FAST-NUCES Admission Test Syllabus Breakdown and Test Dates 2026

Real numbers, complex numbers, algebraic operations, Argand diagram

Types of sets, operations on sets, functions, binary operations, group properties

Matrix types, operations, determinants, inverse matrices, solving linear systems

Solution methods, nature of roots, sum & product of roots, equations in radicals

Resolving proper and improper rational fractions into partial fractions

AP, GP, HP — nth term, sum formulas, arithmetic and geometric means

Factorial notation, nPr, nCr, probability theorems, addition and multiplication rules

Principle of induction, binomial expansion, general term, middle term

Angles, arc length, trigonometric ratios, quadrant signs

Fundamental, double-angle, half-angle, product-to-sum identities

Domain, range, period, graphs of sin/cos/tan and their transformations

Law of sines & cosines, solution of triangles, area of triangle

Domain, range, principal values, graphs of inverse trig functions

General and particular solutions, equations involving multiple angles

Types of functions, composition, inverse, limits, continuity, L'Hôpital's rule

Differentiation rules, derivatives of trig/log/exp, implicit, parametric, higher-order

Indefinite & definite integrals, integration techniques, areas and volumes

Straight lines, circles — equations, properties, tangents and normals

Graphical solution, feasible region, corner point theorem

Parabola, ellipse, hyperbola — standard forms, focus, directrix, eccentricity

2D & 3D vectors, dot and cross products, scalar and vector projections

BODMAS, integers, HCF, LCM, divisibility rules

Conversion, operations, percentage increase/decrease

Direct & inverse proportion, compound ratios, mixing problems

Cost price, selling price, profit %, loss %, discount calculations

Interest formulas, time-value problems, instalment calculations

Relative speed, average speed, upstream/downstream problems

Simplification, factoring, solving one and two-variable equations

Mean, median, mode, weighted average, range

Area, perimeter, volume of 2D and 3D shapes; angles and triangles

Number series, letter series, missing terms, next/previous in pattern

Visual patterns, odd one out, figure completion, matrix reasoning

Letter shifts, number codes, symbol codes, word codes

Family tree problems, relation identification, coded relations

Cardinal directions, turns, distance after movement

All/Some/No statements, Venn diagram reasoning, valid conclusions

Assumptions, inferences, strong/weak arguments, course of action

Bar charts, line graphs, pie charts, tables — reading and computing values

Seating arrangements, scheduling, ranking, floor/building problems

Word analogies, number analogies, odd one out by category

Tenses, parts of speech, subject-verb agreement, active/passive voice, direct/indirect speech, sentence correction

Synonyms, antonyms, word analogies, idioms and phrases, contextual word meaning

Passage analysis, main idea, inference, tone, author's purpose

Fill in the blanks, two-blank sentences, logical and contextual completion