All India Proficiency Oxyopia (AIPO) Syllabus CLASS 10 - National Level Talent Search Examination

INTRA SCHOOL ROUND (First Round)

SCIENCE

MATTER – NATURE AND BEHAVIOUR

Definition of matter; solid, liquid and gas; characteristics – shape, volume, density; change of state-melting (absorption of heat), freezing, evaporation (cooling by evaporation), condensation, sublimation.

Nature of matter:

Elements, compounds and mixtures. Heterogenous and homogenous mixtures, colloids and suspensions.

Particle nature, basic units:

atoms and molecules. Law of constant proportions. Atomic and molecular masses.

Mole Concept:

Relationship of mole to mass of the particles and numbers. Valency. Chemical formula of common compounds.

Structure of atom:

Electrons, protons and neutrons; Isotopes and isobars.

ORGANIZATION IN THE LIVING WORLD

Cell – Basic Unit of life: Cell as a basic unit of life; prokaryotic and eukaryotic cells, multicellular organisms; cell membrane and cell wall, cell organelles; chloroplast, mitochondria, vacuoles, endoplasmic reticulum, Golgi apparatus; nucleus, chromosomes – basic structure, number.

Tissues, Organs, Organ System, Organism:

Structure and functions of animal and plant tissues (four types in animals; meristematic and permanent tissues in plants).

Biological Diversity: Diversity of plants and animals – basic issues in scientific naming, basis of classification. Hierarchy of categories / groups, Major groups of plants (salient features) (Bacteria, Thalophyta, Bryo phyta, Pteridophyta, gymnosperms and Angiosperms). Major groups of animals (salient features) (Non-chordates upto phyla and chordates upto classes).

Health and Diseases: Health and its failure. Infectious and Non-infectious diseases, their causes and manifestation. Diseases caused by microbes (Virus, Bacteria and protozoans) and their prevention, Principles of treatment and prevention. Pulse polio programmes.

MOTION, FORCE AND WORK

Motion: Distance and displacement, velocity; uniform and non-uniform motion along a straight line; acceleration, distance-time and velocity-time graphs for uniform motion and uniformly accelerated motion, equations of motion by graphical method; elementary idea of uniform circular motion.

Force and Newton’s laws: Force and motion, Newton’s laws of motion, inertia of a body, inertia and mass, momentum, force and acceleration. Elementary idea of conservation of momentum, action and reaction forces.

Gravitation: Gravitation; universal law of gravitation, force of gravitation of the earth (gravity), acceleration due to gravity; mass and weight; free fall.

Floatation: Thrust and pressure. Archimedes’ principle, buoyancy, elementary idea of relative density.

Work, energy and power: Work done by a force, energy, power; kinetic and potential energy; law of conservation of energy.

Sound: Nature of sound and its propagation in various media, speed of sound, range of hearing in humans; ultrasound; reflection of sound; echo and SONAR. Structure of the human ear (auditory aspect only).

FOOD PRODUCTION

Plant and animal breeding and selection for quality improvement and management; use of fertilizers, manures; protection from pests and diseases; organic farming.

OUR ENVIRONMENT

Physical resources: Air, Water, Soil. Air for respiration, for combustion, for moderating temperatures; movements of air and its role in bringing rains across India. Air, water and soil pollution (brief introduction). Holes in ozone layer and the probable damages.

Bio-geo chemical cycles in nature: Water, oxygen, carbon and nitrogen.

MATHEMATICS

NUMBER SYSTEMS

Real Numbers

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 √2, √3 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 √x 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 (and their combinations)

ALGEBRA

Polynomials

Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial.

Degree of a polynomial. Constant, linear, quadratic and cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. State and motivate the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of (ax² + bx + c, a + 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem) dt quadratic & cubic polynomial.

Recall of algebraic expressions and identities. Further verification of identities of the type (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx, (x ± y)³ = x³ ± y³ ± 3xy (x ± y), x³ ± y³ = (x ± y) (x² ± xy + y²), x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx) and their use in factorization of polymonials. Simple expressions reducible to these polynomials.

Linear Equations In Two Variables

Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax+by+c=0. Prove that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they seem to lie on a line. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.

GEOMETRY

Introduction To Euclid’s Geometry

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.

Lines And Angles

(Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° 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 180°.
(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.

Triangles

(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).
(Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).
(Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruene).
(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.
(Prove) The angles opposite to equal sides of a triangle are equal.
(Motivate) The sides opposite to equal angles of a triangle are equal.
(Motivate) Triangle inequalities and relation between ‘angle and facing side’ inequalities in triangles.

Quadrilaterals

(Prove) The diagonal divides a parallelogram into two congruent triangles.
(Motivate) In a parallelogram opposite sides are equal, and conversely.
(Motivate) In a parallelogram opposite angles are equal, and conversely.
(Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
(Motivate) In a parallelogram, the diagonals bisect each other and conversely.
(Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and (motivate) its converse.

Area

Review concept of area, recall area of a rectangle.

(Prove) Parallelograms on the same base and between the same parallels have the same area.
(Motivate) Triangles on the same (or equal base) base and between the same parallels are equal in area.

Circles

Through examples, arrive at definitions of circle related concepts, radius, circumference, diameter, chord, arc, secant, sector, segment subtended angle.

(Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
(Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
(Motivate) There is one and only one circle passing through three given non-collinear points.
(Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their repective centers) and conversely.
(Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
(Motivate) Angles in the same segment of a circle are equal.
(Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.
(Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

Constructions

Construction of bisectors of line segments and angles of measure 60°, 90°, 45° etc., equilateral triangles.
Construction of a triangle given its base, sum/difference of the other two sides and one base angle.
Construction of a triangle of given perimeter and base angles.

COORDINATE GEOMETRY

Coordinate Geometry

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane, graph of linear equations as examples; focus on linear equations of the type Ax + By + C = 0 by writing it as y = mx + c.

MENSURATION

Areas

Area of a triangle using Heron’s formula (without proof) and its application in finding the area of a quadrilateral. Area of cyclic quadrilateral (with proof) – Brahmagupta’s formula.

Surface Areas And Volumes

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.

STATISTICS

Introduction to Statistics: Collection of data, presentation of data – tabular form, ungrouped / grouped, bar graphs, histograms (with varying base lengths), frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean, median, mode of ungrouped data.

PROBABILITY

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).

INTER SCHOOL ROUND (Second Round)

MATHEMATICS

NUMBER SYSTEMS

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.

ALGEBRA

Polynomials

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.

Pair Of Linear Equations In Two Variables

Pair of linear equations in two variables and their graphical solution. Geometric representation of different possibilities of solutions/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 must be included. Simple problems on equations reducible to linear equations may be included.

Quadratic Equations

Standard form of a quadratic equation ax²+bx+c=0, (a ≠ 0). Solution of the quadratic equations (only real roots) by factorization, by completing the square and by using quadratic formula. Relationship between discriminant and nature of roots.

Situational problems based on quadratic equations related to day to day activities to be incoporated.

Arithmetic Progressions

Motivation for studying Arithmetic Progression Derivation of standard results of finding the nth term and sum of first n terms and their application in solving daily life problems.

GEOMETRY

Triangles

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 on 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 traingle.

Circles

Tangents to a circle motivated by chords drawn from points coming closer and closer to the point.
(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 circle are equal.

Constructions

Division of a line segment in a given ratio (internally).
Tangent to a circle from a point outside it.
Construction of a triangle similar to a given triangle.

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° and 90°. Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.

Trigonometric Identities

Proof and applications of the identity sin²A + cos²A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

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°.

STATISTICS AND PROBABILITY

Statistics

Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

Probability

Classical definition of probability. Connection with probability as given in Class IX. Simple problems on single events, not using set notation.

COORDINATE GEOMETRY

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.

MENSURATION

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° and 120° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)

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.)

SCIENCE

CHEMICAL SUBSTANCES

Nature and Behaviour Chemical reactions: Chemical equation, Balanced chemical equation, implications of a balanced chemical equation, types of chemical reactions: combination, decomposition, displacement, double displacement, precipitation, neutralization, oxidation and reduction.

ACIDS, BASES AND SALTS

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.

METALS AND NON METALS

Properties of metals and non-metals; Reactivity series; Formation and properties of ionic compounds; Basic metallurgical processes; Corrosion and its prevention.

CARBON COMPOUNDS

Covalent bonding in carbon compounds. Versatile nature of carbon. Homologous series. Nomenclature of carbon compounds containing functional groups (halogens, alcohol, ketones, aldehydes, alkanes and alkynes), difference between saturated hydrocarbons and unsaturated hydrocarbons. Chemical properties of carbon compounds (combustion, oxidation, addition and substitution reaction). Ethanol and Ethanoic acid (only properties and uses), soaps and detergents.

PERIODIC CLASSIFICATION OF ELEMENTS

Need for classification, Modern periodic table, gradation in properties, valency, atomic number, metallic and non-metallic properties.

LIFE PROCESSES

‘Living Being’. Basic concept of nutrition, respiration, transport and excretion in plants and animals. Control and co-ordination in animals and plants: Tropic movements in plants; Introduction of plant hormones;

CONTROL AND CO-ORDINATION IN ANIMALS:

Nervous system; Voluntary, involuntary and reflex action; Chemical co-ordination: animal hormones.

REPRODUCTION

Reproduction in animals and plants (asexual and sexual) reproductive health-need and methods of family planning. Safe sex vs HIV/AIDS. Child bearing and women’s health.

HEREDITY AND EVOLUTION

Heredity; Mendel’s contribution- Laws for inheritance of traits: Sex determination: brief introduction; Basic concepts of evolution.

NATURAL RESOURCES

Different forms of energy, conventional and non-conventional sources of energy: Fossil fuels, solar energy; biogas; wind, water and tidal energy; Nuclear energy. Renewable versus non-renewable sources of Energy.

CONSERVATION OF NATURAL RESOURCES

MANAGEMENT OF NATURAL RESOURCES

Conservation and judicious use of natural resources. Forest and wild life; Coal and Petroleum conservation. Examples of people’s participation for conservation of natural resources.

REGIONAL ENVIRONMENT: Big dams: advantages and limitations; alternatives, if any. Water harvesting. Sustainability of natural resources.

OUR ENVIRONMENT:

Eco-system, Environmental problems, Ozone depletion, waste production and their solutions. Biodegradable and non-biodegradable substances.

EFFECTS OF CURRENT

Electric current, potential difference and electric current. Ohm’s law; Resistance, Resistivity, Factors on which the resistance of a conductor depends. Series combination of resistors, parallel combination of resistors and its applications in daily life. Heating effect of electric current and its applications in daily life. Electric power, Interrelation between P, V, I and R.

MAGNETIC EFFECTS OF CURRENT

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. Electromagnetic induction. Induced potential difference, Induced current. Fleming’s Right Hand Rule, Direct current. Alternating current : frequency of AC. Advantage of AC over DC. Domestic electric circuits.

LIGHT

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; Functioning of a lens in human eye, defects of vision and their corrections, applications of spherical mirrors and lenses. Refraction of light through a prism, dispersion of light, scattering of light, applications in daily life.