UNIT I : NUMBER SYSTEMS
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 decimal expansions of rational
numbers in terms of terminating/non-terminating recurring decimals.
UNIT II : ALGEBRA
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.
2. 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
3. QUADRATIC EQUATIONS
Standard form of a quadratic equation ax2 + bx
+ c = 0, (a ≠ 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 to day to day activities to be incorporated.
4. ARITHMETIC PROGRESSIONS
Motivation for studying AP. Derivation of standard results of finding the
nth term and sum of first n terms.
UNIT III : TRIGONOMETRY
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° & 90°. Values (with proofs) of the trigonometric ratios of 30°, 45° & 60°.
Relationships between the ratios.
2. TRIGONOMETRIC IDENTITIES
Proof and applications of the identity sin2 A + cos2 A =
1. Only simple identities to be given. Trigonometric ratios of complementary
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 30°, 45°, 60°.
UNIT IV : COORDINATE GEOMETRY
1. 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.
UNIT V : GEOMETRY
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
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
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
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 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°, 90° & 120° 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 the following: 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
Mean, median and mode of grouped data (bimodal situation to be avoided).
Cumulative frequency graph.
Classical definition of probability. Connection with probability as given
in Class IX. Simple problems on single events, not using set notation.