Class 10 Maths

The broader objective of class 10 maths is to help the students consolidate the knowledge of mathematical skills and concepts gained at the upper primary stage. It emphasizes visualizing basic concepts, principles, theorems and symbols to master basic algebraic skills. The key topics included in class 10 maths are coordinate geometry, angles, polynomials, linear equations and more.

Class 10 Maths Syllabus

Class 10 maths syllabus is thoroughly prepared to help young learners acquire basic mathematical concepts with ease. It comprises topics related to linear equations, algebra, coordinate geometry and more. Here is the complete syllabus of class 10 maths along with the hierarchy of subtopics.

Number Systems

• Real Numbers
  • Fundamental Theorem of Arithmetic which states "every composite number can be expressed as the product of primes in a unique way"
  • Writing rational numbers as terminating/non-terminating recurring decimals

Algebra

• Polynomials
  • Degree of linear, quadratic, and cubic polynomials
  • Zeroes of a polynomial
  • Relationship between zeroes and coefficients of quadratic and cubic polynomials
  • Division algorithm which states "for two polynomials p(x) and g(x) where g(x) ≠ 0, there exist two polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x), where degree of r(x) is less than that of g(x)"
• Pair of Linear Equations in Two Variables
  • Pair of linear equations in two variables, finding their solution by graphical method, consistency/inconsistency
  • Formula for number of solutions (one solution, no solution, infinitely many solutions)
  • Solution of a pair of linear equations in two variables by substitution and by elimination methods
  • Word problems on pair of linear equations in two variables
• Quadratic Equations
  • The standard form of a quadratic equation ax² + bx + c = 0, (a ≠ 0).
  • Solutions (real roots only) of quadratic equations by factorization, and by using the quadratic formula.
  • Using discriminant to find the nature of roots.
  • Applications of quadratic equations
• Arithmetic Progressions
  • Definition and examples of arithmetic progressions(AP)
  • nth term and sum of arithmetic progressions
  • Applications of AP

Coordinate Geometry

• Straight Lines on Coordinate Plane
  • Graphs of lines
  • Distance formula
  • Section formula (only internal division)

Geometry

• Triangles
  • Similar triangles
• Circles
  • Tangent to a circle
  • The tangent of a circle is perpendicular to the radius through the point of contact (along with proof)
  • The lengths of tangents drawn from an external point to a circle are equal (along with proof)
• Constructions
  • The internal division of a line segment in a given ratio
  • Tangents to a circle from a point outside it

Trigonometry

• Introduction to Trigonometry
  • Trigonometric ratios of an acute angle of a right-angled triangle.
  • Values of the trigonometric ratios of 30°, 45° and 60°.
  • Relationships between the ratios.
• Trigonometric Identities
  • Basic identity sin²x + cos²x = 1 along with its proof and applications
  • Other simple identities
• Heights and Distances (Applications of Trigonometry)
  • The angle of elevation, angle of depression
  • Simple problems on heights and distances involving the angles 30°, 45°, 60° that involve maximum two right triangles

Mensuration

• Areas Related to Circles
  • areas of a circle, sectors and segments
  • Applications on these areas that involve the central angles 60° and 90°, triangles, simple quadrilaterals, etc.
• Surface Areas and Volumes
  • SA and volumes of combinations of the following shapes: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.
  • Applications of these shapes

Statistics and Probability

• Probability
  • Definition of probability
  • Probability of an event
• Statistics
  • Mean, median and mode of grouped data
  • Finding mean by direct method and assumed mean method

Develop Class 10 Maths Skills

Class 10 maths is outlined to impart the knowledge of analytical and practical skills in students. It develops a basic understanding of applying maths, for instance, using trigonometric functions to calculate the height or applying algebraic formulas to solve real-life problems. Students can acquire an understanding of these 10th maths concepts through various interactive activities and visualization. Here are some key class 10 maths skills that students need to develop.

Trigonometric Functions: Trigonometry functions and their applications are important topics covered under class 10 maths that students should understand and apply in solving various problems.

Algebra: Algebra is an important part of class 10 maths that enables students to write, read and apply expressions, rational numbers and polynomials. It also helps students to utilize these skills and knowledge to solve practical problems.

Geometry: It is important for students to understand the geometric transformation covered in mathematics class 10 which involves angles, circles, perpendicular lines, parallel lines, and line segments.

10th Maths Tips and Tricks

Class 10 maths is very important for the students for their future grades and courses. With small tips and tricks the students can make 10th maths easy and they can score very good grades in mathematics class 10.

• Practice Daily: 10th maths is crucial for developing higher-level maths skills thus students must practice daily and track their progress sincerely to improvise their skills.
• Practice Past Years Question Papers: Practicing question papers from past years will help students to get an idea of the complexity level of the exam. It will also benefit students by enhancing their speed and accuracy
• Cover Full Syllabus: Covering full syllabus of class 10 maths is a must for students to clarify all their doubts before exams.
• Refer to Reliable Study material: Refer to reliable study material like textbooks for the preparation of mathematics class 10. These are the best preparation resources as the class 10 maths exam is set according to them.

Class 10 Maths Formulas

Memorizing all formulas of maths class 10 is really very important for the students to score better during board exams. Though the student is able to solve the problem but doesn't remember the formula, all the hard work will go in vain. Especially, students need to pay more attention in remembering trigonometry formulas for class 10 as they are new to trigonometry. Here are some important class 10 maths formulas.

• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a – b)³ = a³ - b³ - 3ab(a – b)
• n^th term of AP, a_n = a + (n - 1) d
• Sum of AP, S_n= n/2 [2a + (n - 1)d]
• Volume of sphere = 4/3 ×π r³
• Total surface area of a sphere = 4πr²
• Volume of right circular cylinder = πr²h
• Total surface area of right circular cylinder = 2πr (r + h)
• Volume of prism = Base area × height
• Lateral surface area of prism (LSA) = perimeter of the base × height

Here are some important trigonometry formulas for class 10.

• sin² θ + cos² θ = 1
• cosec² θ - cot² θ = 1
• sec² θ - tan² θ = 1
• sin θ cosec θ = 1
• cos θ sec θ = 1
• tan θ cot θ = 1
• 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

For the complete list of formulas of class 10 maths, click here.

Class 10 Maths Worksheets

10th maths worksheets are curated by our experts such that they cover all concepts end to end. Further, they cover all types of questions including all difficulty levels. With these worksheets, students can access extra problems to practice mathematics class 10. Moreover, they can identify the areas of their weakness by working on these worksheets and comparing their answers with the answers given in them. This would help them to go back and correct themselves which is very helpful to achieve better grades in maths class 10. Just click here to get the links to the worksheets.