CBSE Class 10 Maths Revision Notes is undoubtedly one of the most important formal education levels. The class and complexity of studies instill in them a sense of seriousness and responsibility. Students tend to mature and stabilize. The most notable characteristic of class 10 Board examinations is that they are the first nationalized external exam for students. Class 10 Maths is one of the toughest subjects to tackle so GeeksforGeeks compiled CBSE Class 10 Maths Notes.
Our CBSE Class 10 Maths NCERT Notes are based on the latest syllabus for Class 10 Boards to help to understand all the concepts of Class 10 Maths chapter-wise. Class 10 Maths NCERT notes comprise all the formulae, theorems, concepts, proofs descriptions, definitions, and graphs, that a student needs to practice and score good marks in their board examinations.
These subject-specific revision notes cover some more important topics like Introduction to Trigonometric Ratios of a Triangle , Heights and Distances , Surface Areas and Volume, etc. Our experts have also covered Class 10 Maths Solutions like NCERT Solutions for Class 10 Maths , and RD Sharma Class 10 Solutions .
If you’re looking for CBSE Class 10 Term 1 Maths Answer Key 2021 Basic Paper to solve maths problems, you can click here .
CBSE Class 10 Maths Notes Chapters List (2023)
Deleted Chapters/Topics from NCERT Class 10th Maths Textbook (2023-2024): The most recent CBSE Class 10th Mathematics syllabus has been changed and reduced by 30% for the upcoming annual assessment in the academic year 2023-2024, you can find the list of all deleted chapters in the table below:
Chapter/Topics Deleted from NCERT Class 10 Maths Textbook 2023-24
Chapter Name
Deleted Topics
Real Number
Euclid’s division lemma, Decimal representation of rational numbers as terminating or non-terminating recurring decimals.
Polynomials
Statements and simple 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
Complete Chapter Deletion
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
Chapter 1: Real Numbers
Any number, barring complex numbers, is a real number. Real numbers include 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.
CBSE Class 10 Maths Notes Chapter 1 – Real Numbers
Revisiting Irrational Numbers
Solved Examples of Real Numbers
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Important Points Explained In Cbse Class 10 Chapter 1- Real Numbers Are:
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 HCF and LCM by prime factorization method:
HCF = Product of the smallest power of each common factor in the numbersLCM = Product of the greatest power of each prime factor involved in the numberHCF (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.
CBSE Class 10 Maths Notes Chapter 2 – Polynomials
Graphical Representations
Geometrical Representation of a Linear Polynomial
Geometrical Representation of a Quadratic Polynomial
Graph of the polynomial of degree n
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Some Important Formulas Of Polynomials Learned In CBSE Class 10 Maths Note Chapter 2 Polynomials:
The general Polynomial Formula is, F (x) = an xn + bxn-1 + an-2 xn-2 + …….. + rx + s
When n is a natural number: an – bn = (a – b)(an-1 + an-2 b +…+ bn-2 a + bn-1 )
When n is even (n = 2a): xn + yn = (x + y)(xn-1 – xn-2 y +…+ yn-2 x – yn-1 )
When n is odd number: xn + yn = (x + y)(xn-1 – xn-2 y +…- yn-2 x + 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. pair of linear equations in two variables
In this chapter notes, the introduction to the pair of linear equations in one variable and the graphical method of their solution , consistency/inconsistency, and algebraic conditions for the number of solutions are covered. Solutions of a pair of linear equations in two variables algebraically – by substitution and by elimination, simple situational problems , and simple problems on equations reducible to linear equations are also explained in this chapter.
CBSE Class 10 Maths Notes – Chapter 3 Pair of Linear Equations in Two Variables
Consistent and Inconsistent System
Equations Reducible to a Pair of Linear Equations in 2 Variables
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Important Points Explained Here In Cbse Class 10 Chapter 3- Pair Of Linear Equations In Two Variables Are:
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 Maths Notes covers the following topics:
Chapter 4: Quadratic Equations
In chapter 4 of Maths NCERT Notes, we’ll cover the Quadratic Equations 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 .
CBSE Class 10 Maths Notes – Chapter 4 Quadratic Equations
Solution of Quadratic Equation
Graphical Representation of a Quadratic Equation
Formation of Quadratic Form its Roots
Sum and Product of Roots of a Quadratic Equation
Solved Exercise Questions
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Important Formulas And Their Conclusions Discussed In Cbse Class 10 Chapter 4- Quadratic Equations Are:
(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) = 0The quadratic equations a1 x2 + b1 x + c1 = 0 and a2 x2 + b2 x + c2 = 0 have;
One common root if (b1 c2 – b2 c1 )/(c1 a2 – c2 a1 ) = (c1 a2 – c2 a1 )/(a1 b2 – a2 b1 )
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
The Arithmetic progression is explained 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 Maths Notes Chapter 5 – Arithmetic Progressions
Basic Adding Patterns of an AP
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Major Formulas Covered In Cbse Class 10 Chapter 5- Arithmetic Progressions Are:
nth term of AP: an = a + (n – 1) d, where an is the nth term.Sum of nth terms of AP: Sn = n/2 [2a + (n – 1)d]
Chapter 6: Triangles
Geometrically, a triangle 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 learned in this chapter.
CBSE Class 10 Maths Notes Chapter 6 – Triangles
Similarity For Polygons having the same number of sides
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Major Topics Explained In Cbse Class 10 Chapter 6- Triangles Are:
Criteria for Triangle Similarity
Angle angle angle (AAA Similarity)
Side angle Side (SAS) Similarity
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 Maths Notes Chapter 7 – Coordinate Geometry
Solved Example of Coordinate Geometry
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Important Formulas Covered In Cbse Class 10 Chapter 7- Coordinate Geometry Are:
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= √[(x2 − x1 )2 + (y2 − y1 )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={[(mx2 + nx1 ) / (m + n)] , [(my2 + ny1 ) / (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 = {(x1 + x2 )/ 2, (y1 +y2 ) / 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 |x1 (y2 − y3 ) + x2 (y3 – y1 ) + x3 (y1 – y2 )|
Chapter 8: Introduction to Trigonometry
Trigonometry 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 Maths Notes Chapter 8 – Introduction to Trigonometry
Trigonometric Ratios
Opposite & Adjacent Sides in a Right-Angled Triangle
Relation Between Trigonometric Rations
Standard values of Trigonometric ratios
Range of Trigonometric Ratios from 0 to 90 degrees
Trigonometric Ratios of Complementary Angles
Complementary Trigonometric Ratio
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Some Major Formulas That Are Learned In Cbse Class 10 Chapter 8- Introduction To Trigonometry Are:
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
sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos2 θ ⇒ cos2 θ = 1 – sin2 θcosec2 θ – cot2 θ = 1 ⇒ cosec2 θ = 1 + cot2 θ ⇒ cot2 θ = cosec2 θ – 1sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
Chapter 9: Some Applications of Trigonometry
Trigonometry 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 Maths Notes Chapter 9 – Some Application of Trigonometry
Introduction
Horizontal Level and Line of Sight
Angle of elevation
Angle of depression
Solved Examples of the Application of Trigonometry
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Important Terms That Are Explained In Cbse Class 10 Chapter 9- Some Applications Of Trigonometry Are:
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 Maths Notes – Chapter 10 Circles
Introduction to Circles
Circle and line in a plane
Tangent Secant
Tangent as a special case of Secant
Two parallel tangents at most for a given diameter
Length of a tangent
Lengths of the tangent drawn from an external point
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Important Theorems Covered In Cbse Class 10 Chapter 10- Circles Are:
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:
There is no tangent to a circle passing through a point lying inside the circle.
There is one and only one tangent to a circle passing through a point lying on the circle.
There are exactly two tangents to a circle through a point lying outside the circle.
Chapter 11: Constructions
Construction helps 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 .
CBSE Class 10 Maths Notes – Chapter 11 Constructions
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Important Constructions Explained In Cbse Class 10 Chapter 11- Constructions Are:
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 Maths Notes – Chapter 12 Areas Related to Circles
Introduction to Areas Related to Circles
Areas of Different plane figures Areas of Combination of Plane Figures
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Important Formulas Covered In Cbse Class 10 Chapter 12- Areas Related To Circles Are:
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 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.
This chapter covers some most important topics of mensuration like the Surface Areas and Volumes of the combination of any 3-D figures (cube , cuboid , sphere , hemispheres, and right circular cylinders , cones ). Along with the practical problems related to the conversion of one type of metallic 3-D solid to another. And various similar everyday life problems related to the surface areas and volumes of 3-D figures .
CBSE Class 10 Maths Notes – Chapter 13 Surface Areas and Volumes
Surface Area and Volume of Cuboid
Surface Area and Volume of Cube
Surface Area and Volume of Cylinder
Surface Area and Volume of Right Circular Cone
Surface Area and Volume of Sphere
Surface Area and Volume of Hemisphere
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Important Formulas Covered In Cbse Class 10 Chapter 13- Surface Areas And Volumes Are:
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 figures-
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 = πr2 h
Volume of a Right circular Cone = 1/3πr2 h
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 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 Maths Notes – Chapter 14 Statistics
Introduction to Statistics
Ungrouped Data
Grouped Data
Frequency
Class Interval
Median
Median for Ungrouped Data
Median of Grouped Data
When class Intervals are not given
When class Intervals are given
Cumulative Frequency
Less than type of Cumulative Frequency distribution
More than type of Cumulative Frequency distribution
Visualizing of Median Graphically Cumulative Frequency Curve – Ogive
Less than type
More than type
Relation between the less than and more than type curve
Mode
Mode for Ungrouped Data
Mode for Grouped Data
When class intervals are not given
When class intervals are given
Visualizing Mode Graphically
Measures of Central Tendency for Grouped Data
Empirical Relationship between Mean, Median, and Mode
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Important Formulas Learned In Cbse Class 10 Chapter 14- Statistics:
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 × hMedian of the grouped data = l + (n/2 – cf) / f × h
Chapter 14 of CBSE Class 10 Maths Notes covers the following topics:
Chapter 15: Probability
The Probability 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 Maths Notes – Chapter 15 Probability
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Important Formulas Covered In CBSE Class 10 Math Chapter 15- Probability Are:
Empirical Probability = Number of Trials which expected outcome come / Total Number of Trials
Theoretical Probability = Number of favourable outcomes to E / Total Number of possible outcomes of the experiment
Important Resources for CBSE Class 10 Maths Notes by GeeksforGeeks:- FAQs on CBSE Class 10 Maths Notes
Question 1: How CBSE Class 10 Maths Notes are helpful for students? Answer:
Students have the ability to construct solid and dependable conceptions by referring to these Class 10 Maths Notes. When attempting a problem, there’s a good chance a pupil won’t be able to finish it because of doubts. Also the NCERT solutions for class 10 maths
Question 2: How to score full marks in Class 10th Maths? Answer:
Following are the useful tips to score good marks in Class 10th Maths:
Understand the syllabus, paper pattern & marking scheme.
First try to solve and understand the concepts explained in NCERT exercises and exemplar questions, before referring to any other textbook.
Learn how to answer problems step-by-step to score better.
Don’t forget to practise the case-study based questions.
Try to solve both Standard and Basic Sample Papers
In order to learn all the formula used in Class 10th board exams, write down them all in one page.
Question 3: List down some important formulae for Maths Class 10 boards.
Answer:
Class 10 math covers a number of key ideas that are necessary for understanding higher-level mathematics. Math formulae are necessary to solve problems quickly and accurately. The first step is to understand how a formula came to be and the concept that governs it. Then you can memorise them and use the formulas to answer questions. The following are some of the key formulas mentioned in NCERT Notes for class 10 math.
(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
an = a + (n – 1) d
S2 = n/2 [2a + (n – 1)d]
sin2 θ + cos2 θ = 1
cosec2 θ – cot2 θ = 1
sec2 θ – tan2 θ = 1
Volume of Sphere = 4/3 ×π r3
Surface Area of Sphere = 4πr2
Total surface area of cuboid = 2(l×b + b×h + l×h)
