IMAT cheat sheet

Syllogism validity depends on form, not truth: 'All A are B; some B are C' yields no necessary conclusion about A and C.

Contrapositive is always equivalent to the original conditional: 'if P then Q' equals 'if not Q then not P'. Converse and inverse are not equivalent.

'Some' in logic means at least one, possibly all; 'no' and 'some not' are not interchangeable with 'not all' in syllogistic conversion.

Set reasoning: 'all A are B' means A is a subset of B, so 'some A are B' follows, but 'some B are A' also follows (existential import assumed).

Numerical series: check differences, then ratios, then alternating subsequences, then squares/cubes/prime offsets before assuming a single rule.

Ordering puzzles: build a table of fixed positions first, then eliminate; a clue of form 'X is immediately before Y' is stronger than 'X is before Y'.

Classic false-premise traps in general knowledge: correlation is not causation; a claim about a majority does not license a claim about every member.

General knowledge anchors: EU founding treaties (Rome 1957, Maastricht 1992), Italian Constitution in force from 1 January 1948, UN founded 1945.

Probability in reasoning items: independent events multiply, mutually exclusive events add; 'at least one' is easiest via 1 minus P(none).

Main-idea questions: the correct answer must cover the whole passage; an option that is true but only about one paragraph is a distractor.

Inference questions allow only what is necessarily supported; outside knowledge, however true, is wrong unless the passage implies it.

Tone and attitude words: identify evaluative adjectives and hedges ('arguably', 'reportedly') to separate the author's claim from reported claims.

Scope words matter: 'all', 'only', 'primarily', 'must' versus 'may'; a single counterexample in the passage defeats an absolute option.

Chronology and cause: distinguish sequence ('then', 'after') from causation ('therefore', 'because'); passages often test this distinction.

School knowledge: Italian literary periods - Dolce Stil Novo (13th c.), Humanism (14th–15th c.), Romanticism (early 19th c.), Verismo (late 19th c.).

Historical anchors: French Revolution 1789, Congress of Vienna 1815, Italian unification proclaimed 1861, First World War 1914–1918.

Answer elimination: reject options that contradict the passage, exceed its scope, or answer a different question than the one asked.

Cell theory: all living things are made of cells, the cell is the basic unit, and cells arise from pre-existing cells by division.

Prokaryotes lack a membrane-bound nucleus and organelles; ribosomes are 70S. Eukaryotes have a nucleus, 80S ribosomes, and membrane-bound organelles.

Mitosis produces two genetically identical diploid cells; meiosis produces four haploid cells with crossing over in prophase I.

Mendel: law of segregation (alleles separate in gametes) and independent assortment (genes on different chromosomes assort independently).

DNA replication is semi-conservative; transcription makes mRNA from a DNA template; translation at the ribosome uses codons matched to tRNA anticodons.

Enzymes are proteins that lower activation energy; they are specific, and activity depends on temperature and pH, with denaturation above an optimum.

Cellular respiration: glycolysis in cytoplasm, Krebs cycle in mitochondrial matrix, oxidative phosphorylation on the inner membrane; net about 30–32 ATP.

Photosynthesis: light reactions in thylakoid membranes produce ATP and NADPH and release O2 from water; Calvin cycle fixes CO2 in the stroma.

Human systems: blood flows right atrium to right ventricle to lungs to left atrium to left ventricle to body; nephron filtration occurs in the glomerulus.

Mole relations: n = m/M, n = N/NA with NA = 6.022×10^23, and at STP 1 mol of ideal gas occupies 22.4 L.

Ideal gas law PV = nRT with R = 8.314 J/(mol·K); at constant T and P, equal volumes of gases contain equal numbers of molecules.

Balancing redox: total electrons lost equal total electrons gained; oxidation number rises on oxidation and falls on reduction.

Acid-base: pH = -log[H3O+]; strong acid/base fully dissociates, weak partially; at 25 °C neutral pH = 7 and Kw = 10^-14.

Equilibrium: Le Chatelier - raising pressure shifts toward fewer gas moles; raising temperature shifts in the endothermic direction.

Periodic trends: atomic radius decreases across a period and increases down a group; electronegativity increases across and decreases down.

Bonding: ionic between metal and non-metal with large electronegativity difference; covalent shares electrons; metallic has delocalised electrons.

Organic functional groups: alcohol -OH, aldehyde -CHO, ketone C=O internal, carboxylic acid -COOH, amine -NH2, ester -COO-.

Stoichiometry decision rule: convert everything to moles first, identify the limiting reagent by mole ratio, then convert back to mass or volume.

Kinematics: v = v0 + at, s = v0t + ½at², v² = v0² + 2as; these apply only for constant acceleration.

Newton's second law F = ma; weight W = mg; friction f = μN opposes relative motion and is independent of contact area for simple models.

Energy: kinetic ½mv², gravitational potential mgh, work W = Fd cosθ; mechanical energy is conserved without non-conservative forces.

Electricity: Ohm's law V = IR; power P = VI = I²R = V²/R; resistors in series add, in parallel reciprocals add.

Waves and optics: v = fλ; refraction obeys Snell's law n1 sinθ1 = n2 sinθ2; total internal reflection occurs above the critical angle.

Quadratic: discriminant Δ = b² - 4ac; two real roots if Δ > 0, one if Δ = 0, none real if Δ < 0; vertex at x = -b/(2a).

Logarithms and exponents: log(ab) = log a + log b, log(a^n) = n log a, a^0 = 1, a^(-n) = 1/a^n.

Trigonometry: sin²θ + cos²θ = 1; sine rule a/sinA = b/sinB; cosine rule a² = b² + c² - 2bc cosA.

Geometry and probability: area of circle πr², circumference 2πr, volume of sphere (4/3)πr³; P(A or B) = P(A) + P(B) - P(A and B).