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

The CBSE Board exam 2024 date sheet has been officially released. The Class 10 board examinations are scheduled to begin on February 19th with the Sanskrit test and end on March 13th, 2024. The Mathematics examination for pupils in the 10th grade has been scheduled for the 11th of March 2024.Decrease reading

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

The CBSE Class 10 Board Exam 2024 date sheet has been released through the official notice. The Class 10 board examinations are scheduled to begin on February 19th, 2024, with the Sanskrit paper and end on March 13th, 2024. The Mathematics examination for pupils in the 10th grade is set to take place on March 11, 2024.
Mathematics is commonly perceived as a daunting discipline due to its substantial significance in board examinations.
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.
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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 formulas

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)


Surface area and volume (mensuration) formulas

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


Arithmetic progression

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.
  • an = a + (n – 1) d, where an is the nth term.
  • Sn= n/2 [2a + (n – 1)d]

Basic Trigonometry formulas

Trigonometry deals with the connections between the sides and angles of a right-angled triangle. Trigonometric ratios are simply the ratios of these sides. Here are some key formulas related to these ratios.
  • 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
Students should be aware that this list is not comprehensive. It is necessary for students to consult their assigned Mathematics textbook in order to get the comprehensive compilation of formulas.

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