COORDINATES

A Cartesian coordinate system specifies each point uniquely in a plane by a pair of coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.

A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.

Quadrants

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the two coordinates are (+,+), II (−,+), III (−,−), and IV (+,−). When the axes are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("northeast") quadrant.

Similarly, a three-dimensional Cartesian system defines a division of space into eight regions or octants, according to the signs of the coordinates of the points. The octant where all three coordinates are positive is sometimes called the first octant; however, there is no established nomenclature for the other octants. The n-dimensional generalization of the quadrant and octant is the orthant.

ALGEBRAIC EXPRESSIONS

Problem:	Jeanne has $17 in her piggy bank. How much money does she need to buy a game that costs $68?
Solution:	Let x represent the amount of money Jeanne needs. Then the following equation can represent this problem:
	17 + x = 68
	We can subtract 17 from both sides of the equation to find the value of x.
	68 - 17 = x
Answer:	x = 51, so Jeanne needs $51 to buy the game.

In the problem above, x is a variable. The symbols 17 + x = 68 form an algebraic equation.

PHYTHAGORAS THEOREM

a²+b²=c²

'The hypotenuse of a right triangle is the side opposite the right angle', sometimes referred to by students as the long side of the triangle. The other 2 sides are referred to as the legs of the triangle.

http://math.

http://math.about.com/od/pythagorean/ss/pythag_3.htm

INTEGER RULES

Here's How:

1. Adding Rules:

   Positive + Positive = Positive: 5 + 4 = 9
   Negative + Negative = Negative: (- 7) + (- 2) = - 9

   Sum of a negative and a positive number: Use the sign of the larger number and subtract

   (- 7) + 4 = -3
   6 + (-9) = - 3
   (- 3) + 7 = 4
   5 + ( -3) = 2

2. Subtracting Rules:

   Negative - Positive = Negative: (- 5) - 3 = -5 + (-3) = -8
   Positive - Negative = Positive + Positive = Positive: 5 - (-3) = 5 + 3 = 8
   Negative - Negative = Negative + Positive = Use the sign of the larger number and subtract(Change double negatives to a positive)
   (-5) - (-3) = ( -5) + 3 = -2
   (-3) - ( -5) = (-3) + 5 = 2

3. Multiplying Rules:

   Positive x Positive = Positive: 3 x 2 = 6
   Negative x Negative = Positive: (-2) x (-8) = 16
   Negative x Positive = Negative: (-3) x 4 = -12
   Positive x Negative = Negative: 3 x (-4) = -12

4. Dividing Rules:

   Positive ÷ Positive = Positive: 12 ÷ 3 = 4
   Negative ÷ Negative = Positive: (-12) ÷ (-3) = 4
   Negative ÷ Positive = Negative: (-12) ÷ 3 = -4
   Positive ÷ Negative = Negative: 12 ÷ (-3) = -4

Tips:

1. When working with rules for positive and negative numbers, try and think of weight loss or poker games to help solidify 'what this works'.
2. Using a number line showing both sides of 0 is very helpful to help develop the understanding of working with positive and negative numbers/integers.

http://math.about.com/od/prealgebra/ht/PostiveNeg.htm

POLYGONS

Shape	Classification
	Triangle 3 sides Tri means three * There are some special triangles that are important to know: Equilateral: All three sides are the same length and all three angles are equal. Isoceles: Two sides have the same length, the angles opposite the equal sides are equal. Scalene: NO two sides have the same length and no two angles are equal. Acute: All three angles are less than a right angle. Obtuse: One angle is greater than a right angle. Right: One angle is 90 degrees - a right angle.
	Quadrilateral 4 sides Quad means four * There are some special quadrilaterals that are important to know: Parallelogram: the opposite sides are parallel. The angles are also equal. Rectangle: all the angles are right angles. Square: all four sides are equal. Rhombus: all four sides are equal, it looks like a square on a slant. Trapezoid: two sides are parallel and two sides are not parallel.
	Pentagon 5 sides Pent means five
	Hexagon 6 sides Hex means 6
	Octagon 8 sides Oct means 8
	Decagon 10 sides Dec means 10

http://math.about.com/library/blpolygons.htm

AREA AND SURFACE FORMULAS

Shapes	Formula
	Rectangle: Area = Length X Width A = lw Perimeter = 2 X Lengths + 2 X Widths P = 2l + 2w
	Parallelogram Area = Base X Height a = bh
	Triangle Area = 1/2 of the base X the height a = 1/2 bh Perimeter = a + b + c (add the length of the three sides)

	Trapezoid Perimeter = area + b1 + b2 + c P = a + b1 + b2 + c
	Circle Try the Online tool. The distance around the circle is a circumference. The distance across the circle is the diameter (d). The radius (r) is the distance from the center to a point on the circle. (Pi = 3.14) More about circles. d = 2r c = pd = 2 pr A = pr2 (p=3.14)
	Rectangular Solid Volume = Length X Width X Height V = lwh Surface = 2lw + 2lh + 2wh
	Prisms Volume = Base X Height v=bh Surface = 2b + Ph (b is the area of the base P is the perimeter of the base)
	Cylinder Volume = pr2 x height V = pr2 h Surface = 2p radius x height S = 2prh + 2pr2
	Pyramid V = 1/3 bh b is the area of the base Surface Area: Add the area of the base to the sum of the areas of all of the triangular faces. The areas of the triangular faces will have different formulas for different shaped bases.
	Cones Volume = 1/3 pr2 x height V= 1/3 pr2h Surface = pr2 + prs S = pr2 + prs =pr2 + pr
	Sphere Volume = 4/3 pr3 V = 4/3 pr3 Surface = 4pr2 S = 4pr2

http://math.about.com/library/blmeasurement.htm