What is the IOE entrance Mathematics syllabus?
Seven areas worth 50 marks: sets and functions, algebra, trigonometry, coordinate geometry, calculus, vectors, and statistics and probability.
Mathematics is the largest single block on the paper at 50 of the 140 marks. These are the seven areas the official syllabus names.
Set, logic and functions. Real number system, intervals, absolute value, connectives and laws of logic. Types of functions: injective, surjective, bijective, algebraic, trigonometric, exponential and logarithmic. Inverse and composite functions.
Algebra. Matrices and determinants, inverse of a matrix. Complex numbers and polynomial equations. Sequence and series, permutation and combination. Binomial theorem, exponential and logarithmic series.
Trigonometry. Trigonometric equations and general values. Inverse trigonometric functions and principal value. Properties of triangles, in-centre, ortho-centre, circum-centre, solution of triangles.
Coordinate geometry. Straight lines and pair of lines. Circles, tangent and normal. Conic sections: parabola, ellipse, hyperbola. Coordinates in space, the plane and its equation.
Calculus. Limits, continuity, indeterminate forms, L’Hospital’s rule. Derivatives and applications: tangent and normal, rate of change, maxima and minima. Integration, definite integrals, area under and between curves. Differential equations of first order and first degree, variable separable, homogeneous, linear and exact, integrating factor.
Vectors and their products. Vectors in plane and space, linear combination, dependence and independence. Scalar and vector products, scalar triple product.
Statistics and probability. Measures of location and dispersion. Correlation and regression. Conditional and compound probability, additive and multiplicative rules, Bayes’ theorem, binomial distribution.
What the paper actually asks
The booklet prints its own model questions, and they are the most useful thing in it for planning revision, because they show the difference between the two sections rather than describing it. Section A carries 60 questions at 1 mark each; Section B carries 40 at 2 marks. The Section A samples are single-step — one identity, one standard result, one substitution. The Section B samples take two or three steps before they reach an option.
Two of the booklet’s own Mathematics samples, reproduced as printed. From Section A: “If the line x + y – 1 = 0 touches the parabola y² = kx, then the value of k is — (a) 4, (b) 2, (c) –2, (d) –4.” From Section B: “If a lottery ticket is drawn at random from a lottery box containing 10 prizes and 25 blanks, what is the probability of getting a prize?” The first is a tangency condition you either know or derive in one line; the second is a probability question that needs the total counted before the ratio is formed.
Where the 50 marks actually sit
The seven areas are not equally represented in the model paper. Calculus and coordinate geometry supply the largest share of the Section A samples, and the Section B samples lean on probability, vectors and applications of the derivative. That is consistent with the syllabus itself, where calculus carries four sub-topics and vectors and statistics carry two and three respectively — but it is worth knowing that the areas with the most sub-topics are also the ones the sample paper returns to most often.
A practical consequence of the 10% negative marking: at 1 mark, a wrong Section A answer costs 0.1 of a mark, and at 2 marks a wrong Section B answer costs 0.2. The penalty scales with the reward, so there is no section where guessing is systematically safer than another. What changes between the sections is the time cost of a wrong guess, not the mark cost.
Summarised from the Detail Syllabus of B.E./B.Arch. Entrance Examination-2083, Mathematics, Full Marks 50, printed page 26 of the booklet. The model questions are transcribed from the booklet’s own Model Questions section, printed pages 29 to 31; the section headers there read “Section A (1*60 = 60)” and “Section B (2*40 = 80)”, which independently confirms the 140-mark structure. These pages are set in Latin type rather than the legacy Nepali fonts used elsewhere in the booklet, so they extract reliably. The booklet carries the full sub-topic wording; where this page and the booklet differ, the booklet governs.
Sources
- IOE B.E./B.Arch Booklet 2083 · published 7 August 2026 · read 18 August 2026
Last reviewed by Ram Raj Thapa, Admissions Officer, Imperial College of Engineering. Every figure on this page is cited to the document it came from.