OFFICIAL SYLLABUS
Mathematics (theory)
UNIT I : NUMBER SYSTEMS
1. Real Number
Euclids division lemma ,Fundamental theorm of Arithmetic -statement after reviewing work done earlier and after illustrating and motivating through examples, Proofs of results, decimal expansions of rational numbers in terms of terminating/nonterminating recurring decimals.
UNIT II : ALGEBRA
1. POLYNOMIALS
Zeros of a polynomial ,relationship between zeros and cofficient of a polynomial with particular reference to 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 equation in two variable ,Geometric representation of different possibilities of solutions/inconsistency. Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically- by substitution, by elimination and by cross multiplication. Simple situational problems must be included. Simple problems on equations reducible to linear equations may be included.
3. QUDRATIC EQUATION
Standered form of solution of the the quadratic equations(only real roots) by factorization and by completing the square, i.e. by using quadratic formula. Relationship between discriminant and nature of roots. Problems related to day to day activities to be incorporated.
4. ARITHMATIC PROGREETION
Motivation for studying AP derivation of standerd result of finding the nth term of sum first in terms.
UNIT III : TRIGONOMETRY
Trignometric ratio of an actuates angle of a right angle tringle .proof there exsistance (well defined); motivate the ratios, whichever are defined at 0o & 90o Values (with proofs) of thetrigonometric ratios of 30o, 45o & 60o. Relationships between the ratios.
2.TEIGNOMETRIC IDENTITIES
Proof the application of the identity sin2 A+cos2A=1.only simple identity to be given .Trigonometric ratios of complementary angles.
3. HEIGHTS AND DISTANCES
Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30o, 45o & 60o.
UNIT IV : COORDINATE GEOMETRY
LINES (In two-dimensions)
Review the concepts of coordinate geometry done earlier including graphs of linear equationsAwareness of geometrical representation of quadratic polynomials. Distance between two
points and section formula(internal). Area of a triangle.
UNIT V : 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 to 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, their 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.
6. (Motivate) 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.
7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
9. (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 traingle.
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
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.
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 areaand perimeter / circumference of the above said plane figures. (In calculating area of segmentof a circle, problems should be restricted to central angle of 60o, 90o & 120o only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)
2. SURFACE AREAS AND VOLUMES
(i) Problems on finding surface areas and volumes of combinations of any two of thefollowing: 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.)
UNIT VII : STATISTICS AND PROBABILITY
1. STATISTICS
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.
2. PROBABILITY
Classical defination of probability ,connection with probability as given in class 10 .simple problems on single event ,not usin set notation
INTERNAL ASSESMENT
Evalution of activities
project wo
...
OFFICIAL SYLLABUS
Mathematics (theory)
UNIT I : NUMBER SYSTEMS
1. Real Number
Euclids division lemma ,Fundamental theorm of Arithmetic -statement after reviewing work done earlier and after illustrating and motivating through examples, Proofs of results, decimal expansions of rational numbers in terms of terminating/nonterminating recurring decimals.
UNIT II : ALGEBRA
1. POLYNOMIALS
Zeros of a polynomial ,relationship between zeros and cofficient of a polynomial with particular reference to 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 equation in two variable ,Geometric representation of different possibilities of solutions/inconsistency. Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically- by substitution, by elimination and by cross multiplication. Simple situational problems must be included. Simple problems on equations reducible to linear equations may be included.
3. QUDRATIC EQUATION
Standered form of solution of the the quadratic equations(only real roots) by factorization and by completing the square, i.e. by using quadratic formula. Relationship between discriminant and nature of roots. Problems related to day to day activities to be incorporated.
4. ARITHMATIC PROGREETION
Motivation for studying AP derivation of standerd result of finding the nth term of sum first in terms.
UNIT III : TRIGONOMETRY
Trignometric ratio of an actuates angle of a right angle tringle .proof there exsistance (well defined); motivate the ratios, whichever are defined at 0o & 90o Values (with proofs) of thetrigonometric ratios of 30o, 45o & 60o. Relationships between the ratios.
2.TEIGNOMETRIC IDENTITIES
Proof the application of the identity sin2 A+cos2A=1.only simple identity to be given .Trigonometric ratios of complementary angles.
3. HEIGHTS AND DISTANCES
Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30o, 45o & 60o.
UNIT IV : COORDINATE GEOMETRY
LINES (In two-dimensions)
Review the concepts of coordinate geometry done earlier including graphs of linear equationsAwareness of geometrical representation of quadratic polynomials. Distance between two
points and section formula(internal). Area of a triangle.
UNIT V : 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 to 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, their 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.
6. (Motivate) 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.
7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
9. (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 traingle.
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
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.
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 areaand perimeter / circumference of the above said plane figures. (In calculating area of segmentof a circle, problems should be restricted to central angle of 60o, 90o & 120o only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)
2. SURFACE AREAS AND VOLUMES
(i) Problems on finding surface areas and volumes of combinations of any two of thefollowing: 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.)
UNIT VII : STATISTICS AND PROBABILITY
1. STATISTICS
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.
2. PROBABILITY
Classical defination of probability ,connection with probability as given in class 10 .simple problems on single event ,not usin set notation
INTERNAL ASSESMENT
Evalution of activities
project work
Countinuous Evalution
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