Maths Formulas For Class 10: Important Class 10 Mathematics Formulas

Maths Formulas For Class 10: Class 10 is one of the most important classes in a student’s life. Class 10 board exam result is a deciding factor in selecting the stream for further studies – PCM, PCB, Commerce, or Arts. Maths is one of the most important subjects as it is a basic requirement for a lot of career choices. Most of the students who are math phobic must know that high school Mathematics is important. Because the concepts covered during this period are asked in various competitive exams, like CAT, MAT, and even government job exams. In this article, we will provide you with the complete list of Maths formulae for Class 10 to help you with board exam preparation.

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Maths Formulas For Class 10 (Chapterwise)

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:

n^th 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:

S_n = n/2 [2a + (n-1) d] or S_n = 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 \(\angle \theta\) is one of the other two angles.

sin θ = \(\frac{Side\, opposite\, to\, angle\, \theta}{Hypotenuse}\) = \(\frac{Perpendicular}{Hypotenuse}\) = P/H

cos θ = \(\frac{Adjacent\, side\, to\, angle\, \theta}{Hypotenuse}\) = \(\frac{Adjacent side}{Hypotenuse}\) = B/H

tan θ = \(\frac{Side\, opposite\, to\, angle\, \theta}{Adjacent\, side\, to\, angle\, \theta}\) = P/B

sec θ = \(\frac{1}{cos\, \theta }\)

cot θ = \(\frac{1}{tan\, \theta }\)

cosec θ = \(\frac{1}{sin\, \theta }\)

tan θ = \(\frac{Sin\, \theta }{Cos\, \theta }\)

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:

\(x=-b\pm\frac{\sqrt{b^2-4ac}}{2a}\)

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: \(\frac{4}{3}\pi r^2\) r = radius
Cylinder	Circumference: 2πr LSA: 2πrh TSA: 2πr (r + h) Volume: πr2h r = radius, h = height
Cone	Slant height: \(l=\sqrt{h^2+r^2}\) LSA: πrl TSA: πr(r + l) Volume:  \(\frac{1}{3}\pi r^2h\) 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 = \(\frac{\sum_{i=1}^{n}f_{i}x_{i}}{\sum_{i=1}^{n}f_{i}}\), where f_i x_i is the sum of observations for i = 1 to n And f_i is the number of observations for i = 1 to n
2. Assumed Mean Method : x̅ = a+\(\frac{\sum_{i=1}^{n}f_{i}d_{i}}{\sum_{i=1}^{n}f_{i}}\)
3. Step Deviation Method : x̅ = a+\(\frac{\sum_{i=1}^{n}f_{i}u_{i}}{\sum_{i=1}^{n}f_{i}}\times h\)

(II) The Mode of Grouped Data: Mode = l +\(\frac{f_{i}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h\)

(III) The median for a grouped data: Median = l+\(\frac{\frac{n}{2}-cf}{f}\times h\)

Some FAQs On Maths Formulas Class 10

Here are some frequently asked questions that students ask regarding Class 10 Maths Formulas.

SOLVE CLASS 10 MATHS PRACTICE QUESTIONS NOW

These are some of the important formulas for Class 10 Maths. These Maths formulas for Class 10 will prove to be helpful in your learning process. You will find them useful while revising the CBSE Class 10 Maths syllabus.

Solve the free Class 10 Maths questions and refer to these formulas to score better in Class 10 board exams:

Maths Formulas For Class 8	Mensuration Formulas
Trigonometry Table	Trigonometric Ratios

If you have any queries regarding this article on Maths formulas for class 10 , feel free to ask in the comment section below. We will get back to you at the earliest.

Embibe wishes you all the best!

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