# 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

#### Linear Equations

[vc_table vc_table_theme=”classic”]One%20Variable,ax%2Bb%3D0,a%E2%89%A00%20and%20a%26b%20are%20real%20numbers|Two%20variable,ax%2Bby%2Bc%20%3D%200,a%E2%89%A00%20%26%20b%E2%89%A00%20and%20a%2Cb%20%26%20c%20are%20real%20numbers|Three%20Variable,ax%2Bby%2Bc%20%3D%200,a%E2%89%A00%20%2C%20b%E2%89%A00%2C%20c%E2%89%A00%20and%20a%2Cb%2Cc%2Cd%20are%20real%20numbers[/vc_table]

#### Pair of Linear Equations in two variables:

[vc_table vc_table_theme=”classic”]a1x%2Bb1%2Bc1%3D0|a2x%2Bb2%2Bc2%3D0[/vc_table]

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 Quadratic Equations:

[vc_table vc_table_theme=”classic”]ax2%2Bbx%2Bc%3D0%20where%20a%20%E2%89%A0%200%0AAnd%20x%20%3D%20%5B-b%20%C2%B1%20%E2%88%9A(b2%20%E2%80%93%204ac)%5D%2F2a[/vc_table]
##### 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;

[vc_table vc_table_theme=”classic”]nth%20term%20%3D%20a%20%2B%20(n-1)%20d[/vc_table]

Sum of nth term in Arithmetic Progression;

[vc_table vc_table_theme=”classic”]Sn%20%3D%20n%2F2%20%5Ba%20%2B%20(n-1)%20d%5D[/vc_table]

#### Trigonometry Formulas

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 θ.

##### Trigonometry Table:
[vc_table vc_table_theme=”classic”][]Angle,[]0%C2%B0,[]30%C2%B0,[]45%C2%B0,[]60%C2%B0,[]90%C2%B0|[]Sin%CE%B8,[]0,[]1%2F2,[]1%2F%E2%88%9A2,[]%E2%88%9A3%2F2,[]1|[]Cos%CE%B8,[]1,[]%E2%88%9A3%2F2,[]1%2F%E2%88%9A2,[]%C2%BD,[]0|[]Tan%CE%B8,[]0,[]1%2F%E2%88%9A3,[]1,[]%E2%88%9A3,[]Undefined|[]Cot%CE%B8,[]Undefined,[]%E2%88%9A3,[]1,[]1%2F%E2%88%9A3,[]0|[]Sec%CE%B8,[]1,[]2%2F%E2%88%9A3,[]%E2%88%9A2,[]2,[]Undefined|[]Cosec%CE%B8,[]Undefined,[]2,[]%E2%88%9A2,[]2%2F%E2%88%9A3,[]1[/vc_table]

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

#### Circles Formulas

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.

• 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

The common formulas from the surface area and volumes chapter in 10th class include the following:

• Sphere Formulas
[vc_table vc_table_theme=”classic”]Diameter%20of%20sphere,2r,Diameter%20of%20sphere|Circumference%20of%20Sphere,2%20%CF%80%20r,Circumference%20of%20Sphere|Surface%20area%20of%20sphere,4%20%CF%80%20r2,Surface%20area%20of%20sphere[/vc_table]
• Cylinder Formulas
[vc_table vc_table_theme=”classic”]Circumference%20of%20Cylinder,2%20%CF%80rh,Circumference%20of%20Cylinder|Curved%20surface%20area%20of%20Cylinder,2%20%CF%80r2,Curved%20surface%20area%20of%20Cylinder|Total%20surface%20area%20of%20Cylinder,Circumference%20of%20Cylinder%20%2B%20Curved%20surface%20area%20of%20Cylinder%20%3D%202%20%CF%80rh%20%2B%202%20%CF%80r2,Total%20surface%20area%20of%20Cylinder|Volume%20of%20Cylinder,%CF%80%20r2%20h,Volume%20of%20Cylinder[/vc_table]
• Cone Formulas
[vc_table vc_table_theme=”classic”]Slant%20height%20of%20cone,l%20%3D%20%E2%88%9A(r2%20%2B%20h2),Slant%20height%20of%20cone|Curved%20surface%20area%20of%20cone,%CF%80rl,Curved%20surface%20area%20of%20cone|Total%20surface%20area%20of%20cone,%CF%80r%20(l%20%2B%20r),Total%20surface%20area%20of%20cone|Volume%20of%20cone,%E2%85%93%20%CF%80%20r2%20h,Volume%20of%20cone[/vc_table]
• Cuboid Formulas
[vc_table vc_table_theme=”classic”]Perimeter%20of%20cuboid,4(l%20%2B%20b%20%2Bh),Perimeter%20of%20cuboid|Length%20of%20the%20longest%20diagonal%20of%20a%20cuboid,%E2%88%9A(l2%20%2B%20b2%20%2B%20h2),Length%20of%20the%20longest%20diagonal%20of%20a%20cuboid|Total%20surface%20area%20of%20cuboid,2(l%C3%97b%20%2B%20b%C3%97h%20%2B%20l%C3%97h),Total%20surface%20area%20of%20cuboid|Volume%20of%20Cuboid,l%20%C3%97%20b%20%C3%97%20h,Volume%20of%20Cuboid[/vc_table]

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.

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