Monday, June 18, 2012

Definitions Relevant To Central Tendency

Mean: The sum of a set of values divided by the number of values in a set.

Median: The middle number of a data set after the data has been arranged in order.

Mode: The most frequently occurring number in a data set.

Range: The positive difference between the largest and smallest values in a data set.

Outlier: A value that is much larger or smaller than the other data values.

Definitions Relevant To Probability

Probability: The chance of an event occurring.

Outcome: One possible result of a probability experiment.

Favourable Outcome: A successful result in a probability experiment.

Independent Event: The outcome of one event that has no effect on the outcome of another event.

Sample Space: All possible outcomes of an experiment.

Random: An event in which every outcome has an equal chance of occurring.

Theoretical Probability: The expected outcome of an event happening.

Experimental Probability: The probability of an event occurring based on experimental results.

Sunday, June 17, 2012

Experimental Probability

Experimental probability is when you do an experiment and get results from the experiment, whether or not they differ from the theoretical probability.

Divisible

Divisible means when a number can be divided by another number with no remainders/ it is a whole number.

The divisibility rules

The rules show when a number is divisible by that number
0- when the number ends in 0
1- All numbers
2- All even numbers
3- If the sum of all the digits equal to something that can be divided by 3, it is.
4- It's divisible by two twice
5- If it ends in 5 or 0.
6- If it is divisible by 2 and 3
8- If divisible by 2 thrice.
9- If the sum of the digits is divisible by 9
10- ends in 0

An outlier

An outlier is a number that is either too small or too big compared to other numbers in a data set.
e.g 5, 5, 6, 7, 1000
The outlier is 1000

Range

The range of a data set is when you subtract the smallest value from the biggest value.
E.g 4, 5, 6, 7
7 - 4 = 3
The range is 3

The Median

The median is the middle number in a data set, or the mean of two middle values
E.g 3, 4, 5 , 6, 7
In this the median is 5
Another e.g 3, 4, 6, 7
4 + 6 = 10
10  ÷ 2 = 5.
The median for this is 5.

The mode

The mode is the easiest for data sets
It is the most frequently shown number in a data set
Example: 1,1,1,1,1,2,2,2,3
The mode is 1.

The mean

To find the mean in a data set, you must take all the values, add them together and then devide that number by the number of values.
Example: 1, 2, 3, 4, 5
1 + 2 + 3 + 4 + 5 = 15
15 ÷ 5 = 3
The mean is 3

Definitions Relevant to Geometry

Parallel lines: Lines in the same plane that never cross or intersect.



Intersecting: Lines in the same plane that meet or cross.


Perpendicular: Lines in the same plane that intersect at a 90 degree angle.

Line Segment: A piece of a line with starting and ending points.


Bisect: To cut in half ("Bi" means "two" and "sect" means "to cut.")

Perpendicular Bisector: A line that divides another segment in half and meets at right (90 degree) angles.

Angle Bisector: A line that divides an angle into two equal parts.








The Basics of a (Mathematical) Circle

The basic definition of a circle: A round two dimensional plane.

Diameter: The distance across a circle through its centre. (usually represented by d)

It is NOT this:


It is this:


Radius (Plural is Radii.): The distance from the centre of a circle to its outer edge (usually represented as r)


(Some random fact: If you measure from the centre to the outer edge of a "perfect" circle all around, the measurements will be virtually the same. This is what fully defines a circle, a round, two-dimensional plane that measured from the centre to the outer edge, the measurements would be equal in distance.)

We can now safely state that 2r=d. This means that 2 radii are needed to make the diameter of a circle.

Circumference: The perimeter around the circle, it is usually represented as C. (this is what I mean by "outer edge".)

To figure out the circumference, multiply the diameter by Pi (π).

Pi is approximate to 3.14.

Some circumference formulas:
C=πd
C=2πr

(I'll also throw in on how to figure out the area.)

Some equivalents to a rectangle or parallelogram:

Length/Height: Radius
Width/Base: Half of the circumference

How to figure out the area of a rectangle or parallelogram: Length x Width (or Base x Height)

Enough Parallelogram talk, to figure out the area of a circle is:

Pi radius square.


















The Basics of Integers.

(Old topic, I know.)

Integers are sets of numbers, their opposites, and zero.
Examples: 1, 2, 3, 4, 0, -1, -2, -3, -4

Remember: Zero is neutral, it is not positive or negative.

Positive numbers are numbers above zero.
Negative numbers are numbers below zero.

A zero pair is a set of integers that equal zero.
Example: 1, -1

Opposite integers have the same numeral but different signs (positive or negative)
They are also the same distance away from zero on a number line.

Friday, June 15, 2012

sectors of circle graphs are made from central angles

if the sector covers 25% of the graph the central angle is 25% of 360 which is 90

mode

mode-the most value that shows up

mean

mean-add up all values divide how many values are there

reflection

mirror image

Rotation

rotation-turn about a fixed point

Translation

translation-slide along a straight line

median

median - the middle number in a set of data after the data have been arranged in order

median of 2,5,6,8,9 is 6

median of 1,3,6,8,9,10 is 7

range

range - the positive difference between the largest and smallest values in the set
range of 4,8,5,6,9,1,3,5,8,6

1,3,4,5,5,6,6,8,8,9


9-1=8
range is 8

mean

mean - a measure of central tendency

the sum of a set of valuesdivided by the number of values in the set
mean of 6,4,8 is

add up all the numbersand divide the result by how many numbers there are

6+4+8=18
18 divided by 3= 6
therefor the mean is 6

Divisibility

Divisibility

Divisible-When a number can be divided by another number with no remainder

Variable

Variable- an unknown number

Possibility

Favourable Outcomes
_________________
Possible Outcomes

Quadrants

(+,+) Quadrant 1
(-,+) Quadrant 2
(-,-) Quadrant 3
(+,-) Quadrant 4

Transformations

Translation- slide along a straight line
Rotation- turn about a fixed point
Reflection- a mirror image

BEDMAS

Brackets
Exponents
Division
Multiplication
Addition
Subtraction

Mode

Mode- most occurring number

Median

Median- The middle number in a set of data.

Mean

Mean- The sum of all the digits divided by the number of values there are.

bedmas

Brackets
Exponents
Division
Multiplication
Addition
Subtraction
 (BEDMAS)

definitions

Translation is a slide along a straight line
Rotation is a turn about a fixed point
Reflection is a mirror image

mode

Mode is the value that shows up the most

probability

favourable outcomes
possible outcomes

quadrents

Quadrant 1 (+,+)
Quadrant 2 (-,+)
Quadrant 3 (-,-)
Quadrant 4 (+,-)

Thursday, June 14, 2012

Circle Graphs

Sectors of circle graphs are made from central angles.

Watch this video for more explanation:

                                  

For more math help go to this sites:

Probability

favourable outcomes
possible outcomes

Watch this video for more explanation:


Math Exam Review

Integers:
Integers - negative numbers represents values below zero and positive numbers represent values aboive zero.
Watch this video for more explanation:


For more math help go to this sites:


Math Exam Review

Central Tendency:
Mean- add up all the values in the set then divide the sum by how many values there are
Median- the middle number in a set of ordered values, might be the mean of 2 middle values
Mode- the value that shows up the most
Range- positive difference between largest and smallest values
Outlier- values that are too big or too small compared to the other values



Watch this video for further explanation:


For more math help go to this sites:


Quadrants

Quadrant 1 (+,+)
Quadrant 2 (-,+)
Quadrant 3 (-,-)
Quadrant 4 (+,-)


For more math help go to this sites:


Math Exam Review

Algebra:
Variable - is an unknown number

Expression contains variables, operations, and numbers, in any combination

Watch this video for more explanation:


For more math help go to this sites:





Math Exam Review


Circles:
Circle Formulas:
c = π d 
c = 2 π r 
d = 2r 
a  = π r 

Area is the measured of space a two dimensional shape covers.

Watch this video for more explanation:

Math Exam Review

Divisibility
Divisibility Rules:
  • 0 - any number ends in 0
  • 1 - any whole number
  • 2 - any even number
  • 3 - sum of the digits is multiple by 3
  • 4 - divisible by 2 twice
  • 5 - any number that ends in 5 or 0
  • 6 - any number that is divisible by 2 and 3
  • 8 - divisible by 2 thrice
  • 9 - sum of the digits is multiple by 9
  • 10 - any number that ends in 0


Watch this video for more explanation:
For more math help go to this sites:


Math Exam Review

Divisibility
Divisible- means when a number can be divided by another number, with no remainder or decimal

It is a whole number


For more math help go to this sites:


Math Exam Review

Probability
Theoretical Probability- what you expect to happen

Watch this video for more explanation:

                                             
For more math help go to this sites:




Math Exam Review

Probability
Experimental Probability- actually doing the trails
Watch this video for more explanation:
For more math help go to this sites:




Math Exam Review

Transformations:
Reflection- mirror image

Watch this for more explanation:

For more math help go to this sites:


Math Exam Review

Transformations:
Rotation- turn about a fixed point

Watch this video to learn more:
For more math help go to this sites:








Variables

Variable is an unknown number.

Expression contains variables, operations and 
numbers in any combination.

Divisible

Divisible- when a number can be divided by another
number with no remainder or decimal.

Variable

Variable is an unknown number.


Expression contains variables, operations and 
numbers in any combination.

Probability

Experimental Probability-actually doing the trails.
Theoretical Probability-what you expect to happen.

Transformations

Translation-slide along a straight line.
Rotation-turn about a fixed point.
Reflection-mirror image.

Range

Range-positive difference between largest and smallest values

3,4,7,9,14,16,18
3-18=15


15 is the range

ALL DIVISIBILITY RULES

0-end inzero
1-all numbers
2-even numbers
3-sum of the digits is 3
4-divisiblility 2 twice
5-ends in a zero or five
6-divisible by 2 and 3
8-divisible by 2 thrice
9-sum of the digits 9
10-ends in zero

Variables

Variable is an unknown number

expression contains variables ,operations, and numbers, in any combination.


Circle Formulas

C=(3.14)d
C=2(3.14)r
D=2r
A=(3.14)r2

PROBABILITY


What is the probability if i were to land on mortage and then roll a six sided die and get a 6
A.)75 percent
B.)60 percent
C.)61 percent
D.)65 percent
E.)67 percent

ANSWER E.)

Integers

negative numbers represent values below zero positive numbers represent values above zero

example-above and below, ground or sea level
(-2)+1=1
3-(-1)=4

Outlier

Outlier-values that are too big or too small compared to the other values

9,28,35,47,69

9 is the smallest
69 is the biggest

NEGITIVE WITH NEGITIVE INTEGERS

Negitive integer are little bit harder than positive with positive intergers.The only thing different is that you would have to swap the integers around and then you would be able to turn in into a positve instead of negitive.

EXAMPLE:

(-9)-(+8)
(+8)+(-9)=-1

Transformation

Transformation

Translation-slide along a straight line
Rotation-turn about a fixed point
Reflection-a mirror image

POSITIVE WITH POSITIVE INTEGERS

Just like adding regular numbers.

EXAMPLE


(+9)+(+8)=+17


(+6)+(+12)=+18

Divisibility Rules

Divisibility-when a number can be divided by another number, with no remainder or decimal; it is a whole number

1-all numbers
2-even numbers
3-sum of the digits is divisible  by 3
4-divisible by 2 twice
5-ends in a 0 or a 5
6-divisible by 2 and 3
7-nothing
8-divisible by 2 thrice
9-sum of the digits is 9
10-ends in 0

HOW TO GET FROM DECIMAL TO FRACTION TO PERCENT

YOUR DECIMAL IS 693

693x100=69300

percent is 69 because i rounded off the extra number 3 to 0 and just used the first 2 numbers.

fraction is 69/100

because if you have your percent you automaticaly have your fraction. 69 percent and 69/100

ANGLE BISECTOR


If you get an angle of 60 degrees and you find the angle bisector the other angles will be 30
 degrees.
60 divided by 2= 30

Median

Median-the middle in a set of data






69 is the median


Mean

Mean-add up all the values then divid by the set of data

1,2,3,4,5,6,7,8,9

1+2+3+4+5+6+7+8+9=45

The mean is 45

THE OUTLIER

OUTLIER- Values that are too big or too small compared to the other values.

EXAMPLE

98,45,23,12,56,34, and 29
Oulier is 98

Math Exam Review

Transformations:
Translation-slide along a straight line


This is how to translate a shape:


outliers

An outlier is any number in a set of data thet is much smaller or much bigger than the others but there is a maximum of 2.
e.g. 12,48,52,54,58,99
the outliers would be 12 and 99
e.g.231,366,3658,369,370,592
the outliers would be 231 and 592
in the examples there were always 2 but there can only be 1 it depends on the set of data.

how to conver fractions ,decimals and percents

if you have a fraction it is easy to convert them to decimals and percents
to get a fraction to a decimal you take numerator (top) and divide it by the denominator (bottom) then you have your decimal, to get that to a percent you then multiply your decimal by 100 and then you have your percent.
to get them to a fraction you have to rememberthat a decimal is any number over 1 and a percent is any number over 100so you can take your percent  you can do any thing to it as a fraction as long as what ever you do to the top you have to do to he bottom.

THE RANGE

RANGE- Positive difference between largest and smallest values.

example

2,4,1,6,7,4, and 6

7-1 = 6

THE MODE

MODE- The value that shows up the most

e.g.

2,2,2,4,5,6,6 and 3

2 is the mode cause it shows up the most.
MEDIAN-The middle number in a set of ordered values, might be the median of 2 middle values

e.g.

10,9,8,7,6,5,4,3,2, and 1

The answer is in between 6 and 5.

The median is 5.5

mode

the mode in a set of data is the most frequently occuring number in the set

e.g.12,13,18,19,22,18,13
there can be numerous modes in this set the mode is 18 and 13.
e.g.3,4,6,8,9,11,13,13,13,22,25
some times it is easier to order the numbers before you figure out the mode

Data sets

Mean- add up all the values in the set then divide the sum by how many values there are
Median- the middle number in a set of ordered values, might be the mean of 2 middle values
Mode- the value that shows up the most
Range- positive difference between largest and smallest values
Outlier- values that are too big or too small compared to the other values

THE MEAN

MEAN- Add up all values divide by how many values there are.

8,7,6,5, and 4

8+7+6+5+4 divided by 5 = 6

So the mean is 6
MEAN- Add up all values divide by how many values there are.

8,7,6,5, and 4    

 8+7+6+5+4 divided by 5 = 6

So the mean is 6

Probabality

favourable outcomes
possible outcomes

p: heads and rolling a 4 with a regular die is

Experimental probabilty- actually doing the trials
Theoretical probability- what you expect to happen

Circle formulas

c=3.14d
c-2 3.14 r
d=2r
a=3.14
2

Integers

Negative numbers represent values below zero and positive numbers represent values above zero
eg. Above and below ground or sea level
1+(-2) = (-1) is an additional statement
3-(-1) = 4 is a subraction statement

Factors of 32

Factors of 32

Formulas

Area of a triangle
A= b x h
vdsfs 2
Area of parallelogram
A= b x h

Converting fractions, decimals, and percent

1/2 = 50%, 0.5

0.75 = 3/4, 75%

80% = 4/5, 0.8  

Integers

Integers
Negative numbers represent values below zero and positive numbers represent numbers above zero.
eg. above and below ground or sea level.
1+(-2)=(-1) is an addition statement.
3-(-1)=4 is a subtraction statement.
Opposite integers have the same numeral but different sign eg. 3 and (-3)

Lines n' stuff

Parellel lines are in the same plane and never meet.
Intersecting lines in the same plan and meet.
Perpendicular is an angle of 90 degrees.
Perpendicular Bisector is a line that cuts a line in half and makes a 90 degree angle.

Variables

Variable-a letter that represents an unknown number.
eg. x,a,n
Expression-any single number or variable, or combination of operations(-,+,x) involving numbers and variables.
Value-a known or calculated amount.
\Constant-a number that does not change and it increases or decreases the value of an expression.
Numerical Coefficient-a number that multiplies the variable.
eg.2t 

Quadrants

(+,+) quadrant I
(-,+) quadrant II
(-,-) quadrant III
(+,-) quadrant IV

Measures of Central Tendency

Mean-add up all values divide by how many there are.

Median-the middle number in a set of ordered values, might be the mean of 2 middle values.

Mode-the value that shows up the most.

Range-positive difference between largest and smallest values.

Outlier-values that are too big or too small compared to the other values.

Transformations

Transformations
Translation-slide along a straight line
Rotation-turn about a fixed point
Reflection-mirror image

range

the positive difference  between the largest and smallest values in the set.

mean

a measure of central tendency

mode

the most frequently occurring number in a set of data.

median

the middle number in a set of data after the data have been arranged in order

transformation

translation -  slide along a straight line.
 rotation - turn about a fixed point.
reflection - mirror image

mode

The most frequently occuring number in a set of data

Mode and Most both have four letters

mode of 3,5,7,7,9, is 7

mode of 2,2,4,6,6,8,11 is 2 and 6

mode of 1,2,3,4,5 is no mode

Mode

Mode is the number that repeats the most in a set of data

34,45,58,70,22,22,22

22 is the mode

Integers

Negative numbers represent values below zero and positive numbers represent values above zero.
eg. above and below ground or sea level

1 + (-2) = (-1) is an addition statement
3 - (-1) = 4 is a subtraction statement

Milton Family's Budget

Food 33%                      If they have $500, how much do they spend on rent?
Misc 21%                                  
Rent 25%                                    25% of 100
Clothing 15%                             0.25 x 500 = $125
Savings 6%

Probabilities

experimental probability- accually doing the trails

Theoretical probability-what you expect to happen

Sread Sheet

A spread sheet organizes data in columns and rows.

Probability

Experiment probability- actually doing the trails
Theoretical probability- what you expect to happen

Spread sheet

A spread sheet organizes data in colums and rows.
Experimental probability- actually doing the trails
Theoretical probability- what you expect to happen  

Variable

Variable is an unknown number

expression contains variables, operations, and numbers, in any combination.

Divisible

Divisible-means when a number can be divided by another number, with no remainder or decimal

it is a whole number

Transformations

Transformations

Translation-slide along a straight line

Rotation-turn around a fixed point

Reflection-mirror image

Integers

Integers

Negative numbers represent values below zero
positive numbers represent values above zero
eg.above and below ground or sea level
1+(-2)=(-1) is a addition statement
3-(-1)=4 is a subtraction statement

Integers

Integers

Negative numbers represent values below zero and positive numbers represent values above zero.

eg. above and below ground or sea level
1+ (-2)=(-1) is an addition statement
3-(-1)=4 is a subtraction statement

Transformations

Translation- slide along a straight line
Rotation- turn about a fixed point
Reflection- mirror image

Transformations

Transformations 
Translation- slide along a straight line
Rotation- turn about a fixed point
Reflection- mirror image

Mean,Meadian,Mode,Range,and Outlier

Mean-Add up all the divide by how many values there are

Median- the middle number in a set of ordered values, might be the mean of the 2 middle numbers

Mode-the value that shows up the most

Range-positive difference between largest and smallest values

Outlier-values that are too big or too small compared to the other values

Divisibilty Rules

Divisibility rules

0- end in zero
1- all numbers
2- even numbers
3- sum of the digits is twice
4- divisible by twice
5- ends in a 0 or 5
6- divisible by 2 and 3
8- divisible by 2 thrice
9- sum of the digits is 9
10- ends in 0

Divisibility Rules

Divisibility - means when a number can be divided by another number, with no remainder or decimal

it is a whole number

Divisibility Rules

 0- end in a zero
1-  all numbers
2- eve numbers
3- sum of the digit is 3
4- divisible by 2 twice
5- ends in a 0  or 5
6- divisible by 2 and 3
8- divisible by 2 twice
9- sum of the digits is 9
10- ends in a zero

Mean, Median, Mode, Range, Outlier definitions

Mean- add up all values divide by how many values there are.

Median- the middle number in a set of ordered values, might be the mean of 2 middle values.

Mode- the value that shows up the most.

Range- positive difference between largest and smallest.

Outlier- values that are too big or too small compared to the other values.