📐 Mathematics (Compulsory Part)
📋 Exam Structure
- Paper 1 (Long questions, ~65%): structured problems; method marks are generous.
- Paper 2 (MC, ~35%): about 45 multiple-choice questions; tests speed and concepts.
- Elective: M1 (Calculus & Statistics) or M2 (Algebra & Calculus) — choose one.
🎯 Three Core Strands
- Number & Algebra: polynomials, indices & logarithms, variation, AP/GP sequences, inequalities.
- Measures, Shape & Space: trigonometry (sine/cosine rules, radians), coordinate geometry, circle equations, vectors, transformations.
- Data Handling: statistics (mean/median/standard deviation), probability (tree diagrams, basic permutations & combinations).
🔑 Key Formulas
- Quadratic discriminant Δ=b²−4ac (Δ>0 two real roots; =0 repeated; <0 none)
- AP aₙ=a₁+(n−1)d; GP aₙ=a₁rⁿ⁻¹; Sₙ=n/2(a₁+aₙ)
- Radian: 180°=π rad; arc s=rθ, sector area A=½r²θ
- Circle (x−h)²+(y−k)²=r²; midpoint ((x₁+x₂)/2, (y₁+y₂)/2)
- Independent P(A∩B)=P(A)P(B); mutually exclusive P(A∪B)=P(A)+P(B)
⚠️ Common Pitfalls
- Forgetting to reverse the sign when dividing an inequality by a negative (e.g. −2x>6 ⇒ x<−3).
- Wrong sign of trig ratios in different quadrants (sin positive in QI,QII; tan negative in QII,QIV).
- Confusing "with replacement" vs "without replacement" in probability.
- Mixing up standard deviation (√variance) with variance.
💡 Tips
- Paper 1 gives many method marks — show the formula and substitution even if the final answer is wrong.
- In Paper 2 MC, use substitution and estimation to save time.
- In geometry, always label coordinates and right-angle marks to avoid misreading conditions.
🧪 Chemistry
📋 Exam Structure
- Paper 1 (MC): core and elective foundational concepts.
- Paper 2 (Structured / reaction / calculation): equations, calculations, reasoning & explanations.
- Paper 3 (Elective): A Industrial Chemistry, B Analytical & Testing, C Reactive Chemistry — choose one.
🎯 Core Topics
- Atoms & bonding: isotopes; distinguishing ionic / covalent / metallic bonds.
- Mole & gas laws: n = m/M = cV; Boyle's, Charles's and Gay-Lussac's laws.
- Acids, bases & salts: indicator colours, titration, acidity/basicity of salts.
- Redox & electrochemistry: oxidation numbers; oxidising/reducing agents; cells & electrolysis.
- Kinetics & equilibrium: rate factors; Le Chatelier's principle.
- Organic chemistry: alkanes/alkenes/alcohols/acids, polymers, nomenclature.
🔑 Key Points
- Mole n = m/M = cV (V in dm³)
- Molar gas volume at STP ≈ 22.4 dm³/mol (RTP ≈ 24)
- Neutralisation: n(H⁺) = n(OH⁻)
- Oxidation: loss of e⁻, oxidation number ↑; Reduction: gain of e⁻, oxidation number ↓
- Galvanic cell: anode oxidation (−), cathode reduction (+)
⚠️ Common Pitfalls
- Confusing oxidising agent (itself reduced, gains e⁻) with reducing agent.
- Electrolysis: cathode (−) deposits metal, anode (+) dissolves — wiring is often reversed.
- Equilibrium: a temperature rise shifts toward the endothermic direction (not exothermic).
- Careless organic nomenclature and isomerism.
💡 Tips
- In calculations, show steps and units — partial credit is given even if an intermediate is wrong.
- For experiment questions, answer as "observation + chemical explanation" in two parts.
- Never omit state symbols (aq)(s)(g)(l) and balancing in equations.
🌿 Biology
📋 Exam Structure
- Paper 1 (MC): broad concepts and graph/diagram interpretation.
- Paper 2 (Short answer / experimental): explanations, comparisons, experimental design.
- Paper 3 (Elective): Human Physiology, Plant Physiology & Reproduction, Microbiology, Biotechnology — choose one.
🎯 Core Topics
- Cell: prokaryote vs eukaryote; organelle functions.
- Transport: diffusion, osmosis, active transport — conditions and examples.
- Enzymes: lower activation energy; affected by pH / temperature (denatured at high heat).
- Photosynthesis & respiration: sites, inputs/outputs, aerobic vs anaerobic.
- Genetics: semi-conservative DNA replication; mitosis/meiosis; Mendel's laws; dominance.
- Human physiology: digestion, circulation, nervous, endocrine, immunity.
🔑 Key Points
- Mitosis: chromosome number unchanged; Meiosis: halved (gametes)
- Photosynthesis: CO₂ + H₂O —light/chloroplast→ glucose + O₂ (thylakoid + stroma)
- Aerobic respiration → CO₂ + H₂O (mitochondria); muscle anaerobic → lactate
- Reflex arc: receptor → sensory neurone → CNS → motor neurone → effector
- Xylem transports water & minerals; phloem transports organic nutrients
⚠️ Common Pitfalls
- Confusing chromosome number vs chromatid number in mitosis/meiosis.
- Errors in dominance and ABO codominance inheritance calculations.
- Writing the reflex arc in reverse; swapping xylem/phloem functions.
- Mixing up respiration products (lactate vs alcohol vs CO₂).
💡 Tips
- For definition questions, "definition + example" is safest.
- In experimental design, clearly state controlled variables, experimental & control groups.
- For graphs, first read the axis variables and units, then describe trend and turning points.
📈 Economics
📋 Exam Structure
- Paper 1 (MC, compulsory): concepts and diagram interpretation.
- Paper 2 (Data / short essays, compulsory): explaining graphs, short arguments.
- Paper 3 (Elective): Microeconomics or Macroeconomics — choose one.
🎯 Core Topics
- Micro: law of demand/supply, price elasticity, consumer/producer surplus, four market structures, externalities & public goods.
- Macro: GDP accounting, types & measurement of unemployment, inflation (demand-pull / cost-push), monetary & fiscal policy, exchange rates, comparative advantage & trade.
🔑 Key Formulas & Concepts
- Price elasticity E_d = %ΔQ / %ΔP (<1 inelastic, >1 elastic)
- Total revenue TR = P × Q
- Unemployment rate = unemployed / labour force × 100%
- Comparative advantage: specialise where opportunity (relative) cost is lower
⚠️ Common Pitfalls
- Confusing change in demand (shift) with change in quantity demanded (movement along).
- Elasticity & total revenue: an inelastic good's price rise raises TR (not lowers).
- Appreciation helps imports, hurts exports; depreciation is the opposite (often reversed).
- Mixing up monetary policy (interest rate) with fiscal policy (G & tax).
💡 Tips
- For diagrams, label both axes (P, Q), draw the shift direction, and don't omit the origin.
- In essays, use economic terms (e.g. "substitution effect", "marginal"), not just common sense.
- For arguments, use a "because… so… leading to…" chain of reasoning.
📜 中國語文
📋 考試結構
- 卷一（閱讀）：文言文與白話文篇章理解、賞析。
- 卷二（寫作）：命題／指定情景，記敘／抒情／議論。
- 卷三（聆聽與綜合）：聽錄音答題、綜合能力運用。
- 卷四（說話）：小組討論與個人短講（口語溝通）。
🎯 核心考點
- 文言文：虛詞（之乎者也）、實詞、特殊句式（判斷／被動／倒裝）、直譯。
- 白話文閱讀：主旨、段意、修辭、寫作手法、詩詞賞析。
- 寫作：審題立意、結構（起承轉合）、描寫與論證。
- 語文基礎：字音字形、標點、成語運用、病句辨析。
🔑 常考提醒
- 修辭：比喻／擬人／誇飾／對偶／借代／排比 的辨識
- 成語：注意感情色彩（褒／貶）與搭配對象
- 虛詞「而」：順承、轉折、修飾、并列 用法
- 書信：稱謂、提稱語、啟封詞（如「鈞啟」「台啟」）
⚠️ 常見失分點
- 文言文實詞古今異義誤解（如「走」＝奔跑）。
- 成語褒貶誤用（如「處心積慮」含貶義用在正面）。
- 病句：缺主語、搭配不當、兩面對一面、邏輯矛盾。
- 寫作離題或結構鬆散，未首尾呼應。
💡 答題技巧
- 閱讀先讀題再回原文定位，節省時間。
- 寫作前列提綱，開頭點題、結尾呼應。
- 說話（卷四）準備立場＋兩個例子，冷靜聆聽他人再回應。
🔤 English
📋 Exam Structure
- Paper 1 (Reading): comprehension of various text types; inference, main idea, vocabulary in context.
- Paper 2 (Writing): essays, emails, proposals, reports — planning & grammar matter most.
- Paper 3 (Listening & Integrated Skills): note-taking, gap-fill, integrated tasks.
- Paper 4 (Speaking): group interaction & individual response.
🎯 Core Areas
- Reading: skimming & scanning, guessing meaning from context, distinguishing fact vs opinion.
- Writing: clear paragraphing, linking words, varied sentences, correct tenses.
- Grammar focus: tenses (incl. present perfect, future), passive voice, conditionals, relative clauses, articles, comparatives, reported speech.
🔑 Key Reminders
- Present perfect: action from past continuing / relevant to now (since, for)
- Passive: be + past participle; future passive = will be + V-pp
- Articles: a/an (one), the (specific / unique)
- Linkers: however (contrast), therefore (result), moreover (add)
⚠️ Common Pitfalls
- Subject–verb agreement after "each", "every", indefinite pronouns.
- Article misuse: missing "the" for unique things (the Moon, the Earth).
- Tense shifts in narrative writing (stay consistent in past).
- Wrong linker: "however" shows contrast, not result.
💡 Tips
- Reading: read the questions first, then scan for keywords.
- Writing: plan → paragraph → check grammar (tense, agreement, spelling).
- Build vocabulary by topic (environment, health, technology, education).