# CBSE 10th Class Mathematics Syllabus

## Course Structure

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

## First Term Course Syllabus

### 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 0o and 90o

• Values (with proofs) of the trigonometric ratios of 30o, 45o and 60o

• 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

## Second Term Course Syllabus

### Unit II: Algebra

• Standard form of a quadratic equation ax2 + 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 9th term and sum of the first ānā 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 30o, 45o, 60o

### 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 60o, 90o and 120o 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.)