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.
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°

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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.