definition of mathematics

Let us learn about definition of mathematics

Mathematics is a study of relationships using different numbers & the study of the relationships between numbers, shapes, & quantities. Mathematics uses signs, symbols, & proofs & includes arithmetic, calculus, algebra, geometry, & trigonometry.

Mathematics is referred as Mathematical operations & processes involved in the solution of a problem or study of some scientific field

Mathematics is a group of related sciences, including geometry, algebra, & calculus, concerned with the study of number, quantity, shape, & space & their interrelationships by using a specialized notation

Mathematics is a science or group of related sciences that deals with the logic of quantity & shape & arrangement

The mathematics is deductive study of shape, quantity, & dependence.

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inequalities calculator

Let us learn how to use inequalities calculator

Add all numbers in left side from the in equality.

Then add all numbers in right side from the inequality.

Add the entire variable with coefficients on the left side from inequality.

Add the entire variable with coefficients on the right side from the inequality.

Subtract all number on left side from both sides of the inequality.

Add all number on the left side from both sides of the inequality

Subtract all variable with a coefficient on the right hand side of the inequality from both sides of the inequality

Add all variable with a coefficient on the right hand side of the inequality from both sides of the inequality.

Simplify by dividing on both sides or by multiplying on both side with reciprocal of inequality.

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sin 30 degrees

Let us learn about sin 30 degrees

Value of 30 Degree

• The value of sin 30 degrees = ½
• The value of cos 30 degrees =√3/2
• The value of tan 30 degree = 1/√3

zero degree angle is known as an acute angle, because the angle of 2 rays Is less than 90 degree & greater than 0 degree.

sin(135) = sqrt(2)/2
cos(135) = -sqrt(2)/2
sin(30) = 1/2
cos(30) = sqrt(3)/2

Note 135 deg is just the 45 deg angle in the upper left quadrant of the unit circle, where sines are postiive & cosines are negative

sin(135-30) = sin135cos30 - cos135sin30
................... = [sqrt(2)/2][sqrt(3)/2] - [-sqrt(2)/2][1/2]
.................. = sqrt(6)/4 + sqrt(2)/4
.................. = [sqrt(6) + sqrt(2)]/4
................... = 0.9659

sin(135) - cos(30) = sqrt(2)/2 - sqrt(3)/2
................................= [sqrt(2) - sqrt(3)]/2
................................= -0.1589

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factoring calculator online

Let us solve problem using factoring calculator online

Factor the given expression, 2x² + 4x
Solution:
= 2x² + 4x
Taking the common terms outside,
= 2x(x + 2)
The solution is 2x (x+2).
Solve 6x² + 18x - 24 = 0 for x.
Solution
Given equation is 6x²+18x-24=0 for x.
Solve the given equation we get
. (6x - 24)(x + 1)=0
Here by equating the values to zero
6x-24=0, x+1=0
Here keep constant terms on 1 side & move the variables to other side.
6x=24, x=-1
The final solution is X=3/2, x = -1.

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college level books

Let us learn about college level books

college level books are very important, helps Student to build our spirit, give information, help to pass time, make us more deep an cultural, helps us to write & think better, help us to chose people, because with college level books student will able to chose the persons that like the same books that student like... Since millions of centuries mankind write it's the way to preserve history, facts that without them all mankind was lost without identity... finally, open our mind to the world & makes us better persons.

College level books are real, true friend. Books provide lot of experience to us. They improve our knowledge. It helps us to collect countless information. It is true that books are our best friend the only thing they cannot talk them but we can read them. Student should always carry college level books while traveling. College level books help a lot to maintain a good vocabulary. Above all these college level books help solve the mystery of life sometimes, so they act as a true companion. Whenever student feels disturbed they should read college level books. College level books are the identity of college level students, a college student is known by the books he/she reads. No books are boring depends on interest of the college grade students declare them as boring or interesting.

College level books give peace to Student mind, increase attention & concentration, increases vocabulary, presence of mind, creativity & above all, college level books gives us knowledge which is considered to be the world's greatest treasure.

college level books make us feel heavenly.

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midpoint formula calculator

Let us learn about midpoint formula calculator

The midpoint formula calculator is very handy while calculating the midpoint between any 2 points & is very commonly used in geometry both practically & during learning. In math, midpoint formula questions are very common & Learner should be well aware of how to use the midpoint formula calculator. The formula to find midpoint using calculator is actually quite logical, if you try to look at it closely, you will find that it is derived from the average of the x coordinates & y coordinates

The midpoint formula calculator is used when you need the point that is exactly between 2 other points. The midpoint formula is used when you need to find a line which bisects a specific line segment. Essentially, the 'middle point' known as the "midpoint"

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square root of 0

Let us learn about square root of 0

The square root of zero would be zero always, because zero multiplied by itself or zero squared & would equal zero.
The best example Question based on what is the square root of 0 is mentioned below that,

Best Example

What is the square root of 0?
The square root of Zero (0) is nothing but √0
The value for √0 = 0

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alphabet of lines

Let us learn about alphabet of lines

The "Alphabet of Lines" defined as the different styles of lines used in drafting such as to show different features about an object which is drawn, hidden, Construction, cutting-plane, visible object, dimension, phantom, center, extention, section, & border. Or alphabet of lines is a geometrical object that is straight, infinitely long & infinitely thin.

Drafting or Computer Aided Drafting: The alphabets of lines are the different line that architects, draftsmen, engineers, et al use when constructing a drawing. The Alphabet of lines is referred as the different types of lines. The use of line types on a drawing is used to describe the various features of an object to the person reading the print. Alphabets of lines help to illustrate & describe the shape of objects which will later become real parts.
The best example, a thick solid line is known an object line and represents the outline of a part on a drawing. A dash line represents an edge which is not visible in a particular view; therefore it is called a hidden line. Other common lines used in drafting include extension lines, dimension lines, construction lines, border lines, center lines, among many others depending on the type of drawing.
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free exam papers

Let us learn how free exam papers helps students in learning math.

Students are well boasted & well encouraged to view the sample answer sheet so that they are familiar with the way they are required to show their solutions in the test.

These free exam papers, past papers have been published to assist students to familiarize themselves with the format of the test & to provide material which will enable them to develop more effective exam technique. Some features of good exam technique include the ability to manage the allocated test time evenly & the understanding that it is better to guess solution than leave it blank.

There are many website which provides free previous math exam papers for students to help them in learning math better. It enables students to understand & establish the type of questions being asked. Student will learn how to manage your time during the exam

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formal charge equation

Let us learn about formal charge equation

a formal charge “FC” is referred as the charge assigned to an atom in a molecule, assuming that electrons in a chemical bond are equally shared between atoms, regardless of relative electronegativity.
Formal charge equation:

FC = V - N - B/2

Where as “V” is the number of valence electrons of the atom in isolation. “B” is the total number of electrons shared in covalent bonds with other atoms in the molecule. “N” is referred as the number of non bonding electrons on this atom in the molecule.

C_f = E_v - (E_u + 1/2E_p)

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gaussian elimination calculator

Let us learn about gaussian elimination calculator

Gaussian elimination calculator is a method to find the inverse of any square matrix. Student simply chooses their matrix’s dimensions & then enters the elements of the matrix student want inverted in the left frame.
Gaussian elimination calculator is a variant of Gaussian Elimination. We are transforming the coefficient matrix into another matrix which is much easier to find solution, & the system represented by the new augmented matrix has the same solution set as the original system of linear equations. In Gaussian elimination calculator, the aim is to transform the coefficient matrix into a diagonal matrix, & the zeros are introduced into the matrix 1 column at a time. We work to eliminate the elements both below & above the diagonal element of a given column in 1 pass through the matrix
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biconditional statement

Let us learn about biconditional statement

If 2 simple statements “p” & “q” are connected by the connective. 'if & only if', then the resulting compound statement is said to be as the biconditional statement. Symbolically it is characterized by p<-> q.

An integer is even if & only if it is divisible by two. Then it is biconditional having the truth value T.

The biconditional statement p <->q is true when either both p & q are true or both p & q are false.

A statement is said to be as biconditional when it expresses the idea which presence of some property is a necessary & sufficient condition for the presence of some other property. Such a statement is usually phrased in the terms "P, if & only if Q." The phrase "if & only if" is often abbreviated as iff.

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perimeter of triangle

Let us learn about perimeter of triangle

The perimeter is the space or distance around a closed plane figure.

The perimeter “P” of a triangle is given by the formula

P = a + b + c
Where a, b & c are the side lengths of the triangle.
Perimeter = a + b+ c. where a, b, and c are sides of triangle.

find the perimeter of a triangle given a = 3 cm, b = 5 cm, and c = 7

P = 3 + 5 + 7 = 15 cm

Find the perimeter when a = 4 cm, b = 8 cm, and c = 12

P = 4 + 8 + 12 = 24 cm

Find the perimeter when a = 1/2 cm, b = 3/2 cm, and c = 6/2

P = 1/2 + 3/2 + 6/2 = ( 1 + 3 + 6)/2 = 10/2 = 5 cm

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linear programming problem

Linear programming problem below, state the dual problem, solve by the simplex or dual simplex method & also states the solutions to both problems.

1. Maximize x1 − 2x2 − 3x3 − x4 subject to the constraints xj ≥ 0 for all j and

x1 − x2 − 2x3 − x4 ≤ 4

2x1 + x3 − 4x4 ≤ 2

−2x1 + x2 + x4 ≤ 1.

2. Minimize 3y1 − y2 + 2y3 subject to the constraints yi ≥ 0 for all i and

2y1 − y2 + y3 ≥ −1

y1 + 2y3 ≥ 2

−7y1 + 4y2 − 6y3 ≥ 1.

3. Maximize −x1 − x2 + 2x3 subject to the constraints xj ≥ 0 for all j and

−3x1 + 3x2 + x3 ≤ 3

2x1 − x2 − 2x3 ≤ 1

−x1 + x3 ≤ 1.

4. Minimize 5y1 − 2y2 − y3 subject to the constraints yi ≥ 0 for all i and

−2y1 + 3y3 ≥ −1

2y1 − y2 + y3 ≥ 1

3y1 + 2y2 − y3 ≥ 0.

5. Minimize −2y2 + y3 subject to the constraints yi ≥ 0 for all i and

−y1 − 2y2 ≥ −3

4y1 + y2 + 7y3 ≥ −1

2y1 − 3y2 + y3 ≥ −5.

6. Maximize 3x1 + 4x2 + 5x3 subject to the constraints xj ≥ 0 for all j and

X1 + 2x2 + 2x3 ≤ 1

−3x1 + x3 ≤ −1

−2x1 − x2 ≤ −1.

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integrated algebra regents

Let us learn about integrated algebra regents

The integrated algebra regents contain the fundamental concepts of algebra like simple expressions, rational, linear equations, & radical expressions. Geometry, Algebra, & Trigonometry are included in the parts of integrated algebra regents examination. The integrated algebra regents test gives the clear idea & picture of solving different types of questions.

Calculators like Graphing calculators are required for the Integrated Algebra Regents examination. During the period the administration of the Regents exam, schools are required to make a graphing calculator available for the exclusive use of each learner. You will need to use your calculator to work with evaluate roots, trigonometric functions of angles, & perform routine calculations. Knowing how to use a graphing calculator gives you an advantage when deciding how to solve a problem. Instead than solving a problem algebraically with paper & pen, it may be easier to solve the same problem using a graph or table created by a graphing calculator. A numerical or graphical solution using a calculator can also be used to help confirm a solution obtained using standard algebraic methods.

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like terms calculator

remainder theorem

Let us learn about remainder theorem

The Remainder Theorem is very useful for calculating, evaluating polynomials at a given value of x, though it might not seem so, at least at 1st blush. This is mainly because the tool is presented as a theorem with a proof & you probably don't feel ready for proofs at this stage in student’s studies. Fortunately, student doesn’t "have" to understand the proof of the Theorem; they just need to understand how to use the remainder theorem. If f(x) is a polynomial in x & it is divided by x-a; the remainder is the value of f(x) at x = a i.e., Remainder = f (a).

Proof of remainder theorem:

Let p(x) be a polynomial divided by (x-a).

Let q(x) is the quotient and R is the remainder.

By division algorithm, Dividend = (Divisor x quotient) + Remainder

P(x) = q(x). (x-a) + R

Substitute x = a,

P (a) = q (a) (a-a) + R

P (a) = R (a - a = 0, 0 - q (a) = 0)

Hence Remainder = p (a).

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Ratio examples

Let us find Ratio examples.

A ratio is a relationship between 2 numbers of the same kind i.e., objects, spoonfuls, units of whatever identical dimension, persons, students, usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the 2, which explicitly indicates how many times the first number contains the second.

The ratio between 2 quantities is 3:7. If first quantity is 15, find the second one.

Let the second quantity be x.
Thus 3:7 = 15:x
Since Product of Extremes = Product of Means
3x = 15*7
=> x = 15/3*7
= 5*7
= 35

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general knowledge

Let us learn about general knowledge & primary resources maths

As easy as ICT
Information & Communication Technology ICT might sound a bit daunting, particularly when the aim & goal is to link it with tutoring mathematics at primary level. However, when put into the context of CD-ROMs, DVDs, & PlayStations, web pages & touch-screen ticket machines — all of which come under the ICT umbrella — perhaps some creative thinking can come out of the different types of resources & software that can be used to solve various mathematics subject problems. ICT at primary level should basically cover 5 main areas:

• learning from expert’s feedback
• observing patterns & extracting ideas
• exploring data
• tutoring the computer through pupil-designed activities
• developing & Improving visual imagery

At Ysgol Frongoch a primary school in North Wales, tutor David Baugh organized a school trip in which student visited a quarry as part of a project to look at the impact of human beings on the environment. Once back at school they developed an online spreadsheet to reflect the consequence. 'When student are actively engaged in the creation process', explains David, 'their ability to gather, manipulate & present information becomes second nature'.
Many multimedia resources are freely available for students, although for Government-funded nursery, primary & secondary schools, money is set aside for equipment in the form of Electronic Learning Credits eLCs. This can cover resources like digital videos & software. The British Educational & Communications & Technology Agency BECTA offers free publications & downloads aimed at helping teachers & teaching assistants at primary & secondary level on some of the best ways to use ICT in the classroom.
Linking ICT with mathematics subject or any other subject can develop students' interest & understanding of ICT in a way that straightforward use of PCs might limit. Special calculators can be applied with overhead projectors to teach student the basic key functions as an addition to their methods of using jottings or mental mathematics subject to find solutions to problems.
Electronic whiteboards also mean that tutors can be at the centre of things & can ask pupils to flash the results of a mathematics student’s problem up onto the board from their keypads. This allows the whole class to be at the same point of a lesson & to discuss their methods & outcomes. This is especially effective when playing number games with shapes & patterns or designing a graph by using collected data as student can relate the visual outcome of each exercise with the solutions to the problems they have tackled.
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add fractions

Let us learn about add fractions

There are 3 easy Steps to add fractions:

• Make sure the bottom numbers which is called as denominators are the same
• Add the top numbers the numerators. Put the solution over the same denominator.
• Simplify the fraction if needed.

Fractions consist of 2 numbers. The top number is said to as the numerator. The bottom number is said to be as denominator.
Numerator
denominator
To add 2 fractions with the same denominator, add the numerators & place that sum over the common denominator.
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time table chart

Let us learn importance of time table chart

A timetable or schedule is a planned or an organized list, which is usually set out in tabular form, providing information about a series of arranged events: in particular, the time at which it is planned these events will take place.

A school timetable is a table for coordinating these 4 elements:

Students, tutors, classrooms, time slots also called periods

Timetable is the easy method or way to list the amount of hours that student have scheduled. Timetable makes it simple to track & bill for your time without keeping a second record outside of learner’s calendar. Students can find trends in their calendars by searching the details of their events & viewing the average, maximum & minimum times that they have spent.

Each school term I put together a student’s timetable. The aim of the student’s timetable is to:

Show the students what their week’s activities are & allow students to take responsibility for having the right equipment on the right days.

To familiarize the preschoolers & early readers with their names, days of the week & other commonly used words & a reminder for parents about what activities they can play with the toddler & preschooler.

The student’s timetable is a very basic document created in Microsoft Word. I like to photocopy this on to A3 size paper & then placing it in a prominent place, making it easy for the student to read.
This term I have refined my process slightly & created 2 timetables:

1. School student – purely text based as both students can read the timetable.
2. Early Learner, Reader & Preschooler – key text & picture based, so they can begin to make connections between the picture & the text.
3. 
   

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equivalent fractions calculator

Let us learn about equivalent fractions calculator


The easiest method to work with math fractions is to use an equivalent fractions calculator. It's a great help & an idea to validate your own calculations.
You can solve including improper fractions, fraction problems, mixed numbers and whole numbers by using equivalent fractions calculator
Properties on Equivalent Fractions Calculator are as follows
This is one of the most important rules used which dealing with a equivalent fractions calculator
The numerator of fraction & the bottom of a fraction must always be the whole number.
The number you choose to divide must be always divided evenly for both bottom and the top numbers.
You have to divide or multiply only, never subtract or add, to get an equivalent fraction
Important things to kept in mind while comparing fractions:

When the denominator is the similar, the bigger fraction is the fraction with the bigger numerator.

The best example, 4/3 is bigger than 2/3

When the numerator is the similar, the bigger fraction is the 1 with the smaller denominator.

The best example, 6/2 is bigger than 6/3

If the denominators or the numerators are not the similar, just look for equivalent fractions with the same denominator. Then, compare the numerators

The best example, compare 3/4 and 2/3

An equivalent fraction for 3/4 is 9/12

An equivalent fraction for 2/3 which has a denominator of 12 is 8/12

Hence 8/12 is smaller 9/12, 2/3 is smaller than 3/4
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Standard form calculator

Let us learn about Standard form calculator


Form of a numbers into expression method is called as Standard form

for example, 3000
3000 = 3x10^3

Standard form calculator is mostly used in because the calculator has less space in display & Standard form calculator is an easy method to make a value in calculator. By using EXP expression command is used in standard form calculator.

Evaluate 0.000 01 3 in standard form
Standard form equation
Given: 0.000 01 3
0.000 01 3 = 1.3 × 10^5
It’s 10^5 are moved to 5 decimal places to the left to get the number to be 1.3
Linear equation, polynomials, quadratic equation, is different forms of Standard form equation

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mean median mode range worksheets

Let us learn about mean median mode range worksheets.

The Mean, Mode, Median, and Range Worksheets are perfect for learning the math topic concerning calculating mean mode median and range for data sets of numbers. The Mean, Mode, Median, and Range Worksheets are valuable resources for students & teachers, home schoolers, moms, & dads looking for some practice with means, modes, medians, and range computations.

Mean Mode Median and Range Definition Worksheets & Mean Missing Number Worksheets. If you need a more help with description of these Mean Mode Median Worksheets then you need to contact tutors who provides online tutoring services free. Mean Mode Median Worksheets are free to download, very flexible & easy to use. The Mean Mode Median Worksheets are randomly generated so when ever we request 1it will be different every time.

The Mean Mode Median Worksheets are a great resource for students in 5th Grade, 6th Grade, 7th Grade and 8th Grade. The Mean Mode Median Worksheets are free printable Math worksheets intended for home study for students.

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area of a parallelogram

Let us learn about area of a parallelogram


Parallelogram is 1 form of quadrilateral that has 4 sides. 2 pair of lines is parallel in the parallelogram. Each side of angle is 90 degree right angle triangle. Total internal angle of parallelogram is 360 degree.
Formula:
Area of triangle = b* h
Where, b = base of the parallelogram,
h = height of the parallelogram.
Perimeter of the parallelogram = 2 (b + h)
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derivatives of trigonometric functions

Let us solve problems on derivatives of trigonometric functions

Find the derivative for the function y = cot 9x.
Solution:
Step 1: Given function
y = cot 9x
Step 2: Differentiate the given function y = cot 9x with respect to ' x '
= - cosec² (9x) (9)

= - 9cosec² (9x)
Example 2:
Find the derivative for the function y = tan^-1 (6x).
Solution:
Step 1: Given function
y = tan^-1 (6x)
Step 2: Differentiate the given function y = tan^-1 (6x) with respect to ' x '
= 1/1+(6x)^2 (6)
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what is an isosceles triangle

Let us learn about isosceles triangle.

what is an isosceles triangle?

A triangle in which two sides and two angles are equal is called an isosceles triangle.

The base of the triangle is always its unequal side. Base angles of triangle are in equal measurement. Here, angles ∠ABC and ∠ACB are often the same. 3rd angle should be a 90^o known as "right isosceles triangle". Perpendicular length between topmost vertex & base = Altitude

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independent variable

Let us learn about independent variable.

Equation in a mathematical or statement whose value determines that of the dependent variable: in y = f(x), x is the independent variable. An experimenter deliberately manipulates to observe its relationship with some other quantity, or that defines the distinct conditions in an experiment.
Continuous variable
Independent variable
Binary variable
Dependent variable
Dummy Variables
Are the types of variable.

An Independent variable is a variable which stands alone and is not effected by the changes of the other variables like Dummy Variables, Dependent variable, so on which we are trying to measure.
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prime numbers up to 100

Let us learn how prime factorization calculator helps in solving math problems.

A Number which is divisible by any other number is called as prime number

prime numbers up to 100

2	3	5	7	11
13	17	19	23	29
31	37	41	43	47
53	59	61	67	71
73	79	83	89	97

A prime factorization calculator is a device or calculator which takes a number as an input and gives the list of prime factorization as its output.

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