S. No | Chapter Name | SubTopics |
1 | Sets, Relations, and Functions | - Sets and their representation: Union, intersection
- 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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2 | 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
- 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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3 | Matrices And Determinants | - Matrices, Algebra of matrices, type of matrices
- Determinants and matrices of order two and three, evaluation of determinants, area of triangles using determinants
- Adjoint, and evaluation of inverse of a square matrix using determinants
- Test of consistency and solution of simultaneous linear equations in two or three variables using matrices
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4 | Permutations And Combinations | - The 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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5 | Binomial Theorem and Its Simple Applications | - Binomial theorem for a positive integral index
- General term and middle term, and simple applications
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6 | Sequence And Series | - Arithmetic and Geometric progressions
- Insertion of arithmetic, geometric means between two given numbers
- Relation between A.M and G.M
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7 | 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.
- Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima, and minima of functions of one variable
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8 | Integral Calculus | - Integral as an antiderivative, Fundamental integral involving algebraic, trigonometric, exponential, and logarithmic functions.
- Integrations by substitution, by parts, and by partial functions. Integration using trigonometric identities.
- Evaluation of simple integrals of the type
\int \frac{d x}{x^2+a^2}, \int \frac{d x}{\sqrt{x^2 \pm a^2}}, \int \frac{d x}{a^2-x^2}, \int \frac{d x}{\sqrt{a^2-x^2}}, \int \frac{d x}{a x^2+b x+c} \int \frac{d x}{\sqrt{a x^2+b x+c}} \int \frac{(p x+q) d x}{a x^2+b x+c} \int \frac{(p x+q) d x}{\sqrt{a x^2+b x+c}} \sqrt{a^2 \pm x^2} d x \\ \sqrt{x^2-a^2} d x - 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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9 | Differential Equations | - Ordinary differential equations, their order, and degree
- The solution of differential equation by the method of separation of variables
- Solution of a homogeneous and linear differential equation of the type dydx+p(x)y=q(x)
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10 | Co-Ordinate Geometry | - Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus, and its equation, the slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate 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
- Coordinate of the centroid, orthocentre, and circumcentre of a triangle
- 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 sections of conics, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms
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11 | Three Dimensional Geometry | - Coordinates of a point in space, the distance between two points, section formula
- Directions ratios, and direction cosines, and the angle between two intersecting lines.
- Skew lines, the shortest distance between them, and its equation. Equations of a line
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12 | Vector Algebra | - Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional space
- Scalar, and vector products
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13 | 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,
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14 | Trigonometry | |
