12th Maths Formulas List

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12th Maths Formulas List

If you are looking for the Class 12th Maths Formulas List, then you at the right place. In 12th grade mathematics, understanding and applying formulas is crucial for success. These formulas serve as powerful tools to solve complex problems and gain insights into various mathematical concepts. By mastering these 12th-grade math formulas, students can enhance their problem-solving skills.

Algebraic formulas, such as the quadratic formula, help find solutions to quadratic equations. Arithmetic and geometric progression formulas enable the computation of sums and terms in these sequences. Trigonometric identities, like the Pythagorean identities, establish relationships between trigonometric functions. Calculus formulas, including derivative and integration rules, are indispensable for analyzing rates of change and calculating areas. Probability and statistics formulas facilitate the interpretation of data and aid in making informed decisions.

Here we have given the list of some formulas for 12th class Math.

Areas

 Square : length of side Rectangle : width  : height Triangle : base  : height Rhombus : large diagonal  : small diagonal Trapezoid : large side  : small side : height Regular polygon : perimeter  : apothem Circle : radius  : perimeter Cone (lateral surface) : radius  : slant height Sphere (surface area) : 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 for 12th Maths

 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±b2-4ac2a Concavity Concave up: a>0a>0 Concave down: a<0a<0 Discriminant Δ=b2−4acΔ=b2-4ac Vertex of the parabola V(−b2a,−Δ4a)V(-b2a,-Δ4a) y=a(x−h)2+ky=a(x-h)2+k Concavity Concave up: a>0a>0 Concave down: a<0a<0 Vertex of the parabola V(h,k)V(h,k) Zero-product property A×B=0⇔A=0∨B=0A×B=0⇔A=0∨B=0 ex : (x+2)×(x−1)=0⇔(x+2)×(x-1)=0⇔ x+2=0∨x−1=0⇔x=−2∨x=1x+2=0∨x-1=0⇔x=-2∨x=1 Difference of two squares (a−b)(a+b)=a2−b2(a-b)(a+b)=a2-b2 ex : (x−2)(x+2)=x2−22=x2−4(x-2)(x+2)=x2-22=x2-4 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 for 12th Maths Formulas

 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¯)=1-P(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×(n-1)×…×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!(n-p)! ex : 6A2=6!(6−2)!=306A2=6!(6-2)!=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!(n-p)!×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(xi-μ)2 Binomial distribution P(X=k)=nCk.pk.(1−p)n−kP(X=k)=nCk.pk.(1-p)n-k ex : B(10;0,6)B(10;0,6) P(X=3)=10C3×0,63×0,47P(X=3)=10C3×0,63×0,47