For some Maths can be fun and for some, it can be a nightmare. Maths Formulas are difficult to memorize and we have curated a list of Maths Formulas for Class 12 PDF State Board just for you. You can use this as a goto sheet whenever you want to prepare Class 12 Maths Formulas. Students can get Formulas on Algebra, Calculus, and Geometry that can be useful in your preparation and help you do your homework.
Here in this article Maths Formulas for Class 12 PDF State Board, we have listed basic Maths formulas so that you can learn the fundamentals of Maths. Our unique way of solving Maths Problems will make you learn how the equation came into existence instead of memorizing it. Solve all the important problems and questions in Maths with the Best Maths Formulas for Class 12.
Maths Formulas for Class 12 PDF State Board
Feel free to directly use the best Maths formulas during your homework or exam preparation. You need to know the list of Class 12 formulas as they will not just be useful in your academic books but also in your daytoday lives.
Remember the Maths Formulas in a smart way by making use of our list. You can practice Questions and Answers based on these Class 12 Maths Formulas. Students can get basic Maths formulas Free PDF Download for Class 12. Candidates can use the handy learning aid Maths Formulas PDF to have indepth knowledge on the subject as per the latest CBSE Syllabus.
CBSE Class 12 Maths Formulas according to the Chapters are prepared by subject experts and you can rely on them during your preparation. Click on the topic you wish to prepare from the list of formulas prevailing.
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12th Maths Formulas List
Areas
Square  A=l2  l : length of side  
Rectangle  A=w×h  w : width h : height 

Triangle  A=b×h2  b : base h : height 

Rhombus  A=D×d2  D : large diagonal d : small diagonal 

Trapezoid  A=B+b2×h  B : large side b : small side h: height 

Regular polygon  A=P2×a  P : perimeter a : apothem 

Circle  A=πr2 P=2πr 
r : radius P : perimeter 

Cone (lateral surface) 
A=πr×s  r : radius s : slant height 

Sphere (surface area) 
A=4πr2  r: radius 
Volumes
Cube  V=s3V=s3  ss: side  
Parallelepiped  V=l×w×hV=l×w×h  ll: length ww: width hh: height 

Regular prism  V=b×hV=b×h  bb: base hh: height 

Cylinder  V=πr2×hV=πr2×h  rr: radius hh: height 

Cone (or pyramid)  V=13b×hV=13b×h  bb: base hh: height 

Sphere  V=43πr3V=43πr3  rr: radius 
Functions and Equations
Directly Proportional  y=kxy=kx k=yxk=yx  kk: Constant of Proportionality 
Inversely Proportional  y=kxy=kx k=yxk=yx  
ax2+bx+c=0ax2+bx+c=0  Quadratic formula  x=−b±b2−4ac−−−−−−−√2ax=b±b24ac2a 
Concavity  Concave up: a>0a>0  
Concave down: a<0a<0  
Discriminant  Δ=b2−4acΔ=b24ac  
Vertex of the parabola  V(−b2a,−Δ4a)V(b2a,Δ4a)  
y=a(x−h)2+ky=a(xh)2+k  Concavity  Concave up: a>0a>0 
Concave down: a<0a<0  
Vertex of the parabola  V(h,k)V(h,k)  
Zeroproduct property  A×B=0⇔A=0∨B=0A×B=0⇔A=0∨B=0  ex : (x+2)×(x−1)=0⇔(x+2)×(x1)=0⇔ x+2=0∨x−1=0⇔x=−2∨x=1x+2=0∨x1=0⇔x=2∨x=1 
Difference of two squares  (a−b)(a+b)=a2−b2(ab)(a+b)=a2b2  ex : (x−2)(x+2)=x2−22=x2−4(x2)(x+2)=x222=x24 
Perfect square trinomial  (a+b)2=a2+2ab+b2(a+b)2=a2+2ab+b2  ex : (2x+3)2=(2x)2+2⋅2x⋅3+32=(2x+3)2=(2x)2+2⋅2x⋅3+32= 4x2+12x+94×2+12x+9 
Binomial theorem  (x+y)n=∑k=0nnCkxn−kyk 
Probability and Sets
Commutative  A∪B=B∪AA∪B=B∪A  A∩B=B∩AA∩B=B∩A 
Associative  A∪(B∪C)=A∪(B∪C)A∪(B∪C)=A∪(B∪C)  A∩(B∩C)=A∩(B∩C)A∩(B∩C)=A∩(B∩C) 
Neutral element  A∪∅=AA∪∅=A  A∩E=AA∩E=A 
Absorbing element  A∪E=EA∪E=E  A∩∅=∅A∩∅=∅ 
Distributive  A∪(B∩C)=(A∪B)∩(A∪C)A∪(B∩C)=(A∪B)∩(A∪C)  A∩(B∪C)=(A∩B)∪(A∩C)A∩(B∪C)=(A∩B)∪(A∩C) 
De Morgan’s laws  A∩B¯¯¯¯¯¯¯¯¯=A¯¯¯∪B¯¯¯A∩B¯=A¯∪B¯  A∪B¯¯¯¯¯¯¯¯¯=A¯¯¯∩B¯¯¯A∪B¯=A¯∩B¯ 
Laplace laws  P(A)=Number of ways it can happenTotal number of outcomesP(A)=Number of ways it can happenTotal number of outcomes  
Complement of an Event  P(A¯¯¯)=1−P(A)P(A¯)=1P(A)  
Union of Events  P(A∪B)=P(A)+P(B)−P(A∩B)P(A∪B)=P(A)+P(B)P(A∩B)  
Conditional Probability  P(A∣B)=P(A∩B)P(B)P(A∣B)=P(A∩B)P(B)  
Independent Events  P(A∣B)=P(A)P(A∣B)=P(A)  P(A∩B)=P(A)×P(B)P(A∩B)=P(A)×P(B) 
Permutation  Pn=n!=n×(n−1)×…×2×1Pn=n!=n×(n1)×…×2×1  ex : P4=4!=4×3×2×1=24P4=4!=4×3×2×1=24 
Permutations without repetition  nAp=n!(n−p)!nAp=n!(np)!  ex : 6A2=6!(6−2)!=306A2=6!(62)!=30 
Permutations with repetition  nA′p=npnAp′=np  ex : 5A′3=53=1255A3′=53=125 
Combination  nCp=nApp!=n!(n−p)!×p!nCp=nApp!=n!(np)!×p!  ex : 5C4=5A44!=55C4=5A44!=5 
Probability Distribution 
Average value  μ=x1p1+x2p2+…+xkpkμ=x1p1+x2p2+…+xkpk 
Standard deviation  σ=∑i=1kpi(xi−μ)2−−−−−−−−−−−−⎷σ=∑i=1kpi(xiμ)2  
Binomial distribution  P(X=k)=nCk.pk.(1−p)n−kP(X=k)=nCk.pk.(1p)nk  ex : B(10;0,6)B(10;0,6) P(X=3)=10C3×0,63×0,47P(X=3)=10C3×0,63×0,47 
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