Maths Formulas for Class 10

It’s obvious that students find Maths as a difficult subject and hard to master in it. But with the correct guidance and proper practice by using standard materials help students to grasp the concept easily and solve any kind of maths problems quickly with the help of Maths Formulas.

First and foremost, students should memorize all concepts formulas perfectly & apply those math formulas while solving the problems. CBSE Class 10 students have to get good on the maths concepts to decide the higher studies field. So, Maths formulas for Class 10 concepts are prevailing here in the form of lists with examples, formula sheets, or tables. Download or Get them offline & recall all those CBSE Class 10 Maths Formulas.

Important Maths Formulas for Class 10 CBSE Students

Maths Formulas for Class 10 presented over here covers important formulas from the mathematics fundamentals of class 10. These Class 10 Maths Formulas helps you solve your homework or assignment problems easier and quicker. So, check out the Onlinecalculator.guru furnished CBSE Maths Formulas for Class 10 from the below sheets, table, or list.

Class 10 Maths Formulas For Arithmetic Progression (AP)

If a1, a2, a3, a4….. 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 the common difference, and l is the last term is given as:

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

Class 10 Maths Formulas For Linear Equations

Linear equations in one, two, and three variables have the following forms:

Linear Equation in one Variableax + b=0Where a ≠ 0 and a & b are real numbers
Linear Equation in Two Variables ax + by + c = 0Where a ≠ 0 & b ≠ 0 and a, b & c are real numbers
Linear Equation in Three Variablesax + by + cz + d = 0Where a ≠ 0, b ≠ 0, c ≠ 0 and a, b, c, d are real numbers

The pair of linear equations in two variables are given as:

a1x+b1+c1=0 and a2x+b2+c2=0

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

Quick Note: Linear equations can also be represented in graphical form.

Trigonometry Formulas For Class 10 Maths

The Trigonometric Formulas for Class 10 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).

Let a right-angled triangle ABC is right-angled at point B and have \(\angle \theta\) is one of the other two angles.

sin θ = \(\frac{Side\, opposite\, to\, angle\, \theta}{Hypotenuse}\) = \(\frac{Perpendicular}{Hypotenuse}\) = P/H

cos θ = \(\frac{Adjacent\, side\, to\, angle\, \theta}{Hypotenuse}\) = \(\frac{Adjacent side}{Hypotenuse}\) = B/H

tan θ = \(\frac{Side\, opposite\, to\, angle\, \theta}{Adjacent\, side\, to\, angle\, \theta}\) = P/B

sec θ = \(\frac{1}{cos\, \theta }\)

cot θ = \(\frac{1}{tan\, \theta }\)

cosec θ = \(\frac{1}{sin\, \theta }\)

tan θ = \(\frac{Sin\, \theta }{Cos\, \theta }\)

The Trigonometric Table comprising the values of these trigonometric functions for standard angles is as under:

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

Some other trigonometric formulas are given below:

  1. sin (90° – θ) = cos θ
  2. cos (90° – θ) = sin θ
  3. tan (90° – θ) = cot θ
  4. cot (90° – θ) = tan θ
  5. sec (90° – θ) = cosecθ
  6. cosec (90° – θ) = secθ
  7. sin2θ + cos2 θ = 1
  8. secθ = 1 + tan2θ for 0° ≤ θ < 90°
  9. Cosecθ = 1 + cot2 θ for 0° ≤ θ ≤ 90°

Class 10 Maths Formulas For Algebra & Quadratic Equations

To know the algebra formulas for Class 10, first, you need to get familiar with Quadratic Equations.

The Quadratic Formula: For a quadratic equation px2 + qx + r = 0, the values of x which are the solutions of the equation are given by:

\(x=-b\pm\frac{\sqrt{b^2-4ac}}{2a}\)

Now you know the basic quadratic equation.

Let us now go through the list of algebra formulas for Class 10:

  1. (a+b)= a+ b+ 2ab
  2. (a-b)= a+ b– 2ab
  3. (a+b) (a-b) = a– b2
  4. (x + a)(x + b) = x2 + (a + b)x + ab
  5. (x + a)(x – b) = x2 + (a – b)x – ab
  6. (a + b)3 = a3 + b3 + 3ab(a + b)
  7. (a – b)3 = a3 – b3 – 3ab(a – b)
  8. (x – a)(x + b) = x2 + (b – a)x – ab
  9. (x – a)(x – b) = x2 – (a + b)x + ab
  10. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
  11. (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
  12. (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
  13. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
  14. x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)
  15. x+ y2 =½ [(x + y)2 + (x – y)2]
  16. (x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc
  17. x3 + y3= (x + y) (x2 – xy + y2)
  18. x3 – y3 = (x – y) (x2 + xy + y2)
  19. x2 + y2 + z2 -xy – yz – zx = ½ [(x-y)2 + (y-z)2 + (z-x)2]

Quick Note: These formulas will be important in higher classes and various comeptitive examninations. So, memorize them and understand them well.

Class 10 Maths Formulas For Circle

Circle formulas act as a base for Mensuration. The Class 10 Maths Circle formulas for a circle of radius r are given below:

  • 1. Circumference of the circle = 2 π r
  • 2. Area of the circle = π r2
  • 3. Area of the sector of angle θ = (θ/360) × π r2
  • 4. Length of an arc of a sector of angle θ = (θ/360) × 2 π r

Class 10 Maths Formulas For Surface Area & Volume

These formulas are very important for successfully solving mensuration questions. Find below the formulas in a tabulated form for your convenience.

Here, LSA = Lateral Surface Area,

TSA = Total Surface Area.

Sphere Diameter: 2r
Circumference: 2 π r
TSA: 4πr2
Volume: \(\frac{4}{3}\pi r^2\)

r = radius
Cylinder Circumference: 2πr
LSA: 2πrh
TSA: 2πr (r + h)
Volume: πr2h

r = radius,
h = height
ConeSlant height: \(l=\sqrt{h^2+r^2}\)
LSA: πrl
TSA: πr(r + l)
Volume:  \(\frac{1}{3}\pi r^2h\)

r = radius,
l = slant height,
h = height
CuboidLSA: 2h(l + b)
TSA: 2(lb + bh + hl)
Volume: lbh

l = length,
b = breadth,
h = height
CubeLSA: 4a2
TSA: 6a2
Volume: a3

a = sides of a cube

Class 10 Maths Formulas For Statistics

Statistics in Class 10 is majorly about finding the Mean, Median, and Mode of the given data. The statistic formulas are given below:

(I) The Mean of Grouped Data can be found by 3 methods.

  1. Direct Method: x̅ = \(\frac{\sum_{i=1}^{n}f_{i}x_{i}}{\sum_{i=1}^{n}f_{i}}\), where fxis the sum of observations for i = 1 to n And fis the number of observations for i = 1 to n
  2. Assumed Mean Method :  = a+\(\frac{\sum_{i=1}^{n}f_{i}d_{i}}{\sum_{i=1}^{n}f_{i}}\)
  3. Step Deviation Method : x̅ = a+\(\frac{\sum_{i=1}^{n}f_{i}u_{i}}{\sum_{i=1}^{n}f_{i}}\times h\)

(II) The Mode of Grouped Data: Mode = l +\(\frac{f_{i}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h\)

(III) The median for a grouped data: Median = l+\(\frac{\frac{n}{2}-cf}{f}\times h\)