## MATH FORMULAS

On this page you can find many math formulas in different topics of math.It is more useful to the students in all grades. Once you memorize this kind of formulas you can solve any difficult in an easy way.We have covered all most all the basic topics in math. After memorizing this formula you can try our worksheets and quiz. We have also given shortcuts to memorize these formulas. In each category you can get many formulas and also shortcut ideas.In each category we have example problems.

 Topics Math Formulas

 a⁄b + c⁄d = (ad + bc) ⁄bd Subtraction formula a⁄b - c⁄d = (ad - bc) ⁄bd Multiplication formula a⁄b x c⁄d = (a x c) ⁄(b x d) Division formula a⁄b / c⁄d = (a x d) ⁄(b x c)

 Algebra Math Formulas

 Formula for square (a + b)² = a² + 2 ab + b²(a - b)² = a² - 2 ab + b²a² - b² = (a + b) (a - b)a² + b² = (a + b)² - 2aba² + b² = (a - b)² + 2aba² + b² = ½ [(a + b)² - (a - b)²]ab = ¼ [(a + b)² - (a - b)²](a - b)² = (a + b)² - 4 ab(a + b)² = (a - b)² + 4 ab(a+b+c)² =a²+b²+c²+2ab+2bc+2ca(a-b+c)² =a²+b²+c²-2ab-2bc+2ca(a-b-c)² =a²+b²+c²-2ab+2bc-2ca Formula for cube (a + b)³ = a³ + 3 a² b  + 3 a b² + b³(a - b)³ = a³ - 3 a² b  + 3 a b² - b³a³ + b³ = (a + b)³ - 3 ab (a + b)a³ - b³ = (a - b)³ + 3 ab (a - b)a³ + b³ = (a + b) (a² - ab + b²)a³ - b³ = (a - b) (a² + ab + b²) (x + a) (x + b) = x² + (a + b) x + ab(x + a) (x + b) (x + c) = x³+(a+b+c) x²+(ab+bc+ca) x+abca² + b² + c² - a b - b c - c a = ½[(a-b)²+(b-c)²+(c-a)²](a+b+c) (a² + b² + c² - a b-b c-c a) = a³ + b³ + c³ - 3 a b c

 Logarithms Math Formulas

 Product rule log ₐ (m n) =  log ₐ m + log ₐ n Quotient rule log ₐ (m/n) =  log ₐ m - log ₐ n Power rule log ₐ m ⁿ = n log ₐ m Change of base rule log ᵤ m = (logᵥm) x (logᵤv) Reciprocal rule log ₐ i = 1/ logᵢ a log ₐ 1 = 0log ₐ a = 1

 Exponents Math Formulas

 Product rule a m x a n = a (m + n) Quotient rule am⁄an = a (m-n) Power rule (am)n = amn Combination Law (am x bm) = (axb)m 1 ⁄a m = a-m a 0 = 1

 Set theory Math Formulas

 Associative law A ∪ (B∪C)=(A∪B) U C       A ∩ (B∩C)=(A∩B) ∩ C Distributive law A ∪ (B∩C) = (A∪B) ∩ (A∪C)     A ∩ (B∪C) = (A∩B) ∪ (A∩C) De Morgan's law (i)(A∪B)'=A'∩B'.       (ii)(A∩B)'=A'∪B'.       (iii)A-(B∪C)=(A-B)∩(A-C)       (iv)A-(B∩C)=(A-B)∪(A-C) Cardinal number of power set n [p(A)] = 2 ⁿ Identity laws A∪∅=A       A∩U=U Domination laws A∪U=U       A∩∅=∅ Idempotent laws A∪A=A       A∩A=A Commutative laws A∪B=B∪A       A∩B=B∩A

 Math Formulas

 General form of an arithmetic progression a,(a+d),(a+2d),(a+3d),........... a - first term d = common difference (t₂ - t₁) nth term or general term of an A.P tn = a + (n - 1)d Sum of n terms of an A.P sn = n⁄2 [2a + (n-1)d] sn = n⁄2 [a + L] L-last term number of terms of an A.P n = (l-a)⁄d + 1 General form of g.p a,ar,ar2,ar3,................. a - first term r = common ratio (t₂/t₁) Sum of n terms of g.p if r≠1 sn = a( 1- rn)⁄( 1 - r) sn = a( rn - 1 )⁄( r - 1) if r = 1 sn = n a Sum of infinite series sn = a ⁄( 1 - r)

 Trigonometry Math Formulas

 Trigonometric ratios sin θ = Opposite side/Hypotenuse sidecos θ = Adjacent side/Hypotenuse sidetan θ = Opposite side/Adjacent side Cosec θ = Hypotenuse side/Opposite sideSec θ = Hypotenuse side/Adjacent sidecot θ = Adjacent side /Opposite side Reciprocal sin θ = 1/Cosec θCosec θ = 1/sin θCos θ = 1/sec θsec θ = 1/cos θtan θ = 1/cot θcot θ = 1/tan θ identities sin² θ  + cos² θ = 1sin² θ  = 1 - cos² θcos² θ = 1 - sin² θSec² θ - tan² θ = 1Sec² θ  = 1 +  tan² θ tan² θ  =  Sec² θ - 1Cosec² θ - cot² θ = 1Cosec² θ = 1 + cot² θcot² θ =  Cosec² θ - 1 Complementary angles Sin (90 - θ) = cos θCos (90 - θ) = sin θTan (90 - θ) = cot θCot (90 - θ) = tan θCosec (90 - θ) = sec θSec (90 - θ) = cosec θ Values of certain angles Double angle formula Sin 2A = 2 Sin A cos ACos 2A = cos² A - Sin² Atan 2A = 2 tan A/(1-tan² A)Cos 2A = 1 - 2Sin² ACos 2A = 2Cos² A - 1 sin 2A = 2 tan A/(1+tan² A)cos 2A = (1-tan² A)/(1+tan² A)sin²A = (1-Cos 2A)/2Cos²A = (1+Cos 2A)/2 Half angle formula Sin A = 2 Sin (A/2) cos (A/2)Cos A = cos² (A/2) - Sin² (A/2) tan A = 2 tan (A/2)/[1-tan² (A/2)]Cos A = 1 - 2Sin² (A/2)Cos A = 2Cos² (A/2) - 1  sin A = 2 tan (A/2)/[1+tan² (A/2)]cos A = [1-tan²(A/2)]/[1+tan² (A/2)] sin²A/2 = (1-Cos A)/2Cos²A/2 = (1+Cos A)/2 tan²(A/2) = (1-Cos A)/(1+Cos A) Compound angle formula Sin (A+B) = Sin A Cos B + Cos A Sin B Sin (A-B) = Sin A Cos B - Cos A Sin B Cos (A+B) = Cos A Cos B - Sin A Sin BCos (A-B) = Cos A Cos B + Sin A Sin Btan (A+B) = [Tan A + Tan B] /(1- Tan A Tan B) tan (A-B) = [Tan A - Tan B] /(1+ Tan A Tan B) Compound angles sum and differences sin(A+B)+Sin (A-B) = 2 Sin A cos Bsin(A+B)-Sin (A-B) = 2 Cos A sin Bcos(A+B)+Cos (A-B) = 2 Cos A cos Bcos(A+B)-Cos (A-B) = -2sin A sin B 3A formula Sin 3A = 3 Sin A - 4 sin³ACos 3A = 4 Cos³A - 3 Cos A tan 3A=(3 tan A - tan³A)/(1-3tan²A) Sum to product formula sin C + sin D = 2 sin [(C+D)/2] cos [(C-D)/2]sin C - sin D = 2 cos [(C+D)/2] sin [(C-D)/2]cos C + cos D = 2 cos [(C+D)/2] cos [(C-D)/2]cos C - cos D = -2 sin [(C+D)/2] sin [(C-D)/2]

 Analytical geometry Math Formulas

 Section formula internally Section formula externally Area of triangle using 1⁄2 {x1(y2-y3) + x2(y3-y1) + x3(y1-y2)} Area of quadrilateral 1⁄2{(x1y2+x2y3+x3y4+x4y1)-(x2y1+x3y2+x4y3+x1y4)} Centroid (x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3 Midpoint of the line segment (x₁ + x₂)/2 , (y₁ + y₂)/2 Distance between two points √(x₂ - x₁) ² + (y₂ - y₁) ² Slope of the line m = tan θm = (y2 - y1)/(x2 - x1)m = - coefficient of x / coefficient of yy = m x + bm-slope Slope intercept form:y = m x + bHere m = slope and b = y-intercept Two point form:(y-y₁)/(y₂-y₁) = (x-x₁)/(x₂-x₁) Point- Slope form:(y-y1) = m (x-x1) Intercept form:(X/a) + (Y/b) = 1 Perpendicular distance a point and a line d=| (ax₁+by₁+c)/ va²+b²| Angle between two lines θ = tan-¹ |(m₁ - m₂)/(1 + m₁ m₂)| Equation of circle (x-h)² + (y-k)² = r² Equation of circle with two endpoints of diameter (x-x₁) (x-x₂) + (y-y₁) (y-y₂) = 0 General equation of circle x² + y² + 2gx + 2fy + c = 0 Length of the tangent √ (x₁² + y₁² + 2gx₁ +2fy₁+c) Condition of two circles touching externally c₁c₂ = r₁ + r₂ Condition of two circles touching internally C₁ C₂ = r₁ - r₂ Orthogonal circles 2 g₁g₂+2f₁f₂=c₁+c₂

 Differentiation Math Formulas

 d(xⁿ) =  n xⁿ⁻¹d(sin x) = cos xd(cos x)  - sin xd(logₐ x) = 1/x log ₐ ed(logₑ x) = 1/xd(tan x) = sec² xd(sec x)= sec x tan xd(cot x)= - cosec²xd(cosec x)= - cosec x cot xd(Sin -¹ x)=  1/√(1-x²)d(Cos -¹ x) = -1/√(1-x²)d(tan -¹ x)= 1/(1+x²)d(Cot -¹ x)= -1/(1+x²)d(Sec -¹ x)=  1/[x√(x² - 1)]d(cosec -¹ x)= -1/[x√(x² - 1)] Product rule (UV)' = UV' + VU' Quotient rule (U/V)' =  [VU' - UV'] /V² Lagrange theorem 1.f(x) is defined and continuous on the closed interval [a,b]  2.f(x) is differentiable on the open interval (a,b). Then there exists at least one point c ∊ (a,b) such that f ' (c) = f (b) - f (a) / (b - a) Rolle's theorem 1.f(x) is defined and continuous on the closed interval [a,b]  2.f(x) is differentiable on the open interval (a,b). 3.f(A) = f(b) then there exists at least one point c ∊ (a,b) such that f ' (c) = 0 Maclaurin series f(x) = f(0) + (f'(0) ⁄1!)x + (f''(0) ⁄2!)x2 + (f'''(0) ⁄3!)x3 + ..........

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 Integration Math Formulas

 ∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c∫ (1/xⁿ) dx = -1/(n - 1) x⁽ⁿ⁻¹⁾  + c∫ (1/x) dx = log x  + c∫ e^(x) dx = e^x  + c∫ a^(x) dx = a^x/(log a)  + c∫ Sin x dx = - Cos x + c∫ Cos x dx = Sin x + c ∫ Cosec ² x dx = - Cot x  + c∫ Sec ² x dx = tan x  + c∫ sec x tan x dx = sec x  + c∫ Cosec x cot x dx = - Cosec x  + c∫ 1/(1 + x ²) dx =  tan ⁻ ¹x  + c∫ 1/ √(1 - x ²) dx = Sin ⁻ ¹x   + c∫ (ax + b)ⁿ dx = (1/a) (ax + b)⁽ⁿ ⁺ ¹⁾/(n + 1)   + c∫ 1/(ax + b) dx = (1/a) log (ax + b) + c∫ e^(ax + b) dx = (1/a) e^ (ax + b) + c∫ Sin (ax + b) dx = -(1/a) Cos (ax + b) + c∫ Cos (ax + b) dx = (1/a) Sin (ax + b) + c∫ Sec ² (ax + b) dx = (1/a) tan (ax + b) + c∫ Cosec ² (ax + b) dx = -(1/a) cot (ax + b) + c∫ Cosec (ax+b)cot (ax+b)dx=-(1/a)Cosec (ax+b) + c∫ sec (ax + b) tan (ax + b) dx = sec (ax + b) + c∫ 1/1+ (ax) ² dx = (1/a) tan ⁻ ¹ (ax) + c∫ 1/ √[1 - (ax ²)] dx = (1/a) Sin ⁻ ¹(ax)   + c Integrating by parts ∫ u dv  = uv - ∫ v du

 Mensuration Formulas

 Area of circle Area of circle = Π r ²Circumference of circle = 2 Π r Area of triangle Area of Equilateral-triangle = (√3/4) a²Perimeter of Equilateral-triangle = 3a Area of scalene triangle Area of scalene triangle = √s(s-a)(s-b)(s-c)Perimeter of scalene triangle = a + b +  c Area of semicircle Area of Semi circle= (1/2) Π r²Perimeter of semi-circle = Πr Area of quadrant Area of quadrant = (1/4) Π r² Area of rectangle Area of rectangle = L x WPerimeter of rectangle=2(l+w) Area of square Area of square = a²Perimeter of square = 4a Area of parallelogram Area of parallelogram = b x h Area of quadrilateral=(1/2) x d x (h₁+h₂) Area of rhombus Area of rhombus =(1/2) x (d₁ x d₂) Area of trapezoid Area of trapezoid =(1/2) (a + b) x h Area of sector Area of the sector = (θ/360) x Π r ² square units (or)  Area of the sector = (1/2) x l r square units   Length of arc = (θ/360) x 2Πr Curved surface area = 2 Π r h Total Curved surface area = 2 Π r (h+r) Volume = Π r²h Cone Curved surface area = Π r l Total Curved surface area = Π r (L+r) Volume = (1/3)Π r²hL² = r² + h² Curved surface area = 4Π r²Volume = (4/3)Π r³ Curved surface area = 2Π r²Total Curved surface area=3Π r²Volume = (2/3)Π r³ Cuboid Curved surface area=4h(l+b)Total surface area = 2(lb+bh+h l)Volume = l x b x h Cube Curved surface area=4a²Total surface area = 6a²Volume = a³

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