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. 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 (Chapterwise)
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
| 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:
| 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
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 a Quadratic Equation is:
| ax2+bx+c=0 where a ≠ 0 And x = [-b ± √(b2 – 4ac)]/2a |
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
- 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 the first n terms in Arithmetic Progression;
| Sn = n/2 [2a + (n-1) d] |
Trigonometry Formulas For Class 10
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
Sin θ=
Cos θ =
Tan θ =
Sec θ =
Cot θ =
Cosec θ =
Tan 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
- 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
The common formulas from the surface area and volumes chapter in 10th 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 | Circumference of Cylinder + Curved surface area of Cylinder = 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
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: x̅ =
∑ni=1fixi∑ni=1fi , where ∑fi xi is the sum of observations from value i = 1 to n And ∑fi is the number of observations from value i = 1 to n - Assumed mean method : x̅ =
a+∑ni=1fidi∑ni=1fi - Step deviation method : x̅ =
a+∑ni=1fiui∑ni=1fi×h
(II) The mode of grouped data:
Mode =
(III) The median for a grouped data:
Median =