Revise Maths

Introduction to Revise maths:
In this article we are discussing about basic maths revise exam problems in which tutor helps the students to get the solutions. Basic maths revise exam problems can solve problems with step by step solutions for all problems. The maths basic problems involved topics such that algebra, geometry, polynomials, trigonometry, data handling and calculus. Let us solve some basic maths revise exam problem with step by step solutions and practice problems are given below. I like to share this Practice Math Problems with you all through my article.

Revise Maths – Example Problems:

Example 1:

John purchased 2 kg 351g apples, 3 kg 800 g mangoes and 1 kg 450 g bananas. What is the total weight of fruits purchased?

Solution:

Weight of apples:        2kg 351 g

Weight of mangoes:    3 kg 800 g

Weight of bananas:    (+) 1 kg 450 g

Total weight: 7k 601 g

Thus, jack purchased 7 kg 601 g fruits.

Example 2:

Find the volume of cuboids of length (l) 5 cm, breadth (b) 2.5 cm and height (h) 3.2 cm

Solution:

Here, length = 5cm

Breadth = 2.5 cm

And height = 3.2 cm

We know that v = l x b h

Hence, v= 5 x 2.5 x 3.2 cu.cm

= 40cu.cm

Example 3:

Find the volume of cubical box of side 5.2 cm.

Solution:

Length of the side of the cube = 5.2 cm

We know that the volume V of the cube = l x l x l

= 5.2 x 5.2 x 5.2cm3

=140.608cm3


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Revise Maths – Practice Problems:
Problem 1: John purchased 3 m 25 cm cloth for the suit, 2 m 80 cm for the shirt and 2m 20 cm for the trouser. Find the total length (l) of the cloth purchased.

Problem 2: Find the volume of cuboids of (l) length 5 cm, breadth (b) 5 cm and height (h) 2 cm

Problem 3: Find the volume of cubical box of side 3 cm.

Revise maths – answer key:

Problem 1: 8 m 25 cm

Problem 2: 50cm3

Problem 3: 27cm3

Postulate Math

Introduction to postulate math:

In general, math postulates are nothing but the math statements, which are assumed as real without any proofs. Math postulates help to understand various concepts involved in the field of mathematics and also useful for the preparation of exam   In this article postulate math, we are going to study few math postulates which will be helpful for the students. Please express your views of this topic Difference of Cubes Formula by commenting on blog.

Math Postulates:
If the two straight lines cross each other, they cross at only one point.

In general, if perpendicular lines cross, four right angles will be formed.

Consider that equal quantities are added to equal quantities, and then their sums will be equal. Likewise, if similar quantities are subtracted to similar quantities, their differences will be equal.

A square is nothing but a parallelogram having four congruent sides and also four right angles.

A rectangle is nothing but a parallelogram having four right angles.

If same quantities are multiplied by same quantities, the products will be equal.

If the two geometric shapes are said to be congruent, then their area must be same.

The addition of the areas of its non-overlapping parts is referred as the area of section.

The addition of the lengths of any two sides of a triangle will be bigger than the length of the third side.

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Additional Math Postulates:

All right angles are said to be congruent according to the Euclid’s postulate.

The addition of interior angles of any triangle will always measure 180 degrees.

Trapezoid is nothing but a quadrilateral, which has single pair of parallel sides.

In general, each and every segment has a single midpoint.

The quotients will be equal if same quantities are divided by equal nonzero quantities.

In general, a line segment can be extended for an indefinite period along a line.

The intersection of planes will be a line, if two planes intersect

If two triangles have equal angles to one another, then the two triangles are similar.

Definition of Slides in Math

Introduction for Math Slides:

Math slides is a transformation which has a plane figure or move across a line. Moving a shape without rotating or flipping is known as slides (translation). A math slides is also known as translation. If any student wants to know about the definition of math slides, they can refer the below examples with definitions Let us see some of the definition and examples for math slides. I like to share this Properties of Exponents with you all through my article.

Definition of Slides in Math – Explanations:

These are the explanations of slides in math with definition and example figure.

Slides are one of the transformations which can translate the image from original direction A, B, C, D and E to other direction as shown.

This means, they can translate the same image to other side A', B', C', D', and E' as shown.

The image of the angle, length and size are not change in them.

The image of the figure translation is its mirror of the image or their translation plane.

Every point in the translation is same distance from the center of the line as shown.

This center line is known as the mirror line.

It has the same size and length from the original image.

The translating image in the opposite side will be always same as the original image as shown in the example figure.

Each point of translation can be marked in them to shows the image length and their sides.

We can show the translation from one place to another in the following example figure.


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Definition of Slides in Math – Example Figure:

These are the example figure for the definition of slides (translation) in math.

Slides in Math:

The example figure below shows the slides in math with the shape of an object.

Elementary Column Operations

Introduction on elementary column operations:

According to the term elementary Column operation are found to be one of the parts in matrix. Elementary is found be defined as Elementary matrix is found to be defined as a simple matrix where it represented in different identity matrix form. Elementary column operation is the operation that is done by post or right multiplication. I like to share this Complex Fractions with you all through my article.

Rules Based on Elementary Column Operations:

Rule 1: To find the sum given, of elementary column operator, the identity matrix operation is applied.

Rule 2: The post multiplication has to be done for carry out elementary column operations.

Rule 3: The column operator is created from multiplying “column * column"

Representation of Column in Matrix:

The column is represented in matrix as :  `[[a],[b],[c]]`

Example Problems Based on Elementary Column Operations:

Example 1:

Elementary column operation on the term “A”, where the identity used in matrix   `A= [[1,6], [4,1], [0,1]]` and identy matrix `x = [[1,0], [0 ,1]]`

Solution:

Given: Identity matrix `x = [[1,0], [0 ,1]]`

`A= [[1,6], [4,1], [0,1]]`

Step 1:  The given identity matrix x is interchanged of fist and second column and the finding result is named it   (x1).

Step 2: To do the elementary column operation on given `A= [[1,6], [4,1], [0,1]]`

Step 3: The operation in matrix is done by [row *column]

`X= [[1,0], [0,1]]`

The first and second column is interchanged and the result is,

`X1= [[0,1], [1,0]].`

Now, the found X1 is calculated with given “A”

`A= [[1,6], [4,1], [0,1]]`

`X1= [[0,1], [1,0]]`

`A*X1` for calculation elementary column operation on

`A*X1`

` [[1,6], [4,1], [0,1]] * [[0,1], [1,0]]`

` [[1*0+6*1 , 1*1+6*0],[4*0+1*1 , 4*1+1*0],[0*0+1*1, 0*1+1*0]]`

`[[0+6, 1+0], [0+1,4+1], [0+1, 0+0]]`

`[[6,1],[1,4],[1,0]]`

Hence ,the elmentary column operation for the given value `A=[[6,1],[1,4],[1,0]]`

Example 2:Based on elementary column operations

Elementary column operation on the term “D”, where `D= [[1,2],[1,1],[0,0]] ` the identity used in matrix   `"x= [[1,0],[0,1]] `

Solution:

Given: Identity matrix `x = [[1,0], [0 ,1]]`

`"D= [[1,2], [1,1],[0,0]], `

Step 1:  The given identity matrix x is interchanged of fist and second column and the finding result is named it   (x1).

Step 2: To do the elementary column operation on given `D=[[1,2],[1,1],[0,0]]`

Step 3: The operation in matrix is done by [row *column]

`X= [[1,0], [0,1]]`

The first and second column is interchanged and the result is,

`"X1= [[0,1],[1,0]]`

Now, the found X1 is calculated with given “A”

`D= [[1,2], [1,1], [0,0]]`

`X1= [[0,1], [1,0]]`

`D*X1` for calculation elementary column operation on

`D*X1`

`[[1,2], [1,1], [0,0]]*[[0,1], [1,0]]`

`[[1*0+2*1 , 1*1+2*0],[1*0+1*1 , 1*1+1*0],[0*0+0*1, 0*1+0*0]]`

`[[0+2, 1+0], [0+1,1+0], [0+0, 0+0]]`

`[[2,1],[1,1],[0,0]]`

Hence ,the elementary column operation for the given value `D=[[2,1],[1,1],[0,0]]`

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Problems to be Solved Based Elementary Column Operations:

Elementary column operation on the term “S”, where  `S ` =  `[[6,2],[2,1],[9,4]]` the identity used in matrix `X` =  `[[1,0],[0,1]] `
Answer: The elementary column operation of  `S` =`[[2,6],[1,2],[4,9]]`

Elementary column operation on the term “Z”, where `Z` =`[[2,1],[3,2],[6,3]]`   the identity used in matrix  `X` = `[[1,0],[0,1]] `

Answer: The elementary column operation of    `Z` =`[[1,2],[2,3],[3,6]]`

Elementary Math Estimation

Introduction to elementary math estimation:

In elementary number theory, integers are studied without use of techniques from other mathematical fields. Questions of divisibility, use of the Euclidean algorithm to compute greatest common divisors, integer factorizations into prime numbers, investigation of perfect numbers and congruence’s belong here. Several important discoveries of this field are Fermat's little theorem, Euler's theorem, the Chinese remainder theorem and the law of quadratic reciprocity. (Source: Wikipedia)

Types of Elementary Math Estimation:

There are four types of basic theory are mainly used in the elementary number theory; these types are classified according to the representation of the number. It will be shown as below,

Addition
Subtraction
Multiplying
Division
In elementary math to estimation it very easy to learning to study. And solve it easy. There are four steps are used in the elementary estimation of the math problems they are solved in the example problems in given below.

Example Problem for Elementary Math

Example 1:

Estimation the example of adding two numbers 163 and 13

Solution:

Let us write the given problem as 163 + 13.

Add the number 163 and 13 we get the sum as,

163 + 13 =176

Therefore, the solution for adding 163 + 13 is 176.

Example 2:

There are 56 peoples travelling in a bus. 17 of them left from the bus in one stopping. Estimation how many people will be left in the bus?

Solution:

Total number of peoples = 56

Number of peoples left from the bus in one stopping = 17

Number of peoples left in the bus = 56 - 17

= 39

Example 3

Estimation the multiplying two numbers 31 and 27

Solution:

The given two numbers 31 and 27

We need to find the product of two numbers

By multiplying 31 and 27

We get 837

So the answer is 837

Problem 4:

Estimation to divide 400 / 4

Solution:

100(quotient)

----

4)  400

400 -

---------

0(remainder)

---------

Practice Example Problem for Elementary Math

1. Estimation of adding 33 and 70

Key: 103

2. Estimation of Subtract 119 and 9

Key: 110

3. Estimation of Multiplying 29 by 20

Key: 580

4. Estimation of Divided 68 by 7

Key: 9.71

Sixth Grade Math Word Problems

Introduction to Sixth Grade math word problems:

Word problem is one of the best ways to turn up children’s towards solving, thinking and analyzing problems. Word problems will enhance this kind of attitude from the childhood stage itself. Sixth grade level includes real numbers,decimal,fraction,charts, graphs, money and basic mathematics like addition,subtraction,multiplication,division .Sixth Grade math word  problems is very essential for the children’s whose age lies between 8-13years old .It will be so fitful ,let us enjoy it, Let us deal about worked problems. Having problem with What is a Trinomial keep reading my upcoming posts, i will try to help you.

Example 1-sixth Grade Math Word Problems

One cat can kill a 10 rat. Then a  how many number of cat can kill  1000 rat?

Given:

1 cat=10 rat

?=1000 rat

Solution:

Step 1:

To find out the no of cat needed to kill a 1000 rat, we have to divide the total no of rat by the no of rat can be killed by single cat.

Step 2:

Division operation is used

The no of cat needed to kill a1000 rat=`1000/10=100 ` cat

Example 2 -Sixth Grade math word problems

One child makes a building with 250 bricks. How many no of bricks needed to make a 5 building?

Given:

1 Building needed=250 bricks

5 Building needed=?

Solution:

Step 1:

To find out the no of bricks needed to make a 5 building, we have to multiply the no of bricks needed to make a one building with 5

Step 2:

Use multiplication

No of bricks needed for to make 5 Building=`5xx25` =1250 bricks

No of bricks needed is 1250 bricks

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Example 3 - Sixth Grade Math Word Problems

A man travels 3 km per hour .So after 5 hour the distance traveled by him?

Given:

Man covered a distance per hour=3 km

Solution:

Step 1:

To find out the distance covered by him, we have to multiply the distance covered in 1 hour with 5

Step 2:

Use Multiplication

The total distance covered in 5hour=`5xx3=15km`

Example 4 - Sixth Grade math word problems

A child has 100 Chocolates and the dog grabbed 20% of it, from the child. How much number of chocolates dog has?

Given:

The number of chocolates Child has at first=100

Grabbed by the dog=20%

Solution:

Step 1:

To find out the 20% of chocolates, multiply the given percent with number of chocolates

=20%of100

Step 2:

Consider % as 1/100

` =(20/100)xx100`

=20

Finally, the dog has 20 chocolates

Univariate Data

Introduction to uni variate data:

Univariate means to equation, expression, polynomial or function of exactly one variable. This term is commonly used in statistics, mean, arithmetic mean to differentiate a distribution of one variable from the distribution of many other variables. Although it could be applied in many other ways as well. Since it is the simpler way to distribute the values. Correspondingly, the “multivariate time series” refers us to the changing values over the time of several quantities. I like to share this Two Way Table with you all through my article.

Properties of Univariate Analysis:

Univariate analysis is been used primarily in descriptive purposes to represent the quantitative analysis and the statistical analysis. It is the easiest method to identify the attributes and the single variable.

Univariate analysis contrasts with the bivariate analysis because it cannot analyse two variables simultaneously – or do multivariate analysis – the analysis of the multiple variables are been done simultaneously.

Univariate analysis is been commonly used in many fields like the scientific research, medical field and in simple hand calculations. Please express your views of this topic free math help online now by commenting on blog.

Data Set (univariate Data):

In our day to day life there may be many simple values that we go across. In those simple values twe can come across problems with only one variable and also with a single column of the data set, these are represented as a list. Mathematically, in the univariate data set there cannot be any repetition (i.e) because it cannot repeat multiple times. In general the order of the univariate data set does not be considered, but collection of those values may be considered to be a multi set rather than the (ordered) list.

Generally, the values might be of any of the kinds described as a level of the measurement. For every variable, the values will be normally of the same kind or similar.  Uni variate data can be as real numbers or the integers. For example, representation of a building's height using the meters. This could also be represented as a nominal data. However, there could also be "missing values", and those values need to be indicated in some representation.

Numerical Form

Introduction to numerical form:

Numerical form is nothing but the conversion of words into numbers. For example, one million can be expanded in numerical form as 1,000,000 or 106. Likewise, one billion can be expanded in numerical form as 1,000,000,000 or 109.  In this article numerical form, we are going to discuss about numerical form through example problems and practice problems. I like to share this Define Numerical Expression with you all through my article.

Example Problems for Numerical Form:

Example 1:

Write two and thirty five thousandths in numerical form.

Solution:

Step 1: thirty five thousandths can be written as .035

Step 2: Here, the whole number is two

Step 3: Hence, the numerical form is 2.035

Example 2:

Write thousand eight hundred million in numerical form.

Solution:

Step 1: one million is equal to 1000,000

Step 2: Thousand eight hundred million will be equal to 1,800,000,000

Step 3: Hence, the numerical form is 1,800,000,000

Example 3:

Write four and forty five thousandths in numerical form.

Solution:

Step 1: forty five thousandths can be written as .045

Step 2: Here, the whole number is four

Step 3: Hence, the numerical form is 4.045.

Example 4:

Write three thousand seven hundred million in numerical form.

Solution:

Step 1: one million is equal to 1000,000

Step 2: three thousand seven hundred million will be equal to 3,700,000,000

Step 3: Hence, the numerical form is 3,700,000,000

Example 5:

Write eight and eighty five thousandths in numerical form.

Solution:

Step 1: Eighty five thousandths can be written as .085

Step 2: Here, the whole number is eight.

Step 3: Hence, the numerical form is 8.085

Example 6:

Write two thousand four hundred billion in numerical form.

Solution:

Step 1: one billion is equal to 1000,000,000

Step 2: two thousand four hundred billion will be equal to 2,400,000,000,000

Step 3: Hence, the numerical form is 2,400,000,000,000


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Practice Problems for Numerical Form:

1) Write five and sixty five thousandths in numerical form.

Answer: Numerical form is 5.065

2) Write thousand hundred million in numerical form.

Answer: Numerical form is 1,100,000,000

3) Write four thousand five hundred billion in numerical form.

Answer: Numerical form is 4,500,000,000,000

Upper Limit Definition

Introduction to upper limit definition:

Real function: Let R be the set of all real numbers, and let X and Y be any two nonempty subsets of R.Then,a rule f which associates to each x ε X,a unique real number f(x) ε Y is called a real function from X to Y and we write, f : X ----> Y.f(x) is called the image of x or the value of the function at x.The sets X and Y are called the domain and co domain of f.Also,the set {f(x):x ε X} is called the range of f.

Limit : A function f(x) is said to tend to a limit L as x tends to 'a' if for every ε > 0,however small,there exists a corresponding positive  real number δ, such that

l f(x) − L l < ε, Whenever 0 < l x -a l < δ

This is denoted symbolically by        `lim_(x->a)` f (x) = L .

It implies that whenever the value of x lies in the open interval (a - δ , a + δ),for δ to be very small, then the value of the function f(x),lies in the open interval (L−ε , L+ε) on the y-axis.

Lower limit and Upper limit : In the limit of a function f(x), as x tends to a, x may approach a from lower side i.e, a < x or from upper side i.e, a > x.The limit of the function f(x),when 'x' tends to 'a' from lower side of a is called lower limit and when 'x' tends to 'a' from upper side of 'a' is called upper limit.

The upper limit and lower limit are represented as shown below.

Upper limit = `lim_(x->a+)` f(x),which implies that x tends to a from upper side of a,i.e, x > a.

lower limit = `lim_(x->a-)` f(x),which implies that x tends to a from lower side of a,i.e, x < a.

Fundamental Theorems of Limit Definition:

1) `lim_(x->a)` { f(x)+g(x)} = {`lim_(x->a)` f(x)} + {`lim_(x->a)` g(x)}.

2) `lim_(x->a)` { f(x)−g(x)} = {`lim_(x->a)` f(x)} − {`lim_(x->a)` g(x)}.

3) `lim_(x->a)` {c . f(x)}  = c. {`lim_(x->a)` f(x)}, where c is constant.

4) `lim_(x->a)` {f(x) . g(x)}  = {`lim_(x->a)` f(x)} . {`lim_(x->a)` g(x)}.

5) `lim_(x->a)` `(f(x))/(g(x))` = `(lim_(x->a)f(x))/(lim_(x->a)g(x))` , where `lim_(x->a)` g(x) ≠ 0.

6) If f(x)≤ g(x) for all x then `lim_(x->a)` f(x) ≤ `lim_(x->a)` g(x).

Example Problems of Upper Limit

Ex 1:  Find the upper limit of  `lim_(x->3 )` `(x^2-9)/(x-3) ` ?

Sol : `lim_(x->3+)` `(x^2-9)/(x-3)` = `lim_(x->3+)` `((x-3)(x+3))/(x-3)`

=  `lim_(x->3+)` `(x+3)`

= ` 6`

Ex 2:  Find the upper limit of `lim_(x->1)` `(x^2-4x+3)/(x-1)` ?

Sol : `lim_(x->1+)` `(x^2-4x+3)/(x-1)` = `lim_(x->1+)` `((x-1)(x-3))/(x-1)`

= `lim_(x->1+)` `(x-3)`

=   ` -2`


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Practice Problems of Upper Limit

Pro 1:  Evaluate `lim_(x->1+)` `(6x^2-4x+3)`

Ans: 5

Pro 2:  Evaluate `lim_(x->7+)` `(x^2-49)/(x-7)`

Ans:   14

Pro 3:  Evaluate `lim_(x->0+)``{(x-2)^2+6}`

Ans: 10

Polygon with all Sides and Angles Congruent

Introduction of polygon with all sides and angles congruent:

Polygon is one of the important shapes in geometry generally; there are two types of polygon. They are regular polygon and irregular polygon,in regular polygon as closed shape the sides of the regular polygon are equal, and the angles are also equal. But in the irregular polygon both angle and sides are not equal. In this article, we have to discuss about polygon with all sides and angles congruent.

Polygon with all Sides and Angles Congruent:

Regular Polygon consist of several types. They are,

Triangle
Square
Pentagon
hexagon
heptagon
octagon
nonagon
decagon
hendecagon, and
dodecagon.


Types of Regular polygon Table:

Description of Polygon with all Sides and Angles Congruent

Triangle:

The equilateral triangle is one of the types of regular polygon because it has three sides, and three angles congruent. The each side of interior and exterior angles is 60o.

Square:

The square is one of the types of regular polygon because it has four sides and four angles are congruent. The each side of interior and exterior angles is 90o

Pentagon:

The pentagon is one of the types of regular polygon because it has five sides and five angles  congruent. The each side of interior and exterior angles is 108o

Hexagon:

The hexagon is one of the types of regular polygon because it has six sides and six angles congruent. The each side of interior and exterior angles is 120o

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Heptagon:

The heptagon is one of the types of regular polygon because it has seven sides and seven angles congruent. The each side of interior and exterior angles is 128.571o

Octagon:

The octagon is one of the types of regular polygon because it has eight sides  and eight angles congruent. The each side of interior and exterior angles is 135o

Nonagon:

The nonagon is one of the types of regular polygon because it has nine sides and nine angles congruent. The each side of interior and exterior angles is 144o

Decagon:

The decagon is one of the types of regular polygon because it has ten sides and ten angles congruent. The each side of interior and exterior angles is 140o

Hendecagon:

The hendecagon is one of the types of regular polygon because it has eleven sides and eleven angles congruent. The each side of interior and exterior angles is 147.273o

Dodecagon :

The dodecagon is one of the types of regular polygon because it has twelve sides and twelve angles congruent. The each side of interior and exterior angles is 150o

Study of Errors in Measurement

Any number when expressed in the form of percentage conveys lot of meaning. Percentage is nothing but a number being expressed as a part of 100. This can be ratio of 100 or also can be termed as fraction. Percentage can be denoted by the symbol % and is very commonly used. Many measurements are made in the real world. So, there can be errors also. When there is deviation from the desired measurement error is obtained. It has to be measured to ascertain its cause and also to seek its remedy. At first the absolute is calculated. This is done by subtracting the value of the measurement obtained and the standard value. This will always be a positive number as absolute value of a number will always be positive. Once the absolute value is obtained the next step is to find the relative error which can be found if the value of the standard measurement is known. The relative error formula is quite simple. It is obtained by dividing the absolute error by the true value. If it has to be found in percentage then the answer obtained is multiplied by 100. So, the relative error equation is absolute error being divided by original value and multiplied by 100. The final answer is obtained in percentage.

This error is very significant and can be very helpful. It can be very useful in making a comparison between two measurements. The symbol percent is very important. One must not forget to write this after the answer is obtained as the answer obtained is in percentage. Also while rounding off the digits it has to be seen that the numbers do not lose their values. The terms relative error and absolute error are inter-related.


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To calculate the former one first the latter one has to be calculated. So, the calculation of absolute error is very important and no mistake must be done while finding it out. To calculate the absolute value the standard value is required. This has to be available and if it is not then the term absolute error cannot be found out and the process cannot be completed. Error occurs in the real world as the instruments used cannot give 100% accuracy. So, the errors cannot be eliminated but they can only be reduced. When an error occurs it means there is deviation from true value.