Math Formulas For Class 10

Maths is considered to be one of the most important and difficult subjects because of its practical nature. This is a subject that consists of a variety of formulas, theories and concepts that are used for problem-solving and that too requires rigorous practice to become a master in Maths concepts and their formulas. 

If you think of a question related to the area or volume of any object, it would not be possible to find the answer without having knowledge of its formulas. Thus, it becomes necessary to learn and revise these formulas regularly if we even talk about basic Maths for class 10.

CREST Champs knows this requirement and therefore we have brought you Math formulas for Class 10 of each chapter to ease the preparation of the students which will help you do regular practice and score better. 

CREST Champs makes sure that all the formulas mentioned are accurate according to the updated syllabus, the latest for the present academic year. 

CBSE Chapter-Wise Important Math Formulas For Class 10

Here’s the list of important formulas for Maths class 10 CBSE chapter-wise. You can find the formulas for the below-mentioned chapters:

  • Real Numbers
  • Polynomials
  • Pair of Linear Equations in Two Variables
  • Quadratic Equations 
  • Arithmetic Progression 
  • Trigonometry 
  • Area of Circle 
  • Surface Area and Volume
  • Algebraic Formulas

Real Numbers Math Formulas For Class 10

  • Natural Numbers 

            N ={ 1, 2,3,4,5 … } 

  • Whole Numbers

             W = { 0, 1, 2, 3, 4, 5… }

  • Rational Numbers - Numbers that can be presented in the a/b form. 

Polynomials Math Formulas For Class 10

Polynomials General Form Formula
Linear ax + b = 0, a ≠ 0 k = {- constant}/{coefficient(x)}
Quadratic ax2 + bx + c = 0, a ≠ 0 k1 + k2 = {coefficient(x)}/{coefficient(x2)}
Cubic ax3 + bx2 + c = 0, a ≠ 0 k1 + k2 + k3 = {coefficient(x2)}/{coefficient(x3)}

Pair of Linear Equations in Two Variables Math Formulas For Class 10

  • a1x+b1y+c1=0
  • a2x+b2y+c2=0

Where

  • a1, b1, c1, a2, b2, and c2 are real numbers and
  • a12+b12 ≠ 0 & a22 + b22 ≠ 0

Quadratic Equations Math Formulas For Class 10

The standard form of a Quadratic Equation is:

ax2+bx+c=0 where a ≠ 0 & x = [-b ± √(b2 – 4ac)]/2a

Arithmetic Progression (AP) Math Formulas For Class 10

If a1, a2, a3….. be the terms of an AP and d be the common difference between each term, then the sequence can be written as: a, a + d, a + 2d, a + 3d, a + 4d…… a + nd.

where a is the first term and (a + nd) is the (n – 1)th term. So, the formula to calculate the nth term of AP is given as:

nth term = a + (n-1)d

The sum for the nth term of AP where a is the 1st term, d is a common difference, and l is the last term is given as:

Sn = n/2[2a + (n-1)d] or Sn = n/2[a + l]

Trigonometry Math Formulas For Class 10

Class 10 Trigonometric formulas covers the basic trigonometric functions for a right-angled triangle i.e. Sine(sin), Cosine(cos) and Tangent(tan) which can be used to derive Cosecant(cos), Secant(sec) and Cotangent(cot).

sinθ = (Side opposite to angle θ)/(Hypotenuse) = Perpendicular/Hypotenuse = P/H

cosθ = (Adjacent side to angle θ)/(Hypotenuse) = Adjacent side/Hypotenuse = B/H

tanθ = (Side opposite to angle θ)/(Adjacent side to angle θ) = P/B

Trignometry Table

Angle 30° 45° 60° 90°
Sinθ 0 1/2 1/√2 √3/2 0
Cosθ 1 √3/2 1/√2 1/2 1
Tanθ 0 1/√3 1 √3 0
Cotθ Undefined √3 1 1/√3 Undefined
Secθ 1 2/√3 √2 2 1
Cosecθ Undefined 2 √2 2/√3 Undefined

Some other trigonometric formulas:

  • sin(90° – θ) = cosθ
  • cos(90° – θ) = sinθ
  • tan(90° – θ) = cotθ
  • cot(90° – θ) = tanθ
  • sec(90° – θ) = cosecθ
  • cosec(90° – θ) = secθ
  • sin2θ + cos2θ = 1
  • sec2θ = 1 + tan2θ for 0° ≤ θ < 90°
  • Cosec2θ = 1 + cot2θ for 0° ≤ θ ≤ 90°

Area Of Circle Math Formulas For Class 10

  • Circumference of the circle = 2πr
  • Area of the circle = πr2
  • Area of the sector of angle θ = (θ/360) × πr2
  • Length of an arc of a sector of angle θ = (θ/360) × 2 π r

Where the radius is denoted by r.

Surface Area & Volume Math Formulas For Class 10

Here, LSA = Lateral Surface Area & TSA = Total Surface Area

  • Sphere
    • Diameter: 2r
    • Circumference: 2πr
    • TSA: 4πr2
    • Volume: 4/3πr3
  • Cylinder
    • Circumference: 2πr
    • LSA: 2πrh
    • TSA: 2πr(r + h)
    • Volume: πr2h
    • r = radius
    • h = height
    • r = radius
  • Cone
    • Slant height: l = √(r2 + h2)
    • LSA: πrl
    • TSA: πr(r + l)
    • Volume: 1/3πr2h
    • r = radius
    • l = slant height
    • h = height
  • Cuboid
    • LSA: 2h(l + b)
    • TSA: 2(lb + bh + hl)
    • Volume: lbh
    • l = length
    • b = breadth,
    • h = height
  • Cube
    • LSA: 4a2
    • TSA: 6a2
    • Volume: a3
    • a = side of a cube

Algebraic Math Formulas For Class 10

  • (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]

Why should you go for all Math Formulas For Class 10?

Formulas are always considered to be the basic requirement for solving any question in Mathematics. Let's go through a few benefits of the Math formulas.

  • The formulas collection works best to revise the chapters & also when the last few days are left before the exam.
  • Students can revise all the important things in one place before any test or exam.

Hope you’ve gained some knowledge through this useful article. These formulas will surely help you in your preparation for the class 10 Maths CBSE exam. At CREST Champs, you can also explore Maths CBSE class 10 courses. These courses are available by many tutors. If you like to take online coaching for Maths, then CREST Champs is the most preferred platform.

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