1. Number Systems |
(i) 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.
|
2. Algebra |
(i) Polynomials |
|
| Zeros of a polynomial. Relationship between zeros
and coefficients of a polynomial with particular reference to
quadratic polynomials. Statement and simple problems on division
algorithm for polynomials with real coefficients. |
(ii) Pair Of Linear Equations In Two Variables |
|
| Pair of linear equations in two variables.
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. |
(iii) Quadratic Equations |
|
| Standard form of a quadratic equation ax2
+ bx + c = 0, (a1 0). Solution of 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 today to day activities to be
incorporated. |
(iV) Arithmetic Progressions |
|
| Motivation for studying AP. Derivation of
standard results of finding the nth term and sum of first n
terms.
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3. Trigonometriy |
(i) Introduction To Trigonometriy |
|
| Trigonometric ratios of an acute angle of a
right-angled triangle. Proof of their existence (well defined);
motivate the ratios, whichever are defined at 0o & 90o.
Values (with proofs) of the trigonometric ratios of 30o, 45o
& 60o. Relationships between the ratios. |
(ii)Trigonometric Identities |
|
| Proof and applications of the identity sin2
A + cos2 A = 1. Only simple identities to be given.
Trigonometric ratios of complementary angles. |
(iii)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.
|
4. Coordinate Geometry |
(i)Lines (In two-dimensions) |
|
| Review the concepts of coordinate geometry done
earlier including graphs of linear equations. Awareness of geometrical
representation of quadratic polynomials. Distance between two points
and section formula (internal). Area of a triangle.
|
5. Geometry |
(i) 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. |
(ii)Circles |
|
| Tangents to a circle motivated by chords drawn
from points coming closer and 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. |
(iii)Constructions (Periods - 8) |
|
| 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.
|
6. Mensuration |
(i) 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
60o, 90o & 120o only. Plane figures
involving triangles, simple quadrilaterals and circle should be
taken.) |
(ii)Surface Areas And Volumes |
|
| (i) Problem on finding surface areas and volumes
of combinations of any two of the following: cubes, cuboids, spheres,
hemispheres and right circular cylinder/cones. Frustum of a cone. |
| (ii) Problems involving converting one type of
metallic solid into another and other mixed problem.(Problems with
combination of not more than two different solids be taken.)
|
7. Statistics And Probability |
(i) Statistics |
|
| Mean, median and mode of grouped data(bimodal
situation to be avoided). Cumulative frequency graph. |
(ii)Probability |
|
| Classical definition of probability. Connection
with probability as given in class IX. Simple problem on single
events, not using set notation. |
