Class 12 Mathematics

Chapters

1. 1Relations and FunctionsLesson: Relations and Functions · 15 sections · chapter quiz

   Students in the same section, lines that are parallel, numbers with the same remainder on division by 5 — these 'sameness' relations split a set into neat groups. Functions that pair inputs and outputs perfectly allow reversing a process, as in encryption.

   • • I can test whether a relation is reflexive, symmetric, transitive and an equivalence relation.
   • • I can describe equivalence classes.
   • • I can prove whether a function is one-one (injective), onto (surjective) or bijective.
2. 2Inverse Trigonometric FunctionsLesson: Inverse Trigonometric Functions · 15 sections · chapter quiz

   A ramp rises 1 m over 4 m — what is its angle? We know the ratio and want the angle; inverse trigonometric functions answer exactly this.

   • • I can explain why trigonometric functions must be restricted to have inverses.
   • • I can state the domains, ranges (principal value branches) and graphs of sin⁻¹, cos⁻¹, tan⁻¹, cot⁻¹, sec⁻¹ and cosec⁻¹.
   • • I can find principal values and simplify simple expressions.
3. 3MatricesLesson: Matrices · 15 sections · chapter quiz

   A spreadsheet of sales by shop and month, the pixels of a photo, and the coefficients of simultaneous equations are rectangular arrays. Matrices let us compute with whole arrays at once.

   • • I can describe matrix notation, order, equality and types of matrices.
   • • I can add, scalar-multiply and multiply matrices and state their properties, including non-commutativity.
   • • I can work with transposes, symmetric and skew-symmetric matrices and prove that an inverse, if it exists, is unique.
4. 4DeterminantsLesson: Determinants · 15 sections · chapter quiz

   Every square matrix has a single number — its determinant — that tells whether the matrix can be inverted, whether a system of equations has a unique solution, and how areas scale.

   • • I can evaluate determinants of order up to 3 and use minors and cofactors.
   • • I can use determinants to find the area of a triangle and test collinearity.
   • • I can find the adjoint and inverse of a matrix and solve linear systems using A⁻¹, deciding consistency.
5. 5Continuity and DifferentiabilityLesson: Continuity and Differentiability · 15 sections · chapter quiz

   A thermometer reading changes without jumps; a taxi fare jumps at each kilometre. Continuity describes smooth, unbroken change; differentiability describes change without sharp corners.

   • • I can test continuity at a point and on an interval.
   • • I can relate differentiability to continuity and differentiate composite, implicit, inverse trigonometric, exponential, logarithmic and parametric functions.
   • • I can use logarithmic differentiation and find second-order derivatives.
6. 6Application of DerivativesLesson: Application of Derivatives · 15 sections · chapter quiz

   How fast is a balloon's radius growing? Which can design uses the least metal? Derivatives turn these questions into calculations.

   • • I can use derivatives as rates of change of related quantities.
   • • I can determine intervals where a function is increasing or decreasing.
   • • I can find local and absolute maxima and minima using the first and second derivative tests and solve optimisation problems.
7. 7IntegralsLesson: Integrals · 15 sections · chapter quiz

   If we know a car's speed at every instant, how far has it travelled? Integration reverses differentiation and adds up tiny pieces to find totals.

   • • I can integrate as the inverse process of differentiation and use standard formulas.
   • • I can integrate by substitution, partial fractions and parts, including the CBSE special forms.
   • • I can evaluate definite integrals using the Fundamental Theorem of Calculus and basic properties.
8. 8Application of IntegralsLesson: Application of Integrals · 15 sections · chapter quiz

   Architects estimate the area of a parabolic arch window; engineers find the area of an elliptical race track. Definite integrals compute areas of curved regions exactly.

   • • I can find the area between a curve and an axis using definite integrals.
   • • I can find areas bounded by lines, circles, parabolas and ellipses in standard form.
   • • I can sketch regions and choose vertical or horizontal strips.
9. 9Differential EquationsLesson: Differential Equations · 15 sections · chapter quiz

   Population growth, cooling of tea and the charge on a capacitor are described by how quantities change. Differential equations connect a quantity with its rate of change.

   • • I can find the order and degree of a differential equation and distinguish general and particular solutions.
   • • I can solve equations by separation of variables and homogeneous first-order equations.
   • • I can solve linear equations dy/dx + Py = Q and dx/dy + P₁x = Q₁ using an integrating factor.
10. 10Vector AlgebraLesson: Vector Algebra · 15 sections · chapter quiz

    Wind blowing north-east at 20 km/h, a force pushing a box, a plane's displacement — these need both size and direction. Vectors capture both and let us calculate with them.

    • • I can describe vectors, their magnitude, direction cosines and direction ratios, and the types of vectors.
    • • I can add vectors, multiply by scalars, use components and position vectors and the section formula.
    • • I can compute and interpret scalar (dot) and vector (cross) products and their applications.
11. 11Three Dimensional GeometryLesson: Three Dimensional Geometry · 15 sections · chapter quiz

    Air-traffic controllers check whether two flight paths could collide or just pass at a safe distance. Lines in space can meet, be parallel, or be skew — and we can compute their closest approach.

    • • I can find direction cosines and ratios of a line through two points.
    • • I can write vector and Cartesian equations of a line and find the angle between two lines.
    • • I can identify skew lines and find the shortest distance between two lines.
12. 12Linear ProgrammingLesson: Linear Programming · 15 sections · chapter quiz

    A furniture maker has limited wood and labour and wants maximum profit; a dietician wants the cheapest diet meeting nutrition needs. Linear programming finds the best choice under constraints.

    • • I can formulate a linear programming problem with decision variables, objective function and constraints.
    • • I can solve two-variable problems graphically using the corner point method.
    • • I can describe feasible and infeasible regions and solutions, bounded and unbounded regions and optimal solutions.
13. 13ProbabilityLesson: Probability · 15 sections · chapter quiz

    A medical test is 99% accurate, yet a positive result may still mean the patient is probably healthy. Conditional probability and Bayes' theorem explain how new information changes probabilities.

    • • I can compute conditional probability and use the multiplication theorem.
    • • I can identify independent events and use the theorem of total probability.
    • • I can state, derive and apply Bayes' theorem.