Multiplication Table

Multiplication Table

x	0	1	2	3	4	5	6	7	8	9	10	11	12
0	0	0	0	0	0	0	0	0	0	0	0	0	0
1	0	1	2	3	4	5	6	7	8	9	10	11	12
2	0	2	4	6	8	10	12	14	16	18	20	22	24
3	0	3	6	9	12	15	18	21	24	27	30	33	36
4	0	4	8	12	16	20	24	28	32	36	40	44	48
5	0	5	10	15	20	25	30	35	40	45	50	55	60
6	0	6	12	18	24	30	36	42	48	54	60	66	72
7	0	7	14	21	28	35	42	49	56	63	70	77	84
8	0	8	16	24	32	40	48	56	64	72	80	88	96
9	0	9	18	27	36	45	54	63	72	81	90	99	108
10	0	10	20	30	40	50	60	70	80	90	100	110	120
11	0	11	22	33	44	55	66	77	88	99	110	121	132
12	0	12	24	36	48	60	72	84	96	108	120	132	144

Monomials, Binomials, and Polynomials

	A monomial is a constant, a variable, or the product of a constant and one or more variables.
	A polynomial is the sum of one or more monomials.

 

"... this means that a monomial is a single term which has NO plus sign (+) or minus sign (-) between entries.  It could be things like  13, 3x, -57, x², 4y², -2xy, or  520x²y²   but NOT (2x+7) or (4x²-2x)." "A polynomial can be one monomial or a bunch of monomials hooked together with plus signs and/or minus signs."

 

Name	Number of Terms	Example
Monomial	1 (mono implies one)	4x²
Binomial	2(bi implies two)	4x² + 3x
Trinomial	3(tri implies three)	4x² + 3x + 5

             


The expression 
4x² is a monomial because it has one term.

The expression
4x² + 3x is a
binomial
because it has two terms.

The expression  4x² +3x + 5 is
a trinomial
because it has three terms.                                                                           

All three
expressions can be
called polynomials.

Solids

Volume
is measured in cubic units.

Surface area is measured in square units.

Volume (V) and
Surface Area (SA) Formulas

	Rectangular Solid V=lwh SA=2lh + 2hw + 2lw
	Cylinder
	Sphere
	Cone

 

If the cross-sectional shape of a solid is the same at every level,  the volume of the solid is the product of  the area of its base and its height:  V = Bh

 

 

	Prism V = Bh
	Pyramid

volume & surface areas of solids

Space Figure

A space figure or three-dimensional figure is a figure that has depth in addition
to width and height. Everyday objects such as a tennis ball, a box, a bicycle, and
a redwood tree are all examples of space figures. Some common simple space figures
include cubes, spheres, cylinders, prisms, cones, and pyramids. A space figure having
all flat faces is called a polyhedron. A cube and a pyramid are both polyhedrons;
a sphere, cylinder, and cone are not.

---

Cross-Section

A cross-section of a space figure is the shape of a particular two-dimensional
"slice" of a space figure.

Example:

The circle on the right is a cross-section of the cylinder on the left.

The triangle on the right is a cross-section of the cube on the left.

---

Volume

Volume is a measure of how much space a space figure takes up. Volume is used
to measure a space figure just as area is used to measure a plane figure. The volume
of a cube is the cube of the length of one of its sides. The volume of a box is
the product of its length, width, and height.

Example:

What is the volume of a cube with side-length 6 cm?

The volume of a cube is the cube of its side-length, which is 6³ = 216
cubic cm.

Example:

What is the volume of a box whose length is 4cm, width is 5 cm, and height is
6 cm?

The volume of a box is the product of its length, width, and height, which is 4 × 5 × 6 = 120
cubic cm.

---

Surface Area

The surface area of a space figure is the total area of all the faces of the figure.

Example:

What is the surface area of a box whose length is 8, width is 3, and height is
4? This box has 6 faces: two rectangular faces are 8 by 4, two rectangular faces
are 4 by 3, and two rectangular faces are 8 by 3. Adding the areas of all these
faces, we get the surface area of the box:

8 × 4 + 8 × 4 + 4 × 3 + 4 × 3 + 8 × 3 + 8 × 3 =


32 + 32 + 12 + 12 +24 + 24=

136.

---

Cube

A cube is a three-dimensional figure having six matching square sides. If L
is the length of one of its sides, the volume of the cube is L³ = L × L × L.
A cube has six square-shaped sides. The surface area of a cube is six times the
area of one of these sides.

Example:

The space figure pictured below is a cube. The grayed lines are edges hidden from
view.

Example:

What is the volume and surface are of a cube having a side-length of 2.1 cm?

Its volume would be 2.1 × 2.1 × 2.1 = 9.261
cubic centimeters.

Its surface area would be 6 × 2.1 × 2.1 = 26.46
square centimeters.

---

Cylinder

A cylinder is a space figure having two congruent circular bases that are parallel.
If L is the length of a cylinder, and r is the radius of one of the
bases of a cylinder, then the volume of the cylinder is L × pi × r²,
and the surface area is 2 × r × pi × L + 2 × pi × r².

Example:

The figure pictured below is a cylinder. The grayed lines are edges hidden from
view.

---

Sphere

A sphere is a space figure having all of its points the same distance from its
center. The distance from the center to the surface of the sphere is called its
radius. Any cross-section of a sphere is a circle.

If r is the radius of a sphere, the volume V of the sphere is given
by the formula V = 4/3 × pi ×r³.


The surface area S of the sphere is given by the formula S = 4 × pi ×r².

Example:

The space figure pictured below is a sphere.

Example:

To the nearest tenth, what is the volume and surface area of a sphere having a
radius of 4cm?

Using an estimate of 3.14 for pi,

the volume would be 4/3 × 3.14 × 4³ = 4/3 × 3.14 × 4 × 4 × 4 = 268
cubic centimeters.

Using an estimate of 3.14 for pi, the surface area would be 4 × 3.14 × 4² = 4 × 3.14 × 4 × 4 = 201
square centimeters.

---

Cone

A cone is a space figure having a circular base and a single vertex.

If r is the radius of the circular base, and h is the height of the
cone, then the volume of the cone is 1/3 × pi × r² × h.

Example:

What is the volume in cubic cm of a cone whose base has a radius of 3 cm, and
whose height is 6 cm, to the nearest tenth?

We will use an estimate of 3.14 for pi.

The volume is 1/3 × pi × 3² × 6 = pi ×18 = 56.52,
which equals 56.5 cubic cm when rounded to the nearest tenth.

Example:

The pictures below are two different views of a cone.

---

Pyramid

A pyramid is a space figure with a square base and 4 triangle-shaped sides.

Example:

The picture below is a pyramid. The grayed lines are edges hidden from view.

---

Tetrahedron

A tetrahedron is a 4-sided space figure. Each face of a tetrahedron is a triangle.

Example:

The picture below is a tetrahedron. The grayed lines are edges hidden from view.

---

Prism

A prism is a space figure with two congruent, parallel bases that are polygons.

Examples:

The figure below is a pentagonal prism (the bases are pentagons). The grayed lines
are edges hidden from view.

The figure below is a triangular prism (the bases are triangles). The grayed lines
are edges hidden from view.

The figure below is a hexagonal prism (the bases are hexagons). The grayed lines
are edges hidden from view..

Tricky Math Questions

Have a go at solving these 15 math questions.




Questions:



1) There are 8 Apples on the table, you take 3. How many do you have?



2) 10 Birds in a field. 2 were shot, how many were left?


3) Take away the first letter, take away the last letter, then take away all the other letters. What do you have left?



4) If you have 4 melons in one hand, and 7 apples in the other - What do you have?



5) A box has nine ears of corn in it. A Squirrel carries out three ears
a day, and yet it takes him nine days to carry out all the corn.
Explain?



6) Why do white sheep eat more than black sheep?



7) A man wanted to plant 4 trees, but all 4 had to be equal distances from each other. How did he do it?



8) I have 2 coins in my hand that add up to 60c. One of the coins isn't a 50c piece. What are the coins?



9) A fisherman was asked how long was the fish he had caught. He said "it is 30cms plus half its length" How long was the fish?



10) A Hammer and a Nail cost $31. If the Hammer cost $30 more than the Nail, what is the cost of each?



11) It takes 7 men 2 hours to build a wall. How long does it take 3 men to build the same wall?



12) "I will bet you $1" said Fred, "that if you give me $2, I will give you $3 in return."
"Done," replied Tom. Was he?



13) "How much will one cost?"

"25 cents"

"How much will fifteen cost?"

"50 cents"

"OK then, I'll take one hundred and sixteen"

"Thank you, that will be 75 cents please"

Explain.



14) What comes next in the following sequence ?
1, 4, 5, 6, 7, 9, 11,...



15) In a scientific context, what could the following phrase mean?
How I want a drink, alcoholic of course, after the heavy chapters involving quantum mechanics


Dont Look for the Answers.




















Answers:



1) If you take 3 then you have 3.



2) 2 - the others flew away.



3) The Mailman.



4) Big hands.



5) He has 2 of his own ears, so he carries out only 1 ear of corn per day.



6) There are more white sheep than black sheep.



7) He planted 3 trees at the corners of an equilateral triangle. He
built a mound in the middle and planted the 4th on the top of the mound
so that it was the same distance from the other 3 trees. (on the points
of a tetrahedron.)



8) 50c and a 10c (The coin that isn't a 50c piece is a 10c. The other coin is the 50c).



9) 60 cms.



10) Hammer $30.50, Nail $0.50



11) No need to bother, the 7 men have already built it.



12) Tom accepts the bet, gives Fred $2. Fred does not give Tom $3 so loses the bet and has to pay Tom $1. Result Fred gains $1.



13) He is buying house numbers, each separate digit costs 25c, so 116 is three digits so 3 x 25c = 75c.



14) 100 (The next number that doesn't contain a "T" in the spelling).



15) The number of letters in each word refers to pi to 14 decimal places, i.e. 3.14159265358979

Marvellous Answer

A mechanic was removing the
cylinder heads from the motor of a car when he spotted the famous heart
surgeon in his shop, who was standing off to the side, waiting for the
service manager to come to take a look at his car. The mechanic shouted
across the garage,"Hello Doctor!! Please come over here for a minute."
The famous surgeon, a bit surprised, walked over to the
mechanic.


The mechanic straightened up, wiped his hands on a
rag and asked argumentatively, "So doctor, look at this. I also open
hearts, take valves out, grind 'em, put in new parts, and when I finish
this will work as a new one. So how come you get the big money, when you
and me is doing basically the same work? "
The doctor leaned over
and whispered to the mechanic...................

*
*
*
*
*
*

       
      He said:
"Try to do it when the engine is running ".

How observant r u??

Readout loud the text inside the triangle below.
 

 

 

 

 

More than likely yousaid, "A bird in the bush," and........

 

if thisIS what YOUsaid, then youfailed to see

 

that the word THE is repeated twice!

 

Sorry, look again.

 

 

Next, let's play with some words.

 

What do yousee?

 

 

 
In
black youcanreadthe word GOOD, in white the word EVIL (inside each
black letter is a white letter). It's all very physiological too,
because it visualize the concept that good can't exist without evil (or
the absence of good is evil ).    
 
 
 
 
 
Now, what do yousee?
 
 
 
 
 
 
 

 
 
 
 
 
 
 
Youmay
not see it at first, but the white spaces readthe word optical, the
blue landscape reads the word illusion. Look again! Canyousee why
thispainting is called an optical illusion?
 
 
 
What do yousee here?
 
 
 
 
 

 
 
 
 
 
Thisone is quite tricky!
 
The word TEACH reflects as LEARN.
 
 
 
 
 
Last one.
 
What do yousee?
 
 
 

 
 
 
Youprobably readthe word ME in brown, but.......
 
when youlook through ME
 
youwill see
 
YOU!
 
 
 
 
 
Do youneed to look again?
 
 
 

---

---

Test Your Brain
Thisis really cool. The second one is amazing so please readall the way though.
 





 
 
                                   
 
 

ALZHEIMERS' EYE TEST Count every "F" in the following text: FINISHED FILES ARE THE RE SULT OF YEARS OF SCIENTI FIC STUDY COMBINED WITH THE EXPERIENCE OF YEARS... (SEE BELOW) HOW MANY ? WRONG, THERE ARE 6 -- no joke. READIT AGAIN ! Really, go Back and Try to find the 6 F's before youscroll down. The reasoning behind is further down. The brain cannot process "OF".                           Incredible or what? Go back and look again!! Anyone who counts all 6 "F's" on the first go is a genius.                                                 Three is normal, four is quite rare. Send thisto your friends. It will drive them crazy.! And keep them occupied For several minutes..!

More Brain Stuff . .  From Cambridge University.   O lny srmat poelpe canraed tihs.     cdnuolt blveiee taht I cluod aulaclty  uesdnatnrd waht I was rdanieg. The phaonmneal pweor of the hmuan mnid, aoccdrnig  to a rscheearch at Cmabrigde Uinervtisy,   it deosn't mttaer in waht oredr the  ltteers in a wrod are, the olny iprmoatnt tihng is taht the frist and lsat  ltteer be in the rghit pclae. The rset canbe a taotl mses and youcansitll  raed it wouthit a porbelm.   Tihs is bcuseae the huamn mnid deos not raed ervey  lteter by istlef, but the wrod as a wlohe. Amzanig huh? yaeh and I awlyas  tghuhot slpeling was ipmorantt! if youcanraed tihs psas it on  !!

Roman Numerals

The Basics

A smaller number in front of a larger number means subtraction, all else means addition. For example, IV means 4, VI means 6. You would not put more than one smaller number in front of a larger number to subtract. For example, IIV would not mean 3. You must separate ones, tens, hundreds, and thousands as separate items. That means that 99 is XCIX, 90 + 9, but never should be written as IC. Similarly, 999 cannot be IM and 1999 cannot be MIM.
I	The numeral one. II is two, III is three. You seldom see IIII as 4, since IV can also mean 4, plus its shorter to write.
V	The numeral 5. IV is 4, VI is 6, VII is 7, VIII is 8.
X	The numeral 10. IX is 9, XI is 11, etc.
L	The numeral 50. XL would be 40.
C	The numeral 100. Think of Century having a hundred years. C is short for the Latin word Centum, but that's not very easy to remember.
D	The numeral 500.
M	The numeral 1000.
Sometimes you will see a numeral with a line over it. That means to multiply it by 1000. A numeral V with a line over it means 5000.

Scatter Plots

Scatter plots are similar to line graphs in that they
use horizontal and vertical axes to plot data points.
However, they have a very specific purpose. Scatter
plots show how much one variable is affected by another.
The relationship between two variables is called their
correlation .

Scatter plots usually consist of a large body of data.
The closer the data points come when plotted to making
a straight line, the higher the correlation between the
two variables, or the stronger the relationship.

If the data points make a straight line going from the
origin out to high x- and y-values, then the variables
are said to have a positive correlation . If
the line goes from a high-value on the y-axis down to
a high-value on the x-axis, the variables have a
negative correlation .

A perfect positive correlation is given the value of 1.
A perfect negative correlation is given the value of -1.
If there is absolutely no correlation present the value
given is 0. The closer the number is to 1 or -1, the
stronger the correlation, or the stronger the relationship
between the variables. The closer the number is to
0, the weaker the correlation. So something that seems
to kind of correlate in a positive direction might have
a value of 0.67, whereas something with an extremely weak
negative correlation might have the value -.21.

An example of a situation where you might find a perfect positive
correlation, as we have in the graph on the left above, would be
when you compare the total amount of money spent on tickets at
the movie theater with the number of people who go. This means
that every time that "x" number of people go, "y" amount of money
is spent on tickets without variation.

An example of a situation where you might find a perfect negative
correlation, as in the graph on the right above, would be if you
were comparing the speed at which a car is going to the amount of
time it takes to reach a destination. As the speed increases, the
amount of time decreases.

On the other hand, a situation where you might find a strong but not
perfect positive correlation would be if you examined the number of
hours students spent studying for an exam versus the grade received.
This won't be a perfect correlation because two people could spend the
same amount of time studying and get different grades. But in general
the rule will hold true that as the amount of time studying increases
so does the grade received.

Let's take a look at some examples. The graphs that were shown
above each had a perfect correlation, so their values were 1 and
-1. The graphs below obviously do not have perfect correlations.
Which graph would have a correlation of 0? What about 0.7? -0.7? 0.3?
-0.3?