12th Maths Formulas List PDF

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12th Maths Formulas List

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

 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

 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