9303753286127016 Maths Formulas for Class 10 (Chapterwise) Download PDF For Free - Goyanka Maths Study

Maths Formulas for Class 10 (Chapterwise) Download PDF For Free - Goyanka Maths Study



Maths Formulas For Class 10

The Maths formulas for Class 10 are the general formulas which are not only crucial for Class 10 but also form the base for higher-level maths concepts. The maths formulas are also important in various higher education fields like engineering, medical, commerce, finance, computer science, hardware, etc. In almost every industry, the most common formulas introduced in class 10 are used.

The class 10 maths formulas include formulas related to real numbers, polynomials, quadratic equations, triangles, circles, statistics, probability, etc. These maths formulas will be extremely helpful for students to be able to solve questions more accurately and quickly.


List of Maths Formulas for Class 10 (Chapterwise)

The basic maths class 10 formulas are almost the same for all the boards. The list of maths formulas are:

  • Pair of Linear Equation in Two Variables Formulas
  • Algebra and Quadratic Equation Formulas
  • Arithmetic Progression Formulas
  • Trigonometry Formulas
  • Circle Formulas
  • Surface Area and Volume Formulas
  • Statistics Formulas
⇒ Download Class 10 Maths Formulas PDF Here:Download Now

Linear Equations

One Variableax+b=0a≠0 and a&b are real numbers
Two variableax+by+c = 0a≠0 & b≠0 and a,b & c are real numbers
Three 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 are all real numbers and
  • a12+b12 ≠ 0 & a2+ b22 ≠ 0

It should be noted that linear equations in two variables can 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 – 4ac)]/2a

Algebraic formulas:

  • (a+b)= a+ b+ 2ab
  • (a-b)= a+ b– 2ab
  • (a+b) (a-b) = a– 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)
  • x+ 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]



Basic formulas for powers

  • px p= pm+n
  • {pm}⁄{pn} = pm-n
  • (pm)= pmn
  • p-m = 1/pm
  • p1 = p
  • P= 1

Arithmetic Progression(AP) Formulas

If a1, a2, a3, a4, a5, a6, are the terms of AP and d is the common difference between each term, then we can write the sequence as; aa+d, a+2d, a+3d, a+4d, a+5d,….,nth term… where a is the first term. Now, nth term for arithmetic progression is given as;

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 Î¸.

Sin θ= Sideoppositetoangleθ=PerpendicularHypotenuse = P/H

Cos θ = Adjacentsidetoangleθ = BaseHypotenuse = B/H

Tan θ = Sideoppositetoangleθ = P/B

Sec θ = cosθ

Cot θ = tanθ

Cosec θ = sinθ

Tan θ = Sinθ

Trigonometry Table:

Angle30°45°60°90°
Sinθ01/21/√2√3/21
Cosθ1√3/21/√2½0
Tanθ01/√31√3Undefined
CotθUndefined√311/√30
Secθ12/√3√22Undefined
CosecθUndefined2√22/√31

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 Î¸ = 1
  • secθ = 1 + tan2θ for 0° ≤ θ < 90°
  • Cosecθ = 1 + cot2 Î¸ for 0° ≤ θ ≤ 90°

Circles Formulas For Class 10

  • Circumference of the circle = 2 Ï€ r
  • Area of the circle = Ï€ r2
  • Area of the sector of angle θ = (θ/360) × Ï€ r2
  • Length of an arc of a sector of angle θ = (θ/360) × 2 Ï€ 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 sphere2r
Surface area of sphere4 π r2
Volume of Sphere4/3 π r3
  • Cylinder Formulas
Curved surface area of Cylinder2 πrh
Area of two circular bases2 πr2
Total surface area of CylinderCircumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr2
Volume of Cylinderπ rh
  • Cone Formulas
Slant height of conel = √(r2 + h2)
Curved surface area of coneπrl
Total surface area of coneπr (l + r)
Volume of cone⅓ Ï€ rh
  • Cuboid Formulas
Perimeter of cuboid4(l + b +h)
Length of the longest diagonal of a cuboid√(l2 + b2 + 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 statistics mostly deals with finding the mean, median and mode of grouped data.

(I) The mean of the grouped data can be found by 3 methods.

  1. Direct Method: x̅ = ni=1fixini=1fi, where ∑fxis the sum of observations from value i = 1 to n And ∑fis the number of observations from value i = 1 to n
  2. Assumed mean method :  = a+ni=1fidini=1fi
  3. Step deviation method : x̅ = a+ni=1fiuini=1fi×h

(II) The mode of grouped data:

Mode = l+f1f02f1f0f2×h

(III) The median for a grouped data:

Median = l+n2cff×h




Balkishan Agrawal

At the helm of GMS Learning is Principal Balkishan Agrawal, a dedicated and experienced educationist. Under his able guidance, our school has flourished academically and has achieved remarkable milestones in various fields. Principal Agrawal’s vision for the school is centered on providing a nurturing environment where every student can thrive, learn, and grow.

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