UNIT I: NUMBER SYSTEMS


REAL NUMBERS

  • Euclid's division lemma
  • The Fundamental theorem of arithmetic
  • Revisiting irrational numbers
  • Revisiting rational numbers and their decimal expansion
  • irrationality of √2, √3, √5

UNIT II: ALGEBRA


Polynomials

  • Geometrical meaning of zeroes of polynomial
  • Relationship between zeroes and coefficients of polynomial
  • Division algorithms for polynomial

Linear Equation in Two Variables

  • Pair of linear equation in two variables
  • Algebraic method of solving pair of linear equation- substitution method
  • Algebraic method of solving pair of linear equation- elimination method
  • Algebraic method of solving pair of linear equation- cross multiplication method
  • Equation reducible to pair of linear equation in two variables

QUADRATIC EQUATIONS

  • Quadratic Equations: ax2+bx+c=0=0, (a ≠ 0)
  • Solution of quadratic equation by factorization
  • Solution of quadratic equation by completing the square
  • Nature of roots
  • Situational problems based on quadratic equations

ARITHMETIC PROGRESSIONS

  • Introduction
  • Arithmetic progressions
  • Derivation of the nth term
  • sum of the first n terms of A.P.
  • application in solving daily life problems

UNIT III: COORDINATE GEOMETRY


LINES (In two-dimensions)

  • Concepts of coordinate geometry
  • Graphs of linear equations
  • Distance formula
  • Section formula (internal division)
  • Area of a triangle

UNIT IV: GEOMETRY


Triangles

  • Similar figures
  • Similarity of triangles
  • Basic Proportionality Theorem
  • Criteria for similarity of triangles
  • Area of similar triangles
  • Pythagoras theorem
  • Converse of Pythagoras theorem

CIRCLES

  • Tangent to a circle
  • Number of tangent from a point to a circle

Constructions

  • Division of a line segment
  • Construction of triangle similar to given triangle
  • Construction of tangents to a circle

UNIT V: TRIGONOMETRY


INTRODUCTION TO TRIGONOMETRY

  • Trigonometry: Introduction
  • Trigonometric ratios of some specific angles
  • Trigonometric ratios of complementary angles
  • Trigonometric identities
  • Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°.
  • Relationships between the ratios

TRIGONOMETRIC IDENTITIES

  • Proof and applications of the identity sin2A + cos2A = 1
  • Trigonometric ratios of complementary angles

HEIGHTS AND DISTANCES

  • Simple and believable problems on heights and distances
  • Angles of elevation / depression of 30°, 45°, 60°.

UNIT VI: MENSURATION


AREAS RELATED TO CIRCLES

  • Perimeter and area of a circle
  • Area of sector and segment of a circle
  • Area of segment of a circle
  • Problems on Area and Perimeter

SURFACE AREAS AND VOLUMES

  • Problems on finding 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


STATISTICS

  • Mean of grouped data
  • Mode of grouped data
  • Median of grouped data
  • Graphical representation of cumulative frequency distribution

Probability

  • Introduction
  • Probability- a theoretical approach