BGCSE cheat sheet

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

Pythagoras: in a right triangle, a² + b² = c², where c is the hypotenuse.

Area: triangle = ½ × base × height; circle = πr²; trapezium = ½(a + b)h.

Volume: cylinder = πr²h; cone = ⅓πr²h; sphere = (4/3)πr³.

Probability: P(A or B) = P(A) + P(B) − P(A and B); for independent events, P(A and B) = P(A)P(B).

Simple interest: I = PRT ÷ 100. Compound amount: A = P(1 + r/n)^(nt).

Interior angle sum of an n-sided polygon = (n − 2) × 180°; exterior angle sum = 360°.

Mean = sum of values ÷ number of values; median = middle ordered value; mode = most frequent value.

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

Passive voice = correct form of 'be' + past participle; the object of the active sentence becomes the subject.

Reported speech shifts tense back one step and changes time markers, e.g. 'today' becomes 'that day'.

Apostrophe: singular possessive = noun + 's; plural possessive ending in s = noun + s'; 'its' is possessive, 'it's' = it is/has.

Comma use: list items, introductory phrases, non-defining relative clauses, and before a coordinating conjunction joining independent clauses.

Subject-verb agreement: singular subject → singular verb; 'either ... or' and 'neither ... nor' agree with the nearer subject.

Simile uses 'like' or 'as'; metaphor states one thing is another; personification gives human qualities to non-human things.

A paragraph normally contains a topic sentence, supporting details, and a concluding sentence.

Inference is a conclusion based on textual evidence; it is not stated directly in the passage.

Formal letter order: sender address, date, recipient address, salutation, body, closing, signature.

Physics: speed = distance ÷ time; acceleration = change in velocity ÷ time; force = mass × acceleration (F = ma).

Physics: weight W = mg, where g ≈ 9.8 N/kg; density = mass ÷ volume; pressure = force ÷ area.

Physics: Ohm's law V = IR; electrical power P = VI = I²R; wave speed v = fλ.

Chemistry: atomic number = protons; mass number = protons + neutrons; isotopes have same protons but different neutrons.

Chemistry: ionic bonds transfer electrons from metals to non-metals; covalent bonds share electron pairs between non-metals.

Chemistry: pH below 7 is acidic, 7 is neutral, above 7 is alkaline; moles n = mass ÷ molar mass.

Biology: photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ using light and chlorophyll.

Biology: aerobic respiration: glucose + oxygen → carbon dioxide + water + energy; diffusion moves particles from high to low concentration.

Biology: in a food chain, energy decreases at each level (about 10% transferred); enzymes are specific biological catalysts.

History: Bechuanaland became a British protectorate in 1885; Botswana became independent on 30 September 1966.

History: Seretse Khama was Botswana's first president; the three chiefs who visited Britain in 1895 were Khama III, Bathoen I, and Sebele I.

History: primary sources originate in the period studied; secondary sources interpret or analyse primary evidence.

Geography: map scale 1:50,000 means 1 cm on the map represents 50,000 cm (0.5 km) on the ground.

Geography: contour lines join points of equal height; close contours indicate steep slopes, widely spaced contours indicate gentle slopes.

Geography: latitude lines run east-west and measure north-south position; longitude lines run north-south and measure east-west position.

Development Studies: GDP measures total output; HDI combines income, life expectancy, and education; sustainable development balances economic, social, and environmental needs.

Development Studies: primary sector extracts raw materials, secondary sector manufactures, tertiary sector provides services.

Setswana noun class prefixes control agreement: mo-/ba- for people (motho/batho), mo-/me- for many objects, le-/ma- for paired or collective nouns.

Setswana greetings: 'Dumela' to one person, 'Dumelang' to more than one; 'Le kae?' means how are you; 'Ke teng' means I am fine.

Setswana question words: eng (what), mang (who), kae (where), leng (when), jang (how).

Setswana numbers 1–5: nngwe, pedi, tharo, nne, tlhano.

Setswana proverb 'Motho ke motho ka batho' means a person is a person through others, stressing community and cooperation.

Setswana politeness: 'Tsweetswee' means please; 'Ke a leboga' means thank you.

French has grammatical gender: nouns are masculine or feminine, and articles/adjectives must agree.

Mandarin Chinese is tonal: the same syllable said with different tones can have different meanings, e.g. ma.

Laboratory safety: wear goggles, tie back hair, know the location of the fire extinguisher, and never taste or smell chemicals directly.

First aid for a sprain: rest, ice, compression, elevation (RICE); do not apply heat in the first 48 hours.

Electrical safety: switch off and unplug before repair; use fuses/circuit breakers; never overload sockets.

Vernier caliper least count is usually 0.02 mm; micrometer least count is usually 0.01 mm; check for zero error before measuring.

Technical drawing: orthographic projection shows front, top, and side views; first-angle projection places the top view below the front view.

Woodwork: saw along the grain with the waste side supported; drill a pilot hole before inserting a screw to prevent splitting.

Food hygiene: keep cold food below 5°C and hot food above 60°C; store raw meat below cooked food to prevent cross-contamination.

Sewing: backstitch is a strong hand stitch; seam allowance is the distance between the fabric edge and the stitching line.