Maths Formulas For Class 10

Before getting into the list of the formulas, let’s check out the major chapters of Class 10 Maths for which formulas are needed:

• 1) Arithmetic Progression Formulas
• 2) Pair of Linear Equation in Two Variables Formulas
• 3) Trigonometry Formulas
• 4) Algebra and Quadratic Equation Formulas
• 5) Circle Formulas
• 6) Surface Area and Volume Formulas
• 7) Statistics Formulas

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 Variable	ax + b=0	Where a ≠ 0 and a & b are real numbers
Linear Equation in Two Variables	ax + by + c = 0	Where a ≠ 0 & b ≠ 0 and a, b & c are real numbers
Linear Equation in Three Variables	ax + by + cz + d = 0	Where 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 & a22 + 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 ∠θ$\mathrm{\angle }\theta$ is one of the other two angles.

sin θ = SideoppositetoangleθHypotenuse$\frac{Sideoppositetoangle\theta }{Hypotenuse}$ = PerpendicularHypotenuse$\frac{Perpendicular}{Hypotenuse}$ = P/H

cos θ = AdjacentsidetoangleθHypotenuse$\frac{Adjacentsidetoangle\theta }{Hypotenuse}$ = AdjacentsideHypotenuse$\frac{Adjacentside}{Hypotenuse}$ = B/H

tan θ = SideoppositetoangleθAdjacentsidetoangleθ$\frac{Sideoppositetoangle\theta }{Adjacentsidetoangle\theta }$ = P/B

sec θ = 1cosθ$\frac{1}{cos\theta }$

cot θ = 1tanθ$\frac{1}{tan\theta }$

cosec θ = 1sinθ$\frac{1}{sin\theta }$

tan θ = SinθCosθ$\frac{Sin\theta }{Cos\theta }$

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

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

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. sec2 θ = 1 + tan2θ for 0° ≤ θ < 90°
9. Cosec2 θ = 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±b2−4ac√2a$x=-b\pm \frac{\sqrt{b^2-4ac}}{2a}$

Now you know the basic quadratic equation.

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

1. (a+b)2 = a2 + b2 + 2ab
2. (a-b)2 = a2 + b2 – 2ab
3. (a+b) (a-b) = a2 – 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. x2 + 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: 43πr2$\frac{4}{3}\pi r^2$ r = radius
Cylinder	Circumference: 2πr LSA: 2πrh TSA: 2πr (r + h) Volume: πr2h r = radius, h = height
Cone	Slant height: l=h2+r2−−−−−−√$l=\sqrt{h^2+r^2}$ LSA: πrl TSA: πr(r + l) Volume:  13πr2h$\frac{1}{3}\pi r^{2}h$ r = radius, l = slant height, h = height
Cuboid	LSA: 2h(l + b) TSA: 2(lb + bh + hl) Volume: lbh l = length, b = breadth, h = height
Cube	LSA: 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 = ∑ni=1fixi∑ni=1fi$\frac{\sum _{i=1}^n{f}_i{x}_i}{\sum _{i=1}^n{f}_i}$, where fi xi is the sum of observations for i = 1 to n And fi is the number of observations for i = 1 to n
2. Assumed Mean Method : x̅ = a+∑ni=1fidi∑ni=1fi$\frac{\sum _{i=1}^n{f}_i{d}_i}{\sum _{i=1}^n{f}_i}$
3. Step Deviation Method : x̅ = a+∑ni=1fiui∑ni=1fi×h$\frac{\sum _{i=1}^n{f}_i{u}_i}{\sum _{i=1}^n{f}_i}\times h$

(II) The Mode of Grouped Data: Mode = l +fi−f02f1−f0−f2×h$\frac{f_i-f_0}{2f_1-f_0-f_2}\times h$

(III) The median for a grouped data: Median = l+n2−cff×h