Question

class 10 all inportant formula maths​

Answer 1

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

Answer 2

Answer:

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