CBSE Syllabus for Class 10 Maths
Course Structure for Maths Class X (2017-18)
| Units | Unit Name | Marks |
| I | Number Systems | 06 |
| II | Algebra | 20 |
| III | Co-ordinate Geometry | 06 |
| IV | Geometry | 15 |
| V | Trigonometry | 12 |
| VI | Mensuration | 10 |
| VII | Statistics & Probability | 11 |
| Total | 80 |
CBSE Syllabus for Class 10 Maths Pdf
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 .
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 n
th
term
and
sum of the first n terms of A.P.
and their application in solving daily life problems.
Unit III: 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 IV: 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.
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 V: 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.
Trigonometric Identities
Proof and applications of the identity sin
2
A + cos
2
A = 1. Only simple identities to be given.
Trigonometric ratios of complementary angles
.
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°, 45°, 60°.
Unit VI: 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°, 90° and 120° 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 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 combination of not more than two different solids be taken.)
Unit VII: Statistics and Probability
1. Statistics
Mean
,
median
and
mode of grouped data
(bimodal situation to be avoided).
Cumulative frequency graph
.
2. Probability
Classical definition of probability. Simple problems on single events
(not using set notation).
Internal Assessment [20 Marks]
- Periodical Test [10 Marks]
- Note Book Submission [05 Marks]
- Lab Practical (lab activities to be done from the prescribed books) [05 Marks]
Prescribed Books
- Mathematics – Textbook for class X – NCERT Publication
- Guidelines for Mathematics laboratory in Schools, class X – CBSE Publication
- Laboratory Manual – Mathematics, secondary stage – NCERT Publication
- Mathematics exemplar problems for class X, NCERT publication.
