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BITSAT Syllabus for Mathematics

1. Algebra

  • 1. Triangle inequality, geometric interpretations, complex numbers, roots of complex numbers, addition, properties of modulus and principal argument, conjugation, multiplication, polar representation.
  • 2. Relation between roots and coefficients, equations reducible to quadratic equations, nature of roots, theory of quadratic equations, quadratic equations in real and complex number system and their solutions.
  • 3. Logarithms and their properties
  • 4. Sums of finite arithmetic and geometric progressions, sums of squares and cubes of the first natural numbers, infinite geometric series, arithmetic, geometric and harmonic means, geometric and harmonic progressions, arithmetico-geometric series.
  • 5. Exponential series
  • 6. Simple applications, Permutations and combinations, combination as selection and permutations as an arrangement.
  • 7. Properties of binomial coefficients, binomial theorem for a positive integral index.
  • 8. Solutions of simultaneous linear equations in two or three variables, matrices and determinants of order two or three, inverse and adjoint of matrices, addition and multiplication of matrices, properties and evaluation of determinants.
  • 9. Functions and relations, equivalence relations, one-one, composition of mappings, sets, algebra of sets applications, mapping, into and onto mappings.
  • 10. Mathematical Induction
  • 11. Solution of linear inequalities in one and two variables, Linear inequalities.

2. Trigonometry

  • 1. Functions and identities, trigonometric ratios
  • 2. Solution of trigonometric equations
  • 3. Properties of triangles and solutions of triangles
  • 4. Inverse trigonometric functions
  • 5. Heights and distances

3. Two-dimensional Co-ordinate Geometry

  • 1. Distance between two points, shift of origin, Cartesian coordinates, section formulae
  • 2. Lines through the point of intersection of two given lines, concurrent lines, equation of the bisector of the angle between two lines, straight lines and pair of straight lines, distance of a point from a line, angle between two lines, equation of straight lines in various forms.
  • 3. Circle and family of circles: intersection of circle with a straight line or a circle, conditions for two intersecting circles to be orthogonal, equation of circle through point of intersection of two circle, equation of circle in various form, parametric equations of a circle, normal and chords, equation of tangent.
  • 4. Conic sections: directrices and foci, equations of tangent and normal, parabola, parametric forms, conditions for y=mx+c to be a tangent and point of tangency, ellipse and hyperbola their eccentricity.

4. Three Dimensional Coordinate Geometry

  • 1. Direction ratios and direction cosines, equation of a straight line in space and skew lines
  • 2. Angle between two lines whose direction ratios are given
  • 3. Distance of a point from a plane, equation of a plane, condition for coplanarity of three lines

5. Differential Calculus

  • 1. Limits and continuity of the sum, product and quotient of two functions, difference, domain and range of a real valued function, differentiability
  • 2. Derivative of the sum, product and quotient of two functions, difference, chain rule, derivate of different of functions (rational, inverse trigonometric, logarithmic, polynomial, trigonometric, exponential, implicit functions).
  • 3. Normals and tangents, geometric interpretation of derivative
  • 4. Minima and maxima of a function, increasing and decreasing functions
  • 5. Mean value theorem and intermediate value theorem, Rollís theorem

6. Integrals Calculus

  • 1. Indefinite integrals of standard functions, integration as the inverse process of differentiation.
  • 2. Methods of integration: integration by parts, integration by substitution, integration by trigonometric identities, integration by partial fractions.
  • 3. Fundamental theorem of integral calculus and its applications, definite integrals and their properties.
  • 4. Application of definite integrals to the determination of areas of regions bounded by simple cuves.
7. Ordinary Differential Equations

  • 1. Variables separable method
  • 2. Solution of homogeneous differential equations
  • 3. Linear first order differential equations
8. Probability

  • 1. Addition and multiplication rules of probability
  • 2. Conditional probability
  • 3. Independent events
  • 4. Discrete random variables and distributions

9. Vectors

  • 1. Scalar multiplication, addition of vectors
  • 2. Cross and dot products of two vectors
  • 3. Scalar triple products and its geometrical interpretations

10. Statistics

  • 1. Measures of skewness and central tendency
  • 2. Measures of dispersion

11. Linear Programming

  • 1. Formulation of linear programming
  • 2. Solution of linear programming using graphical method


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