I Term Units | Topics | Marks |
---|---|---|
I | Number System | 11 |
II | Algebra | 23 |
III | Geometry | 17 |
IV | Trigonometry | 22 |
V | Statistics | 17 |
Total | 90 | |
II Term Units | Topics | Marks |
II | Algebra | 23 |
III | Geometry | 17 |
IV | Trigonometry | 8 |
V | Probability | 8 |
VI | Co-ordinate Geometry | 11 |
VII | Mensuration | 23 |
Total | 90 |
1. Real Numbers
Euclid's division lemma
Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples
Proofs of results - irrationality of √2, √3, √5, decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals
1. Polynomials
Zeros of a polynomial
Relationship between zeros and coefficients of 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 equations in two variables and their graphical solution
Geometric representation of different possibilities of solutions/inconsistency
Algebraic conditions for number of solutions
Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination and by cross multiplication method
Simple situational problems must be included
Simple problems on equations reducible to linear equations
1. Triangles
Definitions, examples, counter examples of similar triangles
(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
(Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side
(Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar
(Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar
(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
(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
(Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides
(Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides
(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 triangle
1. Introduction to Trigonometry
Trigonometric ratios of an acute angle of a right-angled triangle
Proof of their existence (well defined); motivate the ratios, whichever are defined at 0^{o} and 90^{o}
Values (with proofs) of the trigonometric ratios of 30^{o}, 45^{o} and 60^{o}
Relationships between the ratios
2. Trigonometric Identities
Proof and applications of the identity sin2A + cos2A = 1
Only simple identities to be given
Trigonometric ratios of complementary angles
1. Statistics
3. Quadratic Equations
Standard form of a quadratic equation ax^{2} + bx + c = 0, (a ≠ 0)
Solution of the quadratic equations (only real roots) by factorization, by completing the square and by using quadratic formula
Relationship between discriminant and nature of roots
Situational problems based on quadratic equations related to day to day activities to be incorporated
4. Arithmetic Progressions
Motivation for studying Arithmetic Progression Derivation of the 9^{th} term and sum of the first ‘n’ terms of A.P. and their application in solving daily life problems.
2. Circles
Tangents to a circle motivated by chords drawn from points coming closer and closer to the point
(Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact
(Prove) The lengths of tangents drawn from an external point to circle are equal
3. Constructions
3. Heights and Distances
2. Probability
1. Lines (In two-dimensions)
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^{o}, 90^{o} and 120^{o} only
Plane figures involving triangles, simple quadrilaterals and circle should be taken
2. Surface Areas and Volumes
Problems on finding surface areas and volumes of combinations of any two of the following −
Cubes
Cuboids
Spheres
Hemispheres
Right circular cylinders/cones
Frustum of a cone
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.)
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