Mathematics

Half of NET-Engineering and half of NET-Natural Sciences, drawn from the HSSC Part-I and Part-II mathematics syllabus. This is the algebra, calculus and geometry set; the arithmetic-heavy quantitative set that NET-Business uses lives under its own subject.

Chapters

Each chapter with MCQs links straight into its drill: untimed questions with the answer, the working and the common trap on every question. Across the 15 chapters live, 105 MCQs of a typical paper are covered. 10 new-syllabus chapters are marked in preparation until its MCQs land.

01Complex NumbersThe imaginary unit, Argand-plane arithmetic, conjugates, moduli, and conversion between Cartesian and polar form.
02Functions and GraphsDomain and range, one-to-one and onto tests, inverses, composition, and reading transformations off a graph.
03Theory of Quadratic FunctionsRoots, the discriminant, the relationship between roots and coefficients, and equations reducible to quadratic form.
04Matrices and DeterminantsMatrix algebra, determinants, inverses and Cramer's rule for solving linear systems, as tested on the NUST Entry Test.
05Partial FractionsDecomposing a rational fraction into simpler fractions according to the factors of its denominator, covering equations, identities, and the four standard decomposition cases.
06Sequences and SeriesArithmetic, geometric and harmonic sequences, their means, and the sums of finite and infinite series, including the conversion of recurring decimals into fractions.
07Permutations and CombinationsCounting techniques (factorials, permutations, combinations) and the selection rules built on top of them, one of the highest-yield chapters on the Mathematics section.
08Mathematical Inductions and Binomial TheoremThe principle of mathematical induction for proving statements over the natural numbers, and the binomial theorem for expanding $(x+y)^n$ for positive integral, negative and fractional $n$.
09Division of PolynomialsMCQs in preparationLong and synthetic division of polynomials, the remainder and factor theorems, and using them to find zeros and factors.
10Trigonometric IdentitiesFundamental identities, sum and difference formulae, double and half-angle results, and proving identities under exam time pressure.
11Trigonometric Functions and Their GraphsMCQs in preparationPeriod, amplitude and phase shift of sine, cosine and tangent, and reading values and transformations off their graphs.
12Limit and ContinuityEvaluating limits algebraically, one-sided limits, limits at infinity, and the continuity tests NET asks as one-line evaluations.
13DifferentiationRules for finding derivatives of algebraic, trigonometric, exponential, logarithmic and inverse trigonometric functions, and their use in rates, tangents, maxima and minima.
14Vectors in SpacePosition vectors, the dot and cross products, and scalar triple products, tested through direct component computation rather than proof.
15Graphical Representation of FunctionsMCQs in preparationSketching quadratics, exponentials and rational functions from intercepts, asymptotes and turning points, and solving equations graphically.
16Further DifferentiationMCQs in preparationChain rule, implicit and parametric differentiation, higher-order derivatives, and the optimisation and approximation questions built on them.
17IntegrationStandard integrals, substitution, integration by parts, and definite integrals as areas.
18Differential EquationsMCQs in preparationOrder and degree, separable first-order equations, and forming a differential equation by eliminating arbitrary constants.
19Analytical GeometryLines and triangles on Cartesian coordinates, using distance, slope, division of a segment, translation and rotation of axes to answer questions algebraically rather than by drawing.
20Conic SectionConic Section covers the circle, parabola, ellipse and hyperbola as loci defined by a fixed distance or eccentricity relation, together with their standard equations, tangents and normals.
21KinematicsMCQs in preparationDisplacement, velocity and acceleration as functions of time, motion in a straight line, and the calculus that links the three.
22Numerical MethodMCQs in preparationLocating roots of nonlinear equations numerically: bisection, Newton-Raphson iteration, and reading convergence off a table of values.
23Inverse Trigonometric Functions and Their GraphsMCQs in preparationPrincipal values of arcsin, arccos and arctan, their graphs, and simplifying compositions such as $\sin(\arctan x)$.
24Solution of Trigonometric EquationsMCQs in preparationSolving trigonometric equations within a given interval and writing the general solution with the $360^\circ$ / $2\pi$ period term.
25Vector Valued Functions and Their DifferentiationMCQs in preparationVector functions of a single parameter, their derivatives, and velocity and acceleration vectors of a moving point.

Where this subject sits in the papers

A subject can appear on several NET papers at different weights, so the same revision is worth more on one paper than another.

50% weighting

NET-Engineering

50% weighting

NET-Natural Sciences

30% weighting

NET-Architecture

Full official weightings Test dates and series Full-length papers

Mathematics

Chapters

Where this subject sits in the papers

The other 6 subjects