Topics with syllabus and resources
 Introduction of Real Numbers
 Real Numbers Examples and Solutions
 Euclid’s Division Lemma
 Euclid’s division algorithm
 Fundamental Theorem of Arithmetic
1) Statements After Reviewing Work Done Earlier
2) Statements After Illustrating
 Fundamental Theorem of Arithmetic Motivating Through Examples
 Proofs of Irrationality
of Squareroot of 2
 Revisiting Irrational Numbers
Decimal Representation of Rational Numbers in Terms of Termination or Nonterminating Recurring Decimals.
 Revisiting Rational Numbers and Their Decimal Expansions
 Decimal Representation of Rational Numbers in Terms of Terminating Or Nonterminating Recurring Decimals
 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/nonterminating recurring decimals.
 Introduction of System of Linear Equations in Two Variables
 Graphical Method of Solution of a Pair of Linear Equations
 Graphical Method of Solving a System of Linear Equations
 Algebraic Methods of Solving a Pair of Linear Equations
 Equations Reducible to a Pair of Linear Equations in Two Variables
 Equations Reducible to Linear Equations
 Consistency of Pair of Linear Equations
 Inconsistency of Pair of Linear Equations
 Algebraic Conditions for Number of Solutions
 Simple Situational Problems
 Pair of Linear Equations in Two Variables
Pair of Linear Equations in Two Variables Examples and Solutions
 Relation Between Coefficient
 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.
 Arithmetic Progression
 General Term of an Arithmetic Progression
 nth Term of an AP
 general term of the AP
 Sum of First n Terms of an AP
 Sum of the First 'N' Terms of an Arithmetic Progression
 Derivation of the n th Term
 Application in Solving Daily Life Problems
 Arithmetic Progressions Examples and Solutions
 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.
 Quadratic Equations
 Introduction and Standard Form of a Quadratic Equation  ax^{2} + bx + c = 0, (a ≠ 0)
 Solutions of Quadratic Equations by Factorization
 Solutions of Quadratic Equations by Completing the Square
 method of completing the square
 Nature of Roots
 Nature of Roots Based on Discriminant
 two distinct real roots, two equal real roots, no real roots
 Solutions of Quadratic Equations by Using Quadratic Formula and Nature of Roots

Two distinct real roots if b^{2} – 4ac > 0

Two equal real roots if b^{2} – 4ac = 0

No real roots if b^{2} – 4ac < 0
 Relationship Between Discriminant and Nature of Roots
 Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
 Quadratic Equations Examples and Solutions
 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.
 Introduction to Polynomials
 Geometrical Meaning of the Zeroes of a Polynomial
 Relationship Between Zeroes and Coefficients of a Polynomial
 Division Algorithm for Polynomials
 Polynomials Examples and Solutions
 Zeros of a polynomial.
 Relationship between zeros and coefficients of quadratic polynomials.
 Statement and simple problems on division algorithm for polynomials with real coefficients.
 Introduction to Circles
 Tangent to a Circle
Theorem  The tangent at any point of a circle is perpendicular to the radius through the point of contact.
 Number of Tangents from a Point on a Circle
Theorem  The Length of Two Tangent Segments Drawn from a Point Outside the Circle Are Equal
 Circles Examples and Solutions
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.
 Similar Figures
 Similarity of Triangles
 Basic Proportionality Theorem Or Thales Theorem
 Criteria for Similarity of Triangles
 Areas of Similar Triangles
 Pythagoras Theorem
 Pythagoras Theorem : In a rightangled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.
 In a rightangled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.
 Similarity Triangle Theorem
If in a two triangles corresponding angles are equal then their corresponding sides are in same ratio hence two triangle are similar
 Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
 Triangles Examples and Solutions
 Angle Bisector
 Similarity Examples and Solutions
 Ratio of Sides of Triangle
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.
 Division of a Line Segment
 Division of Line Segment in a Given Ratio
 Construction of a Triangle Similar to a Given Triangle
 To divide a line segment in a given ratio
 To construct a triangle similar to a given triangle as per given scale factor
 Construction of Tangents to a Circle
 Construction of Tangent to the Circle from the Point Out Side the Circle
 To construct the tangents to a circle from a point outside it
 Constructions Examples and Solutions
 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.
 Heights and Distances
 Heights and Distances  Angle of Elevation, Angle of Depression
 Height and Distance Examples and Solutions
 line of sight, angle of elevation, angle of depression
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°.
 Trigonometric Ratios of Complementary Angles
We know that complementary angles are the set of two angles such that their sum is equal to 90°. For example: 30° and 60° are complementary to each other as their sum is equal to 90°.The triangle ∆ABC given below, is right angled at B; ∠A and ∠C form a complementary pair.
 Trigonometric Identities
 Proof and applications of the identity sin^{2}A + cos^{2}A = 1. Only simple identities to be given.
 Trigonometric ratios of complementary angles.
 Introduction to Trigonometry
 Introduction to Trigonometry Examples and Solutions
 Trigonometric Ratios
 Trigonometric Ratios of an Acute Angle of a Rightangled Triangle
 Trigonometric Ratios of Some Specific Angles
Trigonometric ratios of some specific angles : For certain specific angles such as 30°, 45° and 60°, which are frequently seen in applications, we can use geometry to determine the trigonometric ratios.
 Trigonometric Ratios of Complementary Angles
We know that complementary angles are the set of two angles such that their sum is equal to 90°. For example: 30° and 60° are complementary to each other as their sum is equal to 90°.The triangle ∆ABC given below, is right angled at B; ∠A and ∠C form a complementary pair.
 Trigonometric Identities
 Proof of Existence
Well Defined
 Relationships Between the Ratios
 Trigonometric ratios of an acute angle of a rightangled 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.
 Introduction to Probability
 Probability  A Theoretical Approach
 Classical Definition of Probability
 Type of Event  Impossible and Sure Or Certain
 assume that all the experiments have equally likely outcomes, impossible event, sure event or a certain event, complementary events,
 Sample Space
 Probability Examples and Solutions
 Concept Or Properties of Probability
 Simple Problems on Single Events
Not using set notation
 Classical definition of probability.
 Simple problems on single events (not using set notation).
 Introduction of Statistics
 Mean of Grouped Data
 Computation of Measures of Central Tendency  Mean
 Direct Method of Mean
 Assumed Mean Method
 Step Deviation Method for Mean
 Stepdeviation method
 Mode of Grouped Data
 Computation of Measures of Central Tendency  Mode
 Median of Grouped Data
 Computation of Measures of Central Tendency  Median of Grouped Data
 cumulative frequency column
 Graphical Representation of Cumulative Frequency Distribution
 Statistics Examples and Solutions
 Ogives (Cumulative Frequency Graphs)
 Mean, median and mode of grouped data (bimodal situation to be avoided).
 Cumulative frequency graph.
 Concepts of Coordinate Geometry
 Coordinate Geometry Examples and Solutions
 Distance Formula
 Section Formula
 Area of a Triangle
We know that Area of a triangle = `1/2 xx "base" xx "altitude"`, but how to find area of a triangle on a plane? Here, we will learn the derivation of a formula to find area of triangle on plane.
 Graphs of Linear Equations
 Basic Geometric Constructions
 Concepts of coordinate geometry, graphs of linear equations.
 Distance formula. Section formula (internal division).
 Area of a triangle.
 Perimeter and Area of a Circle
 Circumference of Circle
 Area of a Circle
 Areas of Sector and Segment of a Circle
 Area of the Sector and Circular Segment
 Length of an Arc
 Areas of Combinations of Plane Figures
 Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle
 Areas Related to Circles Examples and Solutions
 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.)
 Introduction of Surface Areas and Volumes
 Surface Area of a Combination of Solids
 Volume of a Combination of Solids
 Conversion of Solid from One Shape to Another
 Frustum of a Cone
 Surface Areas and Volumes Examples and Solutions
 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.)