Class 10 Mathematics Syllabus 2015-16 CBSE
CBSE Class 10 Mathematics Syllabus of 2015-16 SA1-SA2
This includes both Term 1 and Term 2 mathematics syllabus for Class 10.
Syllabus Information:
- The Question Paper includes value based question to the extent of 3-5 marks.
- As per CCE guidelines, the syllabus of Mathematics for classes IX and X has been divided term wise.
- The units specified for each term will be assessed through both formative and Summative Assessment.
- In each term, there will be two formative assessments, each carrying 10% weightage.
- The Summative Assessment in term I will carry 30% weightage and the Summative Assessment in the term II will carry 30% weightage.
Course Structure
First Term
First Term Units (SA-I) | Marks | |
I. | Number System | 11 |
II. | Algebra | 23 |
III. | Geometry | 17 |
IV. | Trigonometry | 22 |
VI. | Statistics | 17 |
Total | 90 |
Unit I: Number System
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
Zeroes of Polynomial. Relationship between zeroes and coefficients of a polynomial with particular reference to 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 may be included.
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° and 90°. Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.
2. Introduction to Trigonometry
Proof and applications of the identity sin^{2}A + cos^{2}A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.
Unit VI: Statistics
Mean, median and mode of grouped data (bi-modal situation to be avoided). Cumulative frequency graph.
Course Structure
Second Term
Second Term Units (SA-II) | Marks | |
II. | Algebra (contd.) | 23 |
III. | Geometry (contd.) | 17 |
IV. | Mensuration | 23 |
V. | Trigonometry (contd.) | 08 |
VI. | Co-ordinate Geometry | 11 |
VII. | Probability | 08 |
Total | 90 |
Unit II: Algebra (Contd.)
1. 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.
Problems related to day to day activities to be incorporated.
2. Arithmetic Progressions
Motivation for studying Arithmetic Progression Derivation of standard results of finding the nth term and sum of first n terms.
Unit III: Geometry (Contd.)
1. 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.
2. 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: Mensurration
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°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)
2. Surface Areas and Volumes
(i) Problems on finding 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.
(ii) 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.)
Unit V: Trigonometry
1. Height 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°, 45°, 60°.
Unit VI: Probability
Classical definition of probability. Connection with probability as given in Class IX. Simple problems on single events, not using set notation.
You can also download our offline CBSE syllabus of Class 10 Mathematics, see here:
PDF – Click here to download the syllabus