Part 1: Algebra

• Sets:
  • Introduction
  • Methods of writing sets
  • Types of sets
  • Subset - Proper, Improper subset
  • Super set
  • Universal set
  • Venn diagrams
  • Operations on sets
  • Relations between various operations
  • Number of elements in the set and related results
• Real Numbers:
  • Revision of natural numbers, integers, rational numbers and irrational numbers
  • Existence of irrational numbers and their representations on the number line
  • Every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number
  • Properties of real numbers
  • Definition of nth root of a real number
  • Surds - Definition
  • Forms of surds
  • Operations and Laws of surds
  • Rationalization of Surds
  • Absolute value of real numbers
  • Euclid's division Lemma
  • Fundamental theorem of Arithmetic
• Algebraic Expressions:
  • Introduction to algebraic expression
  • Operations on algebraic expressions
  • Methods of factorization of algebraic expression
  • Introduction to polynomials
  • Operations on polynomials
  • Value of polynomials
  • Zeros/roots of polynomial
  • Relation between zeros and coefficient of polynomials
  • Remainder theorem
  • Factor theorem
• Graphs:
  • Cartesian coordinate system
  • Understanding of graphs of lines parallel to axes
  • Graph of line ax + by + c = o
• Linear equations in two variables
  • System of linear equations
  • Solution of system of linear equations in two variables (Algebraic methods)
• Ratio, proportion and variation
  • Introduction to ratio
  • Properties of ratio
  • Properties of equal ratios
  • Theorem on equal ratios
  • Percentage as a ratio
  • Introduction to proportion
  • Introduction to variation
  • Revision of concepts based on Direct
  • Variation, Inverse variation
  • Mixed variation
  • Real life problems based on ratio, proportion and variation
• Statistics:
  • Collection of data
  • Classification and tabulation of data
  • Diagrammatic representation of data
  • Graphical representation of data
  • Mean, median, mode of ungrouped data

Part 2: Geometry

• Lines and Angles:
  • Introductions to line
  • Basic terms and definitions related to line
  • Introduction to Euclid's Geometry
  • Plane separation axiom
  • Introduction to angles in terms of rotation
  • Directed angles, Sexagesimal system
  • Types of angles
  • Zero angle, straight angle, co terminal angle
  • Relation between angles
  • Introduction to mathematical proofs
  • Parallel lines
  • Results on parallel lines and transversal
  • Tests of parallel lines
  • Results on perpendicular lines
  • Distance of a point from a line
• Triangles:
  • Types of triangles
  • Terms related to triangle
  • Properties of triangle
  • Exterior angles and corresponding interior opposite angles
  • Results involving exterior angle and corresponding interior opposite angles
  • Similar triangles
• Congruence of triangles:
  • Criteria of congruent triangles
  • Theorem of an isosceles triangle and its converse
  • Perpendicular bisector theorem
  • Angle bisector theorem
  • Properties of triangles based on inequalities
  • Property of perpendicular drawn from a point outside the line.
• Circle:
  • Introduction to circle and related terms
  • Circle passing through the given points
  • One and only one circle passes through the three non collinear points.
  • Congruence of circles
  • Properties of chords of the circle
• Quadrilateral:
  • Properties of quadrilateral
  • Properties of parallelogram
  • Properties of rectangle
  • Properties of a trapezium
  • Properties of a rhombus
  • Properties of a square
  • Kite
  • Tests for particular quadrilateral
  • Theorem on midpoints of two sides of a triangle and its converse
  • Geometry
• Coordinate Geometry:
  • Distance formula
  • Section formula
  • Area of a triangle
• Geometric constructions:
  • Basic construction – perpendicular bisector of given segment.
  • Construction of a triangle( Sum/difference of two sides and base angles is given Perimeter and base angles are given
• Trigonometry:
  • Introduction to trigonometric ratios
  • Trigonometric Ratios of angles 0o, 30 o, 45 o, 60 o, 90 o
  • Trigonometric identities for complementary angles
• Mensuration:
  • Area of triangle
  • Area of regular hexagon, polygon
  • Area of quadrilaterals
  • If two parallelograms lie between two parallel lines and have the same base then they have the same area. If a triangle and a parallelogram have the same base and lie between the same parallel lines, then the area of the triangle is half the area of the parallelogram.
  • Perimeter of triangle and quadrilateral
  • Area of circle