Kerala Plus Two Mathematics (DHSE) study plan

Derive and apply the binomial expansion for positive integral indices, and compute the general term, middle term, and a specified term coefficient without error.

Solve permutation and combination problems by classifying each as arrangement or selection, handling repetition and restriction conditions explicitly.

Determine whether a given relation is reflexive, symmetric, and transitive, and classify it as an equivalence relation with justification.

Compute domain, range, and composition of two real functions, and test invertibility of a function on a stated interval.

Build a one-page error log recording every mistake type from practice sets on counting and relations.

Compute sums of finite arithmetic and geometric progressions, including infinite geometric sums with the convergence condition stated.

Identify arithmetic and geometric means inserted between given numbers and solve word problems on growth and depreciation.

Perform matrix addition, scalar multiplication, and multiplication, verifying non-commutativity with a concrete counterexample.

Compute determinants of order 2 and 3 by expansion and by properties, and find the inverse of a nonsingular matrix using the adjoint.

Solve a system of three linear equations using matrix inversion and state the consistency condition via determinants.

Compute dot and cross products, and use them to find angle between vectors, projection, and area of a triangle.

Write the vector and Cartesian equations of a line in space from two points and from a point with a direction vector.

Find the shortest distance between two skew lines and the angle between two lines using direction ratios.

Evaluate principal values of inverse trigonometric functions and simplify expressions using the standard identities for sums of arctangents.

Sketch the principal-value branches of the six inverse trigonometric functions and mark their domains and ranges.

Test continuity of piecewise functions at a point using one-sided limits, and classify each discontinuity as removable, jump, or infinite.

Differentiate composite, implicit, inverse trigonometric, and parametric functions using chain rule, logarithmic differentiation, and parametric differentiation.

Apply Rolle's theorem and the mean value theorem to verify hypotheses on a stated interval and locate the guaranteed point.

Find intervals of increase and decrease, local extrema by first and second derivative tests, and absolute extrema on a closed interval.

Solve optimisation word problems involving volume, area, and cost, stating the constraint and the objective function explicitly.

Integrate standard algebraic, trigonometric, exponential, and rational forms using substitution and by parts.

Evaluate definite integrals using properties such as symmetry and periodicity, and apply the fundamental theorem correctly.

Integrate rational functions by partial fractions and complete the square for quadratic denominators.

Compute areas bounded by curves, lines, and the axes by setting up definite integrals, and identify the correct region from an algebraic description.

Assemble a personal table of 25 integrals encountered most often in practice, each verified by differentiating back.

Classify differential equations by order and degree, and form a differential equation from a given family of curves by eliminating parameters.

Solve variable-separable and homogeneous first-order differential equations, and apply linear differential equations with an integrating factor.

Solve particular solutions from initial conditions and interpret the constant of integration in applied contexts.

Apply the addition theorem and conditional probability, and verify independence of two events with a computed check.

Use Bayes' theorem on a stated prior and likelihood setup, and compute mean and variance of a random variable from its probability distribution.

Solve Bernoulli trials problems using the binomial distribution, computing exact and at-least probabilities.

Evaluate the validity of compound statements using truth tables, and identify tautologies, contradictions, and logical equivalences.

Write the converse, contrapositive, and inverse of a conditional statement and test validity of a simple argument.

Compute mean deviation and variance for grouped and ungrouped data, and compare variability of two distributions using coefficients of variation.

Formulate and graphically solve linear programming problems, identifying the feasible region, corner points, and optimal value with the boundedness condition checked.

Complete three full-length timed mock papers under exam conditions and record section-wise time allocation.

Re-derive from memory the highest-frequency formulas across all twelve domains and mark any gap for immediate revision.

Re-solve every item in the accumulated error log and confirm each is now correct without notes.

Practise presentation discipline: stating conditions, showing intermediate steps, and writing final answers with correct units and notation.

Rank domains by residual weakness from mock scores and spend the final sessions only on the bottom three.