All India Proficiency Oxyopia (AIPO) Syllabus CLASS 9 - National Level Talent Search Examination

INTRA SCHOOL ROUND (First Round)

MATHEMATICS

NUMBER SYSTEMS

(i) Rational Numbers:

Properties of rational numbers.(including identities). Usinggeneral form of expression to describe properties. Consolidation of operations on rational numbers. Representation of rational numbers on the number line between any two rational numbers there lies another rational number (Making children see that if we take two rational numbers then unlike for whole numbers, in this case you can keep finding more and more numbers that lie between them.) Word problem (higher logic, two operations, including ideas like area)

(ii) Powers

Integers as exponents. Laws of exponents with integral powers

(iii) Squares, Square roots

Square and Square roots. Square roots using factor method and division method for numbers containing (a) no more than total 4 digits and (b) no more than 2 decimal places

(iii) Cubes, Cube roots.

Cubes and cubes roots (only factor method for numbers containing at most 3 digits), Estimating square roots and cube roots. Learning the process of moving nearer to the required number.

(iv) Playing with numbers

Writing and understanding a² and 3 digit number in generalized form (100a + 10b + c , where a, b, c can be only digit 0-9) and engaging with various puzzles concerning this. (Like finding the missing numerals represented by alphabets in sums involving any of the four operations.) Children to solve and create problems and puzzles. Number puzzles and games. Deducing the divisibility test rules of 2, 3, 5, 9, 10 for a two or three-digit number expressed in the general form.

ALGEBRA

(i) Algebraic Expressions

Multiplication and division of algebraic exp.(Coefficient should be integers), Some common errors (e.g. 2 + x ≠ 2x, 7x + y ≠ 7xy ), Identities (a ± b)² = a²± 2ab + b², a² – b² = (a – b) (a + b) Factorisation (simple cases only) as examples the following types a(x + y), (x ± y)², a² – b², (x + a).(x + b), Solving linear equations in one variable in contextual problems involving multiplication and division (word problems) (avoid complex coefficient in the equations)

(ii) RATIO AND PROPORTION

Slightly advanced problems involving applications on percentages, profit & loss, overhead expenses, Discount, tax. Difference between simple and compound interest (compounded yearly up to 3 years or half-yearly up to 3 steps only), Arriving at the formula for compound interest through patterns and using it for simple problems. Direct variation – Simple and direct word problems, Inverse variation – Simple and direct word problems, Time & work problems– Simple and direct word problems

GEOMETRY

(i) Understanding shapes:

Properties of quadrilaterals – Sum of angles of a quadrilateral is equal to 360^o (By verification)

Properties of parallelogram (By verification)

Opposite sides of a parallelogram are equal,
Opposite angles of a parallelogram are equal,
Diagonals of a parallelogram bisect each other. [Why (iv), (v) and (vi) follow from (ii)]
Diagonals of a rectangle areequal and bisect each other.
Diagonals of a rhombus bisect each other at right angles.
Diagonals of a square are equal and bisect each other at right angles.

(ii) Representing 3-D in 2-D

Identify and Match pictures with objects [more complicated e.g. nested, joint 2-D and 3-D shapes (not more than 2)]. Drawing 2-D representation of 3-D objects (Continued and extended). Counting vertices, edges & faces & verifying Euler’s relation for 3-D figures with flat faces (cubes, cuboids, tetrahedrons, prisms and pyramids)

(iii) Construction:

Construction of Quadrilaterals: Given four sides and one diagonal, Three sides and two diagonals, Three sides and two included angles, Two adjacent sides and three angles

MENSURATION

Area of a trapezium and a polygon. Concept of volume, measurement of volume using a basic unit, volume of a cube, cuboid and cylinder, Volume and capacity (measurement of capacity), Surface area of a cube, cuboid, cylinder.

DATA HANDLING

Reading bar-graphs, ungrouped data, arranging it into groups, representation of grouped data through bar-graphs, constructing and interpreting bar-graphs. Simple Pie charts with reasonable data numbers, Consolidating and generalising the notion of chance in events like tossing coins, dice etc. Relating it to chance in life events. Visual representation of frequency outcomes of repeated throws of the same kind of coins or dice. Throwing a large number of identical dice/coins together and aggregating the result of the throws to get large number of individual events. Observing the aggregating numbers over a large number of repeated events. Comparing with the data for a coin. Observing strings of throws, notion of randomness

INTRODUCTION TO GRAPHS

(i) Preliminaries:

Axes (Same units), Cartesian Plane, Plotting points for different kind of situations (perimeter vs length for squares, area as a function of side of a square, plotting of multiples of different numbers, simple interest vs number of years etc.), Reading off from the graphs, Reading of linear graphs, Reading of distance vs time graph

SCIENCE

CROP PRODUCTION:

Soil preparation, selection of seeds, sowing, applying fertilizers, irrigation, weeding, harvesting and storage; nitrogen fixation, nitrogen cycle.

MICRO ORGANISMS

Useful and harmful.

MATERIALS IN DAILY LIFE

Synthetic clothing materials. Other synthetic materials, especially plastics; usefulness of plastics and problems associated with their excessive use. There are a variety of fibrous materials in use. A material is chosen based on desired property.

METALS AND NON-METALS.

HOW THINGS CHANGE

Combustion, flame All fuels release heat on burning. Fuels differ in efficiency, cost etc. Natural resources are limited. Burning of fuels leads to harmful by products.

THE WORLD OF LIVING

Conservation of biodiversity/wild life/ plants; zoos, sanctuaries, forest reserves etc. flora, fauna endangered species, red data book; endemic species, migration.

THE CELL

Cell structure, plant and animal cells, use of stain to observe, cell organelles – nucleus, vacuole, chloroplast, cell membrane, cell wall.

REPRODUCTION

Sexual reproduction and endocrine system in animals, secondary sexual characters, reproductive health; internal and external fertilisation.

IDEA OF FORCE

push or pull; change in speed, direction of moving objects and shape of objects by applying force; contact and non-contact forces.

FRICTION

factors affecting friction, sliding and rolling friction, moving; advantages and disadvantages of friction for the movement of automobiles, airplanes and boats/ships; increasing and reducing friction.

PRESSURE

Pressure exerted by air/liquid; atmospheric pressure.

SOUND

Various types of sound; sources of sound; vibration as a cause of sound; frequency; medium for propagation of sound; idea of noise as unpleasant and unwanted sound and need to minimise noise.

ELECTRIC CURRENT AND CIRCUITS

Water conducts electricity depending on presence/ absence of salt in it. Other liquids may or may not conduct electricity.
Chemical effects of current.
Basic idea of electroplating.

NATURAL PHENOMENA

Clouds carry electric charge. Positive and negative charges, attraction and repulsion. Principle of lightning conductor.

LIGHT

Laws of reflection, Characteristics of image formed with a plane mirror,
Regular and diffused reflection. Reflection of light from an object to the eye,
Multiple reflection, Dispersion of light, Structure of the eye, Lens becomes opaque, light not reaching the eye, Visually challenged use other senses to make sense of the world around, Alternative technology available, Role of nutrition in relation to blindness.

NIGHT SKY

Idea about heavenly bodies/celestial objects and their classification – moon, planets, stars, constellations. Motion of celestial objects in space; the solar system.

EARTHQUAKES

Phenomena related to earthquakes.

NATURAL RESOURCES

Consequences of deforestation: scarcity of products for humans and other living beings, change in physical properties of soil, reduced rainfall, Reforestation; recycling of paper, Formation of coal and petroleum in nature, Consequences of over extraction of coal and petroleum.

POLLUTION OF AIR AND WATER

Water and air are increasingly getting polluted and therefore become scarce for use. Biological and chemical contamination of water; effect of impure water on soil and living beings; effect of soil containing excess of fertilisers and insecticides on water resources. Potable water.

INTER SCHOOL ROUND (Second Round)

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).

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.