Units | Unit Name | Marks |

I | NUMBER SYSTEMS | 6 |

11 | ALGEBRA | 20 |

III | COORDINATE GEOMETRY | 6 |

IV | GEOMETRY | 15 |

V | TRIGONOMETRY | 12 |

VI | MENSURATION | 10 |

VII | STATISTICS & PROBABILITY | 11 |

INTERNAL ASSESSMENT | 20 | |

Total | 100 |

#### 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 irrationality of 2, 3, 5 . Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

Class 10 Maths – Notes , Important Questions and Solutions – Real Numbers

#### UNIT II : ALGEBRA

1. 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.

Class 10 Maths – Notes , Important Questions and Solutions – Polynomials

2. 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 and by cross multiplication method. Simple situational problems. Simple problems on equations reducible to linear equations.

Class 10 Maths Practice – Pair of Linear Equation in Two variables

3. QUADRATIC EQUATIONS

Standard form of a quadratic equation ax2 + bx + c = 0, (a 0). Solutions of 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 incorporated.

Class 10 Maths – Notes , Important Questions and Solutions – Quadratic Equations

4. ARITHMETIC PROGRESSIONS

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

Class 10 Maths – Notes , Important Questions and Solutions – Arithmetic Progression

#### UNIT III : COORDINATE GEOMETRY

1. LINES (In two-dimensions)

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.

Class 10 Maths – Notes , Important Questions and Solutions – Coordinate Geometry

#### UNIT IV : GEOMETRY

1. TRIANGLES

Class 10 Maths – Notes , Important Questions and Solutions – Similar 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 arc 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 of 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 angle.

2. CIRCLES

Class 10 Maths – Notes , Important Questions and Solutions – Circles

Tangent to a circle at, point of contact

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 a circle are equal.

3. CONSTRUCTIONS

Class 10 Maths – Notes , Important Questions and Solutions – Constructions

1. Division of a line segment in a given ratio (internally). 2. Tangents to a circle from a point outside it. 3. Construction of a triangle similar to a given triangle.

#### UNIT V : TRIGONOMETRY

Class 10 Maths – Notes , Important Questions and Solutions – 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 arc defined at 0° and 90°. Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.

2. TRIGONOMETRIC IDENTITIES

Proof and applications of the identity sin2A + cos2 A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

Class 10 Maths – Notes , Important Questions and Solutions – Height and Distance

3. 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°, 60°.

#### 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 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)

Class 10 Maths – Notes , Important Questions and Solutions – Areas Related to Circle

2. 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. Frustum of a cone.

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).

#### UNIT VII : STATISTICS AND PROBABILITY

1. STATISTICS

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

Class 10 Maths – Notes , Important Questions and Solutions – Statistics

2. PROBABILITY

Classical definition of probability. Simple problems on single events (not using set notation).

Class 10 Maths – Notes , Important Questions and Solutions – Probability