CHSE Odisha Elective Mathematics study plan

Evaluate limits of algebraic, trigonometric, exponential and logarithmic functions using standard limit results, rationalisation and the indeterminate-form techniques tested in CHSE papers.

Test continuity and differentiability of piecewise-defined functions at a given point by computing left-hand and right-hand limits and derivatives separately.

Differentiate composite, implicit, parametric and inverse-trigonometric functions, and state the conditions under which each rule applies.

Classify relations as reflexive, symmetric, transitive or equivalence, and find domain, range, composite and inverse of standard functions.

Build a one-page formula sheet covering limits, standard derivatives and function transformations for later revision.

Integrate standard algebraic, trigonometric, exponential and inverse-trigonometric forms from memory without consulting the textbook.

Apply substitution, integration by parts (including the ILATE order), partial fractions and trigonometric identities to reduce unfamiliar integrands to standard forms.

Evaluate definite integrals using the fundamental theorem and the symmetry and periodic properties, including integrals of the form ∫₀ᵃ f(x)dx rewritten as ∫₀ᵃ f(a−x)dx.

Set up and compute the area bounded by a curve, the x-axis and given ordinates, and the area between two intersecting curves.

Maintain an error notebook listing every integral that required more than two attempts, with the correct first step written out.

Carry out matrix addition, multiplication, transpose and inversion, and verify properties such as (AB)ᵀ = BᵀAᵀ on small numerical examples.

Evaluate determinants of order up to 3×3 using row and column operations and cofactor expansion, and apply the properties of determinants to simplify before expanding.

Solve systems of linear equations in two and three variables by Cramer's rule, matrix inversion and row reduction, and identify inconsistent and infinitely-many-solution cases from the determinant.

Find principal values of inverse trigonometric functions and simplify expressions such as combinations of arcsin, arccos and arctan using triangle and identity methods.

Solve inverse-trigonometric equations and prove standard identities within their valid domains.

Solve arrangements and selections problems with repeated objects, fixed positions and at-least/at-most conditions, justifying whether order matters in each case.

Expand binomials with positive integral indices, find a specified term, the middle term and the term independent of x, and use the general term for coefficient problems.

Identify and sum arithmetic and geometric progressions, including infinite geometric series, arithmetico-geometric series and sums of squares and cubes of the first n natural numbers.

Compute modulus, argument, conjugate and polar form of complex numbers, and apply De Moivre's theorem to powers and roots.

Solve quadratic equations with real and complex coefficients, and relate roots to coefficients including the discriminant-based nature of roots.

Find equations of tangents and normals to curves at given points and at points defined by a condition such as a given slope.

Determine intervals of increase and decrease, locate stationary points and classify local maxima and minima using first and second derivative tests.

Solve applied rate-of-change and maxima–minima problems, including simple optimisation word problems, with the variable and constraint stated explicitly.

Solve first-order differential equations by separation of variables and by the integrating-factor method for linear equations, and form a differential equation from a given family of curves.

Verify every solution found by substituting it back into the original differential equation.

Compute dot and cross products of vectors, and use them to find angles, projections, areas of triangles and parallelograms, and the scalar triple product for volumes.

Write the vector and Cartesian equations of a line and a plane, and calculate the shortest distance between skew lines and the distance of a point from a plane.

Determine whether two lines are parallel, intersecting or skew, and find the angle between two lines and between two planes.

Formulate a linear programming problem from a word problem by defining decision variables, writing the objective function and constraints, and identifying non-negativity conditions.

Solve two-variable linear programming problems graphically, test corner points, and recognise bounded versus unbounded feasible regions and infeasible cases.

Compute conditional probability, apply the multiplication theorem and Bayes' theorem to two-stage experiments, and use the binomial distribution for repeated independent trials.

Calculate mean, variance and standard deviation for raw and grouped data, and interpret the results in the context of the problem.

Re-solve the fifteen hardest integrals from the week 2 portfolio without notes to confirm retention of substitution, parts and partial fractions.

Complete a mixed speed drill combining probability calculations with definite-integral evaluation to practise switching between techniques under time pressure.

Attempt two full-length papers under strict three-hour exam conditions, allocating time according to the domain weightings used in this plan.

Re-derive the standard integrals and determinant properties from memory, and re-solve every question marked wrong in earlier weeks' error logs.

Complete a rapid matrices and determinants revision covering inversion, Cramer's rule and consistency of systems, targeting zero arithmetic slips.

Produce a final one-page revision card of formulas from all twelve domains and review it daily for the last four days before the exam.