Topics to be studied under each chapter for the academic year
||Name of the unit
Pair of linear equations in two variables;
||Introduction to Trigonometry;
Heights and distances.
||Areas related to circles;
Surface areas and volumes.
||Statistics and Probability
Fundamental Theorem of Arithmetic - statements after
reviewing work done earlier and after illustrating and motivating through examples,
Proofs of irrationality of √2 , √3, √5 Decimal representation of rational
numbers in terms of
terminating/non-terminating recurring decimals.
Zeros of a polynomial. Relationship between zeros and
coefficients of quadratic polynomials.
Pair of linear equations in two variables
Pair of linear equations in two variables and graphical
their solution, consistency/inconsistency. Algebraic conditions for number of solutions.
Solution of a pair of linear equations in two variables algebraically - by substitution, by
elimination method. Simple situational problems. Simple problems on equations reducible to
Standard form of a quadratic equation ax2 + bx + c
= 0, (a≠0).
Solutions of quadratic equations (only real roots) by factorization, and by using quadratic
formula. Relationship between discriminant and nature of roots.
Motivation for studying Arithmetic Progression Derivation of
nth term and sum of the first n terms of arithmetic progressions.
Only line in two dimensions. Concepts of coordinate geometry,
graphs of linear equations. Distance formula. Section formula (internal division).
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
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
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
the whole triangle and to each other.
- (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the
on the other two sides.
Tangent to a circle at, point of contact
- (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 a circle are equal.
- Division of a line segment in a given ratio (internally).
- Tangents to a circle from a point outside it.
Introduction to trigonometry
Trigonometric ratios of an acute angle of a right-angled
triangle. Proof of their existence (well defined). Values of the trigonometric ratios of 30°
45°, and 60°. Relationships between the ratios.
Height and distances: Angle of elevation, Angle of Depression.
Simple problems on heights and distances. Problems should not
involve more than two right triangles. Angles of elevation / depression should be only 30°,
Areas related to circles
Motivate the area of a circle; area of sectors and segments
circle. Problems based on areas and perimeter / circumference of the above said plane
(In calculating the area of the segment of a circle, problems should be restricted to a
angle of 60° and 90°only. Plane figures involving triangles, simple quadrilaterals and
should be taken.)
Surface areas and volumes
- Surface areas and volumes of combinations of any two of the following: cubes, cuboids,
spheres, hemispheres and right circular cylinders/cones.
- Problems involving converting one type of metallic solid into another and other mixed
problems. (Problems with combinations of not more than two different solids can be
Mean (step deviation method for finding the mean is
median and mode of grouped data (bimodal situation to be avoided).
Classical definition of probability. Simple problems on
the probability of an event.