CBSE Class 10 Maths Notes PDF: Chapter Wise Notes 2024 (original) (raw)

Last Updated : 21 Aug, 2025

Math is an important subject in CBSE Class 10th Board exam. So students are advised to prepare accordingly to score well in Mathematics. Mathematics sometimes seems complex but at the same time, It is easy to score well in Math. So, We have curated the complete **CBSE Class 10 Math Notes for you to prepare Mathematics for CBSE Class 10th exam 2024.

Our Class 10 Math Note is based on NCERT Pattern and latest syllabus.Take help of our chapter wise CBSE class 10th math notes in order to ace the CBSE class 10 board exam.

CBSE Class 10 Math Notes - Chapter Wise

Below is the chapter wise notes of CBSE Class 10th Math.

Download CBSE Class 10 Math Notes PDF

Click on the link below to download the CBSE Class 10th chapter wise math notes.

**Removed Topics from Class 10th Math Syllabus(2023-2024)

After, Covid, CBSE has reduced the Class 10th Math syllabus by 30% for the upcoming class 10 board exam in the academic year 2023-2024. Below is the list of removed topics form CBSE class 10th board exam.

**Real Number

• Euclid’s division lemma
• Decimal representation of rational numbers

**Polynomials

• Problems on the division algorithm for polynomials with real coefficients.

**Pair of Linear Equations in Two Variables

• Simple problems on equations are reducible to linear equations.

**Triangles

• **The proof of the following theorems is removed.
  • If a perpendicular is drawn from the vertex of a right angle to the hypotenuse of a right triangle, then the triangles on each side of the perpendicular are congruent to the whole triangle and similar to each other.
  • The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
  • In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
  • In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angles opposite to the first side are right angles.

**Construction

• All Chapter is removed

**Trigonometric Identities

• Trigonometric ratios of complementary angles

**Surface Area and Volume

• The frustum of a cone.
• Problems related to the conversion of one type of metallic solid to another and other mixed problems.
• Problems involving the combination of more than two different solids to be taken.

**Statistics

• Step Deviation Method for finding the mean
• Cumulative Frequency graph

**Chapter 1: Real Numbers

Real Numbers are the combination of both rational and irrational numbers. It included positive and negative integers, irrational numbers, and fractions. To put it another way, a real number is any number found in the actual world. Numbers may be found everywhere. Natural numbers are used to count items, integers to measure temperature, rational numbers to represent fractions, and irrational numbers to calculate the square root of a number, among other things.

The chapter Real Numbers include both irrational and rational numbers with all natural numbers, whole numbers, integers, etc., and discuss their characteristics.

**Chapter 1 Real Numbers - Important Points

• **Euclid’s Division Algorithm (lemma): According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integers q and r such that a = bq + r, where 0 ≤ r ≤ b. (Here, a is the dividend, b is the divisor, q is the quotient, and r is the remainder.)
• **Fundamental theorem of arithmetic said that the Composite Numbers are equal to the Product of Primes.
• **HCF and LCM by prime factorization**method:
  • **HCF = Product of the smallest power of each common factor in the numbers
  • **LCM = Product of the greatest power of each prime factor involved in the number
  • **HCF (a,b) × LCM (a,b) = a × b

Chapter 2: Polynomials

**Polynomials are algebraic expressions that consist of coefficients and variables or are indeterminate. An arithmetic operation such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable can be performed on polynomials.

This particular chapter presents the idea of the degree of polynomials, how a polynomial with degree 1 is a linear polynomial, degree 2 is a quadratic polynomial, and degree 3 is a cubic polynomial. Moreover, the most important topics discussed in this chapter are the zeroes of a polynomial and the relationship between zeroes and coefficients of quadratic polynomials only.

**Chapter 2 Polynomials - Important Formulas Of Polynomials

• The general **Polynomial Formula is, **F (x) = a n x n + bx n-1 + a n-2 x n-2 + …….. + rx + s
• • When n is a **natural number: an – bn = (a – b)(an-1 + an-2b +…+ bn-2a + bn-1)
  • When n is **even (n = 2a): xn + yn = (x + y)(xn-1 – xn-2y +…+ yn-2x – yn-1)
  • When n is **odd number: xn + yn = (x + y)(xn-1 – xn-2y +…- yn-2x + yn-1)
• **Algebraic Polynomial Identities
  • (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]
• **Division algorithm for polynomials: If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that p(x) = q(x) × g(x) + r(x)
• where r(x) = 0 or degree of r(x) < degree of g(x). Here p(x) is divided, g(x) is divisor, q(x) is quotient and r(x) is remainder.

Chapter 3: Pair of Linear Equations in Two Variables

An equation of the form ax+by+c, where a, b, and c are real numbers and a, b are not equal to zero, is termed as the **linear equation in two variables. However, in a **pair of linear equations in two variables, there exist two such equations whose solution is a point on the line denoting the equation.

Below are the notes of Math Chapter 2 Pair of Linear Equations in Two Variables.

**Chapter 3 Pair Of Linear Equations In Two Variables - Important Points

An equation which can be put in the form **ax + by + c = 0. Where a, b and c are Pair of Linear Equations in Two Variables, and a and b are not both zero, is called a linear equation in two variables x and y.

Chapter 3 of CBSE Class 10 Math Notes covers the following topics:

• Number of Solutions to a System of Equations Algebraically

Chapter 4: Quadratic Equations

In chapter 4 of Math NCERT Notes, we’ll cover the **Quadratic Equations. The degree 2 polynomial equations in one variable are called **Quadratic equations. The general form of a quadratic equation is ax2 + bx + c where a, b, c, ∈ R and a ≠ 0, where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of the complete equation.

This chapter helps to understand the concept of the standard form of quadratic equations, various methods of solving quadratic equations (by factorization, by completing the square), and the nature of roots.

**Chapter 4 Quadratic Equations - Important Formulas

• **Solution or roots of a quadratic equation are given by the quadratic formula: (α, β) = [-b ± √(b2 – 4ac)]/2ac
• **Roots of the quadratic equation****:** x = (-b ± √D)/2a, where D = b2 – 4ac is known as the Discriminant of a quadratic equation. The discriminant of a quadratic equation decides the nature of roots.
• **Nature of Roots of Quadratic Equation
  • D > 0, roots are real and distinct (unequal).
  • D = 0, roots are real and equal (coincident) i.e. α = β = -b/2a.
  • D < 0, roots are imaginary and unequal i.e α = (p + iq) and β = (p – iq). Where ‘iq’ is the imaginary part of a complex number.
• **Sum of roots: S = α+β= -b/a = coefficient of x/coefficient of x2.
• **Product of roots: P = αβ = c/a = constant term/coefficient of x2.
• **Quadratic equation in the form of roots: x2 – (α+β)x + (αβ) = 0
• The quadratic equations a1x2 + b1x + c1 = 0 and a2x2 + b2x + c2 = 0 have;
  • One common root if (b1c2 – b2c1)/(c1a2 – c2a1) = (c1a2 – c2a1)/(a1b2 – a2b1)
  • Both roots common if a1/a2 = b1/b2 = c1/c2
• In quadratic equation ax2 + bx + c = 0 or [(x + b/2a)2 – D/4a2]
  • If a > 0, minimum value = 4ac – b2/4a at x = -b/2a.
  • If a < 0, maximum value 4ac – b2/4a at x= -b/2a.
• If α, β, γ are roots of cubic equation ax3 + bx2 + cx + d = 0, then, α + β + γ = -b/a, αβ + βγ + λα = c/a, and αβγ = -d/a

Chapter 5: Arithmetic Progressions

**Arithmetic progression is defined as the sequence of numbers where the difference between any two subsequent numbers is a constant. In this chapter, students will learn about the concepts of Arithmetic Progression and its Derivation of the nth term, the Sum of the first n terms of A.P, and their real-life application in solving everyday-life problems.

**CBSE Class 10 Chapter 5 Arithmetic Progressions - Major Formulas

• **n th term of AP: an = a + (n - 1) d, where an is the nth term.
• **Sum of n th terms of AP: Sn= n/2 [2a + (n - 1)d]

Chapter 6: Triangles

A **triangle is defined as a three-sided polygon consisting of three edges and three vertices. The most important and applied property of a triangle is its Angle sum property which means the sum of the internal angles of a triangle is equal to 180 degrees only.

This chapter from geometry is all about the definitions, examples, and examples of similar triangles. Moreover, the **criteria for triangle similarity and some related theorems are also covered in this chapter.

**CBSE Class 10 Chapter 6 Triangles - Major Concepts

• **Criteria for Triangle Similarity
  1. Angle angle angle (AAA Similarity)
  2. Side angle Side (SAS) Similarity
  3. Side-side side (SSS) Similarity
• **Basic Proportionality Theorem: According to this theorem, when a line is drawn parallel to one side of a triangle to intersect the other sides in distinct points, the other two sides are divided in the same ratio.
• **Converse of Basic Proportionality Theorem: According to this theorem, in a pair of triangles when the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.

Chapter 7: Coordinate Geometry

**Coordinate Geometry is defined as the link between geometry and algebra using graphs along with curves and lines. In this way, it provides geometric aspects in Algebra and leads to solving geometric problems. The topics covered in this chapter are the basics of Coordinate Geometry, and graphs of linear equations. Distance formula and Section formula only.

**CBSE Class 10 Chapter 7 Coordinate Geometry - Important Formulas

• **Distance Formula: For a line having two-point A(x1, y1) and B(x2, y2), then the distance of these points is given as: AB= √[(x 2 **− x 1 ) 2 **+ (y 2 **− y 1 ) 2 ]
• **Section Formula: For any point p divides a line AB with coordinates A(x1, y1) and B(x2, y2), in ratio m:n, then the coordinates of the point p are given as: P={[(mx 2 **+ nx 1 ) / (m + n)] , [(my 2 **+ ny 1 ) / (m + n)]}
• **Midpoint Formula: The coordinates of the mid-point of a line AB with coordinates A(x1, y1) and B(x2, y2), are given as: P = {(x 1 **+ x 2 )/ 2, (y 1 +y 2 ) / 2}
• **Area of a Triangle: Consider the triangle formed by the points A(x1, y1) and B(x2, y2) and C(x3, y3) then the area of a triangle is given as: **∆ABC = ½ |x 1 (y 2 **− y 3 ) + x 2 (y 3 **– y 1 ) + x 3 (y 1 **– y 2 )|

Chapter 8: Introduction to Trigonometry

**Trigonometry can be defined as calculations including triangles to study their lengths, heights, and angles. Trigonometry and its functions have an enormous number of uses in our daily life.

The most important topic covered in this chapter is the Trigonometric ratios of an acute angle of a right-angled triangle. Along with the Proof of their existence, Values of the trigonometric ratios of 30 degrees, 45 degrees and 60 degrees, and Relationships between the ratios.

**CBSE Class 10 Chapter 8 Introduction To Trigonometry - Major Formulas

• If in a circle of radius r, an arc of length l subtends an angle of θ radians, then l = r × θ.
  • Radian Measure = π/180 × Degree Measure
  • Degree Measure = 180/π × Radian Measure
• **Trigonometric ratios:
  • sin θ = (Perpendicular (P)) / (Hypotenuse (H)).
  • cos θ = (Base (B)) / ( Hypotenuse (H)).
  • tan θ = (Perpendicular (P)) / (Base (B)).
  • cosec θ = (Hypotenuse (H)) / (Perpendicular (P)).
  • sec θ = (Hypotenuse (H)) / (Base (B)).
  • cot θ = (Base (B)) / (Perpendicular (P))
• **Reciprocal Trigonometric Ratios****:**
  • sin θ = 1 / (cosec θ)
  • cosec θ = 1 / (sin θ)
  • cos θ = 1 / (sec θ)
  • sec θ = 1 / (cos θ)
  • tan θ = 1 / (cot θ)
  • cot θ = 1 / (tan θ)
• **Trigonometric Ratios of Complementary Angles:
  • sin (90**° – θ) = cos θ
  • cos (90**° – θ) = sin θ
  • tan (90**° – θ) = cot θ
  • cot (90**° – θ) = tan θ
  • sec (90**° – θ) = cosec θ
  • cosec (90**° – θ) = sec θ
• **Trigonometric Identities
  • **sin 2 θ + cos 2 θ = 1 ⇒ sin2 θ = 1 - cos2 θ ⇒ cos2 θ = 1 - sin2 θ
  • **cosec 2 θ - cot 2 θ = 1 ⇒ cosec2 θ = 1 + cot2 θ ⇒ cot2 θ = cosec2 θ - 1
  • **sec 2 θ - tan 2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ - 1

Chapter 9: Applications of Trigonometry

**Trigonometry has a lot of practical applications in real life. This part of geometry discusses the line of sight, angle of deviation, angle of elevation, and angle of depression. Using trigonometry and trigonometric ratios the height of a building, or a mountain, from a viewpoint and the elevation angle can be determined easily.

As we have learned the basics of trigonometry in the previous chapter, so now it's time to learn their practical applications. Hence, the topics studied in this chapter will help to understand learners' use of trigonometry. This chapter also helps with the practical concepts of trigonometry like the line of sight, angle of depression, and angle of elevation and to determine height or distance.

**CBSE Class 10 Chapter 9 Some Applications Of Trigonometry - Important Terms

• **Line of Sight - The Line of Sight is the line formed by our vision as it passes through an item when we look at it.
• **Horizontal Line - The distance between the observer and the object is measured by a horizontal line.
• **Angle of Elevation - The angle formed by the line of sight to the top of the item and the horizontal line is called an angle of elevation. It is above the horizontal line, i.e. when we gaze up at the item, we make an angle of elevation.
• **Angle of Depression - When the spectator must look down to perceive the item, an angle of depression is formed. When the horizontal line is above the angle, the angle of depression is formed between it and the line of sight.

Chapter 10: Circles

A **circle is a geometrical shape that is defined as the locus of points that move in a plane so that its distance from a fixed point is always constant. This fixed point is the Centre of the circle while the fixed distance from it is called the radius of the circle.

In this chapter Circles, students will learn about tangents and the different cases when lines touch or bisect circles on a given plane. Also, the concept of point of contact and important theorems related to the same are discussed in this chapter.

**CBSE Class 10 Chapter 10 Circles - Important Theorems

• **Theorem 10.1 **- The tangent at any point of a circle is perpendicular to the radius through the point of contact.
• **Theorem 10.2 **- The lengths of tangents drawn from an external point to a circle are equal.

Different cases for the number of Tangents from a Point on a Circle

1. There is no tangent to a circle passing through a point lying inside the circle.
2. There is one and only one tangent to a circle passing through a point lying on the circle.
3. There are exactly two tangents to a circle through a point lying outside the circle.

**Chapter 11: Constructions

Constructionhelps to understand the approach to constructing different types of triangles for different given conditions using a ruler and compass of required measurements.

Here in the Chapter Construction of Class 10 the major subtopics covered are constructing the line segment in a given ratio internally and drawing a tangent to a circle from a point outside the circle.

**Chapter 11 Constructions

• **Construction 11.1: Construction for the division of a line segment in a given ratio.
• **Construction 11.2: Construction of a triangle similar to a given triangle as per the given scale factor.
• **Construction 11.3: Construction of the tangents to a circle from a point outside it.

Chapter 12: Areas Related to Circles

The area related to circles is the amount of space covered by a circle, which is defined in different ways. Some areas related to a circle are, the area of the circle itself, the Area of the sector, the area of the segment, the area of the triangle or parallelogram, etc. located in a circle.

This chapter included subtopics like the area of a circle; the area of sectors and segments of a circle. Particularly the problems based on the areas and circumference of the circles and related plane figures are explained in depth.

**CBSE Class 10 Chapter 12 Areas Related To Circles - Important Formulas

**Below are some of the important formulas for Chapter 12 Areas related to circles.

• 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
• Distance moved by a wheel in one revolution = Circumference of the wheel.
• The number of revolutions = Total distance moved / Circumference of the wheel.

Chapter 13: Surface Areas and Volumes

**Surface area and volume are the measures calculated for a three-dimensional geometrical shape like a cube, cuboid, sphere, etc. The surface area of any given object is the area occupied by the surface of the object while volume is the amount of space available in an object.

**CBSE Class 10 Chapter 13 Surface Areas And Volumes - Important Formulas

**Total Surface Area (TSA):The whole area covered by the object's surface is called the Total Surface area. Following is the list of the total surface areas of some important geometrical figure.

• TSA of a Cuboid = 2(l x b) +2(b x h) +2(h x l)
• TSA of a Cube = 6a2
• TSA of a Right circular Cylinder = 2πr(h+r)
• TSA of a Right circular Cone = πr(l+r)
• TSA of a Sphere = 4πr2
• TSA of a Right Pyramid = LSA + Area of the base
• TSA of a Prism = LSA × 2B
• TSA of a Hemisphere = 3 × π × r2

**Lateral/Curved Surface Area****:** The curved surface area is the area of only the curved component, or in the case of cuboids or cubes, it is the area of only four sides, excluding the base and top. It's called the lateral surface area for forms like cylinders and cones.

• CSA of a Cuboid = 2h(l+b)
• CSA of a Cube = 4a2
• CSA of a Right circular Cylinder = 2πrh
• CSA of a Right circular Cone = πrl
• LSA of a Right Pyramid = ½ × p × l
• LSA of a Prism = p × h
• LSA of a Hemisphere = 2 × π × r2

**Volume****:** The volume of an object or material is the amount of space it takes up, measured in cubic units. There is no volume in a two-dimensional object, only area. A circle's volume cannot be calculated since it is a 2D figure, while a sphere's volume can be calculated because it is a 3D figure.

• Volume of a Cuboid = l x b x h
• Volume of a Cube = a3
• Volume of a Right circular Cylinder = πr2h
• Volume of a Right circular Cone = 1/3πr2h
• Volume of a Sphere = 4/3πr3
• Volume of a Right Pyramid = ⅓ × Area of the base × h
• Volume of a Prism = B × h
• Volume of a Hemisphere = ⅔ × (πr3)

Here, l is the length, b is the breadth, h is the height, r is the radius, a is the side, p is the perimeter of the base, B is the area of the base of the respective geometrical figure.

**Chapter 14: Statistics

**Statistics is the study of the representation, collection, interpretation, analysis, presentation, and organization of data. In other words, it is a mathematical way to collect and summarize data. The representation of data is different along with the frequency distribution.

This chapter covers subtopics like mean (average), median, and mode from a grouped information set. Another section in this chapter helps to learn the representation of data graphically and to understand trends and their correlations.

**CBSE Class 10 Chapter 14 Statistics - Important Formulas

• Different methods to calculate the **Mean of a grouped data,
  • **Direct method: X = ∑fi xi / ∑fi
  • **Assumed Mean Method: X = a + ∑fi di / ∑fi (where di = xi - a)
  • **Step Deviation Method: X = a + ∑fi ui / ∑fi × h
• **Mode of the grouped data = a + ∑fi ui / ∑fi × h
• **Median of the grouped data = l + (n/2 - cf) / f × h

Chapter 14 of CBSE Class 10 Math Notes covers the following topics

• Step Deviation Method for Finding the Mean with Examples
• Mean, Median, and Mode of grouped data
• Cumulative Frequency Curve

**Chapter 15: Probability

The **Probability in this class includes basic probability theory, which is also used in the probability distribution, to learn the possibility of outcomes for a random experiment and to find the probability of a single event to occur, when the total number of possible outcomes.

**CBSE Class 10 Math Chapter 15 Probability - Important Formulas

**Empirical Probability****:** The probability of events that depends on the experiments and it is defined as,

• **Empirical Probability = Number of Trials which expected outcome come / Total Number of Trials

**Theoretical Probability****:** The probability of events that depends on the experiments and it is defined as,

• **Theoretical Probability = Number of favorable outcomes to E / Total Number of possible outcomes of the experiment

**Important Resources for CBSE Class 10 Math

• **NCERT Solutions Math Class 10
• **RD Sharma Solutions Math Class 10
• **CBSE Class 10 Math Formulas
• **CBSE Physics Class 10 Notes
• **CBSE Class 10 Chemistry Notes
• **CBSE Class 10 Math (Basic) Term 1 Answer Key 2021
• **CBSE Class 10 Math (Standard) Term 1 Answer Key 2021
• **CBSE Class 10 Science Term 1 Answer Key 2021