| Class 10 Maths Marks Distribution |
| Units | Marks |
| Number Systems | 06 |
| Algebra | 20 |
| Coordinate Geometry | 06 |
| Geometry | 15 |
| Trigonometry | 12 |
| Mensuration | 10 |
| Statistics & Probability | 11 |
| Internal Assessment | 20 |
| Total | 100 |
CBSE Class 10 Maths Syllabus
- Real Numbers
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Arithmetic Progressions
- Triangles
- Coordinate Geometry
- Statistics
- Probability
- Introduction to Trigonometry
- Some Applications of Trigonometry
- Circles
- Constructions
- Area Related to Circles
- Surface Areas and Volumes
UNIT I: NUMBER SYSTEMS
1. REAL NUMBER
Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality.
UNIT II: ALGEBRA
- POLYNOMIALS Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.
- PAIR OF LINEAR EQUATIONS IN TWO VARIABLES Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination. Simple situational problems.
- QUADRATIC EQUATIONS Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.
- ARITHMETIC PROGRESSIONS 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.
UNIT III: COORDINATE GEOMETRY
Coordinate Geometry Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).
UNIT IV: GEOMETRY
- TRIANGLES Definitions, examples, counter examples of similar triangles.
1. (Prove) 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.
2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
3.(Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
4.(Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
5.(Motivate) 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. - CIRCLES Tangent to a circle at, point of contact
1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2.(Prove) The lengths of tangents drawn from an external point to a circle are equal.
UNIT V: TRIGONOMETRY
- INTRODUCTION TO TRIGONOMETRY Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0° and 90°. Values of the trigonometric ratios of 30°, 45°, and 60°. Relationships between the ratios.
- TRIGONOMETRIC IDENTITIES Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given.
- HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression. (10)Periods Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, and 60°.
UNIT VI: MENSURATION
- AREAS RELATED TO CIRCLES Area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only.
- SURFACE AREAS AND VOLUMES Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.
UNIT VII: STATISTICS AND PROBABILITY
- STATISTICS Mean, median and mode of grouped data (bimodal situation to be avoided).
- PROBABILITY (10) Periods Classical definition of probability. Simple problems on finding the probability of an event.
PRESCRIBED BOOKS:
- Mathematics - Textbook for class IX - NCERT Publication
- Mathematics - Textbook for class X - NCERT Publication
- Guidelines for Mathematics Laboratory in Schools, class IX - CBSE Publication
- Guidelines for Mathematics Laboratory in Schools, class X - CBSE Publication
- Laboratory Manual - Mathematics, secondary stage - NCERT Publication
- Mathematics exemplar problems for class IX, NCERT publication.
- Mathematics exemplar problems for class X, NCERT publication.
Structure of CBSE Maths Sample Paper for Class 10 is
| Type of Question | Marks per Question | Total No. of Questions | Total Marks |
| Objective Type Questions | 1 | 20 | 20 |
| Short Answer Type Questions - I | 2 | 6 | 12 |
| Short Answer Type Questions - II | 3 | 8 | 24 |
| Long Answer Type Questions | 4 | 6 | 24 |
| Total | 40 | 80 |
For Preparation of board exams students can also check out other resource material
CBSE Class 10 Maths Test Papers
Important Questions for Class 10 Maths Chapter Wise
Maths Revision Notes for class 10
Previous Year Question Paper CBSE Class 10 Maths
What are CBSE Sample Papers?
Sample papers are mainly a kind of mock tests or model test papers which are prepared in accordance with the latest syllabus and guidelines that are issued by the central board. These examination test papers are designed as the replica of the actual papers that are asked in final examinations. All the marking schemes , number of questions , types of questions asked are followed as per board scheme and are issued to students two or three months before the examinations so that students get enough time to practice.
What is the importance of Sample Papers for Students?
In order to access the level of preparation done by any particular student he or she needs to solve CBSE Sample Papers. These papers are the perfect way to practise for the final board exam. If one wants to have a clear idea of how the final exam papers would be in terms of level of difficulty, time and other aspects then , all students must make sure that they do sample papers once their course revision is finished.
Few benefits of solving CBSE sample papers are given below:
- Gauging Self Performance: Understanding and revising the subject is very good, but unless one attempts the sample paper in the lookalike environment as in board exam, seldom can the student identify and check whether the understanding of all concepts of the subject are complete or not. Once students try the question paper in the same time frame he or she is able to judge the capability of solving the paper in the stipulated time frame. It highlights the weak areas if any and gives students ample amount of time to work on those areas and be better prepared before exams.
- Testing Time Criticality: Knowing is not everything as far as board papers are concerned. Sometimes it happens that in spite of knowing everything a student falls short of time to complete the entire paper and thus loses marks. Generally CBSE sample papers are generally of 3 hour duration. So while practicing sample papers it is imperative to create a board like environment at home and ensure that sample paper is attempted only in 3 hours and then check whether it was possible to complete the paper in the desired amount of time. Often at first students take longer than expected, and thus they get early warning to practice more and increase the speed.
- Exam Anxiety: Sometimes sensitive students feel anxious to sit in the examination hall with a 3 hour length paper and for them it becomes a more intense requirement to practice prior to main exams and get rid of any kind of fear. Since they do not know what questions will be asked in the CBSE board they create panic in their mind due to this fear of the unknown and get scared with the idea that they might not be able to do well in exams. Thus such students needs to complete at-least 7-10 sample papers prior to the exams, to gain confidence and get into better frame of mind.
Best Time to Practice Sample Papers
This mainly varies from student to student but in general students should start dealing with sample papers as soon as their book revisions are over. Infact along with sample papers students should also look for model test papers of various publishers and attempt them to get the idea of level of preparation. As the dates of exam are approaching near by that time only samples papers should be mainly considered for practice and in case of any shortcomings those should be thoroughly discussed with teachers freids and other concerned person so that one has clarity before attempting the final paper.