Part 1: Algebra

• Arithmetic Progression:
  • Introduction to Sequence
  • Arithmetic Progression (A.P.) and Geometric Progression (G.P.)
  • General term of an A.P. and G.P.
  • Sum of the first 'n' terms of an A.P. and G.P.
  • Arithmetic Mean and Geometric Mean.
• Quadratic Equations
  • Introduction to quadratic equations
  • Solutions of quadratic equations
  • Nature of roots based on discriminate
  • Relation between roots of the equation and coefficient of the terms in the equation Equations reducible to quadratic form
• Linear equations in two variables
  • System of linear equations in two variables
  • Algebraic methods of solving linear equations in two variables
  • Graphical representation of different possibilities of solutions/Inconsistency
  • Graphical method of solving a system of linear equations
  • Determinant of order two
  • Cramer's rule
  • Consistency of pair of linear equations
• Probability:
  • Introduction to probability and related terms
  • Classical definition of probability
  • Types of events
  • Equally likely outcomes
  • Probability of an event
  • Properties of Probability
  • Addition theorem (without proof)
• Statistics:
  • Brief revision of Tabulation of data, inclusive and exclusive type of tables
  • Mean, median and mode of grouped data
  • Histograms, frequency polygon, frequency curve, pie diagram
  • Ogives (Cumulative frequency graphs)
  • Applications of ogives in determination of median
  • Relation between measures of central tendency
  • Introduction to normal distribution
  • Properties of normal distribution

Part 2: Geometry

• Similarity:
  • Properties of ratios of areas of two triangles
  • Basic proportionality theorem
  • Introduction to similarity
  • Similar triangles
  • Areas of two similar triangles
  • Similarity in right angled triangles
  • Pythagoras theorem and its converse
  • 30o-60o-90o theorem and 45 o-45 o-90 o theorem
  • Application of Pythagoras theorem in acute and obtuse angle.
• Circle:
  • Tangents and its properties
  • Theorem - Tangent at any point to the circle is perpendicular to the radius and its converse
  • Number of tangents from a point to a circle
  • Theorem- The length of two tangent segments drawn from a point outside the circle are equal
  • Touching circles
  • Introduction to an arc
  • Angle subtended by the arc to the centre and to the point on the circle
  • Cyclic quadrilateral
  • Tangent - Secant theorem
• Co-ordinate Geometry:
  • Slope of a line
  • Intercepts made by a line
  • Standard forms of equation of a line
  • General equation of a line.
• Geometric Constructions:
  • Division of line segment in a given ratio
  • Basic geometric constructions
  • Construction of tangent to the circle from the point on the circle and out side the circle.
  • Construction of tangent without using centre
  • Construction of triangle If the base, angle apposite to it and either median altitude is given
  • Construction of a triangle similar to a given triangle
• Trigonometry:
  • Angles in standard position.
  • Trigonometric ratios in terms of coordinates of point
  • Trigonometric Identities (with proof)
  • Use of basic identities and their applications
  • Problems on height and distance
• Menstruation:
  • Length of an arc
  • Area of the sector
  • Area of a Circular Segment
  • Euler's formula
  • Surface area and volume of cuboids Spheres, hemispheres, right circular cylinders cones, frustum of a cone.
  • Problems based on areas and perimeter/circumference of circle, sector and segment of a circle.
  • Problems on finding surface areas and volumes of combinations of any two of the following : cuboids, spheres, hemispheres and right circular cylinders/ cones
  • Problems involving converting one type of metallic solid into another.