### Syllabus Class 10th

#### MATHS Course Structure Class X

**One Paper Time : 2 1/2Hours; Marks : 60**

NITS | CHAPTERS | MARKS |
---|---|---|

I | NUMBER SYSTEMS | 04 |

II | ALGEBRA | 20 |

III | TRIGONOMETRY | 12 |

IV | COORDINATE GEOMETRY | 08 |

V | GEOMETRY | 16 |

VI | MENSURATION | 10 |

VII | STATISTICS AND PROBABILITY | 10 |

TOTAL | 80 |

UNIT I : NUMBER SYSTEMS | |
---|---|

1. 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. | |

UNIT II : ALGEBRA | |

1. POLYNOMIALS | |

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

2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES | |

Pair of linear equations in two variables. Geometric representation of different possibilities of solutions inconsistency. Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically- by substitution, by elimination and by cross multiplication. Simple situational problems must be included. | |

Simple problems on equations reducible to linear equations may be included. | |

3. QUADRATIC EQUATIONS | |

Standard form of a quadratic equation ax2 + bx + c = 0, (a1 0). Solution of the quadratic equations (only real roots) by factorization and by completing the square, i.e. by using quadratic formula. Relationship between discriminant and nature of roots. | |

Problems related today to day activities to be incorporated. | |

4. ARITHMETIC PROGRESSIONS | |

Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms. | |

UNIT III : TRIGONOMETRY | |

1. INTRODUCTION TO TRIGONOMETRIY | |

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0o & 90o. Values (with proofs) of the trigonometric ratios of 30o, 45o & 60o. Relationships between the ratios. | |

2. TRIGONOMETRIC IDENTITIES | |

Proof and applications of the identity sin2 A + cos2 A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles. | |

3. 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 30o, 45o, 60o. | |

UNIT IV : COORDINATE GEOMETRY | |

1. 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. | |

UNIT V : GEOMETRY | |

1. TRIANGLES | |

Definitions, examples, counter examples of similar triangles. | |

1. (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. | |

2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. | |

3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar. | |

4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar. | |

5. (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. | |

6. (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. | |

7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides. | |

8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. | |

9. (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. | |

2. CIRCLES | |

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

1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. | |

2. (Prove) The lengths of tangents drawn from an external point to circle are equal. | |

3. CONSTRUCTIONS | (8) Periods |

1. Division of a line segment in a given ratio (internally) | |

2. Tangent to a circle from a point outside it. | |

3. Construction of a triangle similar to a given triangle. | |

UNIT VI : MENSURATION | |

1. 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 60o, 90o & 120oonly. Plane figures involving triangles, simple quadrilaterals and circle should be taken.) | |

2. SURFACE AREAS AND VOLUMES | |

(i) Problem on finding surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinder/cones. Frustum of a cone. | |

(ii) Problems involving converting one type of metallic solid into another and other mixed problem.(Problems with combination of not more than two different solids be taken.) | |

UNIT VII : STATISTICS AND PROBABILITY | |

1. STATISTICS | |

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

2. PROBABILITY | |

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

INTERNAL ASSESSMENT | 20 MARKS |

Evaluation of activities | 10 Marks |

Project Work | 05 Marks |

Continuous Evaluation | 05 Marks |

#### Science Course Structure Class X (Theory)

**One Paper Time : 2 1/2Hours; Marks : 60**

UNITS | MARKS | |
---|---|---|

I | Chemical Substances | 18 |

II | World of living | 16 |

III | Effects of Current | 10 |

IV | Light | 08 |

V | Natural Resources | 08 |

TOTAL | 60 |

Theme : Materials |
---|

UNIT 1 : CHEMICAL SUBSTANCES - NATURE AND BEHAVIOUR |

Acids, bases and salts : General properties, examples and uses. |

Chemical reactions : Types of chemical reactions : combination, decomposition, displacement, double displacement, precipitation, neutralization, oxidation and reduction in terms of gain and loss of oxygen and hydrogen. |

Metals and non metals : Brief discussion of basic metallurgical processes. Properties of common metals. Elementary idea about bonding. |

Carbon Compounds : Carbon compounds, elementary idea about bonding. Saturated hydrocarbons, alcohols, carboxylic acids (no preparation, only properties). |

Some Important chemical compounds : Soap-cleansing action of soap. |

Periodic classification of elements : Gradations in properties : Mendeleev periodic table. |

Theme : The world of the living |

UNIT 2 : OUR ENVIRONMENT |

Our environment : Environmental problems, their solutions. Biodegradable, non biodegradable, ozone depletion. |

Life Processes : "living" things; Basic concept of nutrition, respiration, transport and excretion in plants and animals. |

Control and Co-ordination in plants and animals : Tropic movements in plants; Introduction to plant hormones; control and co-ordination in animals : voluntary, involuntary and reflex action, nervous system; chemical co-ordination : animal hormones. |

Reproduction: Reproduction in plants and animals. Need for and methods of family planning. Safe sex vs HIV/AIDS. Child bearing and women's health. |

Heridity and evolution : Heridity; Origin of life : brief introduction; Basic concepts of evolution. |

Theme : How things work. |

UNIT 3 : EFFECTS OF CURRENT |

Potential, Potential difference, Ohm's law; Series combination of resistors, parallel combination of resistors; Power dissipation due to current; Inter relation between P, V, I and R. |

Magnets : Magnetic field, field lines, field due to a current carrying wire, field due to current carrying coil or solenoid; Force on current carrying conductor, Fleming's left hand rule. Electro magnetic induction. Induced potential difference, Induced current. Direct current. Alternating current; frequency of AC. Advantage of AC over DC. Domestic electric circuits. |

Theme : Natural Phenomena |

UNIT 4 : LIGHT |

Convergence and divergence of light. Images formed by a concave mirror; related concepts; centre of curvature; principal axis. Optic centre, focus, focal length. Refraction; laws of refraction. Image formed by a convex lens; functioning of a lens in human eye; problems of vision and remedies. Applications of spherical mirrors and lenses. Appreciations of concept of refraction; velocity of light; refractive index; twinkling of stars; dispersion of light. Scattering of light. |

Theme : Natural Resources |

UNIT 5 : NATURAL RESOURCES |

Conservation of natural resources : Management of natural resources. Conservation and judicious use of natural resources. Forest and wild life, coal and petroleum conservation. People's participation. Chipko movement. Legal perspectives in conservation and international scenario. The Regional environment : Big dams : advantages and limitations; alternatives if any. Water harvesting. Sustainability of natural resources. Sources of energy : Different forms of energy, leading to different sources for human use : fossil fuels, solar energy; biogas; wind, water and tidal energy; nuclear energy. Renewable versus non - renewable sources. |