12th Maths Formulas List PDF

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12th Maths Formulas List

Areas

Square Square A=l2 l : length of side
Rectangle Rectangle A=w×h w : width
h : height
Triangle Triangle A=b×h2 b : base
h : height
Rhombus Rhombus A=D×d2 D : large diagonal
d : small diagonal
Trapezoid Trapezoid A=B+b2×h B : large side
b : small side
h: height
Regular polygon Regular polygon A=P2×a P : perimeter
a : apothem
Circle Circle A=πr2
P=2πr
r : radius
P : perimeter
Cone
(lateral surface)
cone A=πr×s r : radius
s : slant height
Sphere
(surface area)
sphere A=4πr2 r: radius

 Volumes

Cube Cube V=s3V=s3 ss: side
Parallelepiped Parallelepiped V=l×w×hV=l×w×h ll: length
ww: width
hh: height
Regular prism Prism V=b×hV=b×h bb: base
hh: height
Cylinder Cylinder V=πr2×hV=πr2×h rr: radius
hh: height
Cone (or pyramid) Cone V=13b×hV=13b×h bb: base
hh: height
Sphere 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±b24ac−−−−−−−√2ax=-b±b2-4ac2a
Concavity Concave up: a>0a>0
Concave down: a<0a<0
Discriminant Δ=b24acΔ=b2-4ac
Vertex of the parabola V(b2a,Δ4a)V(-b2a,-Δ4a)
y=a(xh)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=0A=0B=0A×B=0⇔A=0∨B=0 ex : (x+2)×(x1)=0(x+2)×(x-1)=0⇔
x+2=0x1=0x=2x=1x+2=0∨x-1=0⇔x=-2∨x=1
Difference of two squares (ab)(a+b)=a2b2(a-b)(a+b)=a2-b2 ex : (x2)(x+2)=x222=x24(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+22x3+32=(2x+3)2=(2x)2+2⋅2x⋅3+32=
4x2+12x+94×2+12x+9
Binomial theorem (x+y)n=k=0nnCkxnkyk

 Probability and Sets

Commutative AB=BAA∪B=B∪A AB=BAA∩B=B∩A
Associative A(BC)=A(BC)A∪(B∪C)=A∪(B∪C) A(BC)=A(BC)A∩(B∩C)=A∩(B∩C)
Neutral element A=AA∪∅=A AE=AA∩E=A
Absorbing element AE=EA∪E=E A=A∩∅=∅
Distributive A(BC)=(AB)(AC)A∪(B∩C)=(A∪B)∩(A∪C) A(BC)=(AB)(AC)A∩(B∪C)=(A∩B)∪(A∩C)
De Morgan’s laws AB¯¯¯¯¯¯¯¯¯=A¯¯¯B¯¯¯A∩B¯=A¯∪B¯ AB¯¯¯¯¯¯¯¯¯=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¯¯¯)=1P(A)P(A¯)=1-P(A)
Union of Events P(AB)=P(A)+P(B)P(AB)P(A∪B)=P(A)+P(B)-P(A∩B)
Conditional Probability P(AB)=P(AB)P(B)P(A∣B)=P(A∩B)P(B)
Independent Events P(AB)=P(A)P(A∣B)=P(A) P(AB)=P(A)×P(B)P(A∩B)=P(A)×P(B)
Permutation Pn=n!=n×(n1)××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!(np)!nAp=n!(n-p)! ex : 6A2=6!(62)!=306A2=6!(6-2)!=30
Permutations with repetition nAp=npnAp′=np ex : 5A3=53=1255A3′=53=125
Combination nCp=nApp!=n!(np)!×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(xiμ)2−−−−−−−−−−−−⎷σ=∑i=1kpi(xi-μ)2
Binomial distribution P(X=k)=nCk.pk.(1p)nkP(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

 

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