Exams Counducted Class 9 Medium Grades and Percentage

# Get a Free Demo at your home

Supercharge your learning with personalized analysis and study tips. 90% students find their session to be a game changer.

Sections

Mathematics Class 9 Syllabus

Science Class 9 Syllabus

Reference Books for Class 9

## Mathematics Class 9 Syllabus Stroke 396

Exam Structure

 Units Marks I Number Systems 08 II Algebra 17 III Coordinate Geometry 04 IV Geometry 28 V Mensuration 13 VI Statistics and Probability 10 Total 80
• UNIT I: NUMBER SYSTEMS
• 1. 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.
• Rationalization (with precise meaning) of real numbers of the type 1/(a+b√x) and 1/(√x+√y) (and their combinations) where x and y are natural number and a and b are integers.
• 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.)
• UNIT II: ALGEBRA
• 1. POLYNOMIALS
• Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State 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.
• Recall of algebraic expressions and identities. Verification of identities:
• (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) (x 2 + y2 + z2 - xy - yz - zx) and their use in factorization of polynomials.
• 2. 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 lie on a line. Graph of linear equations in two variables. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.
• UNIT III: COORDINATE GEOMETRY
• 1. COORDINATE GEOMETRY
• The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane.
• UNIT IV: GEOMETRY
• 1. 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.
• 2. 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.
• 3. 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 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.
• (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.
• (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.
• 5. 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.
• 6. 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 respective 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.
• 7. 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.
• UNIT V: MENSURATION
• 1. AREAS
• Area of a triangle using Heron's formula (without proof) and its application in finding the area of a quadrilateral.
• 2. SURFACE AREAS AND VOLUMES
• Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.
• UNIT VI: STATISTICS & PROBABILITY
• 1. 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.
• 2. 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 Class 9 Syllabus

Exam Structure

 Units Marks I Matter - Its Nature & Behaviour 23 II Organisation in the Living World 20 III Motion, Force and Work 27 IV Our Environment 06 V Food; Food Production 04 Total 80
• Unit I: 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.
• Structure of atoms: Electrons, protons and neutrons, valency, chemical formula of common compounds. Isotopes and Isobars.
• Unit II: 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.
• Unit III: 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, Action and reaction forces, Inertia of a body, Inertia and mass, Momentum, Force and Acceleration. Elementary idea of conservation of Momentum.
• 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).
• Unit IV: 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.
• Unit V: Food Production
• Plant and animal breeding and selection for quality improvement and management; use of fertilizers, manures; protection from pests and diseases; organic farming.
• Practicals
• 1. Preparation of:
• a) a true solution of common salt, sugar and alum
• b) a suspension of soil, chalk powder and fine sand in water
• c) a colloidal solution of starch in water and egg albumin/milk in water and distinguish between these on the basis of
• transparency
• filtration criterion
• stability
• 2. Preparation of:
• a) a mixture
• b) a compound
• using iron filings and sulphur powder and distinguish between these on the basis of:
• i. appearance, i.e., homogeneity and heterogeneity
• ii. behaviour towards a magnet
• iii. behaviour towards carbon disulphide as a solvent
• iv. effect of heat
• 3. Separation of the components of a mixture of sand, common salt and ammonium chloride (or camphor).
• 4. Performing the following reactions and classifying them as physical or chemical changes :
• a. Iron with copper sulphate solution in water
• b. Burning of magnesium in air
• c. Zinc with dilute sulphuric acid
• d. Heating of copper sulphate
• e. Sodium sulphate with barium chloride in the form of their solutions in water
• 5. Preparation of stained temporary mounts of (a) onion peel, (b) human cheek cells & to record observations and draw their labeled diagrams.
• 6. Identification of Parenchyma, Collenchyma and Sclerenchyma tissues in plants, striped, smooth and cardiac muscle fibers and nerve cells in animals from prepared slides. Drawing of their labeled diagrams.
• 7. Determination of the melting point of ice and the boiling point of water.
• 8. Verification of the Laws of reflection of sound.
• 9. Determination of the density of solid (denser than water) by using a spring balance and a measuring cylinder.
• 10. Establishing the relation between the loss in weight of a solid when fully immersed in
• a) tap water
• b) strongly salty water, with the weight of water displaced by it by taking at least two different solids.
• 11. Determination of the speed of a pulse propagated through a stretched string / slinky.
• 12. Study of the characteristics of Spirogyra / Agaricus, Moss / Fern, Pinus (either with male or female cone) and an Angiospermic plant. Drawing and providing two identifying features of the groups they belong to.
• 13. Observing the given pictures / charts / models of earthworm, cockroach, bony fish and bird. For each organism, drawing of their picture and recording:
• a) one specific feature of its phylum.
• b) one adaptive feature with reference to its habitat.
• 14. Verification of the law of conservation of mass in a chemical reaction.
• 15. Study of the external features of root, stem, leaf and flower of monocot and dicot plants.

## Reference Books for Class 9

Vagupu is offering some of the best books for CBSE class 9 preparation. If you study with these reference books, there are chances that you will be easily able to top in your class or get 90-100 percent marks

 Subject Book title Publisher/ Author Math Mathematics for Class 9 RD Sharma Math A Textbook of Mathematics for Class 9 Ratna Sagar Physics Physics Class 9 Lakhmir Singh and Manjit Kaur, S Chand Publication Physics Physics Question Bank Oswaal Publications Chemistry Chemistry Class 9 Lakhmir Singh and Manjit Kaur, S Chand Publication Chemistry Chemistry Question Bank Oswaal Publications Biology Super Simplified Science Biology Class IX S. Dinesh Publication Biology Biology Question Bank Oswaal Publications English All in one for English Arihant