# Class 10 Syllabus

### Course Structure

Maths Syllabus for class 10

### Three Hours Max. Marks -90

First Term (SA-I)

 Units Marks I. Number System 11 II. Algebra 23 III. Geometry 17 IV. Trigonometry 22 V. Statistics 17 Total 90

Second Term (SA-II)

 Units Marks II. Algebra (contd.) 23 III. Geometry (contd.) 17 IV. Trigonometry (contd.) 8 V. Probability 8 VI. Co-ordinate Geometry 11 VII. Mensuration 23 Total 90

### First Term Units

#### 1. REAL NUMBERS

• Euclid’s division lemma, Fundamental Theorem of Arithmetic.
• Proofs of results – irrationality of âˆš2, âˆš3, âˆš5, decimal expansions of rational numbers in terms of terminating and non-terminating recurring decimals.

#### 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.
• Problems on equations reducible to linear equations.

#### 1. 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.
• If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
• If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
• If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
• 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.
• 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.

#### 1 . INTRODUCTION TO TRIGONOMETRY

• Trigonometric ratios of an acute angle of a right-angled triangle.
• Proof of their existence; motivate the ratios, whichever are defined at 0Â° and 90Â°.
• Values (with proofs) of the trigonometric ratios of 30Â°, 45Â° and 60Â°. Relationships between the ratios.

#### 2. TRIGONOMETRIC IDENTITIES

Proof and applications of the identity sin2A + cos2A = 1.
Trigonometric ratios of complementary angles.

#### 1. STATISTICS

Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

### Second Term Syllabus

#### UNIT II: ALGEBRA (Contd.)

• Standard form of a quadratic equation ax2+bx+c=0, (a â‰  0).
• Solution of quadratic equations 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 nth term and sum of the first n terms of A.P.

#### 2. CIRCLES

Tangents to a circle motivated by chords drawn from points coming closer and closer to the point.

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 circle are equal.

#### 3. CONSTRUCTIONS

Prove

1. Division of a line segment in a given ratio (internally).
2. Tangent to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.

#### 3. HEIGHTS AND DISTANCES

1. Simple problems on heights and distances.
2. Angles of elevation / depression should be only 30Â°, 45Â°, 60Â°.

#### 2. PROBABILITY

Classical definition of probability. Simple problems on single events.

#### 1. AREAS RELATED TO CIRCLES

• The area of a circle; area of sectors and area of segments of a circle.
• Problems based on areas and perimeter / circumference of the above said plane figures.
• Plane figures involving triangles, simple quadrilaterals and circle.

#### 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.)

#### Practise This Question

A function f such that f(a)=f′′(a)=......f2n(a)=0 and f has a local maximum value b at x = a, if f (x) is