Dear Aspirants, Today we are sharing pdf document of Maths Formulas study material of SSC CGL and other competitive Exams. This e-book very useful for upcoming SSC CGL, CHSL, MTS, Stenographer, IBPS, RRB, Railway and other common written exams. Maths Formula book PDF, includes 1300 Math formula from high school to graduations is for free download. The handbook of Mathematics formulas are very useful for students from high school to engineering and preparing for SSC and other Competitive Exams.
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Ye sabhi ganit ke sutra students ke liye bahut zaruri hote hain. Kyuki koi lambe sawal ko ham fomula ki help se hi asaani se solve kar pate hain. Yahan aap sabhi ki jaankari ke liye bata de ki ye ganit sutra pdf me uplabdh sutra SSC, Railway, UPSC, UP Police etc. Exams ke liye bahut hi mahtvpurn hain. Aap sabhi in sutra ko apne mobile phone me download karke rakh sakte hain aur zarurt ke hisab se kabhi bhi access kar sakte hain. yahan niche hamne ganit ke sutra uplabdh kara diye hain taaki aap sabhi ko ye idea ho jaye ki is book me kis tarah se math formula diye hain.
No.-1.a2 – b2 = (a – b)(a + b)
No.-2.(a+b)2 = a2 + 2ab + b2
No.-3.a2 + b2 = (a – b)2 + 2ab
No.-4.(a – b)2 = a2 – 2ab + b2
No.-5.(a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
No.-6.(a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
No.-7.(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
No.-8.(a – b)3 = a3 – 3a2b + 3ab2 – b3
No.-9.a3 – b3 = (a – b)(a2 + ab + b2)
No.-10.a3 + b3 = (a + b)(a2 – ab + b2)
No.-11.(a + b)3 = a3 + 3a2b + 3ab2 + b3
No.-12.(a – b)3 = a3 – 3a2b + 3ab2 – b3
No.-13.(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
No.-14.(a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
No.-15.a4 – b4 = (a – b)(a + b)(a2 + b2)
No.-16.a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
Number System Quick Maths Formulas
In this post we share complete information about Algebra Formulas PDF for SSC, RRB NTPC Maths Formulas, Math Formula Handwriting PDF, Algebra Formulas for SSC CGL PDF in Hindi.
No.-1. 1 + 2 + 3 + 4 + 5 + … + n = n (n + 1)/2
No.-2. (12 + 22 + 32 + …. + n2) = n (n + 1) (2n + 1) / 6
No.-3. (13 + 23 + 33 + …. + n3) = (n (n + 1)/ 2)2
No.-4. Sum of first n odd numbers = n2
No.-5. Sum of first n even numbers = n (n + 1)
No.-6. (a + b) * (a – b) = (a2 – b2)
No.-7. a + b)*2 = (a2 + b2 + 2ab)
No.-8. (a – b)*2 = (a2 + b2 – 2ab)
No.-9. (a + b + c)*2 = a2 + b2 + c2 + 2(ab + bc + ca)
No.-10. (a3 + b3) = (a + b) * (a2 – ab + b2)
No.-11. (a3 – b3) = (a – b) * (a2 + ab + b2)
No.-12. (a3 + b3 + c3 – 3abc) = (a + b + c) * (a2 + b2 + c2 – ab – bc – ac)
No.-13. When a + b + c = 0, then a3 + b3 + c3 = 3abc
No.-1.A can do a certain work in 12 days. B is 60% more efficient than A. How many days will B and A together take to do the same job?
(A) 80/13
(B) 70/13
(C) 75/13
(D) 60/13
Answer : D
No.-2.A large cube is formed from the material obtained by melting of three cubes 3cm, 4cm and 5cm respectively. Find the ratio of the total surface area of the smaller cubes to the larger cube?
(A) 2:1
(B) 3:2
(C) 25:18
(D) 27:20
Answer : C
List of Important Mathematics Formulas
Given below are the important topics that you need to cover in order to score good marks in mathematics. We have also provided you with the PDF for every part so that you could practice chapter-wise by applying the required formulas –
1. Speed, Distance & Time
This concept has been asked the most in all sorts of competitive exams especially in defence exams and it is also considered to be one of the easiest topics to deal with. however, the type of questions asked in the examinations may have a different variety. But we have provided you with all formulae related to it which will help you to solve every problem related to Speed, distance and time.
No.-1.1 Kmph = (5/18) m/s
No.-2.1 m/s = (18/5) Kmph
No.-3.Speed(S) = Distance(d)/Time(t)
No.-4.Average Speed = Total distance/Total Time = (d1+d2)/(t1+t2)
No.-5.When d1 = d2, Average Speed = 2S1S2/(S1+S2), where S1 and S2 are the speeds for covering d1 and d2 respectively.
No.-6.When t1 = t2, Average Speed = (S1+S2)/2, where S1 and S2 are the speeds during t1 and t2 respectively.
No.-7.Relative speed when moving in the opposite direction is S1+S2
No.-8.Relative speed when moving in the same direction is S1-S2
No.-9.A person goes a certain distance (A to B) at a speed of S1 kmph and returns back (B to A) at a speed of S2 kmph. If he takes T hours in all, the distance between A and B is T(S1S2/(S1+S2)
No.-10.When two trains of lengths l1 and l2 respectively travelling at the speeds of S1 & S2 respectively cross each other in time t, then the equation is given as S1+S2 = (l1+l2)/t
No.-11.When a train of length l1 travelling at a speed of S1 overtakes another train of length l2 travelling at speed S2 in time t, then the equation is given as S1-S2 = (l1+l2)/t
No.-12.When a train of length l1 travelling at a speed of S1 crosses a platform/bridge/tunnel of length l2 in time t, then the equation is given as S1 = (l1+l2)/t
No.-13.When a train of lengths l travelling at a speed s crosses a pole/pillar/flag post in time t, then the equation is given as s = l/t
No.-14.If two persons A and B start at the same time from two points P and Q towards each other and after crossing they take T1 and T2 hours in reaching Q and P respectively, then (A’s speed) / (B’s speed) = √T2 / √T1
Profit & Loss
The profit and Loss formula is used to find out the price of an item and to know how profitable a business is. Every product has a cost price at which an item is purchased and a selling price at which an item is sold and based on the values of these prices, you can easily find out the profit gained or loss incurred on a particular product. Using the formulas given below you can find out the answers to such problems easily –
No.-1.Profit, P = SP – CP; SP>CP
No.-2.Loss, L = CP – SP; CP>SP
No.-3.P% = (P/CP) x 100
No.-4.L% = (L/CP) x 100
No.-5.SP = [(100 + P%)/100] x CP
No.-6.SP = [(100 – L%)/100] x CP
No.-7.CP = [100/(100 + P%)] x SP
No.-8.CP = [100/(100 – L%)] x SP
No.-9.Discount = MP – SP
No.-10.SP = MP -Discount
No.-11.If P% and L% are equal then, %loss = P2/100
No.-12.When the profit is x% and loss is y%, then the net % profit or loss will be: (x-y-xy)/100
No.-13.If a product is sold at x% profit and then again sold at y% profit then the actual cost price of the product will be: CP = [100 x 100 x P/(100+x)(100+y)]. In case of loss, CP = [100 x 100 x P/(100-x)(100-y)]
For false weight, profit percentage will be P% = (True weight – false weight/ false weight) x 100
No.-14.When there are two successful profits say x% and y%, then the net percentage profit equals (x+y+xy)/100
Percentage
Percentage means per hundred. Percentages are a portion or fraction of 100 and it is denoted by the symbol ‘%‘, the percentage is majorly used to compare and find out ratios. The percentage is an interesting and a scoring topic. Once you understand the basics, it becomes easier to solve problems related to percentage –
1. To calculate the percentage of a fraction we have to use the given formula.
Percentage formula = (Numerator/Denominator) ×100
2. To calculate the percentage of a Number.
Percentage /100* Number
3. To express x% as a fraction.
X%/100
To express % as a Fraction, we need to just divide it by 100.
4. To Increase A value or Number by a Given Percentage.
Number * 100+x%/100
5. To Decrease A value or Number by Given Percentage.
Number * 100-x%/100
6. To calculate the percentage Decrement of a number.
Percentage Decreament = Initial value-Final value/ Initial value*100
7. To calculate the percentage increment of a number.
Percentage Increament = Final value – Initial value/ Initial value*100
8. If X% of A is equal to Y% of B.
Z% of A = y*z/x% of B
9. If the passing marks in an examination is P%. If a candidate scores S marks and fails by F marks then Maximum Marks will be.
Maximum Marks = 100*P+S/P
10. If a candidate scores marks and fails by A marks while another candidate scores y% marks and gets B marks more than minimum passing marks, then Maximum Marks will be.
Maximum Marks = Sum of score *100/Difference in % Marks
11.If the price of an item decreases, a person can buy a few Kg more in Y rupees, the actual price of that item.
Actual Price = Rate * Y/100- Rate*X Per Kg
12. If the population of a town is P and it increases at the rate of R% per annum then –Population after ‘n’ years :
Percentage population = P x (1 + R/100)n
13. If the population of a town is P and it decreases at the rate of R% per annum then –Population after ‘n’ years :
Percentage population = P x (1 – R/100)n
14. If the population of a town is P and it increases at the rate of R% per annum then –Population of the town ‘n’ years ago :
Population n years ago = P/(1 + R/100)n
15. If the population of a town is P and it decreases at the rate of R% per annum then –Population of the town ‘n’ years ago:
Population n years ago = P/(1 – R/100)n
16. Cost of Machine
Value of Machine After n years = P x (1 – R/100)n
Value of Machine Before n years = P/(1 – R/100)n
4. Average
Averages can be defined as the central value in a set of data. Average can be calculated simply by dividing the sum of all values in a set by the total number of values. In other words, an average value represents the middle value of a data set. The data set can be of anything like age, money, runs, etc.
No.-1.Average = Sum of quantities/ Number of quantities
No.-2.Sum of quantities = Average * Number of quantities
No.-3.The average of first n natural numbers is (n +1) / 2
No.-4.The average of the squares of first n natural numbers is (n +1)(2n+1 ) / 6
No.-5.The average of cubes of first n natural numbers is n(n+1)2 / 4
No.-6.The average of the first n odd numbers is given by (last odd number +1) / 2
No.-7.The average of first n even numbers is given by (last even number + 2) / 2
No.-8.The average of squares of first n consecutive even numbers is 2(n+1)(2n+1) / 3
No.-9.The average of squares of consecutive even numbers till n is (n+1)(n+2) / 3
No.-10.The average of squares of squares of consecutive odd numbers till n is n(n+2) / 3
No.-11.If the average of n consecutive numbers is m, then the difference between the smallest and the largest number is 2(m-1)
No.-12.If the number of quantities in two groups be n1 and n2 and their average is x and y respectively, the combined average is (n1x+n2y) / (n1+ n2)
No.-13.The average of n quantities is equal to x. When a quantity is removed, the average becomes y.
No.-14.The value of the removed quantity is n(x-y) + y
No.-15.The average of n quantities is equal to x. When a quantity is added, the average becomes y.
The value of the new quantity is n(y-x) + y
Algebra
Algebra is a very important section for all competitive exams. It can be a tricky part to solve but using these given formulas you can ace it in this section. Here we are going to mention the list of some important formulas of algebra that will certainly help you to solve Algebra problems
No.-1.a² – b² = (a-b)(a+b)
No.-2.(a+b)² = a² + 2ab + b²
No.-3.(a-b)² = a² – 2ab + b²
No.-4.a² + b² = (a-b)² +2ab
No.-5.(a+b+c)² = a²+b²+c²+2ab+2ac+2bc
No.-6.(a-b-c)² = a²+b²+c²-2ab-2ac+2bc
No.-7.a³-b³ = (a-b) (a² + ab + b²)
No.-8.a³+b³ = (a+b) (a² – ab + b²)
No.-9.(a+b)³ = a³+ 3a²b + 3ab² + b³
No.-10.(a-b)³ = a³- 3a²b + 3ab² – b³
No.-11.“n” is a natural number, and – bn = (a-b) (an-1 + an-2b +….bn-2a + bn-1)
No.-12.“n” is an even number, an + bn = (a+b) (an-1 – an-2b +….+ bn-2a – bn-1)
No.-13.“n” is an odd number an + bn = (a-b) (an-1 – an-2b +…. – bn-2a + bn-1)
(am)(an) = am+n (ab)m = amn