Sanguine Multimedia Studies

U.No.

Units

Marks

1.

Number systems

10

2.

Algebra

08

3.

Polynomials and Quadratic Equations

17

4.

Geometry

29

5.

Co-ordinate Geometry

08

6.

Trigonometry

15

7.

Mensuration

08

8.

Probability

05

I:

 Number systems                         

 10

Real Numbers

 05

Euclids division lemma, Fundamental Theorem of Arithmetic, Statements after reviewing work done earlier and after illustrating through examples. Proofs of results- irrationality of √2 , √3 √5 decimal expansion of rational numbers in terms of terminating/non terminating recurring decimals.

Arithmetic Progression

 05

Motivation for studying Arithmetic progression. Derivation of standard results of finding the nth term and sum of first n terms.

II:

Algebra

 08

Pair of linear equations in two variables

 08

Pair of Linear Equation in two variables, 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 may be included. Simple problems on equations reducible to linear equation may be included

III:

Polynomials and Quadratic equation    

 17

Polynomials -

 05

Zeroes of a Polynomial, Relationship between zeroes and coefficients of polynomial with particular reference to quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.

Quadratic Equations

 12

Standard form of Quadratic equation ax²+bx+C=0, (a≠0), solution of quadratic equation (only real roots) by factorization and by completing the square, i.e. by using quadratic formulas, Relationship between discriminant and nature of roots.

Problems related to day to day activities to be incorporated

1V:

Geometry

 29

Triangles

 12

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 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 to the hypotenuse, the triangle 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 ratios 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 two sides, the angles opposite to the first side is a right triangle.

Circles

 09

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 length of tangents drawn from an external point to a circle are equal.

Constructions

 08

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

V:

Co-ordinate Geometry

 08

Lines (in two dimensions)

Review the concepts of co-ordinate geometry done earlier including graphs of linear equations. Awareness of geometrical representation of quadratic equations polynomials. Distance between two points and section formula (internal). Area of a triangle.

VI:

Trigonometry

 15

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° and 90°. Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°, Relationship between the ratios.

Trigonometric identities, Proofs and applications of the identity Sin²A+Cos²A=1, Only simple identities to be given. Trigonometric ratios of complementary angles.

Heights and Distances

Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angle of elevation/depression should be only 30°, 45°, 60°.

VII:

Mensuration

 08

Surface Areas and volumes

1. Problems on finding surface areas and volumes of combinations of any two of the following cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.

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.

VIII

Probability

 05

History, Repeated experiments and observed frequency approach to probability. Focus is on empirical probability.

Classical definition of probability. Simple problems on single event, not using set rotation