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
Euclid’s division lemma, Fundamental Theorem of Arithmetic -
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. Statement and simple problems on division algorithms
polynomials with real coefficients.
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, and by cross multiplication method. Simple situational problems. Simple
equations reducible to linear equations.
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. Situational problems based
quadratic equations related to day to day activities to be incorporated.
Motivation for studying Arithmetic Progression Derivation of
nth term and sum of the first n terms of arithmetic progressions.and their
solving daily life problems.
Only line in two dimensions. Concepts of coordinate geometry,
graphs of linear equations. Distance formula. Section formula (internal division). Area of a
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 parallel 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 corresponding 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 to the whole triangle and to each other.
- (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
- (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
- 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 angle.
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.
- Construction of a triangle similar to a given triangle.
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.
Proof and applications of the identity sin2 A + cos2 A = 1.
simple identities to be given. Trigonometric ratios of complementary angles.
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°, 90°, and 120° only. Plane figures involving triangles, simple quadrilaterals
circles 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. Frustum of a cone.
- 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, median, and mode of grouped data (bimodal situation to
avoided). Cumulative frequency graph.
Classical definition of probability. Simple problems on
finding the probability of an event.