10th CBSE history Demo

UNIT I: NUMBER SYSTEMS 
1. REAL NUMBER

• Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of  Decimal representation of rational numbers interms 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 theirsolution, consistency/inconsistency.
• Algebraic conditions for number of solutions. Solution of a pair of linear equations in twovariables algebraically - by substitution, by elimination. Simple situational problems.Simple problems on equations reducible to linear equations

3. QUADRATIC EQUATIONS

• Standard form of a quadratic equation ax2 + 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: COORDINATE GEOMETRY
1. LINES (In two-dimensions) 

• Review: Concepts of coordinate 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 twosides 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 parallelto the third side.
• 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, theircorresponding 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 thesides including these angles are proportional, the two triangles are similar.
• 6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a righttriangle to the hypotenuse, the triangles on each side of the perpendicular are similar 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 thesquares 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 circle 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 theirexistence (well defined). Values of the trigonometric ratios of 300, 450 and 600.Relationships between the ratios.

2. TRIGONOMETRIC IDENTITIES (10) Periods

• Proof and applications of the identity sin2A + cos2A = 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 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°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 methodfor finding the mean to be avoided).

2. PROBABILITY 

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