Study algebra calculus

Introduction to study algebra calculus:

It is the study of algebra calculus is the course that involves relations and its use. This is the Algebra along with the Elementary Algebra course provides a solid foundation to higher mathematics course such as College Algebra, Pre-Calculus and Calculus. To be proficient with the mathematics, we highly recommend you to examine the examples and properties discussed in this course and ponder any of the subtleties encountered in any mathematics problems. I like to share this Definition of Inverse Function with you all through my article.


Definition of study algebra calculus:


Study algebra calculus is the 'Rates of Change'. Calculus as the we know it today was developed in the later half of the seventeenth century by two mathematicians, Gottfried Leibniz and Isaac Newton. There are two main branches of the calculus: Differential Calculus and the Integral Calculus. Differential calculus and the determines the rate of change of a quantity, integral calculus finds the quantity where the rate of change it is known as the algebra calculus.

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Examples on study algebra calculus


When you are studying is the rates of change in mathematics, you are in the branch of mathematics called algebra calculus.

Midpoint Formula:

The Midpoint formula is used when you need of the point that is exactly between two other points. The midpoint formula is a applied when you need to find is a line that bisects a specific line segment. Essentially, the 'middle point' is called the "midpoint".

The midpoint of M of the line segment from p1(x1,y1) to p2(x2,y2)

x1 + y1     x2 + y2

---------  ,    ----------

2                2

Slope Formula:
Sometimes called 'Rise over Run'.

The formula for a slope of the straight line going through the points (x1, y1) and (x 2, y 2) is given by:

y2 - y1

M  =  ----------

x2 - x1

The subscripts refer to the two points.
( m = rise / run )
Parallel lines have equal slope.
Perpendicular lines have negative reciprocal slopes.

Study 7th Grade Pre Algebra

Introduction to pre algebra:

Algebra: Algebra deals with the symbols,usually letters of the alphabet, are used to represent numbers and quantities.

Algebraic expression: a quantity that combines variables, numbers, and operation symbols.

Area: the space occupied inside a two-dimensional shape.

Equation: a mathematical statement in which two or more expressions are set equal to each other.

Inequality: a mathematical statement comparing two or more expressions using <, >, ≤, and ≥.

Like terms: two or more terms that have the same variable raised to the same power.

Linear equation: an equation that represents a line.

Polynomial: an expression made up of terms containing variables with whole number exponents.

Probability: a number from 0 to 1 that gives how likely anevent is to happen.

Real number: any number that can be represented with a point on the real number line.

Solution of an Equation: the value that makes an equation true when the variable is replaced by the value.

Term: a variable, number, or the product of a number and a variable

Variable: a symbol that is used to represent a quantity.

Volume: the amount of space enclosed in a solid object.

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Pre algebra includes different topics:


Natural numbers, arithmetic
Integers, fractions, decimals and negative numbers
factorization of natural numbers
Properties of operations such as associative property, distributive property and commutative property
Roots and powers
Evaluating expressions, such as operator precedence and use of parentheses
Basics of equations, that includes rules for invariant manipulation of equations
Variables and expressions.

Example:


Evaluate the expression for the given values.
2m – 3n + 7 for m = 8 and n = 5
Solution:
2m – 3n + 7 = 2(8) – 3(5) + 7
= 16 – 15 + 7
= 8

2) Evaluate 3x+ 4y - 12 for x =2 and y = - 3

Solution:

=  3(2)+4(-3) -12

= 6-12 -12

= 6 - 24

= -18

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Practice problems for pre algebra:


Evaluate the expression for the given values, 5x – 2y + 13 for x = 3 and y = 7
Evaluate the expression for the given values, 2p – 3q + 56 for p = 7 and q = 3
Evaluate the expression for the given values, 8m – 13n – 18 for m = 7 and n = 5.

Study About Geometric Problems

Introduction to study about geometric problems:

Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metria "measurement") "Earth-measuring" is a part of mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.


Formulas on study about geometric problems:


To study about the formulas of geometric which are givenas below:

Rectangle formulas:

Rectangle Perimeter = l + l + w + w = 2 × l + 2 × w = 2+2w

Area of the Rectangle = l × w

Square formulas:

Perimeter of the square = c + c + c + c = 4 × c = 4c

Area of the square = c* c = c 2

Parallelogram formulas:

Perimeter of the Parallelogram= c + c + d + d = 2 × c + 2 × d = 2c + 2d

Area of the Parallelogram = b × h

Rhombus formulas:

Perimeter of the Rhombus = c + c + c + c = 4 × c = 4c

Area of the Rhombus = b × h

Triangle formulas:

Perimeter of the Triangle = c + d + e

Area of the Triangle = (b × h)/2

Trapezoid formulas:

Perimeter of the Trapezoid = c +d + e + f
Area of the Trapezoid = (c+d) * h / 2

Circle formulas:

Perimeter of Circle = 2 × pi × R or Perimeter = pi × d

Area of the Circle = pi × R 2 or Area = (pi × d2)/4


Problems on study about geometric problems:


Study geometric Square problem:

Problem 1:

Calculate the area and perimeter of square when side length is 8cm?

Solution:

Area of square = (side*side)

=8*8

=>64cm2

Perimeter of square= 4* side

=4*8

= 32cm

Study geometric Rectangle problem:

Problem 2:

Find the area and perimeter of rectangle with length 9cm,width 7 cm?

Solution:

Area of rectangle = Length x width

= 9*7

= 63cm2

Perimeter of rectangle=2(Length +width)

=2(9+7)

= 32cm

Study geometric Triangle problem:

Problem 3:

Find the area and perimeter of triangle Base=8, Height=9, other two sides are 10,11?

Solution:

Area=1/2/(8*9)

=72/2

= 36cm2

Perimeter= (sum of three sides)

= (8+10+11)

= 29 cm

Study About Study Geometry

Introduction to study about study geometry:

Let us study about geometry,

Geometry can be defined as the system of concepts, in which a few ideas were initialized to derive the big ones. These kinds of systems are said to be deductive systems. It tells you the deduction concepts and consequence logic's, which can be applied throughout your life time. In this article, you can learn about the basic terms of geometry. I like to share this Surface Area Cube with you all through my article.

This definition is used in study of geometry.


Study about Basics of Geometry:


Some basics are there to study geometry,

Point:

A point can be defined as the basic object of geometry.

Line:

A line can be defined as the connection of many points. The line having only one dimension, i.e. length. It doesn't have any other dimensions. The two end points name can be used as the line name. Otherwise, it can be named by a single lower case alphabet.

Collinear points:

Collinear points are the points, which lie on the same line. If the point doesn’t lie on the line, then those points are said to be non collinear points.

Plane:

In study of geometry, a plane can be defined as the infinite set of points combined to form a flat surface; it can be extended infinitely in any directions. A plane having infinite length and width, but no height. It’s normally a four side geometric figure. It can be represented by a single upper case letter.

Some basics are there to study geometry,

Point:

A point can be defined as the basic object of geometry. It can be represented by a capital letter or a dot. A point have no dimensions, it just denote a position.

Line:

A line can be defined as the connection of many points. The line having only one dimension, i.e., length. It doesn't have no other dimensions. The two end points name can be used as the line name. Otherwise, it can be named by a single lower case alphabet.

Collinear points:

Collinear points are the points, which lie on the same line. If the points doesn't lie on the line, then those points are said to be non collinear points.

Plane:

In study of geometry,  a plane can be defined as the infinite set of points combined to form a flat surface, it can be extended infinitely in any directions. A plane having infinite length and width, but no height. Its normally a four sided geometric figure. It can be represented by a single upper case letter.

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Study about Other Important Geometry Terms


Some geometry terms are used in study of geometry,

Midpoint:

A midpoint can be defined as a point, which separates a line segment equally from both the end points.

Ray:

A ray can be defined as a line having one fixed end point and an infinite extension on the other end. It is denoted by two upper case letters with an arrow mark on top.

Angles:

An Angle can be formed by two rays having common end point. These rays are said to be the sides of an angle. An Angle is measured by a unit called as degrees. An Angle varies from 0° to 180°.

Right angle:

If an angle is 90°, then the angle is said to be right angle.

Obtuse angle:

If an angle is more than 90° but less than 180°, then the angle is said to be an obtuse angle.

Straight angle:

If an angle is 180°, then the angle is said to be a straight angle.

Study About Tangent

Introduction to study about tangent
A line or plane which touches a curve or surface. If a circle and a line in the same plane contact each other at only one point then the line is called a tangent to the circle. If a tangent to a circle in a plane is also a tangent to another circle in the same plane then, it is called a common tangent to the circles. If the centers of the circles are on the same side of the tangent, it is called external common tangent. If the centers are on opposite sides of the tangent, it is called internal common tangent. If a sphere and a plane contact at only one point, the plane is called tangent plane to the sphere. The point of contact is called point of tangency. Here we are going to study about the properties and theorems about tangents. Having problem with Finding the Volume of a Cylinder keep reading my upcoming posts, i will try to help you.

Tangent chord theorem

Tthe measure of an angle determined by the chord of a circle and the tangents at one of its end points is equal to half of the degree measure of the intercepting arc of that angle.


Formulas to study about tangent:


The following are very common formulas to study about tangent

tan θ = (side adjacent of length side) / (opposite of length).

tan θ = sin θ/ cos θ  = 1/ cot θ

tan2 θ = sec2 θ - 1

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Properties to study about tangent:


A line which touches a circle at exactly one point is called a tangent line and the point where it touches the circle is called the point of contact.
A tangent is the limiting position of a secant when the two points of intersection coincide.
A tangent is the limiting position of a secant when the two points of intersection coincide.
A radius, through the point of contact of tangent to a circle, is perpendicular to the tangent at that point.
From an external point, two tangents can be drawn to a circle.
The lengths of two tangents from an external point are equal.
The tangents drawn from an external point to a circle are equally inclined to the line joining the point to the centre of the circle.
The angles formed in the alternate segments by a chord through the point of contact of a tangent to a circle is equal to the angle between the chord and the tangent.

Discount Rates

This topic has a legendary background. In grand olden days people were using camels to carry heavy loads. When the camel is resting, a heavy load will be placed on its body to its great disliking. After all done, the master will take out a small straw from the load to the notice of the animal and will throw it away. The camel will be extremely happy that the load is much lighter now. I like to share this Discount Rate Formula with you all through my article.

In present days, the above technique is practiced by almost all sellers in the world. Even a billionaire will not accept a sale without discount. Thus, ‘discount’ is a concept that has occupied a place in math. The discount rates are normally expressed as a percentage of the original price. Thus, fundamentally, one has to know the concept of percentages to calculate discount rate. By calculating discount rate, we also come to know how to find discount.

Let us discuss the matter with some practical examples.

In a textile show room, tee shirts are tagged with labels saying that ‘Original price $15, the discount only for today is 10%’. (The today usually remains ever!). Now let us do the math exercise. With the concept on percentages, 10% means a fraction of 10/100. That is, the rate of discount is $10 for every purchase with original price of $100.In other words the rate is 0.1 times the original price. Thus, the discount on the tee shirt originally costing $15 is 0.1 times $15 which works out as $1.5. So what you finally need to pay is $15 - $1.5 = $13.5.

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This is not the case only with show rooms or malls. Even in online transactions we come across the ‘discount rates’. The agent of the seller on chat will mention ‘today we are offering heavy discounts’. In all likelihood, the quoted sentence will be a copy paste from a prepared notepad which may be as old as Bible. In these cases they will not even tax your brain. The complete quote will be like this. ‘Original price $100, offer applicable only on this chat is $79.99 ($80 may seem to be very heavy for the customers even though the difference is just one cent!), amounting to more than 20% discount’. Well, leaving the humorous part of the story, mathematically there is no flaw in this offer. Because the amount of discount is $20.01 and when you work back for the rate of discount, it comes to 20.01%.
Basically this is the concept on discount rates.

Online Study

Introduction to line online study:

In Euclidean geometry, a line is a straight curve. The general form of a line is represented by a equation

Ax + By + C = 0

The above equation of a line can be written as

y = (-`A/B` )x + (-`C/B` )

Plug - A/B  = m and   - C/B = b in the above equation, it becomes

y = mx + b

The above equation is called as slope intercept form of line equation.

Where, m is the slope and

b is the y-intercept

In online, we can study more about this line equation in detail. The example and practice problems are given below which shows how online will helps for your study.

(Source: Wikipedia)

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Example problems of line online:


The following example problems will helps you  to study about line in online.

Example 1:

Find x-intercept of a line y = 4x + 12

Solution:

Step 1: Given line equation

y = 4x + 12

Step 2: Substitute y = 0 in the equation  y = 4x + 12  to find x-intercept.

0 = 4x + 12

Step 3: Solve the above equation for x

Subtract 12 on both side of the equation to cancel 12 from the right hand side of the equation,

-12 = 4x

Multiplying by 4 on both side, we get

- 3 = x

Therefore,

x = - 3

Step 4: Solution

The x-intercept of the given line is (-3, 0)

The following example problems will helps you  to study about line in online.

Example 2:

Find y-intercept of a line 3y = 4x + 12

Solution:

Step 1: Given line equation

3y = 4x + 12

Step 2: Substitute x = 0 in the given equation to find y-intercept.

3y = 4(0) + 12

Step 3: Solve the above equation for y

3y = 0 + 12

Multiplying by 3 on both side, we get

y = 4

Step 4: Solution

The x-intercept of the given line is (0, 4)

Example 3:

Write the following line equation x + 5y = 6 into slope intercept form.

Solution:

Step 1: Given line equation

x + 5y = 6

Step 2: Subtract x on both sides to cancel x from the left hand side of the equation

5y = 6 - x

Step 3: Multiply by 5 on both sides, we get

y = `6/5` - `x/5`

On rearranging, we get

y = - `1/5` x + `6/5`

Step 4: Solution

The slope intercept form of given line equation is y = - `1/5 ` x+ `6/5`

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Practice problems of line online:


1) Find x-intercept of a line y = 8x - 7

2) Find y-intercept of a line 5y = 6x + 15

3) Write the following line equation - x + y = 8 into slope intercept form.

Solution:

1) (7/8, 0)

2) (0, 3)

3) x + 8

Learning Geometric Progression

Introduction to Learning Geometric progression

Learning geometric progression is very easy and can be done very quickly . Geometric progression is a type of progression where the consecutive digits have a common ratio between them . This means that if a G.P (geometric progression ) is present with general term a(i) then for terms  a(i+1) = a(i)* r  , where r is the common ration of the G.P.


MORE OF LEARNING GEOMETRIC PROGRESSION


Take an example .

Lets understand the Geometric Progression in more detail.

Let a Geometric Progression has its first element as 4 and the common ratio be ‘3 ‘. So the next term will be multiplying  first term 4 with common ration 3

i.e 2nd term = 4*3 = 12

Similiarly to find the 3rd term  we multiply the second term by 3 so

3rd term =  12*3 = 36

So we can go on like this .

So the general formula will be that to find ‘nth’ member of the Geometric Progression we can write the formula

a(n)th  term = (first term) * ((common ratio)^(n-1))

so for this example    the a(n) will be  = 4* ((3)^(n-1))

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PROPERTIES OF G.P


In the previous section , the method of finding the Geometric Progression if the initial element and the common ratio is given. Now in this section we will find out how to check it a series of number are in  Geometric Progression.

Lets us suppose that we have three numbers  a, b, c and we have to find that they are in G.P or not. The rule is that  if they are in G.P then

b^2  = a*c

this means that if 2, 4, 8, 16 is a series given then  to find that if it is in common ratio .

4^2  =  8*2    (for 2,4,8)

And  8^2 = 4*16   (for 4,6,8 )

So 2,4,6,8 is in Geometric Progression

Metric Units Math

Introduction to metric units math:

In mathematics, metric units system is one of the important topics. It is used for measuring purpose of an international decimalized system of measurement. In all over world, it is the most common system for measuring different units. For personal, commercial and scientific purposes, it can be used widely. From the base units, it can be used to derive larger and smaller units which may be standard set of prefixes in powers of ten. I like to share this Multiply Fractions Calculator with you all through my article.



Metric units for mass and time in math:


Metric units for mass:

Basic unit for mass is gram.

Some metric units for mass are

1 kilogram = 1000 grams
1 hectogram = 100 grams
1 decagram = 10 grams
1 decigram = 1/10 (or) 0.01 gram
1 centigram = 1/100 (or) 0.001 gram
1 milligram = 1/1000 (or) 0.0001 gram

Some symbolized metric units for mass are

1 kilogram = 1 kg
1 milligram = 1 mg
1 centigram = 1 cg
1 gram = 1 g
1 decigram = 1 dg

Metric units for Time:

Some of the metric units for time are

1 minute = 60 seconds
1 hour = 60 minutes (or) 3600 seconds
1 day = 24 hours (or) 1440 minutes (or) 86400 seconds
1 week = 7 days
1 year = 12 months (or) 52 weeks

Metric units for Length and temparature in math:


Metric units for Length:

Basic unit of length is meter.

Some metric units for length are

1 kilometer = 1000 meters

1 hectometer = 100 meters

1 decameter = 10 meters

1 decimeter = 1/10 (or) 0.01 meter

1 centimeter = 1/100 (or) 0.001 meter

1 millimeter = 1/1000 (or) 0.0001 meter

Some symbolized metric units for length is

1 millimeter = 1 mm

1 centimeter = 1 cm

1 meter = 1 m

1 decimeter = 1 dm

1 kilometer = 1 km

Metric units for Celsius to Fahrenheit:

For converting Celsius to Fahrenheit, multiply the given Celsius temperatures in to 9/5 then we get the Fahrenheit temperature. Celsius is denoted by C

Fahrenheit = 9 /5 Celsius temperature

Metric units for Fahrenheit to Celsius:

For converting Fahrenheit to Celsius, multiply the given Fahrenheit temperatures in to 5/9 then we get the Celsius temperature. Fahrenheit is denoted by F

Celsius = 5/9 Fahrenheit temperature

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Metric units for Volume in math:


Basic unit of a volume is liter.

Some metric units for volume is

1 kiloliter = 1000 liters
1 hectoliter = 100 liters
1 decaliter = 10 liters
1 deciliter = 1/10 (or) 0.01 liter
1 centiliter = 1/100 (or) 0.001 liter
1 milliliter = 1/100 (or) 0.0001 liter

Some symbolize metric units for volume is

1 kiloliter = 1 kl
1 liter = 1 l
1 deciliter = 1 dl
1 centiliter = 1 cl
1 milliliter = 1 ml

Metric units for U .S system of volume:

Basic unit for U.S system of volume is teaspoon

Some of the U. S systems of metric units for volume are

Tablespoons = 3 teaspoons
Fluid ounces = 2 tablespoons (or) 6 teaspoons
Cups = 8 fluid ounces (or) 16 tablespoons
Pints = 2 cups (or) 16 fluid ounces
Quarts = 2 pints (or) 4 cups
Gallons = 4 quarts (or) 8 pints (or) 16 cups.