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All class 10th maths formula |
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Answer» Book mei dekh le Polynomials Formulas(x+y)2=x2+y2+2xy(x−y)2=x2+y2−2xy(x+y)(x−y)=x2−y2(x+y)(x+z)=x2+x(y+z)+yz(x+y)(x−z)=x2+x(y−z)−yzx2+y2=(x+y)2−2xy(x+y)3=x3+y3+3xy(x+y)(x−y)3=x3−y3−3xy(x−y)(x+y+z)2=x2+y2+z2+2xy+2yz+2zx(x−y−z)2=x2+y2+z2−2xy+2yz−2zxx3+y3=(x+y)(x2−xy+y2)x3−y3=(x−y)(x2+xy+y2)x4−y4=(x2)2−(y2)2=(x2+y2)(x2−y2)=(x2+y2)(x+y)(x−y)(x+y+z)2=x2+y2+z2+2xy+2yz+2zx(x+y−z)2=x2+y2+z2+2xy−2yz−2zx(x−y+z)2=x2+y2+z2−2xy−2yz+2zx(x−y−z)2=x2+y2+z2−2xy+2yz−2zxx3+y3+z3−3xyz=[(x+y+z)(x2+y2+z2−xy−yz−zx)]2. Arithmetic Progression Formulasnth Term of an Arithmetic Progression\tan=a+(n−1)×dSum of 1st n Terms of an Arithmetic Progression\tSn=n2[2a+(n−1)d]3. Coordinate Geometry FormulasDistance Formula\tAB=√(x2−x1)2+(y2−y1)2Section Formula\t(mx2+nx1m+n,my2+ny1m+n)Mid-point Formula\t(x1+x22,y1+y22)Area of Triangle\tar(ΔABC)=12×⎡⎢⎣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)⎤⎥⎦4. Trigonometry FormulasTrigonometric Identities\tsin2A+cos2A=1tan2A+1=sec2Acot2A+1=cosec2ARelations between Trigonometric Identities\ttanA=sinAcosAcotA=cosAsinAcosecA=1sinAsecA=1cosATrigonometric Ratios of Complementary Angles\tsin(90∘−A)=cosAcos(90∘−A)=sinAtan(90∘−A)=cotAcot(90∘−A)=tanAsec(90∘−A)=cosecAcosec(90∘−A)=secA Values of Trigonometric Ratios of 0° and 90°∠A0∘30∘45∘60∘90∘sinA0121√2√321cosA1√321√2120tanA01√31√3Not DefinedsecA12√3√22Not Definedcosec ANot Defined\t2√22√31cotANot Defined\t√311√305. Circles FormulasArea of circle\tπr2Diameter of circle\t2rCircumference of circle\t2πrSector angle of circle\tθ=(180×l)(πr)Area of the sector=(θ2)×r2Area of the circular ring=π×(R2−r2)θ=Angle between two radiiR=Radius of outer circler=Radius of inner circle6. Statistics FormulasMean\tam=a1+a2+a3+a44=n∑0 anMedian\tMedian=l+(n2−cff)hMode\tMo=l+(f1−f02f1−f0−f2)h7. Quadratic Equations FormulasQuadratic Equations\tax2+bx+c=0where a≠0Quadratic Polynomial\tP(x)=ax2+bx+c where a≠0Zeroes of the Polynomial P(x)The Roots of the Quadratic Equations are zeroesOne Real Root\tb2−4ac=0Two Distinct Real Roots\tb2−4ac>0No Real Roots\tb2−4ac<08. Triangles FormulasSix elements of triangle\tThree sides and three anglesAngle sum property of triangle\tSum of three angles: ∠A+∠B+∠C=180∘Right angled triangle\tAdjacent SideOpposite SideHypotenusePythagoras Theorem\tH2=AS2+OS2H=HypotenuseAS=Adjacent SideOS=Opposite SideEquilateral Triangles\tAll sides are equalIsosceles Triangle\tTwo sides are equal Congruent Triangles\tTheir corresponding parts are equalSSS Congruence of two triangles\tThree corresponding sides are equalSAS Congruence of two triangles\tTwo corresponding sides and an angle are equalASA Congruence of two triangles\tTwo corresponding angles and a side are equal9. Surface Area and Volume FormulasCuboidVolume of Cuboid (LSA)\tl×b×hLateral Surface Area of Cuboid (LSA)\t2h(l+b)Total Surface Area of Cuboid (TSA)\t2(lb+bh+hl)CubeVolume of Cube\tx3Lateral Surface Area of Cube (LSA)\t4x2Total Surface Area of Cube (TSA)\t6x2SphereVolume of Sphere\t43×πr3Lateral Surface Area of Sphere (LSA)\t4πr2Total Surface Area of Sphere (TSA)\t4πr2Right Circular CylinderVolume of Right Circular Cylinder\tπr2hLateral Surface Area of Right Circular Cylinder (LSA)\t2×(πrh)Total Surface Area of Right Circular Cylinder (TSA)\t2πr×(r+h)Right PyramidVolume of Right Pyramid\t13×[Area of the Base]×hLateral Surface Area of Right Pyramid (LSA)\t12×p×LTotal Surface Area of Right Pyramid (TSA)\tLSA+[Area of the Base]Right Circular ConeVolume of Right Circular Cone\t13×(πr2h)Lateral Surface Area of Right Circular Cone (LSA)\tπrlTotal Surface Area of Right Circular Cone (TSA)\tπr×(r+L)HemisphereVolume of Hemisphere\t23×(πr3)Lateral Surface Area of Hemisphere (LSA)\t2πr2Total Surface Area of Hemisphere (TSA)\t3πr2PrismVolume of Prism\tB×hLateral Surface Area of Prism (LSA)\tp×hTotal Surface Area of Prism (TSA)\tπ×r×(r+L)l=Length, h=Height,b=Breadthr=Radius of SphereL=Slant Height \ufeff |
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