what is a function in math

Let us learn about what is a function in math

A function f from N → N is referred by f(x) = 3x. Find the range of f.

Solution: f = {3, 6, 9, 12, …}

Given f(x) = 4x/(x +1) with domain (–3, –2, 0, 1, 3}. Find the range of f.

Solution: The range of f is (6, 8, 0, 2, 3}

A math function is a 1 of the type of relation. In a function, number two ordered pairs can have the same 1st element & a different 2nd element. That is, for functions, corresponding to every 1^st element of the ordered pairs, there must be a different 2^nd element. That is. In a function we can't have ordered pairs of the form (a₁, b₁) & (a₂, b₂) with a₁ = a₂ & b₁ ≠ b₂. It is called as function in math

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basic operations with polynomials

Let us learn about basic operations with polynomials

A polynomial is referred as a series of terms which are to be added to or subtracted from each other in an equation.

Best example of a trinomial would be 6x2-5x-6. For the ATC apprenticeship mathematics test you will work with factors to create polynomials.

A polynomial is referred as an algebraic expression in which the variables have non-negative integral exponents only.

Best example, all of the following expressions is polynomials:

17 + 2x + x2, x4 + 3x

The 1st & the last are polynomials in 1 variable x. The middle expression is a polynomial in 2 variables x & y. Therefore unless stated otherwise, polynomial will mean a polynomial in 1 variable. Operation of polynomials are classified following ways

a) Addition b) Subtraction c) Multiplication d) Division

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college algebra solver

Let us learn about college algebra solver

College algebra solver calculator reduces student homework time while teaching the concepts critical for success in Mathematics

College algebra solver is important Math equivalents & college algebra solver help to solve algebra word problems so as to make the interpretation of word problems easier.

Add = sum, total of, added to, together, increased by

Subtract =difference between, minus, less than, fewer than

Multiplication = of times, by a factor

Division = per, out of, ratio of, percent

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integration of exponential

Let us learn about integration of exponential


Integration of exponents is referred as the reverse process to differentiation. Integration is known as anti-differentiation. Integration of exponents is applied in many applications. Integration is applied to find the area between 2 curves & amount of work done, etc…Integration of exponential always deals with the exponential functions. Exponents are represented by the power of e. By differentiation of exponents you find the derivative of the mention exponential function, whereas by integration of exponential you find the exponential function whose derivative is called. This is known as the integration of exponential of the given exponential function.
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biconditional

Let us learn about biconditional

If 2 simple statements “p” & “q” are connected by the connective

'if & only if', then the resulting compound statement is known the biconditional statement. Symbolically biconditional is represented by p<-> q.

A biconditional is referred as a truth function which is true only in the case that both parameters are true or both are false.
Symbolically, the biconditional is written as aób or aób
The biconditional function is frequently written as ``iff,'' meaning ``if and only if.''
It gets its name from the fact that it is really 2 conditionals in conjunction,

(a->b)V (b->a)

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p value formula

Let us learn about p value formula

The p-value is referred as the area under the null distribution curve which is in bigger disagreement with the null hypothesis than the observed test statistics.
Best example, the hypothesis test for the mean is:

Imagine you have a large enough sample such that the central limit theorem holds & the mean is normally distributed then to test the null hypothesis H0: μ = Δ

find the test statistic “z” = (x Bar - Δ) / (sx / square root (n)) where “x” bar is the sample average
sx is the sample standard deviation
”n” is the sample size

The p value formula of the test is the area under the normal curve which is in agreement with the alternate hypothesis.

H1: μ > Δ; p-value is the area to the right of z
H1: μ < Δ; p-value is the area to the left of z
H1: μ ≠ Δ; p-value is the area in the tails is always greater than |z|

for a small test for the mean every thing is the same save the test statistic is a t statistic with n - 1 degrees of freedom. In such case the underlying distribution should be normal for this test to be valid.
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numerical coefficient

Let us learn about numerical coefficient
The definition for the numerical coefficient are given below the following section,

• Other name for the numerical coefficient is coefficient.

Best example, a₁ x₁ + a₂ x₂ + a₃ x₃ +……………………. a_n x_n
In the above given example,

• a₁ a₂ a₃ are known as numbers.
• x₁ x₂ x₃ are known as the variables.

Find the numerical coefficient for the product of mentioned terms, (2x² + 3x + 2) (x + 1).
The mentioned problem for numerical coefficient is,
(2x² + 3x + 2) (x + 1)
Next step, we have to product the above mentioned functions,
(2x² + 3x + 2) (x + 1)
= 2x² (x) + 3x(x) +2(x) +2x² + 3x + 2
= 2x³ + 3x² + 2x + 2x² + 3x + 2
= 2x³ + 5x² + 5x+2
Hence, the numerical coefficient is present before the variables.
Numerical coefficient = 2, 5, 5, 2
Thus, this is the required solution for the numerical coefficient.

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math dictionary algebra

Let us learn about math dictionary algebra

Math dictionary algebra is a branch of mathematics that deals in representing numbers through variables. math dictionary algebra also deals with symbols, relations, functions, and equations. Math dictionary algebra is a branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on 1 side of the scale with a number is also done to the other side of the scale. The numbers are the constants.

Math dictionary algebra is a very useful to everybody especially to students, tutors, researchers & etc. math dictionary algebra for students explains over 600 common mathematical terms & math words in simple language. The math dictionary algebra is much more than a compilation of words & definitions. Math dictionary algebra has been organized to reflect the different areas of mathematics taught in elementary & junior high schools. Within each category are all the terms commonly used in this field of math education, concise definitions, & many best examples & illustrations. In addition, the last chapter provides instructions for basic operations & tables of commonly-used facts & equivalents.

Math dictionary algebra may be used effectively in a variety of ways. Math dictionary algebra would definitely be an often sought reference book in any grade 4–9 math classroom, but it offers much more than simple definitions. Math dictionary algebra’s clear style & inclusion of many strategies for success in problem solving make it well adapted for independent instruction.

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permutations and combinations worksheet

Let us learn about permutations and combinations worksheet

In permutations without Repetition, you have to decrease the number of available selections every time. When you have n unlike things then you have to decrease one from the prior term for each time.
This is similar to n * (n-1) * (n-2)….
& if you are asked to select r things from n things, the combination is

n!

P (n, r) = ---------

(n-r)!

Combinations with Repetition for worksheet:
You require to do is change permutations formula to decrease it by how many customs the things could be in order but the order is not significant here.

n!

C (n, r) = ---------

r! (n-r)!

Combinations without Repetition for worksheet:
When you have n unlike things & to chose r things with repetition you have a formula

n+r-1

C (n, r) = -----------

r! (n-r)!

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factoring cubes

Let us learn about factoring cubes

The other 2 special factoring formulas are 2 sides of the same coin: the sum & difference of cubes. These are the formulas used.

a³ + b³ = (a + b)(a² – ab + b2)

a³ – b³ = (a – b)(a² + ab + b2)

The rule for factoring the sum of 2 perfect cubes is almost the same as the rule for factoring the difference between perfect cubes. To change 2 little signs to make it work. The sum of 2 cubes equal to the sum of its roots times the squares of its roots minus the product of the roots that looks like

a³ +b³ = (a+b) (a² –ab +b²)

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everyday math worksheets

Let us learn about everyday math worksheets
Everyday math worksheets make Student to learn better than is usually expected of them. Student comes to school knowing more than they currently get credit for. Mathematics refers more when it is rooted in real-life problems & situations.

Schools should take advantage of the tutoring tools which technology presents

Everyday math worksheets that help students practice graphing, arithmetic, telling time, handling money, & many more. Such activities are a great way to supplement student’s regular mathematics curriculum

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radical calculator

Let us learn about radical calculator

The radical calculator will reduce any number to its principal nth root as well as express it in simplest radical form. The radical of a positive integer “n” is referred as the product of the prime numbers dividing n:

The radical of any integer “n” is the biggest square free divisor of n, & so also described as the square-free kernel of “n” in mathematics.
Radical numbers for the 1st few positive integers are 1, 2, 3, 2, 5, 6, 7, 2, 3, 10, .The function radicals is to multiplicative in mathematics.
. Divide the given radicals : √16 / √4 = √16/ √2 = 4/2 = 2

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log laws

Let us learn about log laws

The "Laws" of Logarithms will allow you to change a single logarithm into the sum, difference, &/or production of logarithms. Logarithms is often easier to refer to the "Laws"

The natural logarithms written as:

log_ex or ln x

Where as e = 2.71828182846 base of natural logarithm

The natural logarithms are explained by the exponent of the power to that a base number must be raised to equal a given number. The solving natural logarithms are also said to be as the inverse of an exponent. In logarithm, it has 2 types of logarithms are the common logarithm, also said to be as the base 10 logarithms, & the natural logarithm, also said to be as the base e logarithm

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fraction reducer

Let us solve problem on fraction reducer

My pet dog is 1/4 years old and my dog is 7/4 years old find the total sums of ages & reducing the fractions
Solution:
Given pet is 1/4 years old
And my dog is 7/4 years old
Now we have to find the total sums of ages
= ¼ + 7/4
= 1 + 7/4
=8/4
By reducing the above fraction we get 2 is the solution
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ordinate abscissa

Let us learn about ordinate abscissa

Ordinate means the y-coordinate of a point: Ordinate’s distance from the x-axis measured parallel to the y-axis.
Abscissa means the x-coordinate of a point: Abscissa’s distance from the y-axis measured parallel to the x-axis.

The 1st element of the ordered pair is called Abscissa & the 2nd element of the ordered pair is called as the Ordinate. A simply X-coordinate point that is on the horizontal line is abscissa and Y-coordinate points on the vertical line are called as the Ordinate.

* Ordinate is said to be as the value of the Y-coordinate or Y-axis on a coordinate plane.

*Ordinate is said to be as the value of the vertical axis on a coordinate plane.

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probability worksheets elementary

Let us learn about probability worksheets elementary

Probability worksheet elementary is a branch of mathematics. Probability is a way of expressing knowledge or belief which is an event will occur or has occurred.

In mathematics the concept has been given an exact definition in probability theory which is used extensively in such areas of study as statistics, finance, mathematics, gambling, science, & philosophy to draw conclusions about the likelihood of potential events & the underlying mechanics of complex systems.

In math, the elementary probability is advance of converse or proposal an event will happen or occurred. The probability worksheet elementary is generally helpful to the study of the mathematics, gambling etc. The elementary math probability problems are performance of fluent familiarity or idea that happening will occur.

1. There are 3 red color balls, & six blue color balls. Then you will select the balls without looking & then put it back. You can do this action for 9 times. Find the best prediction possible for the number of times that you will pick a blue ball.
Solution: There are 9 balls, so the possible out comes is 9.
The number of blue color balls is 6. So, the possible outcomes to pick blue color ball is 6.
The probability = 6 out of 9 or 6/9
You will find 6/9 of 9
6/9 x 9 = 6 The best prediction = 6 out of 9 times Answer: 6 times.
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factors of 108

Let us learn about factors of 108

108 is a composite number because 108 have factors other than 1 & itself. 108 is not a prime number.

The 12 factors of 108 are as follows 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

The factor pairs of 108 are as follows 1 x 108, 2 x 54, 3 x 36, 4 x 27, 6 x 18, & 9 x 12.

The proper factors of 108 are as follows 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, & 54

The prime factors of 108 are as follows 2, 2, 3, 3, & 3.

Points to remember: There is repetition of these factors, therefore if the prime factors are being listed instead of the prime factorization & usually only the distinct prime factors are listed.

The 2 distinct prime factors of 108. They are 2 and 3.

The prime factorization of 108 are as follows 2 x 2 x 3 x 3 x 3 or, in index form 2² x 3³.

Points to remember: There cannot be similar factors, a least common multiple or a greatest common factor because "common" refers to factors or multiples that 2 or more numbers have in common.

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Standard form calculator

Let us learn about Standard form calculator

Evaluate 0.000 01 3 in Standard form calculator

Solution:-

Given: 0.000 01 3

0.000 01 3 = 1.3 × 10^5

Its 10^5 are moved to 5 decimal places to the left to get the number to be 1.3

Standard form is a method of writing down very small numbers or very large number easily. 10³ = 1000, so 4 × 10³ = 4000. So 4000 can be written as 4 × 10³. This idea can be applied to write even larger numbers down easily in standard form.

Small numbers can also be written in standard form. Instead of the index being positive in the given example, the index was 3, it will be negative.

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Free calculus problems

Let us learn about Free calculus problems

Have you ever wish that you had a calculus tutor that was there for you 24/7 (all the time), day or night whenever you wanted, never required an appointment & was willing to go over & 24/7 & over a procedure until you got it right? & in addition cost less than the price of a single tutoring session, or problems book!
Well, now you have! This calculus tutor is even available the night before the test, even the last few minutes before the test.
There are many web site you are about to sample has all these features & more. If you buy a problems calculus book you can read how others do calculus problems. If you go to a calculus problems oriented class you will see how the instructor does the calculus problems. If you hire a calculus tutor you will see how the calculus tutor does the calculus problems. All these types of experiences are great, but what you really want is the skill to do the calculus problems yourself.

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Factor polynomials

Let us learn about Factor polynomials


Factoring polynomial expressions is just not quite the same as factoring numbers but the concept is very similar. When factoring polynomials or factoring numbers you are finding polynomials or numbers that divide out evenly from the original polynomials or numbers. But in the case of polynomials, you are dividing numbers & variables out of expressions not just dividing numbers out of numbers.

When polynomials contain 4 terms it is sometimes easier to group like terms in order to factor.

Student goal is to create a common factor.

Student can also move terms around in the polynomial to create a common factor.

Practice makes student better in recognizing common factors.

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how to do algebra

Let us learn how to do algebra

Algebra is defined as "a branch of mathematics related to the study of structure, relation & quantity." For many learners, algebra is the foreign language of math, rife with equations. The use of letters instead of numbers that demand to be assigned a value appears to add to the complexity. However, algebra can be divided into a series of linked concepts.

Cultivate a "can do" “I can” attitude before Algebra class starts. Remember that practice makes man perfect, so do the homework regularly & practice algebra everyday. Review basic math skills to prepare for algebra.
Start learning the special terms applied in algebra. Understand number sets, elements & learn to identify the numbers which belong to the set of whole numbers, real numbers & natural numbers. Practice writing mathematical statements using the equality signs & inequality signs.
Understand fractions perfectly & thoroughly. Identify the numerator & denominator. Be able to reduce fraction, convert them & find the LCN & least common denominator. Know how to perform math functions, division, addition, subtraction, multiplication, with fractions. Understand prime numbers and prime factorization.
Study the properties of real numbers with interest. Learn about positive numbers & negative numbers, the value of zero & how to multiply by zero & divide by zero. Practice math functions with real numbers. Know how to find the reciprocal of any given number.
Practice reading & drawing graphs, pi chart, including bar, line graphs & double line graphs. Understand the application of each. Know how to create and read a Venn diagram.
Get master simple algebraic expressions & move to more complicated expressions and simplify them. Practice the properties of equality, multiplication & including addition. Advance to linear equations & linear inequalities.
Remember that each concept or topic of algebra is built on another. Make sure to master each concept or a topic before moving to the next. Make the best use of class time, books & ask for help after class & in special tutoring sessions from algebra tutors.

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math word problems worksheets help

Let us learn about math word problems worksheets.

math word problems worksheets help student to solve problems easily.

Math word problems worksheets help make learning engaging for learners. Math Word problems or story problems allow learners to apply what they've learned in math class to real-world situations. Math word problems build critical problem-solving, higher-order thinking, & reasoning skills. All of the printable math word problem worksheets on this site are FREE for parents, students, home school families, & tutors.

The best example: 1. James bought a new camera. He took pictures of birds and squirrels at the park. He took 63 pictures of birds and 24 pictures of squirrels. How many pictures did he take in all?

Answer: 87

2. Joey, John, and Hannah went to the movie theater. Each ticket cost $7.30. What was the total cost of the tickets?

Answer: $21.90

Feature original math word problems worksheets for tutors & parents to copy for their kids. These Math word problems worksheets help in teaching, review & reinforcement. These Math word problems worksheets are most appropriate for grades 4th and 5th, but many are designed to be challenging & informative to older & more advanced learners as well.

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acute triangle problems

Let us solve acute triangle problems.

A triangle whose all angles are less than 90° is called acute triangle

1. The angles of a triangle are 23º, 50º and 80º respectively. Identify what type of triangle is this?

Solution: This triangle is an acute triangle. This is because each of the angles is below 90°.

2. The angles of a triangle are 45º, 56º and 79º. Identify what type of triangle is this?

Solution: This triangle is an acute triangle. This is because each of the angles is below 90°.

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square root chart

Let us find out square root of 25 from square root chart.

Square root is nothing but the exponent of 0.5 to the number or ½ exponents to the number. This type of root gets vanished when the number is squared.

1. The product of two square roots with different numbers inside will be written in a single root with the product of those 2 numbers.

2. When a number gets into the square root, it changes into a square of the number.

3. The square root of a fraction will be written as individual roots.

4. When a perfect square comes out of the root, a perfect square becomes the number without square.

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diameter to circumference

Let us learn diameter to circumference.

The formula used to find the circumference of the circle is given as,
Circumference = 2πr
Where,
r is radius
Radius r = D/2

Find the circumference of the circle when the diameter is 10 cm

Solution:
Diameter of the circle is 10cm
Circumference of the circle is pi*d units
= (3.14)*10
= 31.4 cm.
Circumference of the circle is 31.4 c
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math problems online

Hi Friends!!!

How many of you like to solve math problems online.

Instrument required by both student & tutors to learn math problems online.

Headset, Microphone, webcam, pen drive, digital pen & pad.

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basic probability

Let us learn about basic probability

Formula used for solving basic probability

= Number of favorable out come
Total No. of favorable outcome

basic probability is the method of expressing information or belief that an event will occur or has occurred

1. Two coins are tossed simultaneously, what is the learning basic probability of getting (i) exactly one head
The sample space i s S = {HH, HT, TH, TT}, n(S) = 4
Let A be the event of getting one head A = {HT, TH},
P(A) =n(A)/n(S) =2/4 =1/2
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maths past papers

Hi Friends!!!

How many of you scare to attend exams?

I have few tips and reasons which makes you tension free before attending exams.

Practicing maths past papers is the best way to gain perfection in subject and to complete your revision as you can test yourself under exam conditions, with the same three hour time constraint you'll have in the exam. I can say they are the most valuable resource for carrying out revision. Solving past papers enable students to gauge their subject knowledge and uncover their strengths and weaknesses, enabling you to understand what areas you need to devote more time to and conversely, what areas you can devote less time to.

It is the one of the most effective & easy way of increasing interest in learning and your chances of passing exams at school is to obtain past Test papers.There many websites which provides you free exam paper.
There are 4 reasons to solve maths past papers & English past papers:
1. It enables you to understand & establish the type of questions being asked.
2. How those questions will be marked. For exam some answers carry more points then others
3. You will learn how to manage your time during the exam.
4. It helps you to revise & review information from math books or math notes that are most important for the math exam.
One hand before you obtain past papers the better as it enables you to gear your revision around the typical type of questions that you are likely to get asked.
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grams to kilograms

Let us learn how to convert grams to kilograms.

Grams and kilograms both are the International System of Units, the standard units of measuring weight. Gram is a metric unit of mass which equals to one thousandth (1÷1000) of a kilogram.

Convert 1000 grams to kilograms.

Solution:

We know that one gram is equal to 0.001kilograms.

Therefore 1000 grams= 0.001x 1000 kilograms.

= 1 kilograms.

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Introduction to Analytic Geometry

Let us learn about Analytic Geometry.

Introduction to Analytic Geometry:

In plane analytic geometry, points are defined as ordered pairs of numbers, say, (x, y), while the straight lines are in turn defined as the sets of points that satisfy linear equations.

Analytic Geometry is a branch of algebra that is used to model geometric objects - points, (straight) lines, and circles being the most basic of these. Analytic geometry is a great invention of Descartes and Fermat. Analytical geometry is also known as coordinate geometry or Analytical Cartesian coordinate system.

The study of analytical geometry related to coordinate system and the principles of algebra and analysis. The synthetic approach of Euclidean geometry is the contrast geometry, which treats certain geometric notions as primitive, and uses deductive reasoning based on axioms and theorems to derive truth.

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algebra 1 helper

Hi Friends!!!


What do you think whether books like algebra 1 helper, help on homework , free math answers so on will help you in solving problems or online tutors helps you in learning math better.

Online means it is one of the new way of connectivity it is victimized for introduce the two or author soul in a equal period from that they do the conversation finished the computer, web equivalent that. Here the grad can greet meliorate from the tutor.

online homework help from online tutors proved better learning processes from media of learning. Many students scored good marks in their semesters.

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how to solve math problems

Hi Friends!!!

Math isn’t that hard! In fact it’s probably one of the simpler sciences. That said it could be confusing in case you don’t know what to do. Definitely there's overwhelming issues in math (and even types of math where getting the wrong answer is the whole point!) but most math can be broken down in to simple solvable steps.

now let us learn how to solve math problems

Have you heard any time practice makes man perfect.

Math is an interesting subject. We need to practice daily and we should learn even a simple basic method to solve difficult problems.

There are many websites which provides you free math answers.
If you need more help on homework, online tutoring is best example to make you tension free.
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what does mean in math

what does mean in math ?


In mathematics, an average, central tendency of a data set is a measure of the "middle" or "expected" value of the data set. The average is calculated by combining the values from the set in a specific way and computing a single number as being the average of the set. The most common method is the arithmetic mean

Average or mean =. Sum of all numbers

The count of the number

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division algorithm

Let us learn about division algorithm

In mathematics, polynomials in more than one variable do not form a Euclidean domain, so it is not possible to construct a true division algorithm. Given a polynomial g, polynomials (f₁, ..., f_m) and an order on the monomials in k[x₁, ..., x_n], we construct the reduction of g modulo f₁, ..., f_m by the following algorithm. Let a_i denote the leading term of f_i with respect to the monomial order. Repeatedly apply the following until no monomial term of g is divisible by any of the a_i :

Division Algorithm for Polynomials

Let F is a field, f(x), g(x) e F[x] with g(x) ≠ 0.

In q(x), r(x) in the F[x] such that f(x) = g(x) q(x) + r(x) and r(x) =0

Proof :-
(1) Let f(x) = g(x) q(x) + r(x) with g(x) ≠ 0

(2) If f(x) = 0 or deg f(x) is less than g(x), then r(x)=f(x), q(x)=0.

(3) So, we assume that f(x) ≠ 0 and deg f(x) ≥ deg g(x)

(4) Let f(x) = a_nxⁿ + ... + a₀

(5) Let g(x) = b_mx^m + ... + b₀

(6) Let f₁(x) = f(x) - a_nb_m^-1x^n-mg(x)

(7) We note that deg f₁(x) is <>deg f(x) since:

f(x) - a_nb_m^-1x^n-mg(x)

= a_nxⁿ + ... + a₀ - a_nb_m^-1x^n-m(b_mx^m + ... + b₀)

= a_nⁿ - a_nxⁿ + a_n-1x^n-1 + ... + a₀ - a_nb_m^-1b_m-1x^n-1 - ... - a_nb_m^-1b₀x^n-m

= a_n-1x^n-1 + ... + a₀ - a_nb_m^-1b_m-1x^n-1 - ... - a_nb_m^-1b₀x^n-m

So that f₁(x) has a degree of n-1 while f(x) has a degree of n.

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