Cambridge HSC cheat sheet

Aerobic respiration: C6H12O6 + 6O2 → 6CO2 + 6H2O + ATP; occurs mainly in mitochondria.

Photosynthesis: 6CO2 + 6H2O → C6H12O6 + 6O2; light energy is converted to chemical energy in chloroplasts.

Newton's second law: F_net = ma; acceleration is proportional to net force and inversely proportional to mass.

Ohm's law: V = IR; electrical power P = VI = I²R = V²/R for a resistor.

pH = −log10[H+]; pH < 7 acidic, pH = 7 neutral at 25°C, pH > 7 basic.

Moles: n = m/M; one mole contains 6.022 × 10²³ particles (Avogadro constant).

DNA base pairing: adenine pairs with thymine (A–T) and guanine with cytosine (G–C); RNA uses uracil in place of thymine.

Le Chatelier's principle: a system at equilibrium shifts to oppose a change in concentration, pressure or temperature.

French passé composé: auxiliary avoir or être in present + past participle; with être, the participle agrees with the subject.

French conditional sentences: si + present → future simple; si + imperfect → conditional; never use future or conditional immediately after si.

French adjective agreement: add -e for feminine and -s for plural in regular forms; irregular adjectives have their own forms.

English analytical paragraph: claim → textual evidence → technique → effect on reader or audience.

English modality: modal verbs such as can, may, must and should express possibility, obligation or certainty and position the writer's stance.

Register: vocabulary, syntax and politeness shift according to audience, purpose and context; formal and informal registers are not interchangeable.

Chinese tones: four main tones plus neutral tone; third-tone sandhi changes a third tone before another third tone to a second tone.

Heritage language maintenance: intergenerational transmission, community domains and institutional support affect whether a language is retained.

Quadratic formula: x = (−b ± √(b² − 4ac))/(2a) for ax² + bx + c = 0, a ≠ 0.

Discriminant Δ = b² − 4ac: Δ > 0 two distinct real roots; Δ = 0 one repeated real root; Δ < 0 no real roots.

Derivative: d/dx(x^n) = nx^(n−1); product rule (uv)' = u'v + uv'; quotient rule (u/v)' = (u'v − uv')/v².

Integral: ∫x^n dx = x^(n+1)/(n+1) + C for n ≠ −1; ∫x^(−1) dx = ln|x| + C.

Sine rule: a/sin A = b/sin B = c/sin C; cosine rule: c² = a² + b² − 2ab cos C.

Logarithms: log(ab) = log a + log b; log(a/b) = log a − log b; log(a^n) = n log a.

Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); independent events P(A ∩ B) = P(A)P(B).

Arithmetic sequence: a_n = a + (n−1)d; geometric sequence: a_n = ar^(n−1); sum S_n = a(1−r^n)/(1−r), r ≠ 1.

Accounting equation: Assets = Liabilities + Equity; it must balance after every transaction.

Double-entry rule: every transaction has equal debits and credits; total debits equal total credits in the ledger.

Profit = total revenue − total expenses; gross profit = sales revenue − cost of goods sold.

Break-even units = fixed costs ÷ (unit selling price − unit variable cost).

Straight-line depreciation = (cost − residual value) ÷ useful life.

GDP expenditure approach: GDP = C + I + G + (X − M).

Law of demand: price rises → quantity demanded falls, ceteris paribus; price falls → quantity demanded rises.

Price elasticity of demand = %ΔQd ÷ %ΔP; |PED| > 1 elastic, |PED| < 1 inelastic, |PED| = 1 unit elastic.

Historical source evaluation: origin, purpose, value and limitation (OPVL) assess reliability and usefulness.

Primary source: created during the period by a participant or eyewitness; secondary source: interprets or analyses primary evidence later.

Historical causation: distinguish long-term causes, short-term causes and immediate triggers.

Plate boundaries: divergent boundaries create rifts and new crust; convergent boundaries produce subduction, mountains or volcanoes; transform boundaries cause faulting.

Demographic transition model: Stage 1 high birth/death rates; Stage 2 death rate falls; Stage 3 birth rate falls; Stage 4 low stable rates; Stage 5 may decline.

Separation of powers: legislature makes law, executive implements law, judiciary interprets law.

Rule of law: everyone, including government, is subject to the law and laws are applied consistently and transparently.

Socialisation: family (primary), peers, education, media and religion transmit norms, values and roles.

Design process: define problem → research → ideate → prototype → test → evaluate; iteration may return to earlier stages.

Algorithm control structures: sequence, selection (if/else) and iteration (loops).

Binary: base-2 uses 0 and 1; 1 byte = 8 bits; 1 KiB = 2^10 bytes = 1024 bytes.

Boolean logic: AND true only when both inputs true; OR true when at least one true; NOT inverts; truth tables list all input combinations.

Database keys: primary key uniquely identifies a record; foreign key references a primary key in another table to create a relationship.

Risk control hierarchy: eliminate → substitute → engineer → administrative → PPE; elimination is most effective.

Computational thinking: decomposition, pattern recognition, abstraction and algorithm design.

Network basics: IP address identifies a device; DNS maps domain names to IP addresses; HTTP/HTTPS transfer web content.

Elements of art: line, shape, form, value, texture, colour and space.

Design principles: balance, contrast, emphasis, movement, rhythm, pattern, unity and proportion.

Colour theory: primary colours mix to make secondary colours; complementary colours sit opposite on the colour wheel and create contrast.

Major scale interval pattern: tone–tone–semitone–tone–tone–tone–semitone.

Common chord progression: I–IV–V–I in a major key; tonic (I) establishes home, dominant (V) creates tension.

Sonata form: exposition (themes introduced), development (themes transformed), recapitulation (themes return in tonic key).

Stanislavski: given circumstances, objectives, superobjective and through-line of action guide character choices.

Dramatic tension: created through conflict, stakes, timing, surprise and withheld information.