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Maths Formulas For Class 8/10/12 Vedic/Basic Free List PDF Download

Maths Formulas

Maths is a most difficult subject for some students because solving mathematical problems acquires lots of knowledge and formulas. Well here on this page we are providing you the Maths Formulas of Class 8,9,10, 11 &12 and shortcuts for Learning Maths Formulas. Now most of the Bank, Government and Private Organizations conduct various competitive exams in order to recruit well talented and deserving aspirants for filing up the vacant positions. All these organizations ask many quantities and aptitude questions in these exams which create problem for the job seekers. So now you don’t need to worry more and download the maths formulas PDF of Vedic/Basic Free List for Class 8,10 and 12 and start your preparation accordingly.

When we talk about Mensuration, Trigonometry and calculus, it becomes difficult for solving maths but through the below stated Maths Formulas, you can solve them very easily. When you understand the logic behind every problem and formulas, solving any kind of maths problem becomes easier. All the Formulas Of Maths, maths formulas list, Eamcet Maths Formulas PDF, SSC CGL Maths Formulas, Maths Formulas For IIT JEE PDF, basic formulas in maths for aptitude test, maths formulas for class 8 pdf, integration formulas in maths, maths important formulas, important maths formulas, all maths formulas free download, formulas in maths, maths formulas for class 12 PDF free download, maths formulas for competitive exams PDF and Jee Main Maths Formulas PDF is well mentioned below on this page which is designed by the team members of recruitmentresult.com

Maths Formulas

Shortcut To Solve Maths Question

  • 122= 12+2/22= 14/4 = 144
  • 132= 13+3/32= 16/9 = 169

Question: You can now Multiply 11 with Any Number of 3 Digits. Want to know the trick…

Well here is the trick, let’s take an example

i.e. 352*11 = 3—-(3+5)—-(5+2)—-2 = 3872

How you can apply rule?

  • First of all, you have to Insert the sum of first and second digits
  • Then sum of second and third digits between the two terminal digits of the number

Get Best Answer: How to Prepare for Maths

Maths Formulas For 8th Class

Name of the SolidLateral / Curved Surface AreaTotal Surface AreaVolume
Cuboids2∏(l+b)2(lb+bh+hl)lb∏
Cube4a26a2a3
Right PrismPerimeter of base× heightLateral Surface Area+2(Area of One End)Area of Base× Height

 

Right Circular Cylinder2∏rh2∏r(r+h)∏r2h
Right Pyramid1/2 Perimeter of Base X SlantHeightLateral Surface Area+ Area of the Base13(Area of the Base)×height
Right Circular Cone∏rl∏r(l+r)13∏r2h
Sphere4∏r24∏r243∏r3
Hemisphere2∏r23∏r2

Geometric Area Maths Formula

Geometric AreaGeometric Area Formula
Squarea2
Rectangleab
Circleπr2
Ellipseπr1r2
Triangle1/2bh

Basic Requirements To Solve Maths Numerical

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,—-}

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Maths Formulas for 7th Class:

Check Out: Aptitude Questions & Answers

Maths Formulas for 10th Class:

Maths Algebraic Identities Formula

  • (a+b)2=a2+2ab+b2
  • (a−b)2=a2−2ab+b2
  • (a+b)(a–b)=a2–b2
  • (x+a)(x+b)=x2+(a+b)x+ab
  • (x+a)(x–b)=x2+(a–b)x–ab
  • (x–a)(x+b)=x2+(b–a)x–ab
  • (x–a)(x–b)=x2–(a+b)x+ab
  • (a+b)3=a3+b3+3ab(a+b)
  • (a–b)3=a3–b3–3ab(a–b)
  • (a – b)4= a4 – 4a3b + 6a2b2 – 4ab3 + b4)
  • a– b4= (a – b)(a + b)(a2 + b2)
  • a5 – b5 = (a – b)(a4 + a3b + a2b2+ ab3 + b4)
  • If n is a natural number, a– bn= (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)
  • If n is even (n = 2k), an+ bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
  • If n is odd (n = 2k + 1), an+ bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
  • (a + b + c + …)2 = a2+ b2 + c2 + … + 2(ab + ac + bc + ….

Example:

Question: Which of the following expressions is in the sum-of-products (SOP) form?

  1. (A + B)(C + D)
  2. (A)B(CD)
  3. AB(CD)
  4. AB + CD

Answer: AB + CD

Combination:

Number of combinations of n different things taken r at a time = ⁿCr = n!r!(n−r)!n!r!(n−r)!

ⁿP₀ = r!∙ ⁿC₀.

ⁿC₀ = ⁿCn = 1

ⁿCr = ⁿCn – r

ⁿCr + ⁿCn – 1 = n+1n+1Cr

If p ≠ q and ⁿCp = ⁿCq then p + q = n.

ⁿCr/ⁿCr – 1 = (n – r + 1)/r.

The total number of combinations of n different things taken any number at a time = ⁿC₁ + ⁿC₂ + ⁿC₃ + …………. + ⁿC₀ = 2ⁿ – 1.

The total number of combinations of (p + q + r + . . . .) things of which p things are alike of a first kind, q things are alike of a second kind r things are alike of a third kind and so on, taken any number at a time is [(p + 1) (q + 1) (r + 1) . . . . ] – 1.

Read Also: How to Solve Objective Type Questions

Maths Logarithm Formula

If ax = M then logM = x and conversely.

  • log1 = 0.
  • logaa = 1.
  • alogam = M.
  • logaMN = loga M + loga
  • loga(M/N) = loga M – loga
  • logaMn = n loga
  • logaM = logb M x loga
  • logba x 1oga b = 1.
  • logba = 1/logb
  • logM = logbM/loga

Maths Exponential Series

  • For all x, ex= 1 + x/1! + x2/2! + x3/3! + …………… + xr/r! + ………….. ∞.
  • e = 1 + 1/1! + 1/2! + 1/3! + ………………….. ∞.
  • 2 < e < 3; e = 2.718282 (correct to six decimal places).
  • a= 1 + (logea) x + [(loge a)2/2!] ∙ x+ [(loge a)3/3!] ∙ x3 + …………….. ∞.

Maths Logarithmic Series

  • loge(1 + x) = x – x2/2 + x3/3 – ……………… ∞ (-1 < x ≤ 1).
  • loge(1 – x) = – x – x2/ 2 – x3/3 – ………….. ∞ (- 1 ≤ x < 1).
  • ½ loge[(1 + x)/(1 – x)] = x + x3/3 + x5/5 + ……………… ∞ (-1 < x < 1).
  • loge2 = 1 – 1/2 + 1/3 – 1/4 + ………………… ∞.
  • log10m = µ loge m where µ = 1/loge 10 = 0.4342945 and is a positive number.

Maths Laws of Exponents

  • (am)(an) = am+n
  • (ab)m= ambm
  • (am)n= amn

Maths Fractional Exponents

  • a= 1
  • am/an=am−n
  • am=1/ a−m
  • a−m=1/am

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All Mensuration Formulas In Maths

Maths Trigonometry Formulas:

Basic Formula:

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

Trigonometry Formulas involving Periodicity Identities:

  • sin(x+2π)=sinx
  • cos(x+2π)=cosx
  • tan(x+π)=tanx
  • cot(x+π)=cotx

Trigonometry Formulas involving Cofunction Identities – degree:

  • sin(90∘−x)=cosx
  • cos(90∘−x)=sinx
  • tan(90∘−x)=cotx
  • cot(90∘−x)=tanx

Trigonometry Formulas involving Sum/Difference Identities:

  • sin (x + y) = sin(x) cos(y) + cos(x) sin(y)
  • cos(x + y) = cos(x) cos(y) – sin(x) sin(y)
  • tan(x+y)=tanx+tany1−tanx⋅tany
  • sin(x – y) = sin(x) cos(y) – cos(x) sin(y)
  • cos(x – y) = cos(x) cos(y) + sin(x) sin(y)
  • tan(x−y)=tanx−tany1+tanx⋅tany

Trigonometry Formulas involving Double Angle Identities:

  • sin(2x) = 2 sin(x).cos(x)
  • cos(2x)=cos2(x)–sin2(x),
  • cos(2x)=2cos2(x)−1
  • cos(2x)=1–2sin2(x)
  • tan(2x)=[2tan(x)][1−tan2(x)]

Trigonometry Formulas involving Half Angle Identities:

  • sinx2=±1−cosx2−−−−−−√
  • cosx2=±1+cosx2−−−−−−√
  • tan(x2)=1−cos(x)1+cos(x)−−−−−−√
  • Also, tan(x2)=1−cos(x)1+cos(x)−−−−−−√=(1−cos(x))(1−cos(x))(1+cos(x))(1−cos(x))−−−−−−−−−−−−−√=(1−cos(x))21−cos2(x)−−−−−−−−√=(1−cos(x))2sin2(x)−−−−−−−−√=1−cos(x)sin(x)
  • So, tan(x2)=1−cos(x)sin(x)

Trigonometry Formulas involving Product identities:

  • sinx⋅cosy=sin(x+y)+sin(x−y)2
  • cosx⋅cosy=cos(x+y)+cos(x−y)2
  • sinx⋅siny=cos(x+y)−cos(x−y)2

Trigonometry Formulas involving Sum to Product Identities:

  • sinx+siny=2sinx+y2cosx−y2
  • sinx−siny=2cosx+y2sinx−y2
  • cosx+cosy=2cosx+y2cosx−y2
  • cosx−cosy=−2sinx+y2sinx−y2

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Maths Formulas for 12th Class:

Vectors and Three Dimensional Geometry Formulas for Class 12

Position VectorOP−→−=r⃗ =x2+y2+z2−−−−−−−−−−√
Direction Ratiosl=ar,m=mr,n=cr
Vector AdditionPQ→+QR→=PR→
Properties of Vector AdditionCommutativePropertya⃗ +b⃗ =b⃗ +a⃗

AssociativeProperty(a⃗ +b⃗ )c⃗ +=a⃗ +(b⃗ +c⃗ )

Vector Joining Two Points

 

P1P2−→−−=OP1−→−−OP1−→−
Skew LinesCosθ=∣∣∣a1a2+b1b2+c1c2a21+a21+c21√a22+a22+c22√∣∣∣
Equation of a Linex−x1a=y−y1b=z−z1c

Algebra Formulas For Class 12

  • Ifa⃗=xi^+yj^+zk^ then magnitude or length or norm or absolute value of a⃗  is ∣∣a→∣∣=a=x2+y2+z2−−−−−−−−−−√
  • A vector of unit magnitude is unit vector. If a⃗is a vector then unit vector of a⃗  is denoted by a^ and a^=a^|a^| Therefore a^=a^|a^|a^
  • Important unit vectors are i^,j^,k^, where i^=[1,0,0],j^=[0,1,0],k^=[0,0,1]
  • If l=cosα,m=cosβ,n=cosγ, then α,β,γ, are called directional angles of the vectorsa→and cos+cos+cos=1

Trigonometry Class 12 Formulas

  • Definition
  • θ=sin−1(x)isequivalenttox=sinθ
  • θ=cos−1(x)isequivalenttox=cosθ
  • θ=tan−1(x)isequivalenttox=tanθ
  • Inverse Properties
  • sin(sin−1(x))=x
  • cos(cos−1(x))=x
  • tan(tan−1(x))=x
  • sin−1(sin(θ))=θ
  • cos−1(cos(θ))=θ
  • tan−1(tan(θ))=θ
  • Double Angle and Half Angle Formulas
  • sin(2x)=2sinxcosx
  • cos(2x)=cos2x–sin2x
  • tan(2x)=2tanx1–tan2x
  • sinx2=±1–cosx2−−−−−√
  • cosx2=±1+cosx2−−−−−√
  • tanx2=1−cosxsinx=sinx1–cosx

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