Introduction to Integrated Algebra Help

Introduction to Integrated Algebra Help:

Integrated algebra help introduces the student to help the fundamental concepts of integrated algebra. Integrated algebra help contains a pair of linear equations in two variables, polynomials, factors and factorization and Binomial theorem. Factors and factorization cover HCF and LCM, Surds and Simplification by rationalizing the denominator. Binomial theorem contains General term for positive integral.

Geometry covers area related to circles, circle-constructions, Co-ordinate geometry and Analytical geometry. Area of sector, ring and segment and problems related to circle are some of the areas related to circles.

What are real numbers, sets, sequence and series and linear inequalities are some of the topics cover under Number sense. Sets cover different types of sets, subsets, union and intersection of sets and complement of a set. Sequence and series contain Arithmetic progressions and Geometric progressions

Note on Fractions Calculator

Introduction of Calculating Fractions:

In this section let me help you on fraction calculator. A fraction is a number that represent a part of a whole. For example 1/2. It represents half part. The upper number in a fraction is called numerator and lower number is called denominator So in the example 1/2, 1 is the numerator and 2 is the denominator. A usual fraction is also known as vulgar fraction

Fractions are mainly divided into three:

1) Proper fraction- Numerator is less than denominator eg:- 1/2,4/7

2) Improper fraction- Numerator is greater than denominator eg:-4/3,7/5

3) Mixed fraction:- A combination of a number and proper fraction. eg:- 1 1/2, 2 3/7

This can also help us on

We can do all types of operations using fractions

The different operations are Addition, subtraction, multiplication and division. Here i am explaining only addition. This can also help us on how many triangles puzzle

a) Addition:- To add two fractions the denominator must be same. If in the given two fractions the denominators are not same then we have to convert them to common denominator and then add.

Integrated Algebra Regents

Introduction to Integrated algebra regents:

The integrated algebra regents includes the fundamental concepts of algebra like simple expressions , linear equations, rational and radical expresssions. Algebra, Geometry, and Trigonometry are included in the parts of integrated algebra regents examination. The integrated algebra regents exam gives the clear idea of solving different types of question.

Integrated Algebra Regents:

This will also help us on what is photosynthesis

Integrated algebra regents question 1:

Given:

Q = {0, 1, 2, 4, 6}

W = {0, 1, 2, 3}

Z = {1, 2, 3, 4}

What is the intersection of sets Q, W, and Z?

(1) {1, 2} (3) {1, 2, 3}

(2) {0, 2} (4) {0, 1, 2, 3, 4, 6}

what are rational numbers

In this lesson before we study about what are rational numbers let me take a step in helping you on what is rational numbers?
What is rational numbers?
A rational number is a number that can be in the form p/q where p and q are integers and q is not equal to zero.This also helps on numerator denominator.

Note on Multiplying Integers

Multiplying Integers :

In this lesson let me help you go through more on multiplying integers. Let us start with a quick review of the terms related to multiplication. The numbers to be multiplied are the factors and the result of multiplication is called as product.

4 × 5 = 20

4 and 5 are factors and 20 is the product.

There are four possibilities of multiplying two factors

Case 1: Both the factors are positive: When both the factors are positive, multiply the factors and the product is always positive. 3 × 5 = 15

Case 2: One factor is positive and the other is negative: When one of the factors is negative and the other is positive that is when the factors are of opposite signs, multiply the factors and the product has a negative sign. -3 × 5 = -15 or 3 × -5 = -15

Case 3: Both the factors are negative: When both the factors are negative, multiply the factors and then the product is always positive. -3 × -4 = 12

Case 4: One of the factors is zero: When one of the factors is zero, then the product is always zero. 0 × 6 = 0 or -5 × 0 = 0 Remember that zero is neither positive nor negative.

In short, when we multiply two Integers,

a) If the factors are of the same sign then the product is always positive.

b) If the factors are of the opposite signs then the product is always negative.

Here is an easy way to remember the sign rules for multiplication

(+) × (+) = (+)

(+) × (-) = (-)

(-) × (+) = (-)

(-) × (-) = (+)

Probability

Let me first give you some introduction to Probability,

The mathematical theory of probability deals with patterns that occur in random events. For the theory of probability the nature of randomness is inessential. (Note for the record, that according to the 18th century French mathematician Marquis de Laplace randomness is a perceived phenomenon explained by human ignorance, while the late 20th century mathematics came with a realization that chaos may emerge as the result of deterministic processes.)

An experiment is a process - natural or set up deliberately - that has an observable outcome. In the deliberate setting, the word experiment and trial are synonymous. An experiment has a random outcome if the result of the experiment can't be predicted with absolute certainty.
An event is a collection of possible outcomes of an experiment. An event is said to occur as a result of an experiment if it contains the actual outcome of that experiment. Individual outcomes comprising an event are said to be favorable to that event. Events are assigned a measure of certainty which is called probability (of an event.)

Vector Algebra

Let me first give you some brief introduction to Vector Algebra.

In our day to day life, we come across many queries such as – What is your height? How should a football player hit the ball to give a pass to another player of his team? Observe that a possible answer to the first query may be 1.6 meters, a quantity that involves only one value (magnitude) which is a real number. Such quantities are called scalars. However, an answer to the second query is a quantity (called force) which involves muscular strength (magnitude) and direction (in which another player is positioned). Such quantities are called vectors. In mathematics, physics and engineering, we frequently come across with both types of quantities, namely, scalar quantities such as length, mass, time, distance, speed, area, volume, temperature, work, money, voltage, density, resistance etc. and vector quantities like displacement, velocity, acceleration, force, weight, momentum, electric field intensity etc.

Some Basic Concepts :
Let ‘l’ be any straight line in plane or three dimensional space. This line can be given
two directions by means of arrowheads. A line with one of these directions prescribed
is called a directed line (Fig 10.1 (i), (ii)).

Fig 10.1

Now observe that if we restrict the line l to the line segment AB, then a magnitude
is prescribed on the line l with one of the two directions, so that we obtain a directed
line segment (Fig 10.1(iii)). Thus, a directed line segment has magnitude as well as
direction.

Algebra Word Problems

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Algebra is an important lesson to learn. I would like to take you through on algebra word problems. I would also like to show your some sample problems on algebra word problems so that you understand better with the illustration.
Simple algebra word problems include the problems with multiple choice answers. irrespective of the complexities involved in the problem, one can decide which answer from the multiple choice given is correct.

Find more solved algebra word problems on solving equations

Question - Which of the following equations have x=2, y=3 as solution ?
(a) 8x-y = 12 (b) 2x+3y = 10
Answer - (a) Substitute x=2, y=3 in 8x-y=12
8(2)-3=12
16-3=12

-->13 = 12
x=2, y=3 is not a solution of 8x-y=12
(b) Substitute x=2, y=3 in 2x+3y=10
2(2)+3(3)=10
4+9=10
13=10
x=2, y=3 is not a solution of 2x+3y=10.

develop and solve liner model solutions

To develop and solve liner model solutions ,we should know few basics of polynomials and types of polynomials.

polynomial:-
If p(x) is a polynomial in x.The highest exponent of x in p(x)
is called the degree of polynomial p(x).

For example :- 4x+2 is a polynomial in the unknown x and of degree 1.

This math help gives more explanation along with an example.
To explain more clearly ,a polynomial is a finite length expression constructed from variables (also known as indeterminates and constants, by using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents. For example, x² − 4x + 7 is a polynomial, but x² − 4/x + 7x^3/2 is not, because its second term involves division by the variable x and also because its third term contains an exponent that is not a whole number.

Types of polynomial

Linear :- A polynomial of degree 1 is called linear

Example:-

3x+4x-12=2

 7x-12 = 2

   +12   +12

---------------

   7x = 14

divide with 7 on both sides

we get x=2
Similar

How to solve Percentage problem

What is Percentage : a percentage is a way of expressing a number as a fraction

Here is one simple example which shows , how to solve percentage problem for a number based on a different number .

Problem:

36 is 20 percent of what number?


Solution:

Let the number be X.

36=20% of X

     20
36=  ________  * x   (20*5 =100,so 100 replace as 5)
     100

     1
36=  ______  * x
     5

Multiply with 5 on both sides.

            1
5 * 36= 5 * _____ * x
            5


5 get canceled since 5 times 1 = 5.


5*36 = x

So , x=180