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All the formulas of maths of all chapter of class X cbse |
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Answer» Linear Equations One Variableax+b=0a≠0 and a&b are real numbersTwo variableax+by+c = 0a≠0 & b≠0 and a,b & c are real numbersThree Variableax+by+cz+d=0a≠0 , b≠0, c≠0 and a,b,c,d are real numbers Pair of Linear Equations in two variables: a1x+b1y+c1=0 a2x+b2y+c2=0 Where a1, b1, c1, a2, b2, and c2\xa0are all real numbers and a12+b12\xa0≠ 0 & a22\xa0+ b22\xa0≠ 0 It should be noted that\xa0linear equations in two variables\xa0can also be represented in graphical form. Algebra or Algebraic Equations The standard form of a Quadratic Equation is: ax2+bx+c=0 where a ≠ 0 And x = [-b ± √(b2\xa0– 4ac)]/2a Algebraic formulas: (a+b)2\xa0= a2\xa0+ b2\xa0+ 2ab (a-b)2\xa0= a2\xa0+ b2\xa0– 2ab (a+b) (a-b) = a2\xa0– b2 (x + a)(x + b) = x2\xa0+ (a + b)x + ab (x + a)(x – b) = x2\xa0+ (a – b)x – ab (x – a)(x + b) = x2\xa0+ (b – a)x – ab (x – a)(x – b) = x2\xa0– (a + b)x + ab (a + b)3\xa0= a3\xa0+ b3\xa0+ 3ab(a + b) (a – b)3\xa0= a3\xa0– b3\xa0– 3ab(a – b) (x + y + z)2\xa0= x2\xa0+ y2\xa0+ z2\xa0+ 2xy + 2yz + 2xz (x + y – z)2\xa0= x2\xa0+ y2\xa0+ z2\xa0+ 2xy – 2yz – 2xz (x – y + z)2\xa0= x2\xa0+ y2\xa0+ z2\xa0– 2xy – 2yz + 2xz (x – y – z)2\xa0= x2\xa0+ y2\xa0+ z2\xa0– 2xy + 2yz – 2xz x3\xa0+ y3\xa0+ z3\xa0– 3xyz = (x + y + z)(x2\xa0+ y2\xa0+ z2\xa0– xy – yz -xz) x2\xa0+ y2\xa0=½ [(x + y)2\xa0+ (x – y)2] (x + a) (x + b) (x + c) = x3\xa0+ (a + b +c)x2\xa0+ (ab + bc + ca)x + abc x3\xa0+ y3= (x + y) (x2\xa0– xy + y2) x3\xa0– y3\xa0= (x – y) (x2\xa0+ xy + y2) x2\xa0+ y2\xa0+ z2\xa0-xy – yz – zx = ½ [(x-y)2\xa0+ (y-z)2\xa0+ (z-x)2] Click here to check all algebra formulas Basic formulas for powers pm\xa0x pn\xa0= pm+n {pm}⁄{pn} = pm-n (pm)n\xa0= pmn p-m\xa0= 1/pm p1\xa0= p P0\xa0= 1 Arithmetic Progression(AP) Formulas If a1, a2, a3, a4, a5, a6,…\xa0are the terms of AP and d is the common difference between each term, then we can write the sequence as; a,\xa0a+d, a+2d, a+3d, a+4d, a+5d,….,nth term… where a is the first term. Now, nth\xa0term for\xa0arithmetic progression\xa0is given as; nth\xa0term = a + (n-1) d Sum of the first n terms\xa0in Arithmetic Progression; Sn\xa0= n/2 [2a + (n-1) d] Trigonometry Formulas For Class 10 Trigonometry maths formulas for Class 10 cover three major functions Sine, Cosine and Tangent for a right-angle triangle. Also, in\xa0trigonometry, the functions sec, cosec and cot formulas can be derived with the help of sin, cos and tan formulas. Let a right-angled triangle ABC is right-angled at point B and have\xa0∠θ. Sin θ=\xa0SideoppositetoangleθHypotenuse=PerpendicularHypotenuse\xa0= P/H Cos θ =\xa0AdjacentsidetoangleθHypotenuse\xa0=\xa0BaseHypotenuse\xa0= B/H Tan θ =\xa0SideoppositetoangleθAdjacentsidetoangleθ\xa0= P/B Sec θ =\xa01cosθ Cot θ =\xa01tanθ Cosec θ =\xa01sinθ Tan θ =\xa0SinθCosθ Trigonometry Table: Angle0°30°45°60°90°Sinθ01/21/√2√3/21Cosθ1√3/21/√2½0Tanθ01/√31√3UndefinedCotθUndefined√311/√30Secθ12/√3√22UndefinedCosecθUndefined2√22/√31 Swipe left Other Trigonometric formulas: sin(90°\xa0– θ) = cos θ cos(90°\xa0– θ) = sin θ tan(90°\xa0– θ) = cot θ cot(90°\xa0– θ) = tan θ sec(90°\xa0– θ) = cosecθ cosec(90°\xa0– θ) = secθ sin2θ + cos2\xa0θ = 1 sec2\xa0θ = 1 + tan2θ for 0°\xa0≤ θ < 90° Cosec2\xa0θ = 1 + cot2\xa0θ for 0°\xa0≤ θ ≤ 90° Get complete Trigonometry Formulas list here Circles Formulas For Class 10 Circumference of the circle = 2 π r Area of the circle = π r2 Area of the sector of angle θ = (θ/360) × π r2 Length of an arc of a sector of angle θ = (θ/360) × 2 π r (r = radius of the circle) Surface Area and Volumes Formulas For Class 10 The common formulas from the\xa0surface area and volumes\xa0chapter in 10th\xa0class include the following: Sphere Formulas Diameter of sphere2rSurface area of sphere4 π r2Volume of Sphere4/3 π r3 Cylinder Formulas Curved surface area of Cylinder2 πrhArea of two circular bases2 πr2Total surface area of CylinderCircumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr2Volume of Cylinderπ r2\xa0h Cone Formulas Slant height of conel = √(r2\xa0+ h2)Curved surface area of coneπrlTotal surface area of coneπr (l + r)Volume of cone⅓ π r2\xa0h Cuboid Formulas Perimeter of cuboid4(l + b +h)Length of the longest diagonal of a cuboid√(l2\xa0+ b2\xa0+ h2)Total surface area of cuboid2(l×b + b×h + l×h)Volume of Cuboidl × b × h Here, l = length, b = breadth and h = height In case of Cube, put l = b = h = a, as cube all its sides of equal length, to find the surface area and volumes. Statistics Formulas for Class 10 In class 10, the chapter\xa0statistics\xa0mostly deals with finding the mean, median and mode of grouped data. (I) The mean of the grouped data\xa0can be found by 3 methods. Direct Method: x̅\xa0=\xa0∑ni=1fixi∑ni=1fi, where ∑fi\xa0xi\xa0is the sum of observations from value i = 1 to n And ∑fi\xa0is the number of observations from value i = 1 to n Assumed mean method\xa0:\xa0x̅\xa0=\xa0a+∑ni=1fidi∑ni=1fi Step deviation method : x̅\xa0=\xa0a+∑ni=1fiui∑ni=1fi×h (II) The mode of grouped data: Mode =\xa0l+f1–f02f1–f0–f2×h (III) The median for a grouped data: Median =\xa0l+n2–cff×h Linear EquationsOne Variableax+b=0a≠0 and a&b are real numbersTwo variableax+by+c = 0a≠0 & b≠0 and a,b & c are real numbersThree Variableax+by+cz+d=0a≠0 , b≠0, c≠0 and a,b,c,d are real numbersPair of Linear Equations in two variables:a1x+b1y+c1=0a2x+b2y+c2=0Wherea1, b1, c1, a2, b2, and c2\xa0are all real numbers anda12+b12\xa0≠ 0 & a22\xa0+ b22\xa0≠ 0It should be noted that\xa0linear equations in two variables\xa0can also be represented in graphical form.Algebra or Algebraic EquationsThe standard form of a Quadratic Equation is:ax2+bx+c=0 where a ≠ 0And x = [-b ± √(b2\xa0– 4ac)]/2aAlgebraic formulas:(a+b)2\xa0= a2\xa0+ b2\xa0+ 2ab(a-b)2\xa0= a2\xa0+ b2\xa0– 2ab(a+b) (a-b) = a2\xa0– b2(x + a)(x + b) = x2\xa0+ (a + b)x + ab(x + a)(x – b) = x2\xa0+ (a – b)x – ab(x – a)(x + b) = x2\xa0+ (b – a)x – ab(x – a)(x – b) = x2\xa0– (a + b)x + ab(a + b)3\xa0= a3\xa0+ b3\xa0+ 3ab(a + b)(a – b)3\xa0= a3\xa0– b3\xa0– 3ab(a – b)(x + y + z)2\xa0= x2\xa0+ y2\xa0+ z2\xa0+ 2xy + 2yz + 2xz(x + y – z)2\xa0= x2\xa0+ y2\xa0+ z2\xa0+ 2xy – 2yz – 2xz(x – y + z)2\xa0= x2\xa0+ y2\xa0+ z2\xa0– 2xy – 2yz + 2xz(x – y – z)2\xa0= x2\xa0+ y2\xa0+ z2\xa0– 2xy + 2yz – 2xzx3\xa0+ y3\xa0+ z3\xa0– 3xyz = (x + y + z)(x2\xa0+ y2\xa0+ z2\xa0– xy – yz -xz)x2\xa0+ y2\xa0=½ [(x + y)2\xa0+ (x – y)2](x + a) (x + b) (x + c) = x3\xa0+ (a + b +c)x2\xa0+ (ab + bc + ca)x + abcx3\xa0+ y3= (x + y) (x2\xa0– xy + y2)x3\xa0– y3\xa0= (x – y) (x2\xa0+ xy + y2)x2\xa0+ y2\xa0+ z2\xa0-xy – yz – zx = ½ [(x-y)2\xa0+ (y-z)2\xa0+ (z-x)2]Click here to check all algebra formulasBasic formulas for powerspm\xa0x pn\xa0= pm+n{pm}⁄{pn} = pm-n(pm)n\xa0= pmnp-m\xa0= 1/pmp1\xa0= pP0\xa0= 1Arithmetic Progression(AP) FormulasIf a1, a2, a3, a4, a5, a6,…\xa0are the terms of AP and d is the common difference between each term, then we can write the sequence as; a,\xa0a+d, a+2d, a+3d, a+4d, a+5d,….,nth term… where a is the first term. Now, nth\xa0term for\xa0arithmetic progression\xa0is given as;nth\xa0term = a + (n-1) dSum of the first n terms\xa0in Arithmetic Progression;Sn\xa0= n/2 [2a + (n-1) d]Trigonometry Formulas For Class 10Trigonometry maths formulas for Class 10 cover three major functions Sine, Cosine and Tangent for a right-angle triangle. Also, in\xa0trigonometry, the functions sec, cosec and cot formulas can be derived with the help of sin, cos and tan formulas.Let a right-angled triangle ABC is right-angled at point B and have\xa0∠θ.Sin θ=\xa0SideoppositetoangleθHypotenuse=PerpendicularHypotenuse\xa0= P/HCos θ =\xa0AdjacentsidetoangleθHypotenuse\xa0=\xa0BaseHypotenuse\xa0= B/HTan θ =\xa0SideoppositetoangleθAdjacentsidetoangleθ\xa0= P/BSec θ =\xa01cosθCot θ =\xa01tanθCosec θ =\xa01sinθTan θ =\xa0SinθCosθTrigonometry Table:Angle0°30°45°60°90°Sinθ01/21/√2√3/21Cosθ1√3/21/√2½0Tanθ01/√31√3UndefinedCotθUndefined√311/√30Secθ12/√3√22UndefinedCosecθUndefined2√22/√31Swipe leftOther Trigonometric formulas:sin(90°\xa0– θ) = cos θcos(90°\xa0– θ) = sin θtan(90°\xa0– θ) = cot θcot(90°\xa0– θ) = tan θsec(90°\xa0– θ) = cosecθcosec(90°\xa0– θ) = secθsin2θ + cos2\xa0θ = 1sec2\xa0θ = 1 + tan2θ for 0°\xa0≤ θ < 90°Cosec2\xa0θ = 1 + cot2\xa0θ for 0°\xa0≤ θ ≤ 90°Get complete Trigonometry Formulas list hereCircles Formulas For Class 10Circumference of the circle = 2 π rArea of the circle = π r2Area of the sector of angle θ = (θ/360) × π r2Length of an arc of a sector of angle θ = (θ/360) × 2 π r(r = radius of the circle)Surface Area and Volumes Formulas For Class 10The common formulas from the\xa0surface area and volumes\xa0chapter in 10th\xa0class include the following:Sphere FormulasDiameter of sphere2rSurface area of sphere4 π r2Volume of Sphere4/3 π r3Cylinder FormulasCurved surface area of Cylinder2 πrhArea of two circular bases2 πr2Total surface area of CylinderCircumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr2Volume of Cylinderπ r2\xa0hCone FormulasSlant height of conel = √(r2\xa0+ h2)Curved surface area of coneπrlTotal surface area of coneπr (l + r)Volume of cone⅓ π r2\xa0hCuboid FormulasPerimeter of cuboid4(l + b +h)Length of the longest diagonal of a cuboid√(l2\xa0+ b2\xa0+ h2)Total surface area of cuboid2(l×b + b×h + l×h)Volume of Cuboidl × b × hHere, l = length, b = breadth and h = height In case of Cube, put l = b = h = a, as cube all its sides of equal length, to find the surface area and volumes.Statistics Formulas for Class 10In class 10, the chapter\xa0statistics\xa0mostly deals with finding the mean, median and mode of grouped data.(I) The mean of the grouped data\xa0can be found by 3 methods.Direct Method: x̅\xa0=\xa0∑ni=1fixi∑ni=1fi, where ∑fi\xa0xi\xa0is the sum of observations from value i = 1 to n And ∑fi\xa0is the number of observations from value i = 1 to nAssumed mean method\xa0:\xa0x̅\xa0=\xa0a+∑ni=1fidi∑ni=1fiStep deviation method : x̅\xa0=\xa0a+∑ni=1fiui∑ni=1fi×h(II) The mode of grouped data:Mode =\xa0l+f1–f02f1–f0–f2×h(III) The median for a grouped data:Median =\xa0l+n2–cff×h Chapter ya question ke photo bhejo thabhi to bta payenge Konsa ch ka ek ek kr k pucho aise to aap v confused hoge aur hm sb v |
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