TIPS : find square of a number between 50 and 60

TIPS : find square of a number between 50 and 60

find square of a number between 50 and 60
for example......
56^2=3136
57^2=3249
58^2=3364

there is a 2 steps trick to get the ans
1) add the digit at the units place to 25 and write the sum
2) then calculate the square of units place digit and write it

eg in case of 56^2
we have 25+6=31
and square of 6 is 36
hence the result is 3136 

done by : Nur Edora Binti Kamarul Bahrin 

Why Algebra is so Important! :D

Why algebra matters

It is frequently called the gatekeeper subject. It is used by professionals ranging from electricians to architects to computer scientists. It is no less than a civil right, says Robert Moses, founder of the Algebra Project, which advocates for math literacy in public schools.

Basic algebra is the first in a series of higher-level math classes students need to succeed in college and life. Because many students fail to develop a solid math foundation, an alarming number of them graduate from high school unprepared for college or work. Many end up taking remedial math in college, which makes getting a degree a longer, costlier process than it is for their more prepared classmates. And it means they're less likely to complete a college-level math course. For middle-schoolers and their parents, the message is clear: It's easier to learn the math now than to relearn it later.

The first year of algebra is a prerequisite for all higher-level math: geometry, algebra II, trigonometry, and calculus. According to a study (pdf) by the educational nonprofit ACT, students who take algebra I, geometry, algebra II, and one additional high-level math course are much more likely to do well in college math.

Algebra is not just for the college-bound. Even high school graduates headed straight for the work force need the same math skills as college freshmen, the ACT found. This study looked at occupations that don't require a college degree but pay wages high enough to support a family of four. Researchers found that math and reading skills required to work as an electrician, plumber, or upholsterer were comparable to those needed to succeed in college.

Algebra is, in short, the gateway to success in the 21st century. What's more, when students make the transition from concrete arithmetic to the symbolic language of algebra, they develop abstract reasoning skills necessary to excel in math and science.

Done by, 

Niraanjana :)

BEARING

 

1. In LAND NAVIGATION, a bearing is the angle between a line connecting two points and a north-south line, or meridian. 


2. A MAGNETIC BEARING is measured in relation to magnetic north, that is, using the direction toward the magnetic pole (in northeastern Canada) as a reference.


3. Bearings can be measured in two systems, Mils and Degrees.


4. According to Oxford Dictionary, bearing is the direction or position of something relative to a fixed point, normally measured in degrees and with the magnetic north as zero.

*******************************  

CARDINAL / COMPASS DIRECTION

The 4 major cardinal direction points are : NORTH, SOUTH, EAST & WEST

Intermediate (in other words, intercardinal or ordinal) directions are :

 north-east (NE),

 north-west (NW), 

south-west (SW) 

& 

south-east (SE)

also

DIRECTION CORRESPONDS TO A DEGREE OF A COMPASS 


****************************************

COMPASS 

•  Used to find a direction or bearing
• Invented in ancient China around 247 B.C and was used for navigation by the 11th century.
• DRY COMPASS was invented in medieval Europe around 1300. 
• Early 20th century, came the invention of liquid-filled compass.
• Besides navigational use, compass is used in building orientation, mining and astronomy. 
• Other modern compasses include thumb compass, gyrocompass, solid-state compass, Qibla compass and so on.

Done by, Sharifah. 

circle

Circle Equations

A circle is easy to make: Draw a curve that is "radius" away from a central point. And so: All points are the same distance from the center.

In fact the definition of a circle is

The set of all points on a plane that are a fixed distance from a center.

Let us put that center at (a,b). So the circle is all the points (x,y) that are "r" away from the center(a,b).

Now we can work out exactly where all those points are!

We simply make a right-angled triangle (as shown), and then usePythagoras (a2 + b2 = c2): (x-a)2 + (y-b)2 = r2 And that is the "Standard Form" for the equation of a circle!

You can see all the important information at a glance: the center (a,b) and the radius r.

General Form

But you may see a circle equation and not know it!

Because it may not be in the neat "Standard Form" above.

As an example, let us put some values to a, b and r and then expand it

Start with:		(x-a)2 + (y-b)2 = r2
Set (for example) a=1, b=2, c=3:		(x-1)2 + (y-2)2 = 32
Expand:		x2 - 2x + 1 + y2 - 4y + 4 = 9
Gather like terms:		x2 + y2 - 2x - 4y + 1 + 4 - 9 = 0

And we end up with this:

x² + y² - 2x - 4y - 4 = 0

It is a circle equation, but "in disguise"!

So when you see something like that think "hmm ... that might be a circle!"

In fact we can write it in "General Form" by putting constants instead of the numbers:

x² + y² + Ax + By + C = 0

Going From General Form to Standard Form

Imagine you have an equation in General Form (like the example above):

x² + y² - 2x - 4y - 4 = 0

How could you get it into Standard Form like (x-a)² + (y-b)² = r² ?

The answer is to Complete the Square (better read up on that!) ... for x and for y:

Start with:		x2 + y2 - 2x - 4y - 4 = 0
Put xs and ys together on left:		(x2 - 2x) + (y2 - 4y) = 4
Now to complete the square you take half of the middle number, square it and add it. (Also add it to the right hand side so the equation stays in balance!) And do it for x and y.
Do it for "x":		(x2 - 2x + (-1)2) + (y2 - 4y) = 4 + (-1)2
And for "y":		(x2 - 2x + (-1)2) + (y2 - 4y + (-2)2) = 4 + (-1)2 + (-2)2
Simplify:		(x2 - 2x + 1) + (y2 - 4y + 4) = 9
Finally:		(x - 1)2 + (y - 2)2 = 32

And we have it in Standard Form!

Unit Circle

If we place the circle center at (0,0) and set the radius to 1 we get:

(x-a)2 + (y-b)2 = r2 (x-0)2 + (y-0)2 = 12 x2 + y2 = 1 Which is the equation of the Unit Circle

How to Plot a Circle by Hand

1. Plot the center (a,b)

2. Plot 4 points "radius" away from the center in the up, down, left and right direction

3. Sketch it in!

Example: Plot (x-4)² + (y-2)² = 25

The formula for a circle is (x-a)² + (y-b)² = r²

So the center is at (4,2)

And r² is 25, so the radius is √25 = 5

So we can plot: The Center: (4,2) Up: (4,2+5) = (4,7) Down: (4,2-5) = (4,-3) Left: (4-5,2) = (-1,2) Right: (4+5,2) = (9,2)

Now, just sketch in the circle the best that you can!

How to Plot a Circle on the Computer

You need to rearrange the formula so you get "y=".

You should end up with two equations (top and bottom of circle) that can then be plotted.

Example: Plot (x-4)² + (y-2)² = 25

So the center is at (4,2), and the radius is √25 = 5

Rearrange to get "y=":

Start with:		(x-4)2 + (y-2)2 = 25
Move (x-4)2 to the right:		(y-2)2 = 25 - (x-4)2
Take the square root:		(y-2) = ± √[25 - (x-4)2]
		(notice the "plus/minus" ...  you can have two square roots!)
Move the "-2" to the right:		y = 2 ± √[25 - (x-4)2]

Now, plot the two equations, and you should have a circle:

• y = 2 + √[25 - (x-4)²]
• y = 2 - √[25 - (x-4)²]

Have a look at the plot of this circle

by nur shadzana circlecircle dotdot 

Beauty of Mathematics

Sequential Inputs of numbers with 8

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

Sequential 1's with 9

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 + 10 = 1111111111

Sequential 8's with 9

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888888888

Numeric Palindrome with 1's

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

Without 8

12345679 x 9 = 111111111

12345679 x 18 = 222222222

12345679 x 27 = 333333333

12345679 x 36 = 444444444

12345679 x 45 = 555555555

12345679 x 54 = 666666666

12345679 x 63 = 777777777

12345679 x 72 = 888888888

12345679 x 81 = 999999999

Sequential Inputs of 9

9 x 9 = 81

99 x 99 = 9801

999 x 999 = 998001

9999 x 9999 = 99980001

99999 x 99999 = 9999800001

999999 x 999999 = 999998000001

9999999 x 9999999 = 99999980000001

99999999 x 99999999 = 9999999800000001

999999999 x 999999999 = 999999998000000001

......................................

Sequential Inputs of 6

6 x 7 = 42

66 x 67 = 4422

666 x 667 = 444222

6666 x 6667 = 44442222

66666 x 66667 = 4444422222

666666 x 666667 = 444444222222

6666666 x 6666667 = 44444442222222

66666666 x 66666667 = 4444444422222222

666666666 x 666666667 = 444444444222222222

...................................... Done by ,  Muna

Solid Geometry

Solid Geometry is the geometry of three-dimensional space, the kind of space we live in ...

Three Dimensions

It is called three-dimensional, or 3Dbecause there are three dimensions:width, depth and height.

Properties

Solids have properties (special things about them), such as:

• Volume
• Surface area

Polyhedra and Non-Polyhedra

There are two main types of solids, "Polyhedra", and "Non-Polyhedra":

	Polyhedra : (they must have flat faces)	Platonic Solids Prisms Pyramids
	Non-Polyhedra: (if any surface is not flat)	Sphere Torus Cylinder Cone

DONE BY,

AMEERA LIYANA

Solid Geometry

Solid Geometry is the geometry of three-dimensional space - the kind of space we live in ...

Let us start with some of the simplest shapes:

• Cube <-- CLICK FOR MORE INFO

Cube (Hexahedron)

Cube (Hexahedron) Facts Notice these interesting things: It has 6 Faces Each face has 4 edges, and is actually a square It has 12 Edges It has 8 Vertices (corner points) and at each vertex 3 edges meet And for reference: Surface Area = 6 × (Edge Length)2 Volume = (Edge Length)3 A cube is called a hexahedron because it is a polyhedron that has 6 (hexa-means 6) faces.  Cubes make nice 6-sided dice, because they are regular in shape, and each face is the same size. In fact, you can make fair dice out of all of the Platonic Solids.

• Cuboid <---CLICK FOR MORE INFO

Cuboids, Rectangular Prisms and Cubes

A cuboid is a box-shaped object. It has six flat sides and all angles are right angles. And all of its faces are rectangles. It is also a prism because it has the same cross-section along a length. In fact it is a rectangular prism.

• Volume of a Cuboid <-- CLICK FOR MORE INFO

By: Hananzee

Lets Learn Lines and Planes in 3-Dimension!

The angle between 2 lines

We define the angle between 2 lines to be the angle between their direction vectors placed tail to tail. Notice that this definition works equally well if the lines don't actually cut each other since we then just slide the 2 direction vectors together until their tails meet.

Ways to find the angle between two lines.

The angle between 2 planes

  

• Two planes intersect at a straight line. This line is known as the line of intersection.

• The angle between two planes that intersect is the angle between two lines, one on each planes, that is perpendicular to the line of intersection and from a common point on the line of intersection.

•  Line of intersection = two same letters of the two planes.

                                                     

                     Angle between lines and planes

                                       

                                                     

 

•  A normal to a plane is a straight line that is perpendicular to any line on the plane that     passes through the intersection point of the straight line and the plane.

• The orthogonal projection is the line joining the normal vertex on the plane to the other vertex of the line on the plane.

• The angle between a line and a plane is the angle between the line and its orthogonal projection on the plane.

                                                         

                                           

               

DONE BY,

Adina.