Important Formulas PDF for Class 10 Math Paper: CBSE Board Exam 2024

Analysis of last year question patterns indicates that Quadratic Equations and Arithmetic Progressions have a greater emphasis compared to areas like Polynomials and Real Numbers.

Furthermore, topics that tend to receive high scores encompass Applications of Trigonometry, Triangles, Surface Area, and Volumes, among other subjects.

Mastery of these fundamental concepts, coupled with regular and diligent application, is essential for achieving success in the Mathematics examination. Through diligent and focused practice, the Class 10 board test can be transformed into one of the most fulfilling assessments.

Acquiring proficiency in mathematical formulas throughout Class 10 is crucial for pupils aspiring to achieve outstanding results in board examinations. These formulas serve as the foundational principles that support higher-level mathematical studies, and they play a critical role in determining students’ overall achievement in the subject.

Comprehending Class 10 mathematical formulas enables efficient and precise problem-solving within a limited timeframe. These formulas offer systematic approaches for computing quantities and assessing values, which are valuable in practical scenarios.

Presented below is a compilation of crucial mathematical formulas that will be of significance for the forthcoming CBSE Class 10th Boards Math examination.

Algebra is a branch of mathematics that focuses on equations in which terms are equated. Mastery of algebraic formulas is crucial in the 10th grade curriculum. It facilitates the conversion of verbal problems into mathematical equations. Once you are familiar with these formulas, identifying the type of equation and applying the corresponding rules becomes straightforward. These formulas have distinct inputs and outputs that possess varied interpretations.

Formula	Expression
(a + b)²	a² + 2ab + b²
(a – b)²	a² – 2ab + b²
(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)

Acquiring knowledge of the formulas for area and volume in Class 10 is essential for comprehending the measurements of three-dimensional objects, which play a fundamental role in everyday existence. These formulas are useful for practical activities such as estimating the volume of a container or calculating the surface area of an object.

Shape	Formula
Sphere	Volume = 4/3 × πr³
	Lateral Surface Area (LSA) = 4πr²
	Total Surface Area (TSA) = 4πr²
Right Circular Cylinder	Volume = πr²h
	Lateral Surface Area (LSA) = 2πrh
	Total Surface Area (TSA) = 2πr(r + h)
Hemisphere	Volume = ⅔ × (πr³)
	Lateral Surface Area (LSA) = 2πr²
	Total Surface Area (TSA) = 3πr²
Prism	Volume = B × h
	Lateral Surface Area (LSA) = p × h

Sequences, which are commonly referred to as patterns in daily life, can be categorised into two main types: arithmetic sequences and geometric sequences. Within a sequence, the individual numbers are referred to as terms and are symbolised as a1, a2, a3, and so forth. An arithmetic progression is characterised by a consistent difference between consecutive terms.

• sin(90° – A) = cos A
• cos(90° – A) = sin A
• tan(90° – A) = cot A
• cot(90° – A) = tan A
• sec(90° – A) = cosec A
• cosec(90° – A) = sec A
• sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos2 θ ⇒ cos2 θ = 1 – sin2 θ
• cosec2 θ – cot2 θ = 1 ⇒ cosec2 θ = 1 + cot2 θ ⇒ cot2 θ = cosec2 θ – 1
• sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
• sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1