Christina by stariya

VIEWS: 5 PAGES: 11

									Factor - A factor is a number that divides evenly into another number. 2, 4, 5,20 are all
factors of 20.

Prime Number - A number that can only be divided by one and itself.

Prime Factorization – All the prime factors of a given number. A number can be listed
more than once.

Examples:      20                    100                           54




Greatest Common Factor (GCF) - The greatest common factor is the largest factor
that can be divided into 2 numbers evenly. To find the GCF, find the prime factorization
of both numbers and then line them up. Circle the common factors and then multiply all
the circled numbers on the top row.

Examples: 12,18                      100,225




Try - 250, 500




Least Common Multiple - The smallest multiple that two numbers have in common.
To find the LCM, just find the multiples of each number until you have a match.

Examples: 12, 8                                     100,225
          8- 8,16, 24    LCM =24                    100 – 100,200,300,400,500,…900
          12- 12,24                                 225 – 225,450,675,900
                                                           LCM = 900

Try - 10, 18


1
Order of Operations - Pemdas       Parenthesis, Exponents, Multiplication or Division,
Addition or Subtraction


Examples:




Try:


Integers …-3,-2,-1,0,1,2,3…

Absolute Value- The number of spaces a number is away from 0 on the number line.
The symbol
Examples 5 = 5            -7 = 7          -100 = 100



Adding Integers
Same Sign - Add and keep the sign. Example -25 + -5 = -30
                                             20 + 100 = 125



Try- -15 + -20 =
      25 + 50 =


Different Signs - Take the difference and the use the sign in front of the larger number.
Examples: -25 + 5 = -20
            -10 + 10 = 0
            20 + -8 = 12


Try- 15 + -10
      -6 + 10
     -12 + 20
      40 + -20

Subtracting Integers - Change subtraction to addition. Change the sign of the second
number ( subtrahend) to the opposite. Then add using the integer rules.
Examples - -25 - -10                         -30 - 15
            -25 + +10 = -15                  -30 + -15 = -45
Try: 1) -20 – 8          2) 12 – 5           3) -15 - -10        4) -20 - 14



Multiplying and Dividing Integers - Multiply or divide as usual. Then count up the
number of negative signs. An even number of negative signs is a positive answer and an
odd number of negatives is a negative answer.
Examples- -10 * -2 = 20
            -5 * 4 = -20
            -2 * -3* -5 = -30


Try: 1) -2 * -8 * -2 =
     2) -15 * 2 =
     3) -4 * -5=


Exponents with Integers
(-2) =
(-5) =
( 3) =
(5) =

Algebra
Variable – A variable is a letter that represents a number.
Examples x,w,r,b

Expression – An expression is a math statement without an = sign.
Examples x + 5, 2+3, 5 + n

Equation - An equation is a math sentence with an = sign.
Examples 2 + 3 = 5, x + 6 = 11,       r – 12 = 36

Writing statements in algebraic form – Write a variable for any unknown number and
use symbols for the operations. Also change words to numbers (ten to 10).

Operation words
Adding                   Subtracting         Multiplication               Division
more than                less than           product                      quotient
plus                     minus               times                        divided by
sum                      difference


Examples: A number increased by eleven is twenty.       N + 11 = 20
          Four times a number is forty. 4x=40
            Twice Jan’s salary. 2j
One-Step Equations
Solving
   1. Find the operation used with the variable and use the inverse(opposite) operation
       to solve.

Checking
   1. Rewrite the original equation.
   2. Substitute the number for the letter.
   3. Solve to check.

                 Example:
                        Solve                             Check
                        x + 7 = 14                       x + 7 = 14
                            -7     -7                    7 +7 = 14
                       --------------                     14 =14
                             x=7

                          Solve                            Check
                         N – 5 = 12.5                      N – 5 = 12.5
                             + 5 +5                       17.5 -5 = 12.5
                        -----------------                   12.5 = 12.5
                          N = 17.5


Try: z + 21.4 = 100                                        m – 4 = 12




              Example:
                     Solve                                 Check
                  4z = 16                                  4z= 16
                  4     4                                  4*4=16
                    z= 4                                   16=16



                      w =4                                 w=4
                      2                                     2
                                                           8=4
                      W=8                                  2
                                                            4=4
Try: 5x =20                                  s =12
                                             2




2-Step Equations
Solving
   1. Use the inverse of addition or subtraction to get rid of a number.
   2. Use the inverse of multiplication or division to solve.
Check
   1. Check the same way that you did for the one –step equations.


Example     2x + 7 = 17                              r – 5 = 10
                - 7 -7                               3
            ____________
             2x = 10



Try            4x +16 =20                            p + 12 = 15
                                                     3




Monomials - One term 2x, 4, 10s
Coefficient- The number in front of the variable.
Like terms – Terms with the same variable. Example -2x,4x or 10w,11w
Adding and Subtracting Monomials -
   1. Add the coefficients and keep the same variable.
        Example: 4x + 6x = 10x
                 -3a + 10a = 7a


Try 1) 3a + 70a=              2) -10a + 4a           3) 12c – 6c



Multiplying Monomials
   1. Multiply the coefficients.
   2. Add the exponents of like variables.
Examples:                                                   Try:
Dividing Monomials
   1. Divide the coeffiencts.
   2. Subtract the exponents of like variables.
Examples:                                                    Try:




Simplifying Equations before Solving
   1. Simplify
   2. Solve

Example: 2x + 4x + 12 = 36                                   Try: 12x -10x + 4 = 24
           6x +12 = 36
               -12 -12
           ----------------
          6x = 24
          6         6
             x=4



Geometry

Point – A particular location.   Example .

Line Segment – A line segment is a set of points that starts with an endpoint and ends
with an endpoint. Example ._________________.
                            A                       B

Ray – A set of points that starts with an endpoint and continues in one direction.
 Example

Line – A line is a continuous set of points.
Example


Angle- An angle is formed by two intersecting lines, rays, or line segments.
Example


Degrees – Degrees are used when finding an angle’s measurement.
Right Angle- An angle that measures exactly 90 degrees.
Example
Acute Angle – An angle that measures less than 90 .
Example


Obtuse Angle – An angle that measures more than 90 less than 180.
Example




Straight Angle – An angle that measures exactly 180 degrees.
Example:




Vertical Angles – Angles that are formed by intersecting lines. Opposite angles are
congruent.
Example:


Complementary Angles – Angles that add up to 90 .
Example



Supplementary Angles – Angles that add up to 180 .
Example


Parallel lines cut by a Transversal




Alternate interior angles - Opposite angles located on the interior. They are
congruent.
Example:


Alternate exterior angles- Opposite angles located on the exterior. They are congruent.
Example:
Corresponding Angles - Angles that match up from the bottom to the top. They are
congruent.
Example:




Triangle-

Polygon- Any enclosed figure that has sides.



Triangle- A 3 sided polygon. A triangle has 3 angles that add up to 180 .
Example:



Right triangle- A triangle with one 90 angle.
Example:



Acute Triangle- A triangle with all angles less than 90.
Example:



Obtuse Triangle- A triangle with one obtuse angle.
Example:




Scalene Triangle – A triangle with 3 different sides and angles.
Example:




Isosceles Triangle – A triangle with two congruent sides and angles.
Example:
Equilateral Triangle – A triangle with three congruent sides and angles.
Example:




Area – The inside of a figure.

Perimeter – The distance around the circle.

The Area of a Triangle = base x height    * The base and height always form a 90 angle.
                              2

Examples:




The Perimeter of a Triangle = Side + Side+Side
Examples




Hypotenuse – The longest side of a right triangle.
Legs – The two shorter sides of a right triangle.



Pythagorean Theorem = a2+ b2 = c2             * a and b are the legs, c is the hypotenuse
Page 10


Circle – A circle is a set of points equidistant from a center point.
         There are 360 degrees in a circle.




Radius ( radii) - The radius is the distance between the center point and a point on the
circle.




Diameter - The distance between two points on a circle that also contains the center
point.
* The diameter is twice the size of the radius since it is made up of 2 radii.




Chord – The distance between two points on the circle.




Pi (      ) - 3.141592654… is the number used to help find area and perimeter.



Circumference - is the distance around the circle. The formula to find the circumference
is c =   diameter or c = d




Area – the area is the inside of the circle. The formula to find the area of a circle is A =
where r stands for the radius.
Triangle – 3 sided figure
Quadrilateral – 4 sided figure
Pentagon – 5 sided figure
Hexagon – 6 sided figure
Heptagon – 7 sided figure
Octagon – 8 sided figure
Nonagon – 9 sided figure
Decagon – 10sided figure

								
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