Help your teen with Class 12 Maths, one chapter at a time

Your teen studies reflexive, symmetric and transitive relations, equivalence relations, and one-one, onto and bijective functions, with composition and invertibility.

• reflexive
• symmetric
• transitive
• equivalence relation
• one-one
• onto
• bijection
• composition

Your teen learns the inverse trig functions sin⁻¹, cos⁻¹, tan⁻¹ and others, their domains and principal value ranges, graphs and basic properties.

• inverse function
• principal value
• domain
• range
• restriction

Your teen organises data in matrices, adds and multiplies them, understands order and when multiplication is possible, finds transposes, and works with symmetric and skew-symmetric matrices.

• matrix
• order
• transpose
• symmetric
• skew-symmetric
• identity matrix

Your teen computes 2 × 3 and 3 × 3 determinants, uses them for areas of triangles, finds adjoints and inverses, and solves systems of linear equations with matrices.

• determinant
• minor
• cofactor
• adjoint
• inverse
• singular

Your teen checks continuity, differentiates composite, implicit, inverse trig, exponential and logarithmic functions, uses logarithmic differentiation, and finds second derivatives.

• continuous
• differentiable
• chain rule
• implicit
• logarithmic differentiation
• second derivative

Your teen uses derivatives for rates of change, finds where functions increase or decrease, and solves maxima and minima problems like the largest area for a given fence or cheapest container.

• rate of change
• increasing
• decreasing
• critical point
• maximum
• minimum
• second derivative test

Integration reverses differentiation. Your teen learns standard integrals, substitution, partial fractions and integration by parts, and evaluates definite integrals using the fundamental theorem.

• antiderivative
• constant of integration
• substitution
• by parts
• partial fractions
• definite integral

Your teen uses definite integrals to find areas under curves and between a curve and lines, with circles and parabolas.

• area under a curve
• limits
• definite integral
• bounded region

Your teen forms differential equations, finds order and degree, and solves first-order equations by separating variables, homogeneous methods and linear equations with integrating factors.

• differential equation
• order
• degree
• separable
• homogeneous
• integrating factor

Your teen represents quantities with direction as vectors, adds them, finds magnitudes and unit vectors, and uses dot and cross products for angles, projections and areas.

• vector
• magnitude
• unit vector
• dot product
• cross product
• projection

Your teen uses direction cosines and ratios, writes equations of lines in space in vector and Cartesian forms, finds angles between lines and the shortest distance between skew lines.

• direction cosines
• direction ratios
• vector equation
• Cartesian equation
• skew lines
• shortest distance

Your teen forms linear programming problems from real situations, graphs the feasible region from inequalities, and finds the maximum or minimum of an objective function at corner points.

• objective function
• constraint
• feasible region
• corner point
• optimal solution

Your teen uses conditional probability, the multiplication rule, independence, Bayes’ theorem, and random variables with probability distributions and mean.

• conditional probability
• independent
• Bayes’ theorem
• random variable
• probability distribution
• mean