be asked.

 

The key to this question is the "y" intercept, or the location at which the line crosses (intercepts) the "y" or vertical axis. (For some reason, nobody really cares about the poor old "x" axis. As with all "ex's", they are best left forgotten.)

 

y = x + 6 

 

The free floating number here is the 6. The only line that crosses/intercepts the "y"axis at 6 is line 5. Job done. You are finished.

 

Work SMART, not HARD!



Congruent! Gruesome! Grew Some!

Teacher: "Chris, use the word 'gruesome' in a sentence."
Chris: "A prisoner didn't shave for a week and grew some whiskers."

 

What's this got to do with congruency?

"Congruent" - definition: geometric figures of the same shape and the same size

Note: The figures don't have to be facing in the same direction to be congruent. Think of it as...

"If I cut one shape out, I can rotate it, place it over the top of another shape  and the two shapes will match up exactly."

What if our prisoner above (our con) had a twin brothers who also grew some whiskers....

 

 

Even though con #2 is facing in another direction, he and con #1 are, indeed, congruent.

On the Way to Grandma's House

Look familiar?

7 (x + 2) = 28

 

Solve for x

 

 

This is a Little Red Riding Hood question. Watch out for the...

Little Red Riding Hood decides to take 7 baskets... to Grandma's house. Each basket contains...

   an  X

and 2 apples (or whatever you'd like)

 

Therefore...



 

Little Red Riding Hood will carry a total of 7x and 14

 

 

Now we have a simple equation

 

7x + 14 = 28

 

 

We will employ the dump, shove and divide method to solve it.

 

 

1) DUMP 14 off each side of the equation so you have 7x = 14

 

 

2) SHOVE

the 7 under the 14

 

 

 

14

__

 

 7

 

 

 

 

3)

...14 by 7. Your answer is 2.

 

 

 

 

Done! Work smart, not hard!

 

 





  

 

 

 



10% Rule Part Deux - Using 1%

The 10% Rule RULES! Part Two

A quick review...

 

You can calculate any percentage using the 10% rule.

 

 

 

Example 1: What is 15% of 40?

 

 

Start by finding 10%.

 

To find 10%, think of 40 as 40.0

 

Move your decimal ONE place to the left and you have...

 

 

 

4.0  or 4

 

 

5% is half of 10%. Half of 4 is 2, so you need another

 

2

 

4 + 2 = 6

 

 

 

 

DONE! Work SMART not HARD

 

 

 

 

The 1% rule is just an extension of the 10% rule. 

 

 

Example 2: What is 16% of 40?

 

 

16% is just 10% plus 5 % plus 1%

 

 

 

Start by finding 10%.

 

To find 10%, think of 40 as 40.0

 

Move your decimal ONE place to the left and you have...

 

 

4.0  or 4

 

 

5% is half of 10%. Half of 4 is 2, so you need another

 

2

 

4 + 2 = 6

 

Now you just need that last 1%.

 

To find 1%, think of 40 as 40.0

 

Move your decimal TWO places to the left and you have...

 

 

.4

 

4 + 2 + .4 = 6.4

 

 

DONE! Work SMART not HARD

The 10% Rule RULES! Part One

 

You can calculate any percentage using the 10% rule.

 

No need to remember any rules, formulae or part/whole/percent triangles.

 

Example 1: What is 15% of 40?

 

 

Start by finding 10%.

 

To find 10%,

chop off the "0" in 40 and you have...

 

4

 

 

5% is half of 10%. Half of 4 is 2, so you need another

 

2

 

4 + 2 = 6

 

 

DONE! Work SMART not HARD

 

 

Example 2: What is 15% of 42?

 

 

There's no zero to chop!

 

Think of 42 as "42 decimal" or "42." Move that decimal one place to the left and you have 4.2

 

This is your 10%.

 

5% is half of 10%. Half of 4.2 is 2.1, so you need another

 

2.1

 

4.2 + 2.1 = 6.3

 

DONE! Work SMART not HARD

 

 

 

 

 

 

Neat Trick for Squares - Well Some of Them

If you are squaring a number that ends in 5, your answer will end in 25.

There's the early Christmas present...

That's the easy part. What about the hard part?

There isn't one...

2

15

 

You know your answer will end in 25...

 

Now, multiply the first digit (the 1 in 15) by ONE larger (2)

 

1 x 2 = 2

 

Stick the 2 in front of the 25 and you have your answer...

 

225

 

Try squaring 25...

 

You know your answer will end in 25...

 

Now, multiply the first digit (the 2 in 25) by ONE larger (3)

 

2 x 3 = 6

 

Stick the 6 in front of the 25 and you have your answer...

 

625

 

Still not convinced?

 

Try squaring 35...

 

You know your answer will end in 25...

 

Now, multiply the first digit (the 3 in 25) by ONE larger (4)

 

3 x 4 = 12

 

Stick the 12 in front of the 25 and you have your answer...

 

1225

 

 

 

 

 

 

 

Quick Calculations - Use Half and Double

 

 

                                           X        


Work smart, not hard!

Double the...

... to...

 and halve the ...
 
 
 

... to...

 

 

100 X 8 = 800. Done!

 

Use "7" as your "Key"

Try this trick for multiplying two 2 digit numbers under 20. For example...

First off, make sure the larger number is on top.

Then think of the number 7. Well, the shape of it, anyway.

Now ADD 13 and 2 and stick a zero on the end.

Now cover up everything in the left (or 10's) column.

Now ADD 150 and 6 and you get 156

Done!

Percent Video (Type 5)

Percent Video (Type 5)

I have identified at least 5 distinct types of percent questions. (There may be more...) These include...

1) One number expressed as a % of another

2) Finding a certain % of a given number

3) (For want of a better title) The good old "650 is 15 % of what number" type of question.

4) Percent change

5) Increasing or decreasing a number by a given percentage

 

Here's the link for the 5th of 5 videos in a series on percent questions.