# Shortcuts For Learning Maths Formulas With Example Sample Questions Class 8/10/12

## Maths Formulas

Most of the students find Maths a difficult subject, because to solve mathematical problems, they have to memorize a lot of formulas. These **Maths Formulas** become more complex with time as you reach to Class 8,9,10, 11 &12. So to memorize them, you need to have the Shortcuts for Learning Maths Formulas. Conceptual understanding of Formulas in Maths formulates it simple to learn by heart because learning formulas is not a one-day trick. Here are some of the shortcut With Exam and Sample Questions to memorize Maths formulas forever.

As we all know that, plus, minus, multiplication and division are simple, what if you come across Mensuration, Trigonometry and calculus? You should have Maths Important Formulas to solve them. To learn Maths Formulas, you need to go through this page which is providing the unique way of solving Maths problem, providing the Shortcuts for Learning and applying the formula. We’re going to present you all the Formulas Of Maths, Eamcet Maths Formulas PDF, SSC CGL Maths Formulas, Maths Formulas For IIT JEE PDF and Jee Main Maths Formulas PDF which will let you to execute all important mathematical operations and solve mathematical questions. Take a Look…

**Why We Need To Learn Formulas Of Maths?**

If you’re planning to apply for any competitive exam then you should know that these exams are all about time. Every question paper is designed in the way that a question must be solved in fixed time duration. And in this duration you don’t have much time to remind the formulas. There are many tricks available to perfectly memorize Formulas Of Maths.

To solve questions and answers in any competitive exam, you must have math shortcut tricks and All Maths Formulas to solve problems quickly. You can easilydownload the Maths Formulas List from this page. Learn Maths Basic Formulas, Important Maths Formulas to qualify any exam. By doing so, you can easily score good marks in any competitive papers because math portion is very much important in competitive exams. It doesn’t indicate that other topics are not so important so prepare well for all the subjects equally.

**Read Out: Preparation Kit to Score Higher CGPA**

#### Basic Formulas Of Maths

Maths is very simple and logical, so you can easily score good marks in it then other subjects. Visitors are requested to carefully read all Basic Formulas In Maths from here because these Basic Maths Formulas, Integration Formulas In Maths & 8th Class Maths Formulaswill help you to solve any mathematical problem easily.

__Basic Maths Formulas For Aptitude Test__:

- (a+b)
^{2}=a^{2}+2ab+b^{2} - (a-b)
^{2}=a^{2}-2ab+b^{2} - a
^{2}-b^{2}=(a+b).(a-b) - (a+b)
^{3}=a^{3}+b^{3}+3ab(a+b) - (a-b)
^{3}=a^{3}-b^{3}-3ab(a-b) - a
^{3}+b^{3}=(a+b)(a^{2}+b^{2}-ab) - a
^{3}-b^{3}=(a-b)(a^{2}+b^{2}+ab)

__Basic Requirements To Solve Maths Numerical__:

You need to remember all these things before we do some really handy stuff.

- Whole number={0,1,2,3,4………..}
- Integers={……,-3,-2,-1,0,1,2,3,….}
- Real number={—,2.8,-2,-10,1,1.9,–2,3,3.12,3.13—}
- Even number={2,4,6——}
- Odd number=1,3,5,7——}
- Prime number={2,3,5,7,11,13,17,19,—-}

__Maths Formulas For 7th Class__:

**Get Here: Ways To Get Good Marks In Exam**

##### Maths Algebra Formulas:

An algebraic equation represent a scale, what is made on one side of the scale with a number is also made to either side of the scale. It is a branch of Mathematics that substitute letters for numbers and the numbers are constants. The mathematical term also contains complex numbers, real numbers and matrices and many more. A, B, X, Y, are the most frequently used letters that show the algebraic problems and equation some Maths Formulas to solve Algebric equation as provided below.

__Algebra Formulas__:

Some basic formulas, we discussed earlier and Maths Formulas For Class 8 / 9 / 10 / 12 to solve Algebric equation, take a look and learn them by heart….

- (a + b + c)
^{2}= a^{2 }+ b^{2}+ c^{2}+ 2ab + 2ac + 2bc - (a – b – c)
^{2}= a^{2}+ b^{2}+ c^{2}– 2ab – 2ac + 2bc - (a + b)
^{3}= a^{3}+ 3a^{2}b + 3ab^{2}+ b^{3}; - (a + b)
^{3}= a^{3}+ b^{3}+ 3ab(a + b) - (a – b)
^{3}= a^{3}– 3a^{2}b + 3ab^{2}– b^{3} - (a + b)
^{4}= a^{4}+ 4a^{3}b + 6a^{2}b^{2}+ 4ab^{3}+ b^{4}) - (a – b)
^{4}= a^{4}– 4a^{3}b + 6a^{2}b^{2}– 4ab3 + b^{4}) - a
^{4}– b^{4}= (a – b)(a + b)(a^{2}+ b^{2}) - a
^{5}– b^{5}= (a – b)(a^{4}+ a^{3}b + a^{2}b^{2}+ ab^{3}+ b^{4}) - If n is a natural number, a
^{n}– b^{n}= (a – b)(a^{n-1}+ a^{n-2}b+…+ b^{n-2}a + b^{n-1}) - If n is even (n = 2
^{k}), a^{n}+ b^{n}= (a + b)(a^{n-1}– a^{n-2}b +…+ b^{n-2}a – b^{n-1}) - If n is odd (n = 2
^{k + 1}), a^{n}+ b^{n}= (a + b)(a^{n-1}– a^{n-2}b +…- b^{n-2}a + b^{n-1}) - (a + b + c + …)
^{2}= a^{2}+ b^{2}+ c^{2}+ … + 2(ab + ac + bc + ….

__Laws of Exponents__

- (a
^{m})(a^{n}) = a^{m+n} - (ab)
^{m}= a^{m}b^{m} - (am)
^{n}= a^{mn}

__Fractional Exponents__

- a
^{0 }= 1 - a
^{m}/a^{n}=a^{m−n} - a
^{m}=1/ a^{−m} - a
^{−m}=1/a^{m}

__Some Solved Examples__:

**Question 1: **Find out the value of 5^{2} – 3^{2}

Solution:Using the formula a^{2} – b^{2} = (a – b)(a + b)

- where, a = 5 and b = 3
- (a – b)(a + b)
- = (5 – 3)(5 + 3)
- = 2 × 8
- = 16

**Question 2:** Evaluate the 4^{3} × 4^{2} = ?

Solution: Using the exponential formula (a^{m})(a^{n}) = a^{m+n}

- Where, a = 4
- = 4
^{3}× 4^{2} - = 4
^{3+2} - = 4
^{5} - = 1024

**Read Now: Preparation Tips For Written Exams**

##### All Mensuration Formulas In Maths

Mensuration is branch of Maths, nowadays questions are also coming from this chapter in SSC, Railways and other exams. Here we are going to provide you important Maths Formulas which is used to mensuration’ question, take a look…

__For Example__:

**Question 1:** What is the area of an equilateral triangle of side 16 cm?

__Solution__: Area of an equilateral triangle = √3/4 S^{2}

So if S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm^{2}

**Question 2: **If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?

__Solution__:The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.

Then, Area of the triangle = 1/2 * 24 * 10 = 120 cm^{2}

##### Vedic Maths Formulas

When you’re going to appear in Math exam, there is probability that you can score full marks in this subject. This can be accomplished by using shortcut tricks and practicing more and more. Now check, below provided Vedic Maths Formulas with Examples to solve questions easily…

__Example 1__:

**Question:** How to multiply 123 and 321 in one go?

Answer:

- Let Assume that 123 as ABC & 321 as EFG.
- Now Consider the Vedic Formula i.e. AE/(AF+EB)/(AG+BF+CE)/(BG+CF)/(CG)
- Then Put all digits in this formula such as = 3/8/14/8/3
- Point To Be Noted, 14 is two digit, so add 1 this to 8 – the earlier digit)
- And we get the final Answer that is = 39483

__Example 2__:

**Question:** How to find square of a number ending with 5?

Answer: Suppose, you want to find square of 95, then you may follow the following tricks…

- First of all, multiply 5 by 5 and put 25 as your right part of the answer
- Secondly, multiply 9 by the next higher digit i.e. 10 and put 90 as your left part of the answer.
- Your answer is 9025, so you can use this formula to find square of any number ending with 5.

**Want to Know? How to Study without Distractions**

##### Maths Trigonometry Formulas

The term Trigonometry is used to study the relationships that involve angles and lengths of triangles. It is a branch of mathematics which is as an element of statistics, linear algebra and calculus. So, check below mentioned Maths Formulas, which are being used to solve question of Class 10 / 11.

__Check, Ratio Of Specific Angles__:

__Basic Formula__:

- sin(−θ)=−sinθ
- cos(−θ)=cosθ
- tan(−θ)=−tanθ
- cosec(−θ)=−cosecθ
- sec(−θ)=secθ
- cot(−θ)=−cotθ

**Download From Here: ****Basic Maths Formulas PDF**

##### Tricks and Shortcuts To Learn Maths All Formulas

- Percent implies “for every hundred” so % is read as percentage and x % is read as x per cent.
- To calculate p % of y then solve it as (p/100) x y = (p x y)/100. Learn it as p % of y = y % of p
- To find what percentage of x is y: y/x × 100
- To calculate percentage change in value, then memorize it as Percentage change = {change/(initial value)} x 100
- Percentage point change = Difference of two percentage figures
- Increase N by S % = N( 1+ S/100 )
- Decrease N by S % = N (1 – S/100)
- If the value of an item goes up/down by x%, the percentage reduction/increment to be now made to bring it back to the original point is 100x/ (100 + x) %.
- If A is x% more /less than B, then B is 100x/(100 + x) % less/more than A.
- If the price of an item goes up/down by x %, then the quantity consumed should be reduced by 100x/(100 + x) % so that the total expenditure remains the same.

##### Shortcut To Solve Maths Question

- 12
^{2}= 12+2/2^{2}= 14/4 = 144 - 13
^{2}= 13+3/3^{2}= 16/9 = 169

__Question__: Trick for Multiplication Of 11 With Any Number Of 3 Digits.

- Let me explain this trick by the following example i.e.
- 352*11 = 3—-(3+5)—-(5+2)—-2 = 3872

__How the rule apply__?

- First of all, Insert the sum of first and second digits
- Then sum of second and third digits between the two terminal digits of the number

**Want to Know? Tips To Score +90% Marks In Board**

##### Maths Formulas For Competitive Exams

Nowadays, most of the Bank, Government and Private Organizations conducts competitive exam to recruit fresh and self-motivated contenders to their various work units. All these organizations will end up their selection procedure by recruitment exam followed by group discussions / __Personal Interviews__ etc. The competitive exam will consist of Objective type multiple choice questions with four choices cover up the following sections:

- Quantitative Aptitude/Arithmetic Ability/Numerical Ability
- Reasoning (Verbal & Non-Verbal)
- General English
- General Awareness/General Intelligence
- Technical Ability

Apart from all the above mentioned sections, Quantitative part is amain part of the examination and those who are strong in this section can simply qualify the examination. To help you out, here we are going to provide all the Maths formulas starting from Basic Maths Formulas for Aptitude Test. You can download the Maths Formulas For Class 11 And 12 Pdf, Maths Basic Formulas PDF, Maths Formulas In Hindi from the above links. At the last we have also uploaded the All Maths Formulas PDF so download it and start your practice.

**Read Here- How To Prepare Maths For Competitive Exams**

__Essence Of This Page__:

Additional guidelines based on all Maths Formulas are also available in our site, so you may also get help from it. We’re trying to put all shortcut methods of the given topic. But if you notice that any tricks are missing from the list then please inform us, because your little help will help others.Share This Knowledge with others which are provided by the team of indguru.com and feel free to use our directory of formulas for your homework.