### Class 10 Maths Notes by Toppers for FREE – Download PDF

Here you will get **Maths** Notes for **Class 10 Maths Handwritten Notes **by Toppers. These notes cover every chapter in a detailed way with examples and their Solutions.

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CBSE Class 10 board exam is one of the first milestones in students’ life. This phase of life shapes the future of the students for their next successive years. CBSE board 10th class result acts as the foremost parameter in deciding whether the students will be able to get a preferred stream in 11th Class. Class 10th standard acts as an indicator of a student’s academic performance. Students can refer to the NCERT Solutions to understand the various concepts under the subject.

**Maths Handwritten Notes** is based on the new(reduced) syllabus by **CBSE**.

**Download Class 10 Maths **Handwritten **Notes Chapter-wise**

- Chapter 1 Real Numbers
- Chapter 2 Polynomials
- Chapter 3 Pair of Linear Equations in Two Variables
- Chapter 4 Quadratic Equations
- Chapter 5 Arithmetic Progressions
- Chapter 6 Triangles
- Chapter 7 Coordinate Geometry
- Chapter 8 Introduction to Trigonometry
- Chapter 9 Some Applications of Trigonometry
- Chapter 10 Circles
- Chapter 11 Constructions
- Chapter 12 Areas Related to Circles
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability

Particularly when it comes to the subject of Mathematics, students desire to have an answer key to help them in evaluating their learning and development. Refer to these solutions when practising and solving the Mathematics exercises from NCERT Textbooks.

### Important Tips To Use NCERT Solutions For Class 10

With all the important learning opportunities presented by the NCERT Solutions for Class 10 for all the subjects, we recommend that students follow the below-given simple tips and tricks to effectively use the NCERT Solutions to their advantage.

- NCERT Solutions for Class 10 are self-explanatory in nature. Therefore, if you have confusion in understanding a particular concept, solve an exercise/activity based on it and refer to the explanatory notes in the Solutions to clear the confusion.
- NCERT Solutions for Class 10 for Mathematics consist of explanations and justifications behind the choice of a particular method for solving a problem. These complete explanations can help you learn and develop your own strategies to solve mathematics numerals.
- Refer to the NCERT Solutions for Class 10 as a source of peer-reviewed answer cheat sheets and get all the correct answers. Use this for self-evaluation of the achievement of learning goals.
- Refer to these solutions as short notes for revision before the exam. Instead of studying line by line for each chapter, simply refer to the solutions and sufficient explanations can be found for every important topic.

**Chapter 1 Real Numbers **

**Topics **: Euclid’s division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of **√**2, **√**3, **√**5 Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals

**Chapter 2 Polynomials **

**Topics **: Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithms for polynomials with real coefficients.

**Chapter 3 Pair of Linear Equations in Two Variables**

**Topics :** Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for the number of solutions. The solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method. Simple situational problems. Simple problems on equations reducible to linear equations.

**Chapter 4 Quadratic Equations**

**Topics **:Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization; and by using the quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.

**Chapter 5 Arithmetic Progressions**

**Topics **:Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

**Chapter 6 Triangles**

**Topics **:Definitions, examples, counter-examples of similar triangles.

- If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
- If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
- If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
- If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
- If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
- If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and 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 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 on one side is equal to the sum of the squares on the other two sides, the angle opposite to the first side is a right angle.

**Chapter 7 Coordinate Geometry**

**Topics **:Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.

**Chapter 8 Introduction to Trigonometry**

**Topics **:Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0o and 90o. Values of the trigonometric ratios of 300, 450 and 600. Relationships between the ratios. Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

**Chapter 9 Some Applications of Trigonometry**

**Topics **:Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30°, 45°, 60°.

**Chapter 10 Circles**

**Topics **:Tangent to a circle at, point of contact.

- (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
- (Prove) The lengths of tangents drawn from an external point to a circle are equal

**Chapter 11 Constructions-**

**Topics **:Division of a line segment in a given ratio (internally).

- Tangents to a circle from a point outside it.
- Construction of a triangle similar to a given triangle.

**Chapter 12 Areas Related to Circles**

**Topics **:Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter/circumference of the above-said plane figures. (In calculating the area of a segment of a circle, problems should be restricted to the central angle of 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circles should be taken.)

**Chapter 13 Surface Areas and Volumes**

**Topics : **

- Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.
- Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combinations of not more than two different solids are taken).

**Chapter 14 Statistics**

**Topics **:Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

**Chapter 15 Probability**

**Topics **:The classical definition of probability. Simple problems on finding the probability of an event.

Source of Notes: Garima’s Magical Talks