Maths Formulas for Class 10 PDF - Byju's

Class 10 Maths Formulas PDF

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. Even

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

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:

Linear Equations

One Variable

ax+b=0

a¡Ù0 and a&b are real numbers

Two variable

ax+by+c = 0

a¡Ù0 & b¡Ù0 and a,b & c are real numbers

Three Variable

ax+by+cz+d=0

a¡Ù0 , b¡Ù0, c¡Ù0 and a,b,c,d are real numbers

Pair of Linear Equations in two variables:

a1x+b1+c1=0

a2x+b2+c2=0

Maths Formulas For Class 10 PDF

Where

a1, b1, c1, a2, b2, and c2 are all real numbers and

a12+b12 ¡Ù 0 & a22 + b22 ¡Ù 0

It should be noted that linear equations in two variables

() can also be

represented in graphical form.

Algebra or Elgebraic Equations

The standard form of Quadratic Equations:

ax2+bx+c=0 where a ¡Ù 0

And x = [-b ¡À ¡Ì(b2 ¨C 4ac)]/2ac

Algebraic formulas:

(a+b)2 = a2 + b2 + 2ab

(a-b)2 = a2 + b2 ¨C 2ab

(a+b) (a-b) = a2 ¨C b2

(x + a)(x + b) = x2 + (a + b)x + ab

(x + a)(x ¨C b) = x2 + (a ¨C b)x ¨C ab

(x ¨C a)(x + b) = x2 + (b ¨C a)x ¨C ab

(x ¨C a)(x ¨C b) = x2 ¨C (a + b)x + ab

(a + b)3 = a3 + b3 + 3ab(a + b)

(a ¨C b)3 = a3 ¨C b3 ¨C 3ab(a ¨C b)

(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz

(x + y ¨C z)2 = x2 + y2 + z2 + 2xy ¨C 2yz ¨C 2xz

(x ¨C y + z)2 = x2 + y2 + z2 ¨C 2xy ¨C 2yz + 2xz

(x ¨C y ¨C z)2 = x2 + y2 + z2 ¨C 2xy + 2yz ¨C 2xz

x3 + y3 + z3 ¨C 3xyz = (x + y + z)(x2 + y2 + z2 ¨C xy ¨C yz -xz)

x2 + y2 =? [(x + y)2 + (x ¨C y)2]

(x + a) (x + b) (x + c) = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc

x3 + y3= (x + y) (x2 ¨C xy + y2)

x3 ¨C y3 = (x ¨C y) (x2 + xy + y2)

x2 + y2 + z2 -xy ¨C yz ¨C zx = ? [(x-y)2 + (y-z)2 + (z-x)2]

Click here to check all algebra formulas ()

Basic formulas for powers

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Maths Formulas For Class 10 PDF

pm x pn = pm+n

{pm}?{pn} = pm-n

(pm)n = pmn

p-m = 1/pm

p1 = p

P0 = 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; a, a+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 nth term in Arithmetic Progression;

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

Trigonometry Formulas For Class 10

Trigonometry maths formulas for Class 10 covers 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 ¡Ï¦È.

Sin ¦È=

Side opposite to angle ¦È

Cos ¦È =

Tan ¦È =

Sec ¦È =

Cot ¦È =

H ypotenuse

Adjacent side to angle ¦È

H ypotenuse

Side opposite to angle ¦È

Adjacent side to angle ¦È

P erpendicular

H ypotenuse

=

= P/H

Adjacentside

H ypotenuse

= B/H

= P/B

1

cos ¦È

1

tan ¦È

Cosec ¦È =

Tan ¦È =

=

1

sin ¦È

Sin ¦È

C os ¦È

Trigonometry Table

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Maths Formulas For Class 10 PDF

Angle

0¡ã

30¡ã

45¡ã

60¡ã

90¡ã

Sin¦È

0

1/2

1/¡Ì2

¡Ì3/2

1

Cos¦È

1

¡Ì3/2

1/¡Ì2

?

0

Tan¦È

0

1/¡Ì3

1

¡Ì3

Undefined

Cot¦È

Undefined

¡Ì3

1

¡Ì3/2

0

Sec¦È

1

2/¡Ì3

¡Ì2

2

Undefined

Cosec¦È

Undefined

2

¡Ì2

2/¡Ì3

1

Other Trigonometric formulas

sin(90¡ã ¨C ¦È) = cos ¦È

cos(90¡ã ¨C ¦È) = sin ¦È

tan(90¡ã ¨C ¦È) = cot ¦È

cot(90¡ã ¨C ¦È) = tan ¦È

sec(90¡ã ¨C ¦È) = cosec¦È

cosec(90¡ã ¨C ¦È) = sec¦È

sin2¦È + cos2 ¦È = 1

sec2 ¦È = 1 + tan2¦È for 0¡ã ¡Ü ¦È < 90¡ã

Cosec2 ¦È = 1 + cot2 ¦È for 0¡ã ¡Ü ¦È ¡Ü 90¡ã

Get complete Trigonometry Formulas list here

()

Circles Formulas For Class 10

Circumference of the circle = 2 ¦Ð r

Area of the circle = ¦Ð r2

Area of the sector of angle ¦È = (¦È/360) ¡Á ¦Ð r2

Length of an arc of a sector of angle ¦È = (¦È/360) ¡Á 2 ¦Ð 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

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Maths Formulas For Class 10 PDF

Diameter of sphere

2r

Circumference of Sphere

2¦Ðr

Surface area of sphere

4 ¦Ð r2

Volume of Cylinder

4/3 ¦Ð r2

Cylinder Formulas

Circumference of

Cylinder

2 ¦Ðrh

Curved surface area

of Cylinder

2 ¦Ðr2

Total surface area of

Cylinder

Circumference of Cylinder + Curved surface area of

Cylinder = 2 ¦Ðrh + 2 ¦Ðr2

Volume of Cylinder

¦Ð r2 h

Cone Formulas

Slant height of cone

l = ¡Ì(r2 + h2)

Curved surface area of cone

¦Ðrl

Total surface area of cone

¦Ðr (l + r)

Volume of cone

? ¦Ð r2 h

Cuboid Formulas

Perimeter of cuboid

4(l + b +h)

Length of the longest diagonal of a cuboid

¡Ì(l2 + b2 + h2)

Total surface area of cuboid

2(l¡Áb + b¡Áh + l¡Áh)

Volume of Cuboid

l¡Áb¡Áh

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

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