Related Unit Name
- 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
- Quadratic Equations
- Zeros of a polynomial.
- Pair of linear equations in two variables and their graphical solution.
- Standard form of a quadratic equation ax2+bx+c=0, (a ? 0).
- Motivation for studying Arithmetic Progression
- Relationship between zeros and coefficients of quadratic polynomials?
- Statement and simple problems on division algorithm for polynomials with real coefficients?
- 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?
- Standard form of a quadratic equation ax2+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?
- Definitions, examples, counter examples of similar triangles.
- Tangents to a circle motivated by chords drawn from points coming closer and closer to the point.
- Division of a line segment in a given ratio (internally)
- Tangent to a circle from a point outside it?
- Construction of a triangle similar to a given triangle?
- Motivate the area of a circle;
- 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.
- area of sectors and segments of a circle.
- Problems based on areas mfand perimeter / circuerence of the above said plane figures.
- Problems involving converting one type of metallic solid into another and other mixed problems.