## Topics with syllabus and resources

1 Number Systems

1.01 Real Numbers

syllabus ▼

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

- Concepts :
- Introduction of Real Numbers videos (1)
- Real Numbers Examples and Solutions videos (19) question (6)
- Euclidâ€™s Division Lemma videos (4) question (199)
- Fundamental Theorem of Arithmetic videos (1) question (46)
- Fundamental Theorem of Arithmetic Motivating Through Examples videos (1)
- Proofs of Irrationality videos (1) question (10)
- Revisiting Irrational Numbers question (37)
- Revisiting Rational Numbers and Their Decimal Expansions videos (1) question (60)

2 Algebra

2.01 Arithmetic Progressions

syllabus ▼

- 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.

- Concepts :
- Derivation of the n th Term videos (5)
- Application in Solving Daily Life Problems videos (2)
- Arithmetic Progressions Examples and Solutions videos (52) question (41)
- Arithmetic Progression videos (17) question (176)
- Sum of First n Terms of an AP videos (10) question (383)
- nth Term of an AP question (107)
- General Term of an Arithmetic Progression question (13)

2.02 Quadratic Equations

syllabus ▼

- Standard form of a quadratic equation ax
^{2}+ 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.

- Concepts :
- Quadratic Equations videos (8) question (325)
- Nature of Roots videos (16) question (104)
- Relationship Between Discriminant and Nature of Roots question (113)
- Solutions of Quadratic Equations by Factorization videos (9) question (322)
- Solutions of Quadratic Equations by Completing the Square videos (7) question (81)
- Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated videos (2) question (46)
- Quadratic Equations Examples and Solutions videos (40) question (59)

2.03 Pair of Linear Equations in Two Variables

syllabus ▼

- 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.

- Concepts :
- Introduction of System of Linear Equations in Two Variables videos (3) question (20)
- Graphical Method of Solution of a Pair of Linear Equations videos (10) question (127)
- Consistency of Pair of Linear Equations videos (3)
- Inconsistency of Pair of Linear Equations videos (1) question (1)
- Algebraic Conditions for Number of Solutions
- Algebraic Methods of Solving a Pair of Linear Equations
- Substitution Method videos (6) question (70)

- Elimination Method videos (7) question (19)

- Cross - Multiplication Method videos (5) question (80)

- Simple Situational Problems videos (1) question (12)
- Equations Reducible to a Pair of Linear Equations in Two Variables videos (3) question (69)
- Pair of Linear Equations in Two Variables videos (69) question (215)
- Relation Between Co-efficient videos (2)

2.04 Polynomials

syllabus ▼

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

- Concepts :
- Geometrical Meaning of the Zeroes of a Polynomial videos (6) question (35)
- Division Algorithm for Polynomials videos (1) question (32)
- Polynomials Examples and Solutions videos (27) question (59)
- Introduction to Polynomials videos (2)
- Relationship Between Zeroes and Coefficients of a Polynomial videos (2) question (109)

3 Geometry

3.01 Triangles

syllabus ▼

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.
- (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.
- (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
- (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
- (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.

- Concepts :
- Similar Figures videos (2) question (24)
- Criteria for Similarity of Triangles videos (3) question (60)
- Pythagoras Theorem videos (17) question (76)
- Areas of Similar Triangles videos (1) question (45)
- Similarity of Triangles videos (10) question (84)
- Similarity Triangle Theorem videos (1) question (11)
- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle videos (2) question (44)
- Triangles Examples and Solutions videos (63) question (145)
- Basic Proportionality Theorem Or Thales Theorem videos (4) question (65)
- Angle Bisector videos (8) question (22)
- Similarity Examples and Solutions videos (14) question (50)
- Ratio of Sides of Triangle videos (2)

3.02 Constructions

syllabus ▼

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

- Concepts :
- Division of a Line Segment videos (11) question (48)
- Construction of Tangents to a Circle videos (6) question (63)
- Constructions Examples and Solutions question (15)

3.03 Circles

syllabus ▼

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.

- Concepts :
- Tangent to a Circle videos (4) question (48)
- Number of Tangents from a Point on a Circle videos (4) question (38)
- Circles Examples and Solutions videos (21) question (143)
- Introduction to Circles videos (1) question (1)

4 Trigonometry

4.01 Introduction to Trigonometry

syllabus ▼

- 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° and 90°.
- Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°.
- Relationships between the ratios.

- Concepts :
- Introduction to Trigonometry videos (6) question (3)
- Introduction to Trigonometry Examples and Solutions videos (26) question (1)
- Trigonometric Ratios of an Acute Angle of a Right-angled Triangle question (116)
- Proof of Existence
- Trigonometric Ratios of Some Specific Angles videos (2) question (71)
- Relationships Between the Ratios
- Trigonometric Ratios question (76)

4.02 Heights and Distances

syllabus ▼

**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°.

- Concepts :
- Heights and Distances videos (28) question (261)

4.03 Trigonometric Identities

syllabus ▼

- Proof and applications of the identity sin
^{2}A + cos^{2}A = 1. Only simple identities to be given. - Trigonometric ratios of complementary angles.

- Concepts :
- Trigonometric Ratios of Complementary Angles videos (3) question (188)
- Trigonometric Identities videos (35) question (419)

5 Statistics and Probability

5.01 Statistics

syllabus ▼

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

- Concepts :
- Introduction of Statistics videos (1) question (14)
- Statistics Examples and Solutions videos (24) question (21)
- Median of Grouped Data videos (15) question (83)
- Mean of Grouped Data videos (8) question (113)
- Ogives (Cumulative Frequency Graphs) videos (7) question (16)
- Mode of Grouped Data question (37)
- Graphical Representation of Cumulative Frequency Distribution question (40)

5.02 Probability

syllabus ▼

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

- Concepts :
- Introduction to Probability videos (7)
- Probability Examples and Solutions videos (30) question (223)
- Probability - A Theoretical Approach videos (5) question (257)
- Concept Or Properties of Probability videos (4) question (4)
- Sample Space question (43)
- Simple Problems on Single Events videos (16) question (51)

6 Coordinate Geometry

6.01 Lines (In Two-dimensions)

syllabus ▼

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

- Concepts :
- Coordinate Geometry Examples and Solutions videos (23) question (150)
- Concepts of Coordinate Geometry videos (1) question (125)
- Graphs of Linear Equations
- Distance Formula videos (6) question (102)
- Section Formula videos (3) question (92)
- Area of a Triangle videos (7) question (118)

7 Mensuration

7.01 Areas Related to Circles

syllabus ▼

- 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.)

- Concepts :
- Perimeter and Area of a Circle videos (4) question (40)
- Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle videos (15) question (73)
- Areas Related to Circles Examples and Solutions videos (31) question (184)
- Areas of Sector and Segment of a Circle videos (15) question (54)
- Areas of Combinations of Plane Figures question (39)

7.02 Surface Areas and Volumes

syllabus ▼

- 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.)

- Concepts :
- Surface Area of a Combination of Solids videos (21) question (105)
- Conversion of Solid from One Shape to Another videos (5) question (23)
- Frustum of a Cone videos (5) question (70)
- Introduction of Surface Areas and Volumes videos (1) question (11)
- Surface Areas and Volumes Examples and Solutions videos (31) question (123)
- Volume of a Combination of Solids question (77)

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