Kuwait University Chemistry Aptitude Test cheat sheet

Subject–verb agreement: a singular subject takes a singular verb; intervening prepositional phrases do not change the number (The list of items is long).

Neither/either/each/everyone are singular; both/few/many/several are plural. 'None' may be singular or plural depending on the noun it refers to.

Comma splice = two independent clauses joined only by a comma; fix with a period, semicolon, or coordinating conjunction (for, and, nor, but, or, yet, so).

Restrictive clauses (essential information) take 'that' and no commas; non-restrictive clauses (extra information) take 'which' and commas.

Parallel structure: items joined by and/or/but must share the same grammatical form (reading, writing, and speaking - not reading, writing, and to speak).

Dangling modifier: an introductory participial phrase must describe the subject of the main clause (Walking home, I saw the rain - not Walking home, the rain began).

Active voice is preferred in formal writing; passive voice is correct when the doer is unknown or unimportant.

Affect is a verb (to influence); effect is usually a noun (a result). Its = possessive; it's = it is. Their/there/they're are not interchangeable.

Inference vs. implication: the writer implies; the reader infers. Main-idea questions ask for the point covering the whole passage, not one supporting detail.

Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a. Discriminant b² − 4ac > 0 gives two real roots, = 0 one repeated root, < 0 no real roots.

Slope m = (y₂ − y₁)/(x₂ − x₁); parallel lines have equal slopes, perpendicular lines have slopes whose product is −1.

Laws of exponents: aᵐ·aⁿ = aᵐ⁺ⁿ; aᵐ/aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1 (a ≠ 0); a⁻ⁿ = 1/aⁿ.

Logarithms: log(ab) = log a + log b; log(a/b) = log a − log b; log(aⁿ) = n log a; log_b x = ln x / ln b.

Arithmetic sequence: aₙ = a₁ + (n − 1)d, sum Sₙ = n(a₁ + aₙ)/2. Geometric: aₙ = a₁rⁿ⁻¹, Sₙ = a₁(1 − rⁿ)/(1 − r).

Pythagorean identity sin²θ + cos²θ = 1; sin/cos/tan values at 0°, 30°, 45°, 60°, 90° follow the pattern √0/2, √1/2, √2/2, √3/2, √4/2 for sine.

Area and volume: circle A = πr², circumference 2πr; triangle A = ½bh; sphere V = (4/3)πr³; cylinder V = πr²h.

Probability of independent events multiplies: P(A and B) = P(A)·P(B); P(A or B) = P(A) + P(B) − P(A and B).

Derivative rules: d/dx xⁿ = nxⁿ⁻¹; d/dx sin x = cos x; d/dx eˣ = eˣ; d/dx ln x = 1/x. A zero derivative marks a stationary point.

Mole relations: n = m/M; one mole contains 6.022 × 10²³ particles; at STP one mole of ideal gas occupies 22.4 L.

Ideal gas law PV = nRT with R = 0.0821 L·atm/(mol·K); temperature must be in kelvin (K = °C + 273).

Molarity M = moles of solute / liters of solution; dilution obeys M₁V₁ = M₂V₂.

pH = −log[H₃O⁺]; pH + pOH = 14 at 25 °C; pH < 7 acidic, = 7 neutral, > 7 basic.

Oxidation = loss of electrons (increase in oxidation number); reduction = gain of electrons. In a redox reaction the oxidizing agent is itself reduced.

Le Chatelier: adding reactant shifts right; increasing pressure shifts toward the side with fewer gas moles; raising temperature favors the endothermic direction.

Bond polarity follows electronegativity difference; a molecule is polar only if bond dipoles do not cancel by symmetry (CO₂ nonpolar, H₂O polar).

Strong acids (HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄) ionize completely; weak acids ionize partially and need Ka for pH calculation.

Nomenclature: ionic compounds name cation then anion; molecular prefixes mono-, di-, tri- apply; alkanes follow CnH2n+2 with suffix -ane.

Kinematics: v = u + at; s = ut + ½at²; v² = u² + 2as. These apply only for constant acceleration.

Newton's second law F = ma; weight W = mg with g ≈ 9.8 m/s²; friction f = μN.

Work W = Fd cosθ; kinetic energy KE = ½mv²; gravitational potential energy PE = mgh; power P = W/t.

Conservation of momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ for collisions with no external net force.

Ohm's law V = IR; power P = VI = I²R = V²/R; resistors in series add, in parallel 1/R = 1/R₁ + 1/R₂.

Wave relation v = fλ; for light in vacuum c = 3.0 × 10⁸ m/s; period T = 1/f.

Snell's law n₁ sin θ₁ = n₂ sin θ₂; total internal reflection occurs only when light moves from denser to less dense medium beyond the critical angle.

Ideal gas pressure comes from molecular collisions with walls; average kinetic energy is proportional to absolute temperature (KE ∝ T).

Units: force in newtons (kg·m/s²), energy in joules (N·m), power in watts (J/s), charge in coulombs (A·s).