Relations

New Vocabulary:-

Coordinate system

Coordinate plane

x- and y- axes

Origin

Ordered pair

x- and y- Coordinates

relation

domain

range

independent variable

dependent vaiable

Why?

The deeper in the ocean you are, the greater pressure is on your body. This is because there is more water over you. The force of gravity pulls the water weight down, greater a greater pressure.
The equation that relates the total  pressure of the water to the depth is P=rgh, where
P = the pressure
r = the density of water,g = the acceleration due to gravity, andh = the height of water above you.
Represent a Relation This relationship between the depth and the pressure exerted can be represented by a line on a coordinate grid.
A coordinate system is formed by intersection of two number lines,the horizontal axis and the vertical axis.

A point is represented on a graph using order pairs.

• An order pair is a set of numbers,or coordinates, written in the form (x,y)

• The x- Value, called the x-coordinate, represents the horizontal placement of the point.

• The y- value, or y-coordinate, represents the vertical placement of the point.

A set of ordered pairs is called a relation. A relation can be depicted in several different ways. 

An equation can represent a relation as well as graphs, tables, and mappings.

A mapping illustrates how each elements of the domain is paired with an element in the domain is paired with an element in the range.
The set of the first numbers of the ordered pairs is the domain. The set of second numbers of the ordered pairs is the range  of the relation. This mapping represent the ordered pairs.

In a relation,
The value of the variable that determines the output is called the independent variable.
The variable with a value that is dependent on the value of the independent variable is called the dependent variable.
The domain contains values of the independent variable.
The range contains the values of the dependent variable.

Mean, Median ,Mode Range, and Quartiles

Mean, Median ,Mode Range, and Quartiles

Measures of central tendency  are numbers used to represent a set of data. Three types of measures of central tendency are 

Mean 

Median

Mode

Mean : The mean is the sum of the numbers in a set of data divided by the numbers of items.

Median: The median is the middle number in a set if data when the data are arranged in numerical order. If there is an even number of data, the median is the mean of the two middle numbers.

Mode: The mode is the number or numbers that appears most often, the set has no mode.

Measures of variation: are used to describe the distribution of the data. One measure, the difference between the greatest and the least data values, is called the range.

Distribution Data: The measures of variation including range describe how the data in a set vary. This is another way to describe data.

In a set of data, the quartiles are values that separate the data into four equal subsets, eachj containing one fourth of the data. Q1, Q2, and Q3 are used to represent the three quartiles. Q1 is the lower quartiles. It divides the lower half of the data into two equal parts. Q2 is the median since it separates the data into two equal parts. q3 is the upper quartile. it divides the upper half if the data into two equal parts.

The Percent Proportion

The Percent Proportion

New Vocabular

A percent is a ratio that compares a number to 100. To write a percent as a fraction. express the ratio as a fraction with a denominator of 100. Fraction should be expressed in simplest form.

In the percent proportion, the ratio of a part of something to the whole (base) is equal to the percent written as a fraction.

Operation with integers

Operation With Integers

Objective 

Add, Subtract, multiply, and divide integers.

New Vocabulary:

Absolute Value
Opposites
additive inverses

Number Line

Absolute Value  :   You Can also use absolute value to add integers. The absolute value of a number is its distance from 0 on the number line.

Additive Inverse: Every positive intergers can be paired with negative integers.These pairs are called opposites. A number and its opposite are additive inverses. Additive inverses can be used when you subtract integers.

Rules for Addition

Rules for Addition
Positive + Positive	Positive
Positive + Negative	Depends
Negative + Positive	Depends
Negative + Negative	Negative

Rules for Multiplication Rules for Multiplication Positive x Positive Positive Positive x Negative Negative Negative x Positive Negative Negative x Negative Positive

Algebra 1

Algebra 

Algebra is very easy.

we Learn Algebra in easy way step by step

1. The part of mathematics in which letters and other symbols are used to represent numbers and quantities in formula and equations.
2. A system of this based on given axioms.

Plan for Problem Solving

Step 1 Understand the problem.

Step 2 Plan the solution.

Step 3 Solve the problem.

Step 4 Check the solution.

Step 1 Understand the Problem:

To solve a verbal problem, first read the problem carefully and explore what the problem is about.

• Identify what information is given.
• Identify what you need to find.

Step 2  Plan the Solution:

• One strategy you can is to write an equation. Choose a Variable to represent one of the unspecified numbers in the problems in the problem. This is called defining a variable. Then use the variable ti write expression for the other unspecified numbers in the problem.

Step 3 Solve the Problem

• Use the strategy you chose in step 2 to solve the problem.

Step 4 Check the Solution

Check your answer in the context of the original problem.

• Does your answer makes any sense.
• Does it fit the information in the problem?

What is Real Number?

Real Number A number line can be used to show the sets of natural numbers, whole numbers, integers,and rational numbers. values greater than 0, or positive numbers, are listed to the right 0, and values less than 0, or negative numbers, are listed ti the left of 0

natural numbers: 1,2,3,...

whole numbers:0,1,2,3,...

integers: .....,-3,-2,-1,0,1,2,3....

rational numbers: number that can be expressed in the form a/b, where a and b are integers and b  ≠ (not equal to) 0

A Square root : 


                    is one of two equal factors of a number. For example, one square root of 64, written as  √64, is since 8 . 8 or 8² is 64. The nonnegative square root of a number is the principal square root. Another square root of 64 is -8 science (-8). (-8) or (-8)²  is also 64. A number like 64, with a square root  that is a rational number is called a perfect square. The square roots of a perfect square are irrational numbers.

A number such as √3  is the square root of  a number that is not a perfect square. It cannot be expressed as a terminating or repeating decimal;  √3  ͌  1.73205... Numbers that cannot be expressed as terminating or repeating decimals, or in the form a/b, where a and b are integers and b≠0, are called irrational numbers. Irrational numbers and rational numbers together form the set of real numbers.