class 10 all inportant formula maths
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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
Sum of the first n terms in Arithmetic Progression;
Sn = 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 trigonometry, 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 ∠θ.
Sin θ= SideoppositetoangleθHypotenuse=PerpendicularHypotenuse = P/H
Cos θ = AdjacentsidetoangleθHypotenuse = BaseHypotenuse = B/H
Tan θ = SideoppositetoangleθAdjacentsidetoangleθ = P/B
Sec θ = 1cosθ
Cot θ = 1tanθ
Cosec θ = 1sinθ
Tan θ = SinθCosθ
Trigonometry Table:
Angle 0° 30° 45° 60° 90°
Sinθ 0 1/2 1/√2 √3/2 1
Cosθ 1 √3/2 1/√2 ½ 0
Tanθ 0 1/√3 1 √3 Undefined
Cotθ Undefined √3 1 1/√3 0
Secθ 1 2/√3 √2 2 Undefined
Cosecθ Undefined 2 √2 2/√3 1Swipe left
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°
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 surface area and volumes chapter in 10th class include the following:
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
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 statistics mostly deals with finding the mean, median and mode of grouped data.
(I) the main three methods
(II) The mode of grouped data:
Mode = l+f1–f02f1–f0–f2×h
(III) The median for a grouped data:
Median = l+n2–cff×h
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