European Baccalaureate Physics cheat sheet

Paper structure typically has two parts: a comprehension/analysis task on an unseen text and a written production task (essay, opinion piece, or argumentative response) assessed on content, organisation, and language accuracy.

Language accuracy is usually marked separately from content: keep a running error log of your own recurring faults (articles, tense agreement, register) and check only those in the final five minutes.

Text analysis vocabulary: register (formal/informal/neutral), tone, irony, hyperbole, euphemism, anaphora, rhetorical question, antithesis, and the writer's stance (thesis, implicit assumption, concession).

Commentary structure: introduce the text (author, type, date, topic), state the dominant effect or argument, then support with quotation plus analysis of the linguistic device used and its effect on the reader.

Quotations should be short (three to eight words), integrated syntactically into your sentence, and always followed by interpretation, never left as bare evidence.

Essay planning: thesis in the introduction, one idea per paragraph, topic sentence first, evidence and analysis in the middle, and a conclusion that answers the question rather than summarising.

Word-count discipline: plan paragraph targets in advance (for example 5 paragraphs of roughly equal length) so the conclusion is not lost to over-long early paragraphs.

Cohesion markers to vary: however, nevertheless, whereas, thereby, consequently, by contrast, indeed, arguably; avoid repeating the same connector more than once per paragraph.

L2 assessment in the European Baccalaureate is split into written and oral components; the written paper typically contains a listening or reading comprehension section and a written production section.

Comprehension questions often require reformulation, not copying: answer in your own words and match the number of elements the question asks for (give two reasons means exactly two).

Written production is graded on task achievement, coherence, range of vocabulary and structures, and grammatical accuracy; a short accurate text usually outscores a long inaccurate one.

Register control: choose formal connectors for essays (furthermore, in addition, nevertheless) and avoid oral fillers (well, you know, actually) in written work.

Oral exam routine: prepare a short structured statement on the topic, then be ready to defend it; examiners reward interaction strategies such as asking for clarification or reformulating.

False friends are a common scoring trap across European languages (for example German aktuell = current, not actual; French actuel = current; Italian attuale = current).

Subjunctive and conditional sequences appear in formal writing in Romance languages; check the sequence of tenses after expressions of doubt, wish, or hypothesis.

Paraphrase toolkit: synonym substitution, word-class change (verb to noun), clause restructuring (active to passive), and generalisation or specification.

Quadratic formula: for ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / 2a; the discriminant Δ = b² − 4ac gives two real roots (Δ > 0), one double root (Δ = 0), or no real roots (Δ < 0).

Derivative rules: (xⁿ)′ = nxⁿ⁻¹; (eˣ)′ = eˣ; (ln x)′ = 1/x; (sin x)′ = cos x; (cos x)′ = −sin x; product rule (uv)′ = u′v + uv′; quotient rule (u/v)′ = (u′v − uv′)/v².

Chain rule: d/dx f(g(x)) = f′(g(x))·g′(x); integration by substitution reverses it, and integration by parts is ∫u dv = uv − ∫v du.

Definite integral equals the signed area under the curve; the Fundamental Theorem gives ∫ₐᵇ f(x) dx = F(b) − F(a) where F′ = f.

Logarithm laws: ln(ab) = ln a + ln b; ln(a/b) = ln a − ln b; ln(aⁿ) = n ln a; used to solve exponential equations by taking logs of both sides.

Trigonometric identities: sin²x + cos²x = 1; sin 2x = 2 sin x cos x; cos 2x = cos²x − sin²x = 1 − 2sin²x = 2cos²x − 1.

Arithmetic sequence: uₙ = u₁ + (n − 1)d, sum Sₙ = n(u₁ + uₙ)/2; geometric: uₙ = u₁·rⁿ⁻¹, sum Sₙ = u₁(1 − rⁿ)/(1 − r) for r ≠ 1.

Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); conditional P(A|B) = P(A ∩ B)/P(B); independence means P(A ∩ B) = P(A)·P(B).

Vectors: dot product a·b = |a||b|cos θ, zero for perpendicular vectors; cross product magnitude |a||b|sin θ gives the area of the parallelogram spanned.

History essays are marked on use of evidence, argument coherence, and historiographical awareness; every claim needs a date, place, or named example.

Causation language in L2: distinguish long-term structural causes, short-term triggers, and precipitating events; examiners reward explicit weighting of causes.

Source criticism framework: origin (who, when, where), purpose (why produced, intended audience), value (what it reveals), and limitations (bias, silence, reliability).

Key twentieth-century anchor dates: 1919 Treaty of Versailles; 1929 Wall Street Crash; 1945 end of World War II and founding of the United Nations; 1949 NATO and the two German states; 1989 fall of the Berlin Wall; 1991 dissolution of the USSR.

European integration milestones: 1951 ECSC Treaty of Paris; 1957 Treaties of Rome (EEC and Euratom); 1992 Maastricht Treaty creating the European Union; 2002 euro cash introduction.

Geography: population structure is read from population pyramids; a wide base indicates high birth rates and a youthful population, a narrow base indicates ageing.

Demographic transition model stages: high stationary (high birth and death rates), early expanding, late expanding, low stationary, and declining population.

Plate tectonics: divergent boundaries create rift valleys and mid-ocean ridges; convergent boundaries produce subduction zones, fold mountains, and volcanic arcs; transform boundaries produce strike-slip earthquakes.

Climate and biome links: latitude controls insolation and therefore temperature belts; continentality and ocean currents modify rainfall and seasonal range.

Physics kinematics: v = u + at; s = ut + ½at²; v² = u² + 2as; use these only for constant acceleration, and fix a positive direction before substituting signs.

Newton's second law F = ma; momentum p = mv is conserved in collisions absent external forces; impulse equals change in momentum, FΔt = Δp.

Energy: kinetic ½mv², gravitational potential mgh, elastic ½kx²; power P = W/t = Fv; efficiency = useful output / total input × 100%.

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

Waves: v = fλ; refraction obeys Snell's law n₁sin θ₁ = n₂sin θ₂; for a converging lens 1/f = 1/v + 1/u with the thin-lens sign convention stated explicitly.

Chemistry moles: n = m/M; n = cV for solutions (V in dm³); at standard conditions one mole of gas occupies about 24 dm³ (22.4 dm³ at STP).

Acid–base: pH = −log₁₀[H⁺]; strong acid and strong base neutralise in the ratio given by the balanced equation; titration uses n(acid)/n(base) from stoichiometry.

Organic functional groups: alcohols (OH), carboxylic acids (COOH), aldehydes (CHO), ketones (C=O between carbons), esters (COO), amines (NH₂); oxidation of a primary alcohol gives an aldehyde then a carboxylic acid.

Biology: enzyme activity depends on temperature and pH, denaturing above the optimum; photosynthesis equation 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂; aerobic respiration releases far more ATP per glucose than anaerobic.

Argument anatomy: premises, inference, conclusion; validity concerns form only, soundness requires validity plus true premises, so a valid argument can still have a false conclusion if a premise is false.

Common fallacies to name precisely: ad hominem, straw man, false dilemma, begging the question, post hoc ergo propter hoc, appeal to authority, and hasty generalisation.

Deductive versus inductive reasoning: deduction guarantees the conclusion if premises are true; induction makes the conclusion probable only, so it can be strong or weak rather than valid or invalid.

Descartes' method of doubt reaches the cogito (I think, therefore I am) and argues for a distinction between mind and body; the weakness is the move from indubitability to real existence.

Kant's distinction: analytic judgements are true by meaning, synthetic judgements extend knowledge; the categorical imperative tests maxims for universalisability and treats persons as ends, not merely means.

Utilitarianism (Bentham, Mill) judges acts by consequences and total welfare; standard objections are the utility monster, the sacrifice of minority rights, and the difficulty of measuring happiness.

Kantian deontology judges acts by duty and the maxim behind them, not consequences; the standard objection is that it may forbid morally required lies in extreme cases.

Hume's is–ought gap: descriptive statements about what is the case do not by themselves entail prescriptive statements about what ought to be done.

Essay method: state the thesis, reconstruct the strongest version of the opposing view, apply a specific objection, then evaluate rather than merely describe.

Paper structure typically has two parts: a comprehension/analysis task on an unseen text and a written production task (essay, opinion piece, or argumentative response) assessed on content, organisation, and language accuracy.

Language accuracy is usually marked separately from content: keep a running error log of your own recurring faults (articles, tense agreement, register) and check only those in the final five minutes.

Text analysis vocabulary: register (formal/informal/neutral), tone, irony, hyperbole, euphemism, anaphora, rhetorical question, antithesis, and the writer's stance (thesis, implicit assumption, concession).

Commentary structure: introduce the text (author, type, date, topic), state the dominant effect or argument, then support with quotation plus analysis of the linguistic device used and its effect on the reader.

Quotations should be short (three to eight words), integrated syntactically into your sentence, and always followed by interpretation, never left as bare evidence.

Essay planning: thesis in the introduction, one idea per paragraph, topic sentence first, evidence and analysis in the middle, and a conclusion that answers the question rather than summarising.

Word-count discipline: plan paragraph targets in advance (for example 5 paragraphs of roughly equal length) so the conclusion is not lost to over-long early paragraphs.

Cohesion markers to vary: however, nevertheless, whereas, thereby, consequently, by contrast, indeed, arguably; avoid repeating the same connector more than once per paragraph.

L2 assessment in the European Baccalaureate is split into written and oral components; the written paper typically contains a listening or reading comprehension section and a written production section.

Comprehension questions often require reformulation, not copying: answer in your own words and match the number of elements the question asks for (give two reasons means exactly two).

Written production is graded on task achievement, coherence, range of vocabulary and structures, and grammatical accuracy; a short accurate text usually outscores a long inaccurate one.

Register control: choose formal connectors for essays (furthermore, in addition, nevertheless) and avoid oral fillers (well, you know, actually) in written work.

Oral exam routine: prepare a short structured statement on the topic, then be ready to defend it; examiners reward interaction strategies such as asking for clarification or reformulating.

False friends are a common scoring trap across European languages (for example German aktuell = current, not actual; French actuel = current; Italian attuale = current).

Subjunctive and conditional sequences appear in formal writing in Romance languages; check the sequence of tenses after expressions of doubt, wish, or hypothesis.

Paraphrase toolkit: synonym substitution, word-class change (verb to noun), clause restructuring (active to passive), and generalisation or specification.

Quadratic formula: for ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / 2a; the discriminant Δ = b² − 4ac gives two real roots (Δ > 0), one double root (Δ = 0), or no real roots (Δ < 0).

Derivative rules: (xⁿ)′ = nxⁿ⁻¹; (eˣ)′ = eˣ; (ln x)′ = 1/x; (sin x)′ = cos x; (cos x)′ = −sin x; product rule (uv)′ = u′v + uv′; quotient rule (u/v)′ = (u′v − uv′)/v².

Chain rule: d/dx f(g(x)) = f′(g(x))·g′(x); integration by substitution reverses it, and integration by parts is ∫u dv = uv − ∫v du.

Definite integral equals the signed area under the curve; the Fundamental Theorem gives ∫ₐᵇ f(x) dx = F(b) − F(a) where F′ = f.

Logarithm laws: ln(ab) = ln a + ln b; ln(a/b) = ln a − ln b; ln(aⁿ) = n ln a; used to solve exponential equations by taking logs of both sides.

Trigonometric identities: sin²x + cos²x = 1; sin 2x = 2 sin x cos x; cos 2x = cos²x − sin²x = 1 − 2sin²x = 2cos²x − 1.

Arithmetic sequence: uₙ = u₁ + (n − 1)d, sum Sₙ = n(u₁ + uₙ)/2; geometric: uₙ = u₁·rⁿ⁻¹, sum Sₙ = u₁(1 − rⁿ)/(1 − r) for r ≠ 1.

Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); conditional P(A|B) = P(A ∩ B)/P(B); independence means P(A ∩ B) = P(A)·P(B).

Vectors: dot product a·b = |a||b|cos θ, zero for perpendicular vectors; cross product magnitude |a||b|sin θ gives the area of the parallelogram spanned.

History essays are marked on use of evidence, argument coherence, and historiographical awareness; every claim needs a date, place, or named example.

Causation language in L2: distinguish long-term structural causes, short-term triggers, and precipitating events; examiners reward explicit weighting of causes.

Source criticism framework: origin (who, when, where), purpose (why produced, intended audience), value (what it reveals), and limitations (bias, silence, reliability).

Key twentieth-century anchor dates: 1919 Treaty of Versailles; 1929 Wall Street Crash; 1945 end of World War II and founding of the United Nations; 1949 NATO and the two German states; 1989 fall of the Berlin Wall; 1991 dissolution of the USSR.

European integration milestones: 1951 ECSC Treaty of Paris; 1957 Treaties of Rome (EEC and Euratom); 1992 Maastricht Treaty creating the European Union; 2002 euro cash introduction.

Geography: population structure is read from population pyramids; a wide base indicates high birth rates and a youthful population, a narrow base indicates ageing.

Demographic transition model stages: high stationary (high birth and death rates), early expanding, late expanding, low stationary, and declining population.

Plate tectonics: divergent boundaries create rift valleys and mid-ocean ridges; convergent boundaries produce subduction zones, fold mountains, and volcanic arcs; transform boundaries produce strike-slip earthquakes.

Climate and biome links: latitude controls insolation and therefore temperature belts; continentality and ocean currents modify rainfall and seasonal range.

Physics kinematics: v = u + at; s = ut + ½at²; v² = u² + 2as; use these only for constant acceleration, and fix a positive direction before substituting signs.

Newton's second law F = ma; momentum p = mv is conserved in collisions absent external forces; impulse equals change in momentum, FΔt = Δp.

Energy: kinetic ½mv², gravitational potential mgh, elastic ½kx²; power P = W/t = Fv; efficiency = useful output / total input × 100%.

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

Waves: v = fλ; refraction obeys Snell's law n₁sin θ₁ = n₂sin θ₂; for a converging lens 1/f = 1/v + 1/u with the thin-lens sign convention stated explicitly.

Chemistry moles: n = m/M; n = cV for solutions (V in dm³); at standard conditions one mole of gas occupies about 24 dm³ (22.4 dm³ at STP).

Acid–base: pH = −log₁₀[H⁺]; strong acid and strong base neutralise in the ratio given by the balanced equation; titration uses n(acid)/n(base) from stoichiometry.

Organic functional groups: alcohols (OH), carboxylic acids (COOH), aldehydes (CHO), ketones (C=O between carbons), esters (COO), amines (NH₂); oxidation of a primary alcohol gives an aldehyde then a carboxylic acid.

Biology: enzyme activity depends on temperature and pH, denaturing above the optimum; photosynthesis equation 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂; aerobic respiration releases far more ATP per glucose than anaerobic.

Argument anatomy: premises, inference, conclusion; validity concerns form only, soundness requires validity plus true premises, so a valid argument can still have a false conclusion if a premise is false.

Common fallacies to name precisely: ad hominem, straw man, false dilemma, begging the question, post hoc ergo propter hoc, appeal to authority, and hasty generalisation.

Deductive versus inductive reasoning: deduction guarantees the conclusion if premises are true; induction makes the conclusion probable only, so it can be strong or weak rather than valid or invalid.

Descartes' method of doubt reaches the cogito (I think, therefore I am) and argues for a distinction between mind and body; the weakness is the move from indubitability to real existence.

Kant's distinction: analytic judgements are true by meaning, synthetic judgements extend knowledge; the categorical imperative tests maxims for universalisability and treats persons as ends, not merely means.

Utilitarianism (Bentham, Mill) judges acts by consequences and total welfare; standard objections are the utility monster, the sacrifice of minority rights, and the difficulty of measuring happiness.

Kantian deontology judges acts by duty and the maxim behind them, not consequences; the standard objection is that it may forbid morally required lies in extreme cases.

Hume's is–ought gap: descriptive statements about what is the case do not by themselves entail prescriptive statements about what ought to be done.

Essay method: state the thesis, reconstruct the strongest version of the opposing view, apply a specific objection, then evaluate rather than merely describe.

Paper structure typically has two parts: a comprehension/analysis task on an unseen text and a written production task (essay, opinion piece, or argumentative response) assessed on content, organisation, and language accuracy.

Language accuracy is usually marked separately from content: keep a running error log of your own recurring faults (articles, tense agreement, register) and check only those in the final five minutes.

Text analysis vocabulary: register (formal/informal/neutral), tone, irony, hyperbole, euphemism, anaphora, rhetorical question, antithesis, and the writer's stance (thesis, implicit assumption, concession).

Commentary structure: introduce the text (author, type, date, topic), state the dominant effect or argument, then support with quotation plus analysis of the linguistic device used and its effect on the reader.

Quotations should be short (three to eight words), integrated syntactically into your sentence, and always followed by interpretation, never left as bare evidence.

Essay planning: thesis in the introduction, one idea per paragraph, topic sentence first, evidence and analysis in the middle, and a conclusion that answers the question rather than summarising.

Word-count discipline: plan paragraph targets in advance (for example 5 paragraphs of roughly equal length) so the conclusion is not lost to over-long early paragraphs.

Cohesion markers to vary: however, nevertheless, whereas, thereby, consequently, by contrast, indeed, arguably; avoid repeating the same connector more than once per paragraph.

L2 assessment in the European Baccalaureate is split into written and oral components; the written paper typically contains a listening or reading comprehension section and a written production section.

Comprehension questions often require reformulation, not copying: answer in your own words and match the number of elements the question asks for (give two reasons means exactly two).

Written production is graded on task achievement, coherence, range of vocabulary and structures, and grammatical accuracy; a short accurate text usually outscores a long inaccurate one.

Register control: choose formal connectors for essays (furthermore, in addition, nevertheless) and avoid oral fillers (well, you know, actually) in written work.

Oral exam routine: prepare a short structured statement on the topic, then be ready to defend it; examiners reward interaction strategies such as asking for clarification or reformulating.

False friends are a common scoring trap across European languages (for example German aktuell = current, not actual; French actuel = current; Italian attuale = current).

Subjunctive and conditional sequences appear in formal writing in Romance languages; check the sequence of tenses after expressions of doubt, wish, or hypothesis.

Paraphrase toolkit: synonym substitution, word-class change (verb to noun), clause restructuring (active to passive), and generalisation or specification.

Quadratic formula: for ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / 2a; the discriminant Δ = b² − 4ac gives two real roots (Δ > 0), one double root (Δ = 0), or no real roots (Δ < 0).

Derivative rules: (xⁿ)′ = nxⁿ⁻¹; (eˣ)′ = eˣ; (ln x)′ = 1/x; (sin x)′ = cos x; (cos x)′ = −sin x; product rule (uv)′ = u′v + uv′; quotient rule (u/v)′ = (u′v − uv′)/v².

Chain rule: d/dx f(g(x)) = f′(g(x))·g′(x); integration by substitution reverses it, and integration by parts is ∫u dv = uv − ∫v du.

Definite integral equals the signed area under the curve; the Fundamental Theorem gives ∫ₐᵇ f(x) dx = F(b) − F(a) where F′ = f.

Logarithm laws: ln(ab) = ln a + ln b; ln(a/b) = ln a − ln b; ln(aⁿ) = n ln a; used to solve exponential equations by taking logs of both sides.

Trigonometric identities: sin²x + cos²x = 1; sin 2x = 2 sin x cos x; cos 2x = cos²x − sin²x = 1 − 2sin²x = 2cos²x − 1.

Arithmetic sequence: uₙ = u₁ + (n − 1)d, sum Sₙ = n(u₁ + uₙ)/2; geometric: uₙ = u₁·rⁿ⁻¹, sum Sₙ = u₁(1 − rⁿ)/(1 − r) for r ≠ 1.

Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); conditional P(A|B) = P(A ∩ B)/P(B); independence means P(A ∩ B) = P(A)·P(B).

Vectors: dot product a·b = |a||b|cos θ, zero for perpendicular vectors; cross product magnitude |a||b|sin θ gives the area of the parallelogram spanned.

History essays are marked on use of evidence, argument coherence, and historiographical awareness; every claim needs a date, place, or named example.

Causation language in L2: distinguish long-term structural causes, short-term triggers, and precipitating events; examiners reward explicit weighting of causes.

Source criticism framework: origin (who, when, where), purpose (why produced, intended audience), value (what it reveals), and limitations (bias, silence, reliability).

Key twentieth-century anchor dates: 1919 Treaty of Versailles; 1929 Wall Street Crash; 1945 end of World War II and founding of the United Nations; 1949 NATO and the two German states; 1989 fall of the Berlin Wall; 1991 dissolution of the USSR.

European integration milestones: 1951 ECSC Treaty of Paris; 1957 Treaties of Rome (EEC and Euratom); 1992 Maastricht Treaty creating the European Union; 2002 euro cash introduction.

Geography: population structure is read from population pyramids; a wide base indicates high birth rates and a youthful population, a narrow base indicates ageing.

Demographic transition model stages: high stationary (high birth and death rates), early expanding, late expanding, low stationary, and declining population.

Plate tectonics: divergent boundaries create rift valleys and mid-ocean ridges; convergent boundaries produce subduction zones, fold mountains, and volcanic arcs; transform boundaries produce strike-slip earthquakes.

Climate and biome links: latitude controls insolation and therefore temperature belts; continentality and ocean currents modify rainfall and seasonal range.

Physics kinematics: v = u + at; s = ut + ½at²; v² = u² + 2as; use these only for constant acceleration, and fix a positive direction before substituting signs.

Newton's second law F = ma; momentum p = mv is conserved in collisions absent external forces; impulse equals change in momentum, FΔt = Δp.

Energy: kinetic ½mv², gravitational potential mgh, elastic ½kx²; power P = W/t = Fv; efficiency = useful output / total input × 100%.

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

Waves: v = fλ; refraction obeys Snell's law n₁sin θ₁ = n₂sin θ₂; for a converging lens 1/f = 1/v + 1/u with the thin-lens sign convention stated explicitly.

Chemistry moles: n = m/M; n = cV for solutions (V in dm³); at standard conditions one mole of gas occupies about 24 dm³ (22.4 dm³ at STP).

Acid–base: pH = −log₁₀[H⁺]; strong acid and strong base neutralise in the ratio given by the balanced equation; titration uses n(acid)/n(base) from stoichiometry.

Organic functional groups: alcohols (OH), carboxylic acids (COOH), aldehydes (CHO), ketones (C=O between carbons), esters (COO), amines (NH₂); oxidation of a primary alcohol gives an aldehyde then a carboxylic acid.

Biology: enzyme activity depends on temperature and pH, denaturing above the optimum; photosynthesis equation 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂; aerobic respiration releases far more ATP per glucose than anaerobic.

Argument anatomy: premises, inference, conclusion; validity concerns form only, soundness requires validity plus true premises, so a valid argument can still have a false conclusion if a premise is false.

Common fallacies to name precisely: ad hominem, straw man, false dilemma, begging the question, post hoc ergo propter hoc, appeal to authority, and hasty generalisation.

Deductive versus inductive reasoning: deduction guarantees the conclusion if premises are true; induction makes the conclusion probable only, so it can be strong or weak rather than valid or invalid.

Descartes' method of doubt reaches the cogito (I think, therefore I am) and argues for a distinction between mind and body; the weakness is the move from indubitability to real existence.

Kant's distinction: analytic judgements are true by meaning, synthetic judgements extend knowledge; the categorical imperative tests maxims for universalisability and treats persons as ends, not merely means.

Utilitarianism (Bentham, Mill) judges acts by consequences and total welfare; standard objections are the utility monster, the sacrifice of minority rights, and the difficulty of measuring happiness.

Kantian deontology judges acts by duty and the maxim behind them, not consequences; the standard objection is that it may forbid morally required lies in extreme cases.

Hume's is–ought gap: descriptive statements about what is the case do not by themselves entail prescriptive statements about what ought to be done.

Essay method: state the thesis, reconstruct the strongest version of the opposing view, apply a specific objection, then evaluate rather than merely describe.

Paper structure typically has two parts: a comprehension/analysis task on an unseen text and a written production task (essay, opinion piece, or argumentative response) assessed on content, organisation, and language accuracy.

Language accuracy is usually marked separately from content: keep a running error log of your own recurring faults (articles, tense agreement, register) and check only those in the final five minutes.

Text analysis vocabulary: register (formal/informal/neutral), tone, irony, hyperbole, euphemism, anaphora, rhetorical question, antithesis, and the writer's stance (thesis, implicit assumption, concession).

Commentary structure: introduce the text (author, type, date, topic), state the dominant effect or argument, then support with quotation plus analysis of the linguistic device used and its effect on the reader.

Quotations should be short (three to eight words), integrated syntactically into your sentence, and always followed by interpretation, never left as bare evidence.

Essay planning: thesis in the introduction, one idea per paragraph, topic sentence first, evidence and analysis in the middle, and a conclusion that answers the question rather than summarising.

Word-count discipline: plan paragraph targets in advance (for example 5 paragraphs of roughly equal length) so the conclusion is not lost to over-long early paragraphs.

Cohesion markers to vary: however, nevertheless, whereas, thereby, consequently, by contrast, indeed, arguably; avoid repeating the same connector more than once per paragraph.

L2 assessment in the European Baccalaureate is split into written and oral components; the written paper typically contains a listening or reading comprehension section and a written production section.

Comprehension questions often require reformulation, not copying: answer in your own words and match the number of elements the question asks for (give two reasons means exactly two).

Written production is graded on task achievement, coherence, range of vocabulary and structures, and grammatical accuracy; a short accurate text usually outscores a long inaccurate one.

Register control: choose formal connectors for essays (furthermore, in addition, nevertheless) and avoid oral fillers (well, you know, actually) in written work.

Oral exam routine: prepare a short structured statement on the topic, then be ready to defend it; examiners reward interaction strategies such as asking for clarification or reformulating.

False friends are a common scoring trap across European languages (for example German aktuell = current, not actual; French actuel = current; Italian attuale = current).

Subjunctive and conditional sequences appear in formal writing in Romance languages; check the sequence of tenses after expressions of doubt, wish, or hypothesis.

Paraphrase toolkit: synonym substitution, word-class change (verb to noun), clause restructuring (active to passive), and generalisation or specification.

Quadratic formula: for ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / 2a; the discriminant Δ = b² − 4ac gives two real roots (Δ > 0), one double root (Δ = 0), or no real roots (Δ < 0).

Derivative rules: (xⁿ)′ = nxⁿ⁻¹; (eˣ)′ = eˣ; (ln x)′ = 1/x; (sin x)′ = cos x; (cos x)′ = −sin x; product rule (uv)′ = u′v + uv′; quotient rule (u/v)′ = (u′v − uv′)/v².

Chain rule: d/dx f(g(x)) = f′(g(x))·g′(x); integration by substitution reverses it, and integration by parts is ∫u dv = uv − ∫v du.

Definite integral equals the signed area under the curve; the Fundamental Theorem gives ∫ₐᵇ f(x) dx = F(b) − F(a) where F′ = f.

Logarithm laws: ln(ab) = ln a + ln b; ln(a/b) = ln a − ln b; ln(aⁿ) = n ln a; used to solve exponential equations by taking logs of both sides.

Trigonometric identities: sin²x + cos²x = 1; sin 2x = 2 sin x cos x; cos 2x = cos²x − sin²x = 1 − 2sin²x = 2cos²x − 1.

Arithmetic sequence: uₙ = u₁ + (n − 1)d, sum Sₙ = n(u₁ + uₙ)/2; geometric: uₙ = u₁·rⁿ⁻¹, sum Sₙ = u₁(1 − rⁿ)/(1 − r) for r ≠ 1.

Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); conditional P(A|B) = P(A ∩ B)/P(B); independence means P(A ∩ B) = P(A)·P(B).

Vectors: dot product a·b = |a||b|cos θ, zero for perpendicular vectors; cross product magnitude |a||b|sin θ gives the area of the parallelogram spanned.

History essays are marked on use of evidence, argument coherence, and historiographical awareness; every claim needs a date, place, or named example.

Causation language in L2: distinguish long-term structural causes, short-term triggers, and precipitating events; examiners reward explicit weighting of causes.

Source criticism framework: origin (who, when, where), purpose (why produced, intended audience), value (what it reveals), and limitations (bias, silence, reliability).

Key twentieth-century anchor dates: 1919 Treaty of Versailles; 1929 Wall Street Crash; 1945 end of World War II and founding of the United Nations; 1949 NATO and the two German states; 1989 fall of the Berlin Wall; 1991 dissolution of the USSR.

European integration milestones: 1951 ECSC Treaty of Paris; 1957 Treaties of Rome (EEC and Euratom); 1992 Maastricht Treaty creating the European Union; 2002 euro cash introduction.

Geography: population structure is read from population pyramids; a wide base indicates high birth rates and a youthful population, a narrow base indicates ageing.

Demographic transition model stages: high stationary (high birth and death rates), early expanding, late expanding, low stationary, and declining population.

Plate tectonics: divergent boundaries create rift valleys and mid-ocean ridges; convergent boundaries produce subduction zones, fold mountains, and volcanic arcs; transform boundaries produce strike-slip earthquakes.

Climate and biome links: latitude controls insolation and therefore temperature belts; continentality and ocean currents modify rainfall and seasonal range.

Physics kinematics: v = u + at; s = ut + ½at²; v² = u² + 2as; use these only for constant acceleration, and fix a positive direction before substituting signs.

Newton's second law F = ma; momentum p = mv is conserved in collisions absent external forces; impulse equals change in momentum, FΔt = Δp.

Energy: kinetic ½mv², gravitational potential mgh, elastic ½kx²; power P = W/t = Fv; efficiency = useful output / total input × 100%.

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

Waves: v = fλ; refraction obeys Snell's law n₁sin θ₁ = n₂sin θ₂; for a converging lens 1/f = 1/v + 1/u with the thin-lens sign convention stated explicitly.

Chemistry moles: n = m/M; n = cV for solutions (V in dm³); at standard conditions one mole of gas occupies about 24 dm³ (22.4 dm³ at STP).

Acid–base: pH = −log₁₀[H⁺]; strong acid and strong base neutralise in the ratio given by the balanced equation; titration uses n(acid)/n(base) from stoichiometry.

Organic functional groups: alcohols (OH), carboxylic acids (COOH), aldehydes (CHO), ketones (C=O between carbons), esters (COO), amines (NH₂); oxidation of a primary alcohol gives an aldehyde then a carboxylic acid.

Biology: enzyme activity depends on temperature and pH, denaturing above the optimum; photosynthesis equation 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂; aerobic respiration releases far more ATP per glucose than anaerobic.

Argument anatomy: premises, inference, conclusion; validity concerns form only, soundness requires validity plus true premises, so a valid argument can still have a false conclusion if a premise is false.

Common fallacies to name precisely: ad hominem, straw man, false dilemma, begging the question, post hoc ergo propter hoc, appeal to authority, and hasty generalisation.

Deductive versus inductive reasoning: deduction guarantees the conclusion if premises are true; induction makes the conclusion probable only, so it can be strong or weak rather than valid or invalid.

Descartes' method of doubt reaches the cogito (I think, therefore I am) and argues for a distinction between mind and body; the weakness is the move from indubitability to real existence.

Kant's distinction: analytic judgements are true by meaning, synthetic judgements extend knowledge; the categorical imperative tests maxims for universalisability and treats persons as ends, not merely means.

Utilitarianism (Bentham, Mill) judges acts by consequences and total welfare; standard objections are the utility monster, the sacrifice of minority rights, and the difficulty of measuring happiness.

Kantian deontology judges acts by duty and the maxim behind them, not consequences; the standard objection is that it may forbid morally required lies in extreme cases.

Hume's is–ought gap: descriptive statements about what is the case do not by themselves entail prescriptive statements about what ought to be done.

Essay method: state the thesis, reconstruct the strongest version of the opposing view, apply a specific objection, then evaluate rather than merely describe.

Paper structure typically has two parts: a comprehension/analysis task on an unseen text and a written production task (essay, opinion piece, or argumentative response) assessed on content, organisation, and language accuracy.

Language accuracy is usually marked separately from content: keep a running error log of your own recurring faults (articles, tense agreement, register) and check only those in the final five minutes.

Text analysis vocabulary: register (formal/informal/neutral), tone, irony, hyperbole, euphemism, anaphora, rhetorical question, antithesis, and the writer's stance (thesis, implicit assumption, concession).

Commentary structure: introduce the text (author, type, date, topic), state the dominant effect or argument, then support with quotation plus analysis of the linguistic device used and its effect on the reader.

Quotations should be short (three to eight words), integrated syntactically into your sentence, and always followed by interpretation, never left as bare evidence.

Essay planning: thesis in the introduction, one idea per paragraph, topic sentence first, evidence and analysis in the middle, and a conclusion that answers the question rather than summarising.

Word-count discipline: plan paragraph targets in advance (for example 5 paragraphs of roughly equal length) so the conclusion is not lost to over-long early paragraphs.

Cohesion markers to vary: however, nevertheless, whereas, thereby, consequently, by contrast, indeed, arguably; avoid repeating the same connector more than once per paragraph.

L2 assessment in the European Baccalaureate is split into written and oral components; the written paper typically contains a listening or reading comprehension section and a written production section.

Comprehension questions often require reformulation, not copying: answer in your own words and match the number of elements the question asks for (give two reasons means exactly two).

Written production is graded on task achievement, coherence, range of vocabulary and structures, and grammatical accuracy; a short accurate text usually outscores a long inaccurate one.

Register control: choose formal connectors for essays (furthermore, in addition, nevertheless) and avoid oral fillers (well, you know, actually) in written work.

Oral exam routine: prepare a short structured statement on the topic, then be ready to defend it; examiners reward interaction strategies such as asking for clarification or reformulating.

False friends are a common scoring trap across European languages (for example German aktuell = current, not actual; French actuel = current; Italian attuale = current).

Subjunctive and conditional sequences appear in formal writing in Romance languages; check the sequence of tenses after expressions of doubt, wish, or hypothesis.

Paraphrase toolkit: synonym substitution, word-class change (verb to noun), clause restructuring (active to passive), and generalisation or specification.

Quadratic formula: for ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / 2a; the discriminant Δ = b² − 4ac gives two real roots (Δ > 0), one double root (Δ = 0), or no real roots (Δ < 0).

Derivative rules: (xⁿ)′ = nxⁿ⁻¹; (eˣ)′ = eˣ; (ln x)′ = 1/x; (sin x)′ = cos x; (cos x)′ = −sin x; product rule (uv)′ = u′v + uv′; quotient rule (u/v)′ = (u′v − uv′)/v².

Chain rule: d/dx f(g(x)) = f′(g(x))·g′(x); integration by substitution reverses it, and integration by parts is ∫u dv = uv − ∫v du.

Definite integral equals the signed area under the curve; the Fundamental Theorem gives ∫ₐᵇ f(x) dx = F(b) − F(a) where F′ = f.

Logarithm laws: ln(ab) = ln a + ln b; ln(a/b) = ln a − ln b; ln(aⁿ) = n ln a; used to solve exponential equations by taking logs of both sides.

Trigonometric identities: sin²x + cos²x = 1; sin 2x = 2 sin x cos x; cos 2x = cos²x − sin²x = 1 − 2sin²x = 2cos²x − 1.

Arithmetic sequence: uₙ = u₁ + (n − 1)d, sum Sₙ = n(u₁ + uₙ)/2; geometric: uₙ = u₁·rⁿ⁻¹, sum Sₙ = u₁(1 − rⁿ)/(1 − r) for r ≠ 1.

Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); conditional P(A|B) = P(A ∩ B)/P(B); independence means P(A ∩ B) = P(A)·P(B).

Vectors: dot product a·b = |a||b|cos θ, zero for perpendicular vectors; cross product magnitude |a||b|sin θ gives the area of the parallelogram spanned.

History essays are marked on use of evidence, argument coherence, and historiographical awareness; every claim needs a date, place, or named example.

Causation language in L2: distinguish long-term structural causes, short-term triggers, and precipitating events; examiners reward explicit weighting of causes.

Source criticism framework: origin (who, when, where), purpose (why produced, intended audience), value (what it reveals), and limitations (bias, silence, reliability).

Key twentieth-century anchor dates: 1919 Treaty of Versailles; 1929 Wall Street Crash; 1945 end of World War II and founding of the United Nations; 1949 NATO and the two German states; 1989 fall of the Berlin Wall; 1991 dissolution of the USSR.

European integration milestones: 1951 ECSC Treaty of Paris; 1957 Treaties of Rome (EEC and Euratom); 1992 Maastricht Treaty creating the European Union; 2002 euro cash introduction.

Geography: population structure is read from population pyramids; a wide base indicates high birth rates and a youthful population, a narrow base indicates ageing.

Demographic transition model stages: high stationary (high birth and death rates), early expanding, late expanding, low stationary, and declining population.

Plate tectonics: divergent boundaries create rift valleys and mid-ocean ridges; convergent boundaries produce subduction zones, fold mountains, and volcanic arcs; transform boundaries produce strike-slip earthquakes.

Climate and biome links: latitude controls insolation and therefore temperature belts; continentality and ocean currents modify rainfall and seasonal range.

Physics kinematics: v = u + at; s = ut + ½at²; v² = u² + 2as; use these only for constant acceleration, and fix a positive direction before substituting signs.

Newton's second law F = ma; momentum p = mv is conserved in collisions absent external forces; impulse equals change in momentum, FΔt = Δp.

Energy: kinetic ½mv², gravitational potential mgh, elastic ½kx²; power P = W/t = Fv; efficiency = useful output / total input × 100%.

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

Waves: v = fλ; refraction obeys Snell's law n₁sin θ₁ = n₂sin θ₂; for a converging lens 1/f = 1/v + 1/u with the thin-lens sign convention stated explicitly.

Chemistry moles: n = m/M; n = cV for solutions (V in dm³); at standard conditions one mole of gas occupies about 24 dm³ (22.4 dm³ at STP).

Acid–base: pH = −log₁₀[H⁺]; strong acid and strong base neutralise in the ratio given by the balanced equation; titration uses n(acid)/n(base) from stoichiometry.

Organic functional groups: alcohols (OH), carboxylic acids (COOH), aldehydes (CHO), ketones (C=O between carbons), esters (COO), amines (NH₂); oxidation of a primary alcohol gives an aldehyde then a carboxylic acid.

Biology: enzyme activity depends on temperature and pH, denaturing above the optimum; photosynthesis equation 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂; aerobic respiration releases far more ATP per glucose than anaerobic.

Argument anatomy: premises, inference, conclusion; validity concerns form only, soundness requires validity plus true premises, so a valid argument can still have a false conclusion if a premise is false.

Common fallacies to name precisely: ad hominem, straw man, false dilemma, begging the question, post hoc ergo propter hoc, appeal to authority, and hasty generalisation.

Deductive versus inductive reasoning: deduction guarantees the conclusion if premises are true; induction makes the conclusion probable only, so it can be strong or weak rather than valid or invalid.

Descartes' method of doubt reaches the cogito (I think, therefore I am) and argues for a distinction between mind and body; the weakness is the move from indubitability to real existence.

Kant's distinction: analytic judgements are true by meaning, synthetic judgements extend knowledge; the categorical imperative tests maxims for universalisability and treats persons as ends, not merely means.

Utilitarianism (Bentham, Mill) judges acts by consequences and total welfare; standard objections are the utility monster, the sacrifice of minority rights, and the difficulty of measuring happiness.

Kantian deontology judges acts by duty and the maxim behind them, not consequences; the standard objection is that it may forbid morally required lies in extreme cases.

Hume's is–ought gap: descriptive statements about what is the case do not by themselves entail prescriptive statements about what ought to be done.

Essay method: state the thesis, reconstruct the strongest version of the opposing view, apply a specific objection, then evaluate rather than merely describe.