Class 10 Mathematics : Master the Logic…

Complete step-by-step Understanding

Unit 1: Number Systems

REAL NUMBERS

1. Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples.
2. Proofs of irrationality of √2, √3, √5.

Unit-II: Algebra

POLYNOMIALS

1. Zeros of a polynomial
2. Relationship between zeros and coefficients of quadratic polynomials.

PAIR OF LINEAR EQUATIONS IN
TWO VARIABLES

1. Pair of linear equations in two variables and graphical method of their solution,
consistency/inconsistency.
2. Algebraic conditions for number of solutions.
3. Solution of a pair of linear equations in two variables algebraically by substitution, by elimination. Simple situational problems.

QUADRATIC EQUATIONS

1. Standard form of a quadratic equation $𝑎𝑥^{2}+𝑏𝑥+𝑐=0, (𝑎 \ne 0)$.
2. Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots.
3. Situational problems based on quadratic equations related to day-to-day activities to be incorporated.

ARITHMETIC PROGRESSIONS

1. Motivation for studying Arithmetic Progression
2. Derivation of the nth term and sum of the first n terms of AP and their application in
solving daily life problems.

UNIT III: COORDINATE GEOMETRY

Coordinate Geometry

1. Review: Concepts of coordinate geometry. Distance formula. Section formula (internal division).

UNIT IV: GEOMETRY

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. State (without proof) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
3. State (without proof) If in two triangles, the corresponding angles are equal, their
corresponding sides are proportional and the triangles are similar.
4. State (without proof) If the corresponding sides of two triangles are proportional,
their corresponding angles are equal and the two triangles are similar. State (without proof) 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.

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.

UNIT V: TRIGONOMETRY

INTRODUCTION TO TRIGONOMETRY

1. Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their
existence (well defined)
2. Motivate the ratios whichever are defined at 0° and 90°. Values of the trigonometric ratios of 30°, 45° and 60°.
3. Relationships between the ratios.
TRIGONOMETRIC IDENTITIES
1. Proof and applications of the identity $sin^2{A}+cos^2{A}=1$.
2. Only simple identities to be given.

Some Applications of Trigonometry

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°, and 60°.

UNIT VI: MENSURATION

AREAS RELATED TO CIRCLES

1. Area of sectors and segments of a circle.
2. 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.

SURFACE AREAS AND VOLUMES

Surface areas and volumes of combinations of any two of the following: cubes, cuboids,
spheres, hemispheres and right circular cylinders/cones.

UNIT VII: STATISTICS AND PROBABILITY

STATISTICS

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

Probability

1. Classical definition of probability.
2. Simple problems on finding the probability of an event.

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