Syllabus

Class- 9^th

“Mathmatics”

Unit	Unit Name	Marks
I	Number Systems	10
II	Algebra	20
III	Coordinate Geometry	04
IV	Geometry	27
V	Mensuration	13
VI	Statistics	06
Total		80

1. Number Systems

• Real Numbers:
  • Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/terminating decimals. Operations on real numbers.
  • Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, π, and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.
  • Definition of nth root of a real number.
  • Rationalization (with precise meaning) of real numbers of the type 1/(√a + √b) and (√a – √b)/(√a + √b) (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.)

1. Algebra

• 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: (a + b)² = a² + 2ab + b², (a – b)² = a² – 2ab + b², a² – b² = (a + b)(a – b) and their use in factorization of 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. Explain 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.

III. Coordinate Geometry

• Coordinate Geometry:
  • The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.

1. 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. 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) Lines which are parallel to a given line are parallel.
• 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. (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.
• 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 in half of it and (motivate) its converse.
• Circles:
  • (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) 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.

1. Mensuration

• Areas:
  • Area of a triangle using Heron’s formula (without proof)
• Surface Areas and Volumes:
  • Surface areas and volumes of spheres (including hemispheres) and right circular cones.

1. Statistics

• Statistics:
  • Bar graphs, histograms (with varying base lengths), and frequency polygons.

“Science”

Unit No.	Unit	Marks
I	Matter – Its Nature and Behaviour	25
II	Organization in the Living World	22
III	Motion, Force and Work	27
IV	Food; Food Production	06
Total		80
Internal Assessment		20
Grand Total		100

Theme: Materials

• 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. Heterogeneous and homogenous mixtures, colloids and suspensions. Physical and chemical changes (excluding separating the components of a mixture).
  • Particle nature and their basic units: Atoms and molecules, Law of Chemical Combination, Chemical formula of common compounds, Atomic and molecular masses.
  • Structure of atoms: Electrons, protons and neutrons, Valency, Atomic Number and Mass Number, Isotopes and Isobars.

Theme: The World of the Living

• 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 and cell inclusions; 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 (only four types of tissues in animals; Meristematic and Permanent tissues in plants).

Theme: Moving Things, People and Ideas

• 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, 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.
  • 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.
  • Work, Energy and Power: Work done by a Force, Energy, power; Kinetic and Potential energy; Law of conservation of energy (excluding commercial unit 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.

Theme: Food

• Unit IV: Food Production
  • Plant and animal breeding and selection for quality improvement and management; Use of fertilizers and manures; Protection from pests and diseases; Organic farming.

Internal Assessment: 20 Marks Grand Total: 100 Marks

Class 10^th

“Mathematics”

Unit No.	Unit Name	Marks
I	Number Systems	06
II	Algebra	20
III	Coordinate Geometry	06
IV	Geometry	15
V	Trigonometry	12
VI	Mensuration	10
VII	Statistics & Probability	11
Total		80

1. Number Systems

• Real Numbers:
  • Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of √2, √3

1. Algebra

• Polynomials:
  • Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.
• Pair of Linear Equations in Two Variables:
  • Pair of linear equations in two variables and graphical method of 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.
  • Simple situational problems.
• Quadratic 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 the quadratic formula.
  • Relationship between discriminant and nature of roots.
  • Situational problems based on quadratic equations related to day-to-day activities.
• Arithmetic Progressions:
  • Motivation for studying Arithmetic Progression.
  • Derivation of the nth term and sum of the first n terms of A.P.
  • Application in solving daily life problems.

III. Coordinate Geometry

• Coordinate Geometry:
  • Review: Concepts of coordinate geometry, graphs of linear equations.
  • Distance formula.
  • Section formula (internal division).

1. 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.
• Circles:
  • 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.

1. Trigonometry

• 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°, 90°.
  • Values 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.
• Heights 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°, 45°, and 60°.

1. Mensuration

• Areas Related to Circles:
  • 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.)
• 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.

VII. Statistics and Probability

• Statistics:
  • Mean, median and mode of grouped data (bimodal situation to be avoided).
• Probability:
  • Classical definition of probability.
  • Simple problems on finding the probability of an event.

“Science”

Unit No.	Unit	Marks
I	Chemical Substances-Nature and Behaviour	25
II	World of Living	25
III	Natural Phenomena	12
IV	Effects of Current	13
V	Natural Resources	05
Total		80
Internal Assessment		20
Grand Total		100

Theme: Materials

• Unit I: 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, endothermic exothermic reactions, oxidation and reduction.
  • Acids, bases and salts: Their definitions in terms of furnishing of H+ and OH– ions, General properties, examples and uses, neutralization, 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 nonmetals: 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.

Theme: The World of the Living

• Unit II: World of Living
  • 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: (topics excluded – evolution; evolution and classification and evolution should not be equated with progress).

Theme: Natural Phenomena

• Unit III: Natural Phenomena
  • 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 (excluding colour of the sun at sunrise and sunset).

Theme: How Things Work

• Unit IV: 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, Direct current. Alternating current: frequency of AC. Advantage of AC over DC.
  • Domestic electric circuits.

Theme: Natural Resources

• Unit V: Natural Resources
  • Our environment: Eco-system, Environmental problems, Ozone depletion, waste production and their solutions. Biodegradable and non-biodegradable substances.

Internal Assessment: 20 Marks Grand Total: 100 Marks

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