STUDY MATERIALS

What are Synthetic Fibres? Types of Synthetic Fibres Characteristics of Synthetic Fibres Plastics Plastics as Materials of Choice Plastics and the Environment

Conservation and judicious use of natural resources. Forest and wildlife; Coal and Petroleum conservation. Examples of people’s participation for conservation of natural resources. Big dams: advantages and limitations; alternatives, if any. Water harvesting. Sustainability of natural resources

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 combination of not more than two different solids be taken)

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) In a right triangle, the square on the hypotenuse is equal to the sum of the squares 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

Their definitions in terms of furnishing of H+ and OH- ions, General properties, examples and uses, concept of pH scale (Definition relating to logarithm not required), importance of pH in everyday life; preparation and uses of Sodium Hydroxide, Bleaching powder, Baking soda, Washing soda and Plaster of Paris.

Force: A push or a Pull Forces are due to an Interaction Exploring Forces A Force can Change the State of Motion Force can Change the Shape of an object Contact Forces Non-contact Forces Pressure Pressure Exerted by Liquids and Gases Atmospheric Pressure

Magnetic field, field lines, field due to a current carrying conductor, field due to current carrying coil or solenoid; Force on current carrying conductor, Fleming’s Left Hand Rule, Electric Motor, Electromagnetic induction. Induced potential difference, Induced current. Fleming’s Right Hand Rule.

Reflection of light by curved surfaces; Images formed by spherical mirrors, centre of curvature, principal axis, principal focus, focal length, mirror formula (Derivation not required), magnification. Refraction; Laws of refraction, refractive index. Refraction of light by spherical lens; Image formed by spherical lenses; Lens formula (Derivation not required); Magnification. Power of a lens. Refraction of light through a prism, dispersion of light, scattering of light, applications in daily life.

(Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180o and the converse. (Prove) If two lines intersect, vertically opposite angles are equal. (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines.(Motivate) Lines which are parallel to a given line are parallel.(Prove) The sum of the angles of a triangle is 180o. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles

(Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence). (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle (RHS Congruence).(Prove) The angles opposite to equal sides of a triangle are equal. (Motivate) The sides opposite to equal angles of a triangle are equal

History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem, for example: (Axiom) 1. Given two distinct points, there exists one and only one line through them. (Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common.

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of an A.P.

History, Repeated experiments and observed frequency approach to probability Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real - life situations, and from examples used in the chapter on statistics)

Review of representation of natural numbers Integers Rational numbers on the number line Representation of terminating / non-terminating recurring decimals, on the number line through successive magnification Rational numbers as recurring/terminating decimals Examples of non-recurring / non-terminating decimals Existence of non-rational numbers (irrational numbers) such as v2, v3 and their representation on the number line Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number Existence of vx for a given positive real number x (visual proof to be emphasized) Definition of nth root of a real number Recall of laws of exponents with integral powers Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws) Rationalization (with precise meaning) of real numbers of the type 1/(a+bvx) and 1/(vx+vy) (and their combinations) where x and y are natural number and a and b are integers