Материалдар кітапханасы

Convert between SI units and reason about compound rates (speed, density, pressure) without losing track of the units.

Collect like terms, expand brackets, factorise, and simplify algebraic fractions — the building block under almost every later math topic.

Index laws, fractional and negative powers, and how to manipulate expressions like $a^{m/n}$ confidently.

Split quantities by ratio, scale recipes, and recognise direct vs inverse proportion in disguise.

Direct, inverse, joint, and combined variation — set up the constant from one data point, then answer any question.

Increase, decrease, reverse, and compound percentages without falling into the most common traps.

A reliable 4-step framework for translating English into algebra without missing details.

Solve linear inequalities and compound systems, and remember the rule about flipping the sign.

Compute slopes, write line equations in three forms, and recognise parallel and perpendicular lines instantly.

How translation, reflection, stretch, and rotation act on graphs $y = f(x)$.

Three forms of a quadratic, the discriminant, and the quadratic formula — when to use which.

Worked NUET-style problems applying the three forms — projectile, area, and pricing scenarios.

Read everything you need from a parabola: vertex, axis of symmetry, intercepts, direction, width.

Sign analysis on a parabola — find roots, then test intervals.

Add, subtract, multiply, and divide expressions of the form $\dfrac{p(x)}{q(x)}$ — and watch the domain.

Arithmetic and geometric sequences — general term, sum formulas, and how to spot the pattern.

Equations with squares, square roots, or absolute values — substitution and squaring tactics.

Core geometry: angle facts, parallel-line theorems, similarity, and the area/volume zoo.

Growth and decay, the natural exponential, and basic logarithms.

NUET's defined-symbol problems: a custom operator like $a \diamond b = 2a - b$. Treat symbols as plug-in instructions.

Pythagoras, congruence/similarity rules, special right triangles, and triangle inequality.

2D vector arithmetic, magnitude, and the dot product — geometry without diagrams.

Three-digit compass bearings: always clockwise from north. Combine with trig and Pythagoras for navigation problems.

Interior/exterior angle formulas, regular vs irregular, and the angle sum trap.

Circumference, area, sector and arc length, plus the must-know circle theorems.

Surface area and volume of prisms, pyramids, cylinders, cones, and spheres — plus the diagonals.

Sin, cos, tan ratios, the special angles, sine/cosine rules, and the identities you actually need.

Read an argument like an examiner: separate premises from conclusions, then judge the logic.

Match the wording of the right answer to what the passage actually concluded — no more, no less.