Here is the latest Syllabus for class 10 Mathematics. Entire course is divided into two parts . Term 1 and Term 2 we have given syllabus for the both terms. Sometimes these terms are also referred as semester 1 and semester 2 i.e. sa1 and sa2.
[h]Course Structur math class 10[/h]
I Term Units | Topics | Marks |
---|---|---|
I | Number System | 11 |
II | Algebra | 23 |
III | Geometry | 17 |
IV | Trigonometry | 22 |
V | Statistics | 17 |
Total | 90 | |
II Term Units | Topics | Marks |
II | Algebra | 23 |
III | Geometry | 17 |
IV | Trigonometry | 8 |
V | Probability | 8 |
VI | Co-ordinate Geometry | 11 |
VII | Mensuration | 23 |
Total | 90 |
[h]First Term sa1 Syllabus of Math[/h]
Unit I: Number Systems
1. Real Numbers
- Euclid’s division lemma
- Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples
- Proofs of results – irrationality of √2, √3, √5, decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals
Unit II: Algebra
1. Polynomials
- Zeros of a polynomial
- Relationship between zeros and coefficients of quadratic polynomials
- Statement and simple problems on division algorithm for polynomials with real coefficients
2. Pair of Linear Equations in Two Variables
- Pair of linear equations in two variables and their graphical solution
- Geometric representation of different possibilities of solutions/inconsistency
- Algebraic conditions for number of solutions
- Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method
- Simple situational problems must be included
- Simple problems on equations reducible to linear equations
Unit III: Geometry
1. Triangles
- Definitions, examples, counter examples of similar triangles
- (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
- (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side
- (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar
- (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar
- (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
- (Motivate) 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
- (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides
- (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides
- (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right triangle
Unit IV: Trigonometry
1. 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^{o} and 90^{o}
- Values (with proofs) of the trigonometric ratios of 30^{o}, 45^{o} and 60^{o}
- Relationships between the ratios
2. Trigonometric Identities
- Proof and applications of the identity sin2A + cos2A = 1
- Only simple identities to be given
- Trigonometric ratios of complementary angles
Unit V: Statistics and Probability
1. Statistics
- Mean, median and mode of grouped data (bimodal situation to be avoided)
- Cumulative frequency graph
[h]Cbse Class 10 Math Sa2 syllabus[/h]
Unit II: Algebra
3. Quadratic Equations
- Standard form of a quadratic equation ax^{2} + bx + c = 0, (a ≠ 0)
- Solution of the quadratic equations (only real roots) by factorization, by completing the square 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
4. Arithmetic Progressions
- Motivation for studying Arithmetic Progression Derivation of the 9^{th} term and sum of the first ‘n’ terms of A.P. and their application in solving daily life problems.
Unit III: Geometry
2. Circles
- Tangents to a circle motivated by chords drawn from points coming closer and closer to the point
- (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 circle are equal
3. Constructions
- Division of a line segment in a given ratio (internally)
- Tangent to a circle from a point outside it
- Construction of a triangle similar to a given triangle
Unit IV: Trigonometry
3. Heights and Distances
- Simple and believable problems on heights and distances
- Problems should not involve more than two right triangles
- Angles of elevation / depression should be only 30^{o}, 45^{o}, 60^{o}
Unit V: Statistics and Probability
2. Probability
- Classical definition of probability
- Simple problems on single events (not using set notation)
Unit VI: Coordinate Geometry
1. Lines (In two-dimensions)
- Concepts of coordinate geometry, graphs of linear equations
- Distance formula
- Section formula (internal division)
- Area of a triangle
Unit VII: Mensuration
1. Areas Related to Circles
- 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 area of segment of a circle, problems should be restricted to central angle of 60^{o}, 90^{o} and 120^{o} only
- Plane figures involving triangles, simple quadrilaterals and circle should be taken
2. Surface Areas and Volumes
- Problems on finding surface areas and volumes of combinations of any two of the following −
- Cubes
- Cuboids
- Spheres
- Hemispheres
- Right circular cylinders/cones
- Frustum of a cone
- Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken.)