TS Class 10 Maths Syllabus with Videos & PDFs
In this post, Digital Teacher explains the SSC Class 10 Maths textbook in Telangana, from âReal Numbers,â to Chapter 14 of âStatisticsâ. It discusses the definition, properties, and conditions of real numbers such as integers, decimals, and fractions. It also underlines their classification and importance, allowing for arithmetic operations and representation on the number line.
Students looking for Telangana 10th-class courses may get the whole Telangana (TS) SSC lessons here. The Telangana TS 10th Class Syllabus is accessible for all courses. The Class 10 TS maths syllabus is divided into 1 to 14 units.Telangana State Board Syllabus -Digital Teacher
Telangana (TS) Board Class 10 Syllabus for Maths
The following are the Telangana State TS Maths Class 10 lessons. Since we have covered every significant topic for the exam, students can check here. The table below lists the chapter names for the Class 10 Mathematics course, which includes Real Numbers, Sets, Polynomials, and more.Unit 1Â Real NumbersUnit 2 SetsUnit 3 PolynomialsUnit 4 Pair of Linear Equations in Two VariablesUnit 5 Quadratic EquationsUnit 6 ProgressionsUnit 7 Coordinate GeometryUnit 8 Similar TrianglesUnit 9 Tangents and Secants to a CircleUnit 10 MensurationUnit 11 TrigonometryUnit 12 Applications of TrigonometryUnit 13 ProbabilityUnit 14 Statistics
In the sections below, we will try to explain each class 10th Mathematics unit in detail so that you can understand what you need to study on the syllabus. Now, read it!
Class 10 Maths TS Units in Detailed:
Real Numbers:Â This unit covers the fundamental properties of real numbers, including the Euclidean algorithm, rational and irrational numbers, and decimal expansions.
Definition:Â (Real numbers) encompass both rational and irrational numbers within the number system. They can be both positive or negative and are represented by the symbol âRâ. All natural numbers, decimals, and fractions fall under this category.
Irrational Constants: â2
Here is a Detailed Explanation: (Real Numbers Example)
Real numbers encompass both rational and irrational numbers within the number system. Rational numbers can be expressed as fractions of integers, while irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions. Real numbers allow for various arithmetic operations and can be represented on the number line. In contrast, imaginary numbers, which are also used in mathematics, cannot be plotted on the number line and are denoted by multiples of the imaginary unit âiâ. Examples such as 17 (integer), -8 (integer), 3.14 (decimal number), 1/3 (fractional number), and â2 (irrational constant) illustrate the diversity of real numbers, ranging from whole numbers to fractions and transcendental constants like â2 and Ď. This comprehensive understanding of real numbers is essential in various mathematical contexts, from basic arithmetic to advanced calculus.
Full Video Lesson in The Below (Real Numbers)
TS class 10 Maths Unit 2 & 3: (Sets & Polynomials)
Mathematics Unit-2: (Sets) or (Set of Real Numbers) Real numbers are classified into several categories, including natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
Natural numbers are infinitely long counting numbers, whereas whole numbers encompass both zero and the whole natural number set. Integers are the sum of whole integers and their negatives, including values such as -â, -4, -3, -2, -1, 0, 1, 2, 3, 4, and up to +â. Rational numbers may be stated as p/q, such as 1/2, 5/4, and 12/6, however, irrational numbers cannot be written as fractions and have non-repeating and non-terminating decimal expansions, such as â2.
In Telangana Ts Class 10 Unit 3, weâll explore polynomials. Think of them as math expressions made up of different parts like letters (which we call variables), numbers (which we call coefficients), and powers. We can add, subtract, and multiply them, but we canât divide them by variables.
Imagine this: ???? 2 + ???? â 12 x 2 +xâ12. Here, we have three parts: ???? 2 x 2, ???? x, and â 12 â12.
A polynomial is like a bunch of terms (like ???? 2 x 2 , ???? x, and â 12 â12) all added, subtracted, or multiplied together. We use these terms to build expressions that represent different situations in math.
Constants are just regular numbers, like 1, 2, 3, and so on.
Variables are letters that stand for numbers we donât know yet, like ???? g, â h, ???? x, ???? y, and so on.
Exponents are little numbers that tell us how many times to use the variable, like 5 in ???? 5 x 5.
Letâs break down a simple example into a table:Term TypeExampleDescriptionConstant1Regular numberVariablexLetter representing an unknown valueExponent5The little number indicates repetition
Pair of Linear Equations in Two Variables (Unit-4)
Substitution, elimination, and graphical representation are methods used in the solution of linear equations. In Unit 4, the emphasis is on solving equation pairs involving straight lines by utilizing graphing, substitution, and elimination techniques to determine where the lines cross.
Equation: An equation is a statement that two mathematical expressions having one or more variables are equal.
Linear Equation: Unit 4 focuses (Linear Equation) on solving pairs of equations with each equation being a straight line, utilizing techniques such as substitution, elimination, and graphing to determine where these lines intersect, ensuring that the degree of a linear equation is always one.
Letâs Explore the Fundamentals of Maths:
Equation: Itâs like a balancing scale, indicating that two items are equal. For instance, the equation 2 ???? + 3 = 7 2x+3=7 states that 2 ???? + 3 2x+3 equals 7 7.
Linear equations have a maximum power of 1 for the variable (e.g., ???? x or ???? y). They produce straight lines when graphed. The equation 3 ???? + 2 ???? = 5 is linear since the powers of ???? x and ???? y are both 1.
Comprehending these fundamentals will aid us in resolving issues when determining the intersection of two lines is required.
Unit-5: Quadratic Equations
In Class 10, âQuadratic Equations,â Chapter 4, is an important component of algebra. It gives an overview of quadratic equations and demonstrates several methods for solving them, including factoring, using formulas, and completing the square. Acquiring these techniques is essential as they serve as the foundation for more complex math problems in the near future!
In This Chapter, Students Will Study These Topics:
Quadratic equations are special equations in which the variableâs maximum power is two.
A quadratic polynomial is a unique equation, such as ???? ???? 2 + ???? ???? + ???? ax 2 +bx+c, where ???? a, ???? b, and ???? c are real values and ???? an is not zero.
Understanding these ideas will enable you to answer issues expertly and score your tests!
6th Unit â Progressions (or) Arithmetic Progression (AP)
This lesson focuses on Arithmetic Progressions (AP), a series of consistent terms that includes both arithmetic and geometric progressions, as well as determining the nth term and the sum of the first n terms.
Here are a few basic concepts:
Sequences are lists of numbers that follow a certain pattern. For example, 1, 2, 3, 4, 5⌠is a natural number sequence
Series: It is the sum of all the numbers in a series. The natural number sequence is represented by 1+2+3+4+5âŚ
Progressions are sequences in which we may put out a rule or formula for determining any term.
Now, letâs explore Arithmetic Progression:
What is Arithmetic Progression-AP?
It is a sequence in which each term after the first is determined by adding a set integer to the preceding term. For example, 2, 5, 8, 11, 14, and so on, with each addition of three.
Common Difference: This is the number that we keep adding to go from one word to the next. If itâs positive, the AP is rising; if itâs zero, the AP is stable; and if itâs negative, the AP is dropping.
For example, in the sequence 2, 5, 8, 11, 14,âŚ, the common difference is 3 since we are adding three each time.
Understanding (Arithmetic Progression) APs enable students to solve many real-world situations and prepare students for higher-level math topics.
Please let me know if you need any more clarity on any aspect of this topic! Now letâs look into 7th Unit Coordinate Geometry.
Unit-7 Coordinate Geometry
Chapter 7 of Class 10 Mathematics: Coordinate Geometry, a branch that discusses the position of points on a plane, including the Cartesian plane, distance formula, section formula, and triangle area.
Comprehending Coordinates:Â A pair of integers, represented as (x, y), may be used to identify any point on a plane. In this case, âxâ stands for the distance from the y-axis (also known as the abscissa) and âyâ for the distance from the x-axis (also known as the ordinate).
Distance Formula:Â Weâll understand how to use this helpful formula to determine the distance between two sites. We may calculate the length of a line segment between any two locations on a coordinate plane using this formula.
Area Calculation:Â If we know the coordinates of a triangleâs vertices, we can also use the distance formula to get the triangleâs area.
For example: Coordinate Geometry
Letâs think about the point R(4, 3). In this instance, â4â denotes the objectâs separation from the y-axis, and â3â is the objectâs separation from the x-axis. Knowing Coordinate Geometry helps us see and understand mathematical topics by allowing us to accurately describe and evaluate objects and figures on a graph!
Please do comment! if you want any further explanation or examples!
Similar Triangles (Unit 8th)
Students in Class 10 Mathâs eighth unit study the idea of Similar triangles, which is an important test topic. The lesson explores the requirements for triangle similarity along with its theorems.
Similar triangles, such as âABC and âPQR, have the same form but may differ in size. For this to be true:
(i) Angles A, B, and C must be equal (A = P, B = Q, and C = R).
(ii) Their corresponding sides are proportional, suggesting that the length ratios of the corresponding sides stay constant.
Example with Answer: (Similar Triangles)
Q) For example, Consider two triangles, âDEF and âGHI, where âDEF ~ âGHI. If DE = 4 cm, EF = 6 cm, and GH = 8 cm, what is the length of side HI?
Ans)Â To find the length of side HI in triangle âGHI, given that triangle âDEF is similar to triangle âGHI, we can use the properties of similar triangles.
Since triangles âDEF and âGHI are similar, their corresponding sides are proportional.
We can set up the proportions:Â GH/DEâ=HI/EFâ
Substituting the given values: 4 /8 = 6 /HI
Now, letâs solve for HI:
8/4 = HI/6
â4ĂHI=6Ă84ĂHI=48&HI= 48/4
HI=12Â cm
So, the length of side HI is 12 cm.
Unit-9 Tangents and Secants to a Circle
In Chapter 9 of Class 10 Math, we look at Tangents and Secants, focusing on their properties and practical applications. Let us put it in simpler terms:
Understand Tangents and Secants:
Tangent:Â Imagine a line that only touches a circle at one place. That is what we call a tangent.
Secant:Â Draw a line that cuts through the circle and intersects it at two different points. That is a secant.
When a tangent touches a circle, it only touches it at one place, known as the point of contact.
The tangent is always perpendicular to the radius of the circle at the point of contact.
If you draw tangents from an external point to a circle, they will be the same length.
We may also determine the area of a circle segment using an angle and radius formula.
Q)Â Consider a circle with a radius 5 cm. A tangent is drawn to the circle from a point outside the circle, and it intersects the circle at point P. If the distance from the point to the centre of the circle is 8 cm, what is the length of the tangent segment, i.e., the length of line segment PT?
Ans)Â To find the length of the tangent segment PT, we can use the property that the length of the tangent segment from an external point to a circle is equal to the radius of the circle drawn perpendicular to the tangent line.
Given that the distance from the point to the center of the circle is 8 cm and the radius of the circle is 5 cm, we can use the Pythagorean theorem to find the length of the tangent segment PT.
Letâs denote the length of PT as ???? x. According to the Pythagorean theorem:
uare)
x2=132â5(square)
x2=169â25
x2=144
Taking the square root of both sides:
x= 144â
x=12
10th Class Maths: Mensuration (Unit-10)
In Ts Class 10 Mathematics, we look at mensuration, which is the process of determining the areas and volumes of geometric forms including triangles, quadrilaterals, circles, and solids, as well as their properties such as area, length, volume, and surface area.
Defining Mensuration: Mensuration is a field of geometry concerned with quantifying the area, volume, and size of different forms and figures in both two and three dimensions (3D and 2D).
Shapes in Two(2D) and (3D) Three Dimensions:
Two categories of forms are encountered in the field of mensuration:
2D forms are flat shapes like squares, circles, triangles, and rectangles that only have length and breadth.
3D Three-dimensional forms have three dimensions: length, breadth, and height. Cones, spheres, cylinders, and cubes are a few examples.
We examine a variety of formulae for calculating the characteristics of 2D and 3D shapes. These formulae assist us in determining areas, volumes, surface areas, and other characteristics required for problem-solving with geometric forms.
Mensuration formulae may be used to compute the volume and surface area of a rectangular box with dimensions of 10 cm long, 5 cm wide, and 3 cm high.
Understanding mensuration gives us the tools we need to tackle real-world measuring and geometry issues, making it an important aspect of 10th-class mathematics.
If you want more information or examples, please continue reading! the following table!ShapeParameterFormulaSquareAreaArea = side2RectangleAreaArea = length Ă widthPerimeterPerimeter = 2 Ă (length + width)TriangleAreaArea = 0.5 Ă base Ă heightPerimeterPerimeter = side1Â + side2Â + side3CircleAreaArea = Ď Ă radius2CircumferenceCircumference = 2 Ă Ď Ă radius
Moving on to our next topic, letâs look into the interesting area of trigonometry.
Unit-11 Trigonometry (TS Class 10 Maths Syllabus)
Introduction to Trigonometry:
The study of triangles and their relationships is known as trigonometry, and it is covered in this section. It concentrates on triangles with one 90-degree angle, or right-angled triangles. Trigonometric functions, such as sine, cosine, and tangent, may be determined by analyzing side ratios. These functions are important in a variety of domains, including physics, engineering, astronomy, and navigation.
Trigonometric Ratios:Â These ratios define the relationship between the angles and sides of a right triangle. The main trigonometric ratios are:
Sine (sin): Opposite/Hypotenuse
Cosine (cos): Adjacent/Hypotenuse
Tangent (tan): Opposite/Adjacent
Pythagorean Identity: This fundamental identity relates the lengths of the sides of a right triangle: (sin2θ+cos2θ=1)
Throughout this unit, weâll explore a range of trigonometric formulas and identities, including:
Area of a Triangle Using Trigonometry
Angle of Elevation and Depression
