| Units |
Topics |
| Sets, Relations, and Functions |
- Sets and their representation: Union, intersection, and complement of sets and their algebraic properties
- Power set: Relation, Type of relations, equivalence relations, functions
- One-one, into and onto functions, the composition of functions.
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| Complex Numbers and Quadratic Equations |
- Complex numbers as ordered pairs of reals
- Representation of complex numbers in the form a + ib and their representation in a plane
- Argand diagram
- Algebra of complex number
- Modulus and argument (or amplitude) of a complex number
- Square root of a complex number
- Triangle inequality
- Quadratic equations in real and complex number system and their solutions
- Relations between roots and coefficient, nature of roots, the formation of quadratic equations with given roots.
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| Matrices and Determinants |
- Matrices
- Algebra of matrices
- Type of matrices,
- Determinants and matrices of order two and three
- Properties of determinants
- Evaluation of determinants
- Area of triangles using determinants
- Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations
- Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices
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| Permutations and Combinations |
- Fundamental principle of counting
- Permutation as an arrangement and combination as section,
- Meaning of P (n,r) and C (n,r)
- Simple applications.
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| Binomial Theorem and its Simple Applications |
- Binomial theorem for a positive integral index
- General term and middle term
- Properties of Binomial coefficients and simple applications.
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| Sequence and Series |
- Arithmetic and Geometric progressions
- Insertion of arithmetic
- Geometric means between two given numbers,
- Relation between A.M and G.M sum up to n terms of special series
- Sn, Sn2, Sn3
- Arithmetico-Geometric progression
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| Limit, Continuity and Differentiability |
- Real-valued functions
- Algebra of functions
- polynomials, rational, trigonometric, logarithmic and exponential functions
- Inverse function. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions.
- Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions;
- Derivatives of order up to two
- Rolle’s and Lagrange’s Mean value Theorems, Applications of derivatives
- Rate of change of quantities, monotonicI ncreasing and decreasing functions,
- Maxima and minima of functions of one variable, tangents and normal.
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| Integral Calculus |
- Integral as an anti-derivative
- Fundamental Integrals involving algebraic, Trigonometric, exponential and logarithms functions.
- Integrations by substitution, by parts and by partial functions.
- Integration using trigonometric identities. Integral as limit of a sum.
- The fundamental theorem of calculus, properties of definite integrals.
- Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.
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| Differential Equations |
- Ordinary differential equations, their order and degree,
- Formation of differential equations
- Solution of differential equation by the method of separation of variables
- Solution of a homogeneous and linear differential equation.
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| Co-ordinate Geometry |
- Cartesian system of rectangular coordinates in a plane
- Distance formula, sections formula
- Locus and its equation,
- Translation of axes, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis.
- Straight line: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, the distance of a point form a line, equations of internal and external by sectors of angles between two lines co-ordinate of the centroid, orthocentre and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines.
- Circle, Conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and central, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent, sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for Y = mx +c to be a tangent and point (s) of tangency
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| 3D Geometry |
- Coordinates of a point in space
- Distance between two points
- Section formula, directions ratios and direction cosines, the angle between two intersecting lines.
- Skew lines, the shortest distance between them and its equation.
- Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.
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| Vector Algebra |
- Vectors and scalars,
- Addition of vectors, components of a vector in two dimensions and three-dimensional space
- Scalar and vector products, scalar and vector triple product.
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| Statistics and Probability |
- Measures of discretion
- Calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
- Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and binomial distribution.
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| Trigonometry |
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