Section A1 — Algebra
- Matrices and their types; equality, transpose, symmetric and skew-symmetric matrices; algebra of matrices; determinants; inverse; simultaneous equations using the matrix method.
Source: 2026 syllabus PDF, page 2
Section A1 — Calculus, Integration and Differential Equations
- Derivatives up to second order; increasing and decreasing functions; maxima and minima.
- Indefinite integrals of simple functions, evaluation of indefinite integrals, definite integrals, and area under a simple curve.
- Order and degree of differential equations; variable-separable differential equations.
Source: 2026 syllabus PDF, page 2
Section A1 — Probability and Linear Programming
- Simple probability.
- Graphical solutions in two variables; feasible and infeasible regions; optimal feasible solutions.
Source: 2026 syllabus PDF, page 2
Section B1: Mathematics — Unit I: Relations and Functions
- Reflexive, symmetric, transitive and equivalence relations; one-to-one and onto functions.
- Inverse trigonometric functions: definition, domain, range, principal value branches and graphs.
Source: 2026 syllabus PDF, page 3
Section B1: Mathematics — Unit II: Algebra
- Matrices: notation, order, equality, types, zero matrix, transpose, symmetric and skew-symmetric matrices, addition, multiplication and scalar multiplication; properties, non-commutativity, non-zero matrices with zero product (order 2); invertible matrices and uniqueness of inverse with real entries.
- Determinants up to order 3; minors, cofactors, triangle area, adjoint, inverse, consistency and number of solutions; solving unique systems in two or three variables using inverse matrices.
Source: 2026 syllabus PDF, page 3
Section B1: Mathematics — Unit III: Calculus
- Continuity and differentiability, chain rule, inverse trigonometric, implicit, exponential and logarithmic derivatives; logarithmic differentiation, parametric derivatives and second-order derivatives.
- Applications: rates of change, increasing/decreasing functions, maxima and minima, first and second derivative tests and real-life problems.
- Integration as the inverse of differentiation; substitution, partial fractions and integration by parts; standard integral forms listed in the PDF; fundamental theorem of calculus without proof; definite integrals and their properties.
- Area under lines, circles, parabolas and ellipses in standard form.
- Differential equations: definition, order, degree, general and particular solutions; separation of variables, first-order first-degree homogeneous equations and linear equations. See PDF page 4 for exact integral and differential-equation formulae.
Source: 2026 syllabus PDF, pages 3, 4
Section B1: Mathematics — Unit IV: Vectors and Three-dimensional Geometry
- Vectors and scalars, magnitude, direction, direction cosines and ratios; equal, unit, zero, parallel and collinear vectors; position and negative vectors, components, addition, scalar multiplication, division of a segment; scalar and vector products, interpretations, properties and applications.
- Direction cosines and ratios of a line; Cartesian and vector equations, skew lines, shortest distance between lines and angles between lines.
Source: 2026 syllabus PDF, page 5
Section B1: Mathematics — Unit V: Linear Programming
- Constraints, objective function, optimisation; graphical solutions in two variables; bounded/unbounded feasible and infeasible regions and solutions; optimal feasible solutions with up to three non-trivial constraints.
Source: 2026 syllabus PDF, page 5
Section B1: Mathematics — Unit VI: Probability
- Conditional probability, multiplication theorem, independent events, total probability and Bayes’ theorem.
Source: 2026 syllabus PDF, page 5
Section B2: Applied Mathematics — Unit I: Numbers, Quantification and Numerical Applications
- Modulo arithmetic and congruence modulo; alligation and mixtures; real-life numerical problems; boats and streams; pipes and cisterns; races and games; numerical inequalities.
Source: 2026 syllabus PDF, pages 5, 6
Section B2: Applied Mathematics — Unit II: Algebra
- Matrices and types, equality, transpose, symmetric and skew-symmetric matrices; addition, subtraction, matrix and scalar multiplication; determinants and elementary properties, singular/non-singular matrices and determinant of a product; inverse by cofactors and inverse properties; non-homogeneous simultaneous equations in up to three variables.
Source: 2026 syllabus PDF, pages 6, 7
Section B2: Applied Mathematics — Unit III: Calculus
- Derivatives up to second order, parametric and implicit differentiation, rate of change, marginal cost and revenue; increasing/decreasing functions, critical points, local and absolute extrema and applications.
- Indefinite integrals as antiderivatives and families of curves; substitution, partial fractions, integration by parts; definite integrals as area under non-trigonometric curves; fundamental theorem and definite-integral properties; consumer and producer surplus.
- Recognising, formulating and verifying differential equations; order, degree and simple solutions.
Source: 2026 syllabus PDF, pages 7, 8
Section B2: Applied Mathematics — Unit IV: Probability Distributions
- Random variables and discrete probability distributions; mathematical expectation, variance and standard deviation; Bernoulli trials and binomial distribution; Poisson conditions, mean and variance; normal distribution, standard normal variate and area relationships.
Source: 2026 syllabus PDF, page 8
Section B2: Applied Mathematics — Unit V: Time Based Data
- Time series, components, univariate time-series analysis and interpretation; secular trend and methods of measuring trend.
Source: 2026 syllabus PDF, page 8
Section B2: Applied Mathematics — Unit VI: Inferential Statistics
- Population and sample, representative samples, simple and systematic random sampling; parameters and statistics, limitations of generalisation, statistical significance and inference; Central Limit Theorem and population–sampling distribution–sample relationships.
- One-sample t-test for small samples: hypotheses, null and alternative hypotheses, degrees of freedom, testing and inference.
Source: 2026 syllabus PDF, pages 8, 9
Section B2: Applied Mathematics — Unit VII: Financial Mathematics
- Perpetuity and sinking funds; EMI; returns and nominal rate of return; compound annual growth rate; linear depreciation, cost, residual value and useful life; bond valuation using the present-value approach.
Source: 2026 syllabus PDF, pages 9, 10
Section B2: Applied Mathematics — Unit VIII: Linear Programming
- Terminology, mathematical formulation, types of linear programming problems; graphical solutions of inequalities in two variables; feasible, infeasible and bounded regions; feasible, infeasible and optimal feasible solutions.
Source: 2026 syllabus PDF, page 10