PSLE RME cheat sheet

Place value: each position is ten times the value of the position to its right; 4 in 3 472 means 400, in 3 742 it means 40.

Order of operations: work through brackets, then powers, then multiplication and division left to right, then addition and subtraction left to right.

Fraction operations: to add or subtract, rewrite over a common denominator; to multiply, multiply numerators and denominators; to divide, multiply by the reciprocal.

Percentage: part = percentage ÷ 100 × whole; to find the whole from a part, divide the part by the percentage expressed as a decimal.

Area and perimeter: rectangle area = length × width; triangle area = ½ × base × height; circle area = π × radius², circumference = 2πr.

Volume: cuboid = length × width × height; cube = side³; 1 litre = 1 000 cm³ and 1 m³ = 1 000 000 cm³.

Average (mean) = total of all values ÷ number of values; total = mean × number of values.

Ratio: simplify by dividing all terms by their highest common factor; share a quantity by dividing it by the total number of parts, then multiplying.

Speed = distance ÷ time; distance = speed × time; time = distance ÷ speed; average speed uses total distance over total time.

Angle facts: angles on a straight line sum to 180°, angles at a point sum to 360°, angles in a triangle sum to 180°, vertically opposite angles are equal.

Subject–verb agreement: a singular subject takes a singular verb (she walks); a plural subject takes the plural form (they walk); compound subjects joined by 'and' take a plural verb.

Tenses: simple past uses verb + -ed or an irregular form; present perfect uses has/have + past participle for actions linked to now.

Direct to reported speech: shift the tense back one step (present to past, past to past perfect) and change pronouns and time words (today becomes that day).

Active to passive: move the object to the subject position and use be + past participle (The dog bit the boy becomes The boy was bitten by the dog).

Punctuation: commas separate items in a list and mark off non-defining clauses; apostrophes show possession (the girl's bag) or contraction (don't).

Question tags: a positive statement takes a negative tag and vice versa (She is late, isn't she?); the tag repeats the auxiliary verb.

Comprehension strategy: read the question first, locate the relevant sentence, and answer in a full sentence using the words of the question.

Inference: an answer not stated directly must be supported by clues in the text; quote or paraphrase the evidence.

Vocabulary in context: replace the target word with each option and check that the sentence still makes sense.

Summary writing: keep only main points, use your own words, and stay within the word limit.

Nouns fall into classes marked by prefixes; class 1 (motho, person) takes the subject concord o, class 2 (batho, people) takes ba.

Subject concords must match the noun class: 'Mosadi o a ja' (the woman eats) versus 'Basadi ba a ja' (the women eat).

The present tense uses the subject concord + a + verb, with 'a' often changing form before vowels, e.g. 'ke a bona' (I see).

The negative present is formed with ga + subject concord + verb ending in -e: 'Ga ke bone' means 'I do not see'.

The past tense marker is -ile or -ne: 'Ke ne ke ithuta' means 'I was learning'; 'O ile a tsamaya' means 'He/She went'.

The future tense uses tla or tloo with the subject concord: 'Ke tla ya' means 'I will go'.

Possession uses the concord of the possessed noun plus the possessor: 'buka ya me' (my book), 'bana ba rona' (our children).

Questions: 'eng' asks what, 'mang' asks who, 'leng' asks when, 'kae' asks where, and 'jang' asks how.

Idioms and proverbs carry fixed meanings; for example, 'A e telele e tswa kae' is a rhetorical expression rather than a literal question.

Cells are the basic unit of life; plant cells have a cell wall, chloroplasts and a large vacuole, while animal cells do not have a cell wall or chloroplasts.

Photosynthesis: carbon dioxide + water, using light energy absorbed by chlorophyll, produces glucose and oxygen; it occurs in chloroplasts.

Respiration releases energy from glucose; aerobic respiration uses oxygen and produces carbon dioxide and water, while anaerobic respiration in muscles produces lactic acid.

Food chains begin with a producer, arrows show the direction of energy flow, and decomposers break down dead material and return nutrients to the soil.

States of matter: solids have fixed shape and volume, liquids have fixed volume but take the shape of the container, gases fill any container; heating causes expansion and melting or evaporation.

Forces: a force can change an object's speed, direction or shape; weight = mass × gravitational field strength (about 10 N/kg on Earth); friction opposes motion.

Electricity: a series circuit has one path so current is the same everywhere; a parallel circuit has branches so components work independently; metals are conductors, plastics are insulators.

Light travels in straight lines; it is reflected at equal angles and refracted (bent) when passing between media of different density.

The water cycle: evaporation, condensation, precipitation and collection; the Sun provides the energy driving it.

Fair testing: change only one variable, keep all others constant, and repeat measurements to improve reliability.