class 10 maths full fromula
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Answer:
Algebraic formulas:
(a+b)2 = a2 + b2 + 2ab
(a-b)2 = a2 + b2 – 2ab
(a+b) (a-b) = a2 – b2
(x + a)(x + b) = x2 + (a + b)x + ab
(x + a)(x – b) = x2 + (a – b)x – ab
(x – a)(x + b) = x2 + (b – a)x – ab
(x – a)(x – b) = x2 – (a + b)x + ab
(a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – b3 – 3ab(a – b)
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
(x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
(x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
(x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
x2 + y2 =½ [(x + y)2 + (x – y)2]
(x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
x3 + y3= (x + y) (x2 – xy + y2)
x3 – y3 = (x – y) (x2 + xy + y2)
x2 + y2 + z2 -xy – yz – zx = ½ [(x-y)2 + (y-z)2 + (z-x)2]
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Basic formulas for powers
pm x pn = pm+n
{pm}⁄{pn} = pm-n
(pm)n = pmn
p-m = 1/pm
p1 = p
P0 = 1
nth term = a + (n-1) d
Sn = n/2 [2a + (n-1) d]
Other Trigonometric formulas:
sin(90° – θ) = cos θ
cos(90° – θ) = sin θ
tan(90° – θ) = cot θ
cot(90° – θ) = tan θ
sec(90° – θ) = cosecθ
cosec(90° – θ) = secθ
sin2θ + cos2 θ = 1
sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
Cosec2 θ = 1 + cot2 θ for 0° ≤ θ ≤ 90°
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)
Sphere Formulas
Diameter of sphere 2r
Surface area of sphere 4 π r2
Volume of Sphere 4/3 π r3
Cylinder Formulas
Curved surface area of Cylinder 2 πrh
Area of two circular bases 2 πr2
Total surface area of Cylinder Circumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr2
Volume of Cylinder π r2 h
Cone Formulas
Slant height of cone l = √(r2 + h2)
Curved surface area of cone πrl
Total surface area of cone πr (l + r)
Volume of cone ⅓ π r2 h
Cuboid Formulas
Perimeter of cuboid 4(l + b +h)
Length of the longest diagonal of a cuboid √(l2 + b2 + h2)
Total surface area of cuboid 2(l×b + b×h + l×h)
Volume of Cuboid l × b × h