1.4.1 Mensuration and counting notes

1. 1.4.1.1Mensuration: perimeter, area, volume and surface area

   Mensuration is a short list of formulas for flat figures (perimeter, area) and solids (surface area, volume); exam questions test the formula, unit conversion, percentage change in a dimension, and melting one solid into another.

   Advanced · 7 min · Full course
2. 1.4.1.2Permutations, combinations and probability: basics

   Permutation counts arrangements (order matters), combination counts selections (order does not), and probability is favourable outcomes ÷ total outcomes when all outcomes are equally likely.

   Advanced · 7 min · Full course
3. 1.4.1.3Plane areas: triangles, quadrilaterals, circles, sectors and paths

   Every plane-area question reduces to a handful of formulas (triangle, quadrilateral, circle and its parts) plus one habit: find the bigger shape and subtract the smaller one.

   Advanced · 8 min · Full course
4. 1.4.1.4Area word problems: fencing, flooring, painting and borders

   In cost questions the only decision is what is being paid for: fencing and borders run along the perimeter, flooring and painting cover an area, and carpets are sold by length of a fixed width.

   Advanced · 6 min · Full course
5. 1.4.1.5Solids: cuboid, cylinder, cone, sphere, hemisphere and frustum

   For each solid learn three things: volume, curved (lateral) surface and total surface; most questions give one of them and ask for another, or join two solids together.

   Advanced · 6 min · Full course
6. 1.4.1.6Melting, recasting, water flow and percentage change in dimensions

   When a solid is melted, poured, dug out or flows through a pipe, volume is conserved; when its size is scaled, lengths change by k, areas by k² and volumes by k³.

   Advanced · 6 min · Full course

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