Units, Perimeter & Area Problems

OC runs perimeter backwards. OC style: 64 cm of ribbon bent into a rectangle with two sides of 12 cm — find one of the other sides. Forward thinking says add sides; reverse thinking subtracts: the two known sides consume 24 cm, leaving 40 cm for the other two — 20 cm each. The trap answer 40 (forgetting there are TWO of them) is in the options, of course. Rectangle sides come in PAIRS: use it forwards and backwards.

Burn this in: perimeter and area are INDEPENDENT. A 1×6 rectangle and a 2×3 rectangle both hold 6 squares of area — but their perimeters are 14 and 10! Long thin shapes carry more fence per grass; compact shapes carry less. OC asks both directions: 'same area, biggest perimeter?' (the thinnest one) and 'same perimeter, biggest area?' (the squarest one). Intuition points you; a quick computation confirms.

A hard perimeter question: attach a 2×1 rectangle to a 5×3 rectangle so the perimeter grows by exactly 4 — which positions work? The physics: attaching hides the CONTACT edges on both shapes and adds the piece's other edges. Contact of length 2 (long side flat): new exposed edges 1+1+2 = 4, hidden 2+2 = 4 → net +2... careful accounting matters! Rule of thumb: perimeter change = (perimeter of piece) − 2 × (contact length). A 2×1 piece has P=6: contact 2 → +2; contact 1 → +4. So the answer is the positions touching by a SHORT side.

A favourite late-paper question: a ruler has only marks at 0, 3, 4 and 9 — which length can you NOT draw between two marks? Every drawable length is a DIFFERENCE of two marks. Robot-list the pairs: 3, 4, 9 (from 0), 1 (4−3), 6 (9−3), 5 (9−4). Possible: 1, 3, 4, 5, 6, 9 — so of the lengths offered, 7 is the one you cannot draw. Difference-set thinking plus systematic listing: two skills you already own, combined. That's what late-paper OC questions are — combinations.

Units are where OC hides easy marks and easy errors. The conversions you must own cold: ×10 (mm→cm), ×100 (cm→m), ×1000 (m→km, g→kg, mL→L). Questions lean on 2½ kg = 2500 g and on reading scales — where the first job is always 'what is ONE gap worth?' (the practice-test jug counted in 10 mL steps; the walking grid in 10 m squares). Golden rule: convert everything to one unit BEFORE any arithmetic. Quiz and exercises!