Maths Formulas for Class 10 (Chapterwise)

 

Linear Equations

Video Lecture: Previous Year Questions- https://youtu.be/BuTcfAQ8Vww

One Variable	ax+b=0	a≠0 and a&b are real numbers
Two variable	ax+by+c = 0	a≠0 & b≠0 and a,b & c are real numbers
Three Variable	ax+by+cz+d=0	a≠0 , b≠0, c≠0 and a,b,c,d are real numbers

Pair of Linear Equations in two variables

Video Lecture revision : https://youtu.be/vqe_td0aYxQ

a1x+b1y+c1=0 a2x+b2y+c2=0

Where

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

Quadratic Equation and Formula

Revision Video Lectures: https://youtu.be/ALrcbAOrOKs     https://youtu.be/5nsD6R6BYh4

The standard form of a Quadratic Equation is:

ax2+bx+c=0 where a ≠ 0 and

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]

 

Basic formulas for powers

• p^m x pⁿ = p^m+n
• {p^m}⁄{pⁿ} = p^m-n
• (p^m)ⁿ = p^mn
• p^-m = 1/p^m
• p¹ = p
• P⁰ = 1

Arithmetic Progression(AP) Formulas

Revision Video Lectures: https://www.youtube.com/watch?v=GtZaXP3ckMU     https://youtube.com/live/agPz7ia-ln4

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; a_, a+d, a+2d, a+3d, a+4d, a+5d,….,nth term… where a is the first term. Now, n^th term for arithmetic progression is given as;

nth term = a + (n-1) d

Sum of the first n terms in Arithmetic Progression;

Trigonometry Formulas For Class 10                                                   

Quick Revision Video Lecture: https://www.youtube.com/watch?v=FwgMLfxbIQ0

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.

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	1

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°

Circles Formulas For Class 10

Revision Video Lecture: https://youtu.be/k8G9ao6FcZk

• 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             

Revion Video Lecture: https://www.youtube.com/watch?v=_QReteWl5DA

The common formulas from the  surface area and volumes chapter in 10^th 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	Curved surface area of Cylinder + Area of Circular bases = 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  

Revision Video Lecture:  https://www.youtube.com/watch?v=C5BIfZT_F7A

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.

Direct Method:

where ∑f_i x_i is the sum of observations from value i = 1 to n

And ∑f_i is the number of observations from value i = 1 to n

Assumed mean method :

where a is assumed mean and d_i is deviation of a from each of the x_i.

Also, d_i = x_i – a

Step deviation method :

where 

and h is class size

(II) The mode of grouped data:

l=lower limit of modal class.

h= size of the class interval

f₁= frequency of modal class.

f₀= frequency of the class preceding the modal class.

f₂= frequency of the class succeeding the modal class.

(III) The median for a grouped data:

l=lower limit of median class.

n= number of observations.

cf= cumulative frequency of class preceding the median class.

f= frequency of median class

h= class size