**Exam adhyayan 10th science **

**Exam adhyayan 10th math **[MATHEMATICS : CLASS 10]

**UNIT I: NUMBER SYSTEMS**

1. REAL NUMBERS

Fundamental Theorem of Arithmetic statements after reviewing work done earlier and

after illustrating and motivating through examples, Proofs of irrationality of V2, V3.5.

Decimal representation 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.

2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Pair of linear equations in two variables and graphical method of their solution,

consistency/inconsistency.

Algebraic conditions for number of solutions. Solution of a pair of linear equations in

two variables algebraically-by substitution, by elimination. Simple situational problem.

Simple problems on equations reducible to linear equations.

3. QUADRATIC EQUATIONS

Standard form of a quadratic equation a2+bx+c = 0, (a + 0). Solutions of quadratic

equations (only real roots) by factorization, and by using quadratic formula. Relationship

between discriminant and nature of roots.

4. ARITHMETIC PROGRESSIONS

Motivation for studying Arithmetic Progression. Derivation of the nth term and sum of

the first n terms of A. P.

**UNIT III : CO-ORDINATE GEOMETRY**

1. LINES (IN TWO-DIMENSIONS)

Review: Concepts of co-ordinate geometry, graphs of linear equations. Distance formula.

Section formula (Internal division).

**UNIT IV : GEOMETRY**

1. TRIANGLES

Definitions, examples, counter examples of similar triangles,

1. (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.

2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel

3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding

sides are proportional and the triangles are similar.

4. (Motivate) If the corresponding sides of two triangles are proportional, theie

corresponding angles are equal and the two triangles are similar.

5. (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. 1. ST

6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right M

triangle to the hypotenuse, the triangle on each side of the perpendicular are similar ta

to the whole triangle and to each other.

7. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the

squares on the other two sides.

2. CIRCLES

Tangent to a circle at, point of contact

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 a circle are equal

3. CONSTRUCTIONS

1. Division of a line segment in a given ratio (Internally).

2. Tangents to a cirice from a point outside it.

**UNIT V : TRIGONOMETRY**

1. INTRODUCTION TO TRIGONOMETRY

Trigonometric ratios of an acute angle of a right-angled triangle Proof of their existence

(well defined); 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 sinA+ cos2 A = 1. Only simple identities to be

given.

3. HEIGHTS AND DISTANCES : Angle of elevation, Angle of Depression

Simple 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

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% and

90° only. Plane figures involving triangles, simple quadrilaterals and circle should be

taken.

2. SURFACE AREAS AND VOLUMES

1. Surface areas and volumes of combinations of any two of the following : Cubes,

cuboids, spheres, hemispheres and right circular cylinders/cones.

2. 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 and step deviation method

for finding the mean to be avoided).

2. PROBABILITY

Classical definition of probability. Simple problems on finding the probability of an

event.

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